QUANTIFICATION OF PHARMACOKINETICS IN SMALL ANIMALS WITH MOLECULAR IMAGING AND COMPARTMENT MODELING ANALYSIS YU HUA FANG

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1 QUANTIFICATION OF PHARMACOKINETICS IN SMALL ANIMALS WITH MOLECULAR IMAGING AND COMPARTMENT MODELING ANALYSIS BY YU HUA FANG Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Thesis Adviser: Dr. Raymond F. Muzic, Jr. Department of Biomedical Engineering CASE WESTERN RESERVE UNIVERSITY May 2009

2 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of candidate for the degree *. (signed) (chair of the committee) (date) *We also certify that written approval has been obtained for any proprietary material contained therein.

3 To Yu Ting

4 TABLE OF CONTENTS List of Tables. 3 List of Figures... 4 List of Abbreviations 6 Abstract. 7 Chapter 1 Introduction 9 Molecular imaging in biomedicine 9 PET imaging MRI and dynamic contrast-enhanced MRI 12 Image quantification.. 14 Measuring the glucose metabolic rate with FDG.. 15 Input function measurement in PET Existing methods for estimating input functions for FDG-PET. 24 Kinetic models for DCE-MRI The mathematics of a perfusion model Flow-limited case.. 27 The mathematics of a perfusion model Permeability-limited case. 30 Measuring concentration in DCE-MRI.. 33 Existing methods for estimating input functions for DCE-MRI 34 Software implementation for modeling and imaging. 35 Introduction to COMKAT.. 36 Limitations of COMKAT Specific aims.. 37 Biomedical context 39 Thesis organization. 40 Chapter 2 Spillover and Partial-Volume Correction for Image-Derived Input Functions for Small-Animal 18 F-FDG PET Studies.. 46 Abstract Introduction 50 Materials and Methods Results 63 Discussion Conclusion.. 70 Acknowledgement.. 70 Reference 71 Tables 73 1

5 Figures 77 Chapter 3 Simultaneous Measurement of the Arterial Input Function and Tissue Uptake of Gd-DTPA with Single-Frame Inversion Recovery turboflash Sequences for Kinetic Modeling Analysis Abstract Introduction 87 Materials and Methods Results 107 Discussion Conclusion Acknowledgement Reference 118 Tables. 122 Figures 125 Chapter 4 Integrated software environment based on COMKAT for analyzing tracer pharmacokinetics with molecular imaging 133 Abstract Introduction 136 Materials and Methods Results 149 Discussion Conclusion Acknowledgement Reference 158 Tables. 161 Figures 166 Chapter 5 Conclusion Summary 172 Limitations Future developments Closing statements Reference 189 Bibliography

6 LIST OF TABLES Chapter 2 1 Initial values and bounds for parameter estimation to obtain the MCIF 73 2 Direct comparison of estimated input functions Comparison of Ki estimates from measured and estimated input functions from rat data. 75 Comparison of Ki estimates from measured and estimated input functions from mouse data Chapter 3 1 Quantities and symbols Simulation results Parameter estimation settings and statistics of estimated values for animal data Chapter Summary and comparison of functionalities of COMKAT distributions Data formats supported by COMKAT GUI and COMKAT Image Tool Summary of computation speed for major functions in COMKAT Summary of computation speed for parametric imaging

7 LIST OF FIGURES Chapter 1 1 FDG 2 compartment model Glucose 2 compartment model Perfusion model in the flow limited scenario Perfusion model in the permeability limited scenario Chapter 2 1 Typical placement of the ventricular and myocardium ROIs The comparison between the measured input function and the IDIF in one rat Estimation plots of one rat with zero-sample MCIF estimation Estimation results of one mouse with zero-sample MCIF estimation Box plot of the Ki error percentage of zero-sample and one-sample MCIF 81 Box plot of the Ki error percentage of zero-sample and one-sample estimation for mouse data 82 Chapter 3 1 Simulated intensity versus T Simulated intensity curves for flowing blood and tumors Curve fitting results for intensities of a brain ROI from preparation scans Images of a rat study Arterial intensity data and curve fitting results of one rat Arterial intensity data and curve fitting results of one rat Brain intensity data and curve fitting results

8 8 Comparison of estimated input function to a standard input function. 132 Chapter 4 1 Framework of COMKAT software Screen capture of the layout of COMKAT GUI when initialized Screen capture of the COMKAT Input Function GUI The appearance of COMKAT Image Tool when micropet images are loaded COMKAT GUI with all necessary information specified

9 List of Abbreviations CA COMKAT DCE MRI EES FDG FDG 6P Gd DTPA GUI IDIF LC LOR ODE PGI RSI MCIF MRI PET SD ROI VOI Contrast agent Compartment Model Kinetic Analysis Tool Dynamic contrast enhanced magnetic resonance imaging Extra vascular, extra cellular space 2 [ 18 F]fluoro 2 deoxy D glucose 2 [ 18 F]fluoro 2 deoxy D glucose 6 phosphate gadolinium diethylenetriaminopentaacetic acid Graphical User Interface Image derived input function Lump constant Line of response Ordinary different equation Phosphoglucose isomerase Relative signal intensity Model corrected input function Magnetic resonance imaging Positron emission tomography Standard deviation Region of interest Volume of interest 6

10 Quantification of Pharmacokinetics in Small Animals with Molecular Imaging and Compartment Modeling Analysis Abstract BY YU-HUA FANG In the recent years molecular imaging has become an important tool in biomedical research. To quantify physiology from image data, compartment modeling has been shown to be useful by analyzing the pharmacokinetics from molecular images. However, some challenges still exist and limit the application of compartment modeling in a routine basis. Methods to resolve some of the existing challenges are proposed and validated in this thesis. First, non invasive methods are developed to measure the input functions required in compartment modeling and parameter estimation for positron emission tomography (PET) and dynamic contrast enhanced magnetic resonance imaging (DCE MRI) studies. Methods for imagederived input functions are developed and validated against the reference input functions. Second, a software environment is established to integrate functions that handle image analysis and modeling analysis based on COmpartment Model Kinetic Analysis Tool (COMKAT). Methods to enhance speed and interface for COMKAT have been implemented as described in this thesis. With the methods and software 7

11 developed in this thesis, researchers can quantify in vivo pharmacokinetics with molecular imaging methods to measure the physiology and metabolism noninvasively in a routine basis. 8

12 Chapter 1 Introduction 9

13 Molecular imaging in biomedicine Over the past decade, imaging has emerged as a powerful tool for biomedical research. Advances in imaging instrumentation now allow scientists to look at the in vivo physiology of humans and animal models at the molecular level. Traditionally, imaging was used to detect the anatomy with X ray or computed tomography (CT) images. With new imaging methods developed for tracing specific molecules, scientists began to acquire functional images that reveal the physiologic function of organs, tissues and even cells. Often these functional images would require a specific imaging tracer to mark target molecules or physiological reactions. To be distinguished from being either functional or anatomical, the term molecular imaging is now commonly adapted to describe the imaging methods that can quantitatively monitor specific molecules or biological processes (1). Molecular imaging has been found to be useful in both clinical and pre clinical applications. In clinical studies, molecular imaging techniques can be used for diagnosis, treatment planning, and treatment evaluation. For research purposes, molecular imaging also has been widely applied to study the physiology and metabolism of humans and animals. For researchers who use animal models, molecular imaging methods are highly appealing because imaging procedures can be repeated without having to sacrifice the animal. On the other hand, as many animal models like rodents are much smaller in size compared to human, technological challenges exist in the attempt to acquire the same relative level of detail in small animal imaging. 10

14 PET imaging Since first development in 1970s PET has become a popular modality in both clinical and pre clinical imaging (2). PET is mainly characterized by its ability for functional imaging in contrast to other medical imaging techniques to visualize anatomical structures. Clinically PET has been proved to be very helpful especially in neurology, cardiology and oncology applications. Over the past 20 years, dedicated PET scanners have been developed for animal models, mainly rodents and primates, for research imaging. These animal scanners provide better spatial resolution that is a critical factor for acquiring images for small animals and therefore serve as a useful tool for pre clinical research. The major principle of PET is to image the annihilation photons emitted during positron decay. Radionuclides, such as 18 F or 15 O, are labeled to specific compounds to make a so called tracer. This tracer can be injected into humans or animals and continuously releases positrons. Within a short range a positron interacts with an electron and the two annihilate. Two 511 kev photons are produced and emitted at approximately 180 degrees to each other. Scintillation crystals are used to build detector rings to capture those photons. When two photons are detected within a short time interval of each other (the coincidence window), the event is called a coincidence. The line between the involved detectors includes the site of annihilation and is called the line of response (LOR). LORs encode the information about the radioactivity distribution as projection (Radon Transform) data which may be reconstructed to produce 3D or 4D kinetic data set of images. 11

15 In addition to functional imaging capabilities, PET has also been regarded with advantages of high sensitivitiy (10 11 ~10 12 M) (1) and absolute quantification. With careful calibration and quality control, PET scanner can measure the concentration of tracer in the field of view. However, there are some disadvantages with PET. For example, the spatial resolution of PET scanners (~1 2 mm for small animal scanners) is worse than CT or MRI (~ um) (1). MRI and DCE MRI Compared to PET, MRI has much better spatial resolution and anatomical contrast to differentiate soft tissues. The contrast in an MR image comes from the difference in proton density and magnetic relaxation properties of tissue. As protons can be treated as a dipole, their spins are aligned by the external magnetic field in the MRI scanner. While those dipoles return to their original orientation after being excited by RF pulses, a signal or so called echo is produced. This echo signal induces current changes in MR coils. The scanner system can therefore detect this signal and use the collected data to reconstruct images. Conventional MRI scans generally produce anatomical images with resolution of μm. However, the disadvantages of clinical MRI scanners compared to PET include the limited temporal resolution (~minutes depending on the pulse sequence) and sensitivity (10 3 ~10 5 M) (1). Also with most pulse sequences it is challenging to convert the pixel intensity to molar concentration for specific molecules. 12

16 Dynamic contrast enhanced (DCE) MRI has been widely used to improve the image contrast, providing functional and molecular information for an MRI study (3, 4). For a DCE MRI study, images are taken before and after the injection of a contrast agent. The images taken before the injection are often denoted as the baseline scans. After the injection, the image pixel intensity under gradient echo sequences is increased because of the reduction of T 1 relaxation time caused by the contrast agent. DCE MRI has been widely used in oncology studies because these MR images provide useful information about vascular permeability and blood flow information of the tumor (5). There are different levels of detail for image analysis of DCE MRI images. Qualitative analysis can be achieved by visual interpretation. Semi quantitative and quantitative analyses are based on the time concentration curves of the contrast agents either pixel wise or region wise. Semi quantitative analysis includes measuring the relative signal intensity (RSI) or slope of time concentration curves (6, 7). Such semi quantitative analysis has been applied to study tumor perfusion (6 9). These statistics are simple to obtain, but they may differ significantly from scanner to scanner and even coil to coil. Quantitative analysis uses compartment modeling, often a perfusion model, to fit experimental data and estimate the physiological parameters (6, 7). Such quantitative analysis has been shown to be feasible on small animals (6 9). As the compartment modeling estimates the parameters that are independent of the hardware, the quantitative analysis provides researchers with a fair basis for comparison of in vivo physiology. 13

17 Image quantification One common limitation in almost every molecular imaging modality is the physiological interpretation of images. In most imaging methods, the signal intensity or pixel value of acquired images is a function of instrumentation parameters, subject physiology, tracer properties and external environment, etc. Usually pixel values are not directly proportional to quantitative measures of metabolism, hemodynamics, or other physiologic parameter. Therefore, post processing methods have to be applied to extract truly physiological information from the images. The derived information can be qualitative, semi quantitative or quantitative. In general, the more quantitative certain analysis is, typically the more work has to be done for such analysis. However, obtaining absolute quantification of molecular functions provides better understanding of physiology and a fair way to compare inter subject variability. In addition, the absolute quantification facilitates the comparison of images collected at different institutions or longitudinal studies because the physiologic measurement is independent on the instruments and scan protocols. This thesis focuses on the quantification of two major molecular imaging technologies: PET and DCE MRI. New methods to quantify 2 [ 18 F]fluoro 2 deoxy Dglucose (FDG) metabolism with PET and the pharmacokinetics of Gadolinium(III) diethyltriamine pentaacetic acid (Gd DTPA) with DCE MRI are proposed and evaluated. Compartment modeling is used as the approach to quantify 14

18 pharmacokinetics for both types of images. Another common feature is the need for an input function as is detailed below. Compartment modeling is one of the best accepted methods for the quantification of molecular image analysis. As previously described, a PET scanner measures the absolute activity concentration of a tracer. This activity concentration can be easily converted to molar concentration with decay correction and specific activity. Although, in MRI, this conversion is not so straight forward, molar concentration can also be measured for a contrast agent based on its ability to enhance the proton relaxation rates. With a compartment model to describe the transport of molecules between different steps of metabolism or uptake, measured tracer or contrast agent concentration can be fitted to a compartment model for parameter estimation of the rate constants. Those rate constants can be further used to interpret the data in a quantitative and objective way. Two common models, perfusion and glucose metabolic models, are explained in the following sections. Measuring the glucose metabolic rate with FDG FDG is currently the most commonly used PET tracer FDG is an analog of glucose. Similar to glucose, FDG is transported into cells by glucose transporters and becomes phosphorylated to FDG 6 phosphate (FDG 6P) by hexokinase. Unlike glucose 6P, which is the phosphorylated product of natural glucose that is further metabolized in the glycolytic pathway, FDG 6P is not further metabolized and becomes trapped within cells. Consequently, a high amount of FDG and FDG 6P 15

19 radioactivity accumulates in tissues with high glucose metabolism making these tissues appear as bright areas in the PET images. This character makes FDG extremely powerfulin oncology as tumors often would excessively take up and metabolize glucose. The early attempts to measure the metabolic rate of glucose with radioisotopelabeled compounds used [ 14 C]glucose (10). By replacing one carbon in the glucose molecule with 14 C, [ 14 C]glucose is expected to be metabolized in the same pathway of glycolysis by tissues. Therefore, [ 14 C]glucose can serve as a glucose analog to study glucose metabolism and [ 14 C]glucose tissue concentration can be measured with autoradiography methods. The disadvantages of the [ 14 C]glucose tracer, however, is the fast metabolism which converts [ 14 C]glucose to CO 2 and water. As CO 2 is quickly removed from the tissue, the accumulation of radioactivity in tissue is small and difficult to measure (11). This limitation made deoxyglucose (DG), a glucose derivative, a better candidate for measuring the glucose metabolism. Due the difference in chemical composition of the replacement for the C 2 hydroxyl group with a hydrogen, DG participates only part of the glucose metabolic pathway. Unlike glucose, once DG is metabolized by hexokinase to DG 6 phosphate, the phosphorylated DG cannot be further metabolized but remains mostly trapped within cells (12). Therefore, Sokoloff et al. (12) used [ 14 C]deoxyglucose ( 14 C DG) to first develop modeling methods to measure the glucose metabolic rate with autoradiography methods because the trapped 14 C DG 6P was much easier to measure than [ 14 C]glucose. 16

20 As the autoradiography method is impossible to use to measure the in vivo tracer concentration, use of PET scanners and positron emitting tracers emerged for research and clinical applications in studying the in vivo glucose metabolism. 11 C DG (13) and 2 [ 18 F]fluoro deoxy glucose ( 18 F DG or FDG) (5) were among the first candidates to be applied in clinical usage. Eventually FDG was found to be more convenient in clinical use. One major reason is that, since not all hospitals have cyclotrons to produce tracers, PET tracers are often synthesized in one site and then transported to the imaging centers. The activity decay due to transportation can be a significant loss to the original activity. Therefore, the longer half life of FDG (~110 min) compared to 11 C DG (~20 min) leads to less activity loss during transportation and makes FDG preferable to 11 C DG for clinical PET studies. Although FDG is structurally different from DG, FDG is considered to be very similar to DG in the in vivo uptake and metabolism (5). Therefore, Phelps et al. (5) adopted the 14 C DG model developed by Sokoloff et al. (12) for estimating the FDG kinetics and showed that FDG PET with modeling methods could be reliably applied to measure the glucose metabolic rate. In the following paragraphs, detailed derivation of how to measure glucose metabolism with FDG is demonstrated. To derive the governing equations of FDG and glucose uptake, first the compartment models have to be defined for FDG and glucose. The FDG metabolism in tissue can be represented by a 2 compartment model shown in Fig. 1. and denote the respective extravascular FDG concentration and intracellular 2 [ 18 F]fluoro deoxy glucose 6 phosphate (FDG 6P) concentration. The FDG distributes in the extra vascular extracellular space or EES (5) as well as in the intra cellular space. FDG inside the cell 17

21 may be phosphorylated by hexokinase to form FDG 6P which is trapped within the cell. Similarly, glucose metabolism can be described by a 2 compartment model as shown in Fig. 2. As the parameters and model names in the glucose model are identical as in the FDG model, a nomenclature of * is used to identify these symbols in the glucose model. This model entails two compartments, and, which are the glucose and glucose 6P concentration in tissue. Unlike FDG 6P, glucose 6P is further metabolized following the glycolysis pathway by phosphoglucose isomerase (PGI). The further breakdown of glucose 6P is simply represented by a single rate constant in this model because in most tissues, the enzyme PGI responsible for converting glucose 6P to fructose 6 phosphate has a fast reaction rate and makes this conversion nearly irreversible (14). 18

22 k 1 k 3 C p (FDG in plasma) C e FDG in tissue k 4 C m FDG-6P in tissue k 2 FIGURE 1. FDG 2 compartment model C p * (glucose in plasma) k 1 * C e * glucose in tissue k 2 * k 3 * k 4 * C m * glucose-6p in tissue k 5 * FIGURE 2. Glucose 2 compartment model. The FDG transport is described by the state equations Eq. 1 and 2: dc dt e k ( C k C Eq.1 1 C p k2 k3) e 4 m dc dt m k k C Eq.2 3Ce 4 m 19

23 State equations of the glucose model are: dc dt * e kc ( k k) C kc * * * * * * * 1 p 2 3 e 4 m Eq.3 dc dt * m kc ( k k) C Eq.4 * * * * * 3 e 4 5 m The glucose metabolic rate is defined as the net rate at which glucose is metabolized in tissue. In the steady state, glucose metabolic rate is equal to the net rate of phosphorylation: Eq.5 Here a constant is defined as: 1 The constant is the fraction of the phosphorylated glucose (glucose 6P) that is further metabolized. It has been shown that is very close to unity in the brain (12), showing that very little phosphorylated glucose would be dephosphorylated again. In other tissues, is also considered to be approximately one because the catalyzation of glucose 6P is normally much faster than the dephosphorylation ( ) since rate of glucose 6P dephosphorylation is increased (mainly in liver and muscle) only when the blood glucose is excessive. With the definition of, Eq. 22 can be re written as: 20

24 As it is much easier to measure glucose concentration in plasma than in tissue, is expressed in terms of by assuming glucose is in a steady state (no net accumulation of glucose in tissue) which implies requires: 0. According to Eq. 3 this Eq.6 which can be algebraically rearranged to obtain: Eq.7 Using Eq. 7, can be expressed in terms of and : Eq.8 With the definition of, can be expressed in terms of as 1 /. Using this relation in Eq. 8, the relation between and is obtained as: Eq.9 This relationship can be used in Eq. 5 to express in terms of and thus obtain an expression for the metabolic rate of glucose MR glc in terms of by: Eq.10 21

25 A difficulty of using Eq.10 is that values for the rate constants ~ for glucose have to be determined. Since the direct measurement of them are quite challenging, FDG PET image data are used to estimate those parameters from FDG. To do so, first the glucose metabolic rate MR glc is expressed in terms of the rate constants of FDG ~. By multiplying Eq.10 equation with one, we get: /, which equals to / / Eq. 11 where and / /. The term is given the name lumped constant (LC) which represents the factor by which metabolism of glucose differs from that of FDG. With the definition of LC, the rate of glucose metabolism can be expressed as: / / Eq.12 where Ki is defined as k 1 k 3 /(k 2 +k 3 ). This makes the MR glc a simple equation that involves the FDG rate constants k 1, k 2, and k 3, plasma glucose concentration under steady state and the lumped constant LC. Although there are a number of terms involved in the representation of LC, the easiest way to understand it is to simply treat it as a constant that accounts for the difference in metabolic rates between glucose and FDG. The value of the lumped 22

26 constant depends on the insulin level (dietary status) and species. However, it is found that in the same dietary status and species, the value of LC is similar across different types of tissues and subjects (5 10). In summary, to measure the glucose metabolic rate with FDG PET, three parameters must be determined: Ki, blood glucose level and the lumped constant LC. As blood glucose level is fairly constant and LC also is a simple constant, the key information is the determination of Ki which is directly proportional to glucose metabolic rate. Therefore, Ki alone is treated as the most important and robust parameter for evaluating the glucose metabolic rate, and the proposed method in this thesis for input function estimation is validated by examining the accuracy and precision of Ki estimates. Input function measurement in PET Although compartment modeling with FDG PET images is very helpful in interpreting imaging data, the main challenge for this analysis is the invasive measurement of the input function C p. The gold standard to measure the C p is from arterial blood samples. Initially this is achieved via a continuous blood sampling and activity monitor in order to capture the fast dynamics of the first few minutes of tracer time activity curves. The continuous sampling is followed by the manual blood sampling for several samples. This blood sampling requirement has several disadvantages. For clinical studies, blood sampling increases the discomfort of patients and risks because of arterial catheterization. In small animals, blood vessels 23

27 are small and the amount of blood that may be withdrawn is limited. Furthermore, blood loss may perturb the animal physiology and affect the experimental outcome. There have been micro devices developed specifically for sampling and counting blood activity for small animals (15, 16). However, surgery is still required to catheterize the arteries or insert plastic tubing into the arteries. As a result, in practice most researchers prefer to avoid the blood sampling for PET studies and use non invasive methods to estimate the input function if compartment modeling is desired. Existing methods for estimating input functions for FDG PET To estimate the input function without extensive blood sampling, various methods have been proposed. For FDG PET, these methods can be summarized into four categories: (i) image derived input functions, (ii) factor analysis methods, (iii) standardized input functions and (iv) simultaneous estimation. Image derived input functions (IDIFs) are the time activity curves obtained from regions over the major vascular structures, such as the ventricular cavity, aorta, or large arteries (17, 18). This method is relatively simple to use in principle and applicable to a variety of tracers (19, 20). However, in small animal PET imaging, hearts and arteries are small compared to the scanner s spatial resolution. Consequently, significant amount of vascular radioactivity is blurred into adjacent tissues and vice versa. Also, the cardiac and respiratory motion creates additional signal cross contamination between vascular structures and surrounding tissues. As 24

28 a result, curves obtained from regions drawn over the vascular space are mixture of the input functions and surrounding tissue time activity curves. Herein, for a ventricular IDIF, spillover denotes the activity in the myocardium that gets blurred into the ventricles, while the partial volume effect denotes the underestimation of activity in the ventricles from being blurred into the myocardium. Some methods have been proposed to correct the spillover and partial volume effect for imagederived input functions using three or more blood samples in clinical studies (21, 22), but these methods have not yet been validated for small animal PET imaging. Factor analysis (FA) methods have been applied to separate the arterial blood component from the myocardial tissue component in the dynamic heart images. In these methods it is assumed that a heart image is a summation of three or more factors that typically include left and right ventricles and the myocardium. Principle component analysis is applied to find these components and therefore obtain an estimate of the input function. Such method has been used to extract the input function for rats and mice using just one blood sample (23) or two to three blood samples (24), showing good correlation between the measured and extracted input function. FA methods have the advantage of being robust and requiring few blood samples. However, the ambiguity still exists in this method whether the factors found by FA represents the true blood component without spillover and partial volume effects, especially in mice (23). Standardized input function methods assume that all input functions have an identical curve shape. Under this assumption, a standard input function with fixed 25

29 curve shape is used to approximate the individual input function when its magnitude is scaled to match the concentration measured in one or two blood samples or adjusted by the injection dose normalized to the subject size. It has been used in clinical (25 28) and small animal FDG PET (29). However, the input function curve shape varies between subjects based on several factors, including the injection speed, dietary state, individual metabolic difference and the renal clearance rates. As the standardized input function is obtained from a population of animals, it only represents the average curve shape and therefore lacks the ability to account for the individual difference in curve shapes, especially in animals with abnormal metabolism. In addition, the standardized input function method has not yet been tested on mice. Simultaneous estimation was originally proposed to estimate the input function for human brain studies (30). It is assumed that an input function can be described by a mathematical function with multiple parameters that can be estimated simultaneously with the fitting of multiple regions or interest, typically three. Few, usually two late blood samples are required in the simultaneous estimation process to provide information of the input function magnitude. The main challenge of this method is the large number of parameters (>25) that need to be estimated compared to the data available and this often leads to parameter identifiability issues. Moreover, this method has not been validated on small animal PET studies. Kinetic models for DCE MRI 26

30 For MR contrast agents that are not metabolized, often a single compartment kinetic model can be used to describe its transport between intra and extra vascular spaces. However, depending on the characteristics of a specific contrast agent, whether its transport is limited by blood flow or permeability determines the parameter definition in physiology for the rate constants in the kinetic model. Flowlimited contrast agents can permeate through the capillary wall so fast that the amount of contrast agent that enters the extra vascular space is mainly determined or limited by the rate of blood flow. Conversely, contrast agents are described as permeability limited when blood flow is relatively much faster than permeation so that the extra vascular amount of contrast agent is primarily determined by permeability. In the following paragraphs both cases are examined for the derivation of mathematics of the kinetic model and relating model parameters to physiology. The mathematics of a perfusion model Flow limited case For an inert radiotracer or a contrast agent used to measure perfusion, a onecompartment model can be used to describe its transport. (For convenience, in this section we only describe transport of a contrast agent. The model of transport of a radiotracer is analogous; transport depends on chemical properties.) For MRI contrast agents that are not transported into cells or metabolized after entering the EES, the model shown in Fig. 3 represents the transport of contrast agent under flow limited conditions and uses the standardized nomenclature as proposed by 27

31 Tofts et al. (7). In this model, blood flow F (ml/min/g) is defined as volume of blood flowing through per gram of tissue per minute. F is assumed to be the same entering and leaving the tissue so that there is no net accumulation of blood in tissue. Specifically, the rate for the contrast agent to leak out the capillary is determined by the product of F, tissue volume V t (ml) and the tissue density ρ (g/ml). C a (tracer/agent concentration in arterial blood) FρV t (blood flow) C t tracer in tissue FρV t FIGURE 3. Perfusion model in the flow limited scenario. With a constant blood flow, the net rate of contrast agent accumulation in the tissue can be described by the product of (1) the blood volume flowing through the tissue and (2) the molar concentration difference between the arterial and venous blood. Therefore the state equation for mass balance can be expressed as: dm dt t F V C C ) Eq.16 t ( a v 28

32 where M t is the quantity in moles of contrast agent per V t ml of tissue. is the molar concentration of contrast agent in the arterial blood and C v is the concentration in the venous blood. If the contrast agent is well mixed in the EES with a high permeability across the capillary so that its venous plasma concentration equilibrates with that in the EES in one capillary pass, is related to the EES concentration C e by: C ( 1 Hct ) C (1 Hct ) C v p e Eq.17 where Hct is the hematocrit which is the fraction of blood volume attributed to red blood cells. C e is the contrast agent concentration in the EES. By replacing the term in Eq.16 with Eq.17, the state equation for mass balance in Eq.16 becomes: dm dt t F V C (1 Hct) C ] Eq.18 t[ a e By dividing both sides by V t, this equation can be expressed in terms of the concentration of contrast agent in tissue: dc dt t F C (1 Hct) C ) Eq.19 ( a e where is the molar concentration in the extravascular tissue space including both intracellular space and EES. Alternatively can be expressed as a weighted summation of the intracellular concentration and the EES concentration by: C v C ( 1 v ) C t e e e i Eq.20 29

33 where Ci is the intracellular concentration. is the volume fraction of the EES which is dimensionless with value between zero and one. For those MR contrast agents that largely remain within EES after permeating from the capillary bed and do not enter the cells, can be simplified as: v e Ci can be neglected. As C i is neglected in the tissue, Eq. 20 C v C Eq.21 t e e With the arterial blood concentration C a related to the arterial plasma concentration C p by C a ( 1 Hct ) C p, Eq.19 can then be re written as: dct dt F (1 Hct)( C C ) Eq.22 p e With Eq. 21, in Eq. 22 can be replaced in terms of : dct dt Ct F (1 Hct)( Cp ) KtransCp kepct Eq.23 v e where 1 and k / ep K trans ve. If the plasma concentration C p and the tissue concentration C t can be measured from MR images, K trans and k ep can be estimated by adjusting their values to achieve the best correspondence of modelpredicted and measured C t values. The mathematics of a perfusion model Permeability limited case 30

34 When the molecular size of the contrast agent is sufficiently larte, lood tissue exchange may be primarily limited by the permeability of the capillary. The exchange equations are derived similarly to this above and again, it is assumed that the contrast agent is not trapped or metabolized within the cells so a onecompartment model is used as shown in Figure 4. C p (tracer/agent concentration in arterial plasma) (permeation) C e tracer in the EES (permeation) FIGURE 4. Perfusion model in the permeability limited scenario. The net permeation of the contrast agent across the endothelium can be described by a flux of. P is the permeability rate, expressed as the distance (cm) of permeation per minute. S is the capillary surface area (cm 2 /gram of tissue). The product PS is then the volume (ml) of fluid permeation per gram of tissue per minute. The perfusion of contrast agent is determined by the product of PS, the tissue density (g/ml) and volume of the tissue including the cells and EES (ml). The net rate of contrast agent accumulation equals the product of this permeation flux and the concentration difference between plasma and EES concentration. Eq.24 31

35 is the net quantity of contrast agent (mole) that accumulates in the EES. is the contrast agent concentration in the arterial plasma. is the concentration of contrast agent in tissue EES. By dividing both sides of Eq. 24 by EES volume, it becomes: / Eq.25 is the EES volume and is the volume fraction of EES. Again Eq. 21 is used to express in terms of : / Eq.26 This equation has the same format as in Eq. 23. Therefore, Eq. 23 can again be used to express the model mathematically with a different definition of and the same definition of k ep as k ep K trans / ve. In this thesis, a permeability limited contrast agent Gd DTPA is used to evaluate the permeability of the capillary. It is important to note that K trans is a composite rate constant. Its physiologic interpretation depends on whether the transport is limited by blood flow or permeability. In the case of permeability limited contrast agents such as Gd DTPA, and density. k ep K trans is a product of tissue permeability, capillary surface area, on the other hand, can be used to determine the volume fraction of the EES space v K / k e trans ep. When the contrast agent is excluded from the intracellular space, v e can be used to determine the intra and extra cellular volumes. This can be informative for tumor physiology because the immature tumor 32

36 structure often has an EES fraction that is greater than normal (31). been shown to be a useful index in clinical oncology studies(32, 33). k ep also has Measuring concentration in DCE MRI Gadolinium based contrast agents are effective in reducing the longitudinal recovery time constant T 1 by the dipole dipole reaction between the proton and paramagnetic gadolinium. Tissue relaxivity R 1 (which equals 1/T 1 ) depends on the concentration of Gd DTPA [CA] by: R 1, post R 1, pre r[ca] Eq.27 where R 1,pre and R 1,post are the R 1 pre and post contrast agent injection. [CA] is the molar concentration of contrast agent. r is the calibration factor dependent on the scanner and coil instrumentation. It should be noted that the concentration of Gd DTPA is not directly measured but derived based on the increase in proton relaxation rate caused by the presence of Gd DTPA. The compartment modeling of DCE MRI also requires an input function which is the concentration of contrast agent in blood as a function of time. Ideally, this input function should be measured from blood samples. However, the blood sample T 1 differs from T 1 of the in vivo blood because of changes in temperature, oxygen levels, hemoglobin and denaturing of blood proteins (34 36). As a result, researchers tend to use alternative methods to measure the input function for DCE MRI studies other than blood sampling. 33

37 Existing methods for estimating input functions for DCE MRI The most common representation of input function is the tri exponential function: C () t Ae A e Ae p Lt 1 L2t L3t Eq.28 In practice, this tri exponential function is used as a standardized input function, whose curve shape is fixed and magnitude is scaled by the normalized injection dose (mmol/kg body weight) (37, 38). Therefore, this method for using fixed curve shapes has the limitation of neglecting the subject specific curve shapes. Since its magnitude is scaled by injected dose instead of a blood sample, the accuracy of magnitude may also be incorrect in some subjects (39). Given the spatial resolution of MR images, arterial input functions can be obtained with much less spillover and partial volume contamination from vascular structures. There have been several reports on the image derived input function for human studies that obtain the input function with gated cardiac images (40, 41), from aorta (42) and large arteries (41, 43). The major challenge for such methods is the socalled bright blood effect. Because the blood is flowing during data acquisition, between each RF excitation some blood flows into the coil range. As the MR signal comes from all the spins that resonate at a specific frequency decided by spatial encoding within the coil, all the resonating blood spins within the coil range contribute to the intensity of generated echo. But since those spins experience different levels of excitation when the signal is acquired at the center of k space, the 34

38 intensity is different than the intensity measured from stationary blood. In gradientecho sequences, flowing blood causes greatly increased intensity that makes T 1 and the input function difficult to measure. Software implementation for modeling and imaging As described previously, obtaining quantitative physiological interpretation of image data is an important challenge for biomedical image analysis. Previous sections have shown how compartment modeling can be applied to help quantify the pharmacokinetics for measuring physiology. Other than the limitations in image acquisition and getting the input functions, another challenge for many researchers is the lack of a software environment for processing the image data through modeling approaches. Most software provided by the scanner vendor has extensive functions for displaying or post processing the images but lacks the capabilities for compartment modeling. Most pharmacokinetic modeling packages, on the other hand, require the user to customize the packages for imaging analysis or to be integrated into imaging software. For researcherss that are inexperienced in computer programming, making their own software for analyzing images in a quantitative way can be a challenging and time consuming task. Therefore, we have continued to develop a software package to help researchers apply compartment modeling in the context of molecular imaging. The approach we took is to pursue the development of such software package based on COMKAT (44). 35

39 Introduction to COMKAT COMKAT was firstly developed as a MATLAB toolbox for compartment modeling analysis (44). COMKAT was designed to allow a user to build and solve compartment models with simple commands and even a graphical user interface. COMKAT also included parameter estimation functions to allow users to estimate model parameters with simulated or experimental data. With the model solving functions being compiled based on CVOdes (45), a fast ODE solver package developed by Lawrence Livermore National Library, COMKAT has a spectacular improvement on the speed of solving differential equations for model output compared to the build in ODE solver in MATLAB. Over the years, our group has made numerous efforts to extend the functions of COMKAT hoping to adapt it for imaging needs. For example, our group has implemented COMKAT Image Tool for loading, displaying and co registering images. To make COMKAT even more powerful in modeling analysis for molecular images and more useful for a larger audience, a few limitations have to be resolved. Limitations of COMKAT First, the user interface for COMKAT may be improved by adding more graphical user interfaces (GUIs), especially for compartment modeling. Data handling from COMKAT Image Tool to the modeling GUI should be efficient and simple for the user, so that users can easily use the modeling GUI to process data from images. Common models for pharmacokinetics need to be implemented as templates to streamline 36

40 data analysis. The GUI also serves as a foundation to add functions such as parameter estimation, quality of fit analysis, or graphical methods for analyzing transformed data, etc. Another important function is to generate parametric images. In a parametric image data set, pixel values are represented as measures of physiological quantities. This would often entail modeling analysis on a pixel wise level to convert pixel intensities to model parameters that have physiological meaning. As image volumes have on the order of 10 5 or 10 6 pixels, one can imagine how large the amount of computation would be required in this mode. Although COMKAT has a very sophisticated solver, pixel wise operations are still required and therefore excessive computing time is necessary. New computation methods have to be adapted to improve the speed of generating parametric images. In addition, functions and interfaces also have to be designed to calculate and display parametric images efficiently. Specific aims This thesis includes three specific aims: Specific aim 1: Estimate input functions for FDG PET small animal imaging with zero or one blood sample. A method in developed in this thesis to derive the input function from images for compartment modeling to avoid blood sampling required by conventional methods 37

41 for input function measurement. Such procedures were invasive and might perturb the animal physiology due to the required surgery and blood loss. This method is based on the input functions derived from left ventricles over the images. Typically those image derived input functions contained significant contamination from tissue tracer uptake, and necessary correction had to be developed to obtain a correct estimation of input functions. The estimated input functions were validated against input functions measured from blood samples from invasive blood sampling. Animal studies including cannulation surgeries and scans were performed by myself during data collection. Specific aim 2: Quantify Gd DTPA concentration and in vivo permeability for DCE MRI in small animals This project included two types of experiments. First, parameter estimation was achieved by a novel method that directly fits experimental data of MR intensity curves from the DCE MRI images. This was achieved by modeling the signal intensities as functions of concentrations of Gd DTPA and physiologic parameters in both tissue and blood. The flowing effect on signal intensities was accounted for and modeled as mathematical equations that described the intensities of arterial blood. Second, the arterial input functions and tissue uptake were estimated from measured intensity. This involved designing of a complete imaging protocol, developing modeling methods for parameter estimation and validation against reference input functions and tissue parameters. Simulation and animal studies were used to validate the proposed methods. 38

42 Specific aim 3: Develop software with enhanced speed and graphical user interfaces for quantifying molecular images. Based on COMKAT a software environment was established to meet imaging and modeling needs. Several functions were added to COMKAT. First, graphical user interfaces (GUIs) were designed and programmed for image processing and modeling analysis. These GUIs would allow users without much programming experience to easily use COMKAT for analyzing image data by compartment modeling. Second, various analysis tools were integrated into COMKAT including the methods developed for quantifying FDG PET and DCE MRI studies. Third, support for distributed computing capabilities was added into COMKAT to enhance the speed for parametric imaging. Finally, a website based on wiki for COMKAT dissemination was established to provide users better support in user manuals and examples for COMKAT applications. This wiki based website even allowed user to edit its web pages so that users may provide their examples and feedback. Biomedical context Methods and software were developed in this thesis to perform kinetic modeling to analyze and quantify physiology seen in images. To be more specific, with the methods developed in this thesis, the glucose metabolic rates, vascular fraction and capillary permeability can be measured in vivo for small animals. Being able to quantify those physiologic processes is very helpful in pre clinical research. For example, in evaluating drug effects or therapies for tumors, it is common to observe 39

43 the reduction in glucose metabolism or metabolism of other nutrients after treatment. However, it is often hard to differentiate whether such metabolism reduction is due to reduction of blood flow (by destruction of vasculature or blockage of arteries), direct kill of cells or reduction of relevant enzymes. If permeability and vascular fraction can be measured, they can serve as indication of how perfusion and vasculature is modified and therefore provide evidence to evaluate whether reduced blood flow or cell death is more significant in the therapy. Such information may help to interpret the physiologic or pathological changes in a quantitative way and can be further used to modify the treatment to maximize its effect. The other reason for developing these methods is that they may be useful for clinical studies in the future. It is often advantageous to first attempt novel methods on animals before applying these methods on humans. Working on animals avoids the possible risks to human subjects and validates the safety and efficacy of new methods. Researchers may have more flexibility to evaluate and validate different approaches and experimental details on animals compared to a clinical trial. By developing and validating new methods in animal models, we not only solve problems encountered in small animal imaging but also prototype methods that may be applicable to clinical studies. We discuss the possible future application of the methods proposed in this thesis in more details in the last chapter of this thesis. Thesis organization 40

44 This thesis is divided into five chapters. This first chapter is the Introduction, including background, motivations and specific aims. Chapters Two to Four are manuscripts that describe the three projects included in this thesis. Chapter Two describes the FDG PET input function estimation project. The work has been published in Journal of Nuclear Medicine (46). Chapter Three is on the DCE MRI kinetic modeling and input function measurement. A manuscript will be submitted to Magnetic Resonance in Medicine. The development of COMKAT is illustrated in Chapter Four and a manuscript has been submitted to Journal of Nuclear Medicine. Chapter Five is the conclusion. It summarizes for each project and discusses limitations and future improvements. 41

45 REFERENCE 1. Massoud TF, Gambhir SS. Molecular imaging in living subjects: seeing fundamental biological processes in a new light. Genes Dev. Mar ;17(5): Wenick MN, Aarsvold JN. Emission tomography - the fundamentals of PET and SPECT. First ed. San Diego: Elsevier Academic Press; Choyke PL, Dwyer AJ, Knopp MV. Functional tumor imaging with dynamic contrast-enhanced magnetic resonance imaging. Journal of Magnetic Resonance Imaging. 2003;17(5): Padhani AR, Gapinski CJ, Macvicar DA, et al. Dynamic contrast enhanced MRI of prostate cancer: correlation with morphology and tumour stage, histological grade and PSA. Clin Radiol. 2000;55(2): Choyke PL, Dwyer AJ, Knopp MV. Functional tumor imaging with dynamic contrast-enhanced magnetic resonance imaging. J Magn Reson Imaging. May 2003;17(5): Roberts C, Issa B, Stone A, Jackson A, Waterton JC, Parker GJ. Comparative study into the robustness of compartmental modeling and model-free analysis in DCE- MRI studies. J Magn Reson Imaging. Apr 2006;23(4): Tofts PS, Brix G, Buckley DL, et al. Estimating kinetic parameters from dynamic contrast-enhanced T(1)-weighted MRI of a diffusable tracer: standardized quantities and symbols. J Magn Reson Imaging. Sep 1999;10(3): Brix G, Kiessling F, Lucht R, et al. Microcirculation and microvasculature in breast tumors: pharmacokinetic analysis of dynamic MR image series. Magn Reson Med. Aug 2004;52(2): Galbraith SM, Lodge MA, Taylor NJ, et al. Reproducibility of dynamic contrastenhanced MRI in human muscle and tumours: comparison of quantitative and semiquantitative analysis. NMR Biomed. Apr 2002;15(2): Hawkins RA, Miller AL, Cremer JE, Veech RL. Measurement of the rate of glucose utilization by rat brain in vivo. J Neurochem. Nov 1974;23(5): Sacks W. Cerebral metabolism of isotopic glucose in normal human subjects. J Appl Physiol. Jan 1957;10(1): Sokoloff L. Localization of functional activity in the central nervous system by measurement of glucose utilization with radioactive deoxyglucose. J Cereb Blood Flow Metab. 1981;1(1):

46 13. MacGregor RR, Fowler JS, Wolf AP, Shiue CY, Lade RE, Wan CN. A synthesis of 2-deoxy-D-[1-11C]glucose for regional metabolic studies: concise communication. J Nucl Med. Sep 1981;22(9): Voet D, Voet JG, Pratt CW. Fundamentals of biochemistry. Upgrade ed. New York: Wiley; Wu HM, Sui G, Lee CC, et al. In vivo quantitation of glucose metabolism in mice using small-animal PET and a microfluidic device. J Nucl Med. May 2007;48(5): Convert L, Morin-Brassard G, Cadorette J, Archambault M, Bentourkia M, Lecomte R. A new tool for molecular imaging: the microvolumetric beta blood counter. J Nucl Med. Jul 2007;48(7): van der Weerdt AP, Klein LJ, Boellaard R, Visser CA, Visser FC, Lammertsma AA. Image-derived input functions for determination of MRGlu in cardiac (18)F-FDG PET scans. J Nucl Med. Nov 2001;42(11): Hoekstra CJ, Hoekstra OS, Lammertsma AA. On the use of image-derived input functions in oncological fluorine-18 fluorodeoxyglucose positron emission tomography studies. Eur J Nucl Med. Nov 1999;26(11): Hove JD, Iida H, Kofoed KF, Freiberg J, Holm S, Kelbaek H. Left atrial versus left ventricular input function for quantification of the myocardial blood flow with nitrogen-13 ammonia and positron emission tomography. Eur J Nucl Med Mol Imaging. Jan 2004;31(1): Sanabria-Bohorquez SM, Maes A, Dupont P, et al. Image-derived input function for [11C]flumazenil kinetic analysis in human brain. Mol Imaging Biol. Mar-Apr 2003;5(2): Chen K, Bandy D, Reiman E, et al. Noninvasive quantification of the cerebral metabolic rate for glucose using positron emission tomography, 18F-fluoro-2- deoxyglucose, the Patlak method, and an image-derived input function. J Cereb Blood Flow Metab. Jul 1998;18(7): Ohtake T, Kosaka N, Watanabe T, et al. Noninvasive method to obtain input function for measuring tissue glucose utilization of thoracic and abdominal organs. J Nucl Med. Jul 1991;32(7): Kim J, Herrero P, Sharp T, et al. Minimally invasive method of determining blood input function from PET images in rodents. J Nucl Med. Feb 2006;47(2):

47 24. Su Y, Welch MJ, Shoghi KI. The application of maximum likelihood factor analysis (MLFA) with uniqueness constraints on dynamic cardiac micropet data. Phys Med Biol. Apr ;52(8): Eberl S, Anayat AR, Fulton RR, Hooper PK, Fulham MJ. Evaluation of two population-based input functions for quantitative neurological FDG PET studies. Eur J Nucl Med. Mar 1997;24(3): Shiozaki T, Sadato N, Senda M, et al. Noninvasive estimation of FDG input function for quantification of cerebral metabolic rate of glucose: optimization and multicenter evaluation. J Nucl Med. Oct 2000;41(10): Tsuchida T, Sadato N, Yonekura Y, et al. Noninvasive measurement of cerebral metabolic rate of glucose using standardized input function. J Nucl Med. Sep 1999;40(9): Wakita K, Imahori Y, Ido T, et al. Simplification for measuring input function of FDG PET: investigation of 1-point blood sampling method. J Nucl Med. Sep 2000;41(9): Meyer PT, Circiumaru V, Cardi CA, Thomas DH, Bal H, Acton PD. Simplified quantification of small animal [18F]FDG PET studies using a standard arterial input function. Eur J Nucl Med Mol Imaging. Aug 2006;33(8): Wong KP, Feng D, Meikle SR, Fulham MJ. Simultaneous estimation of physiological parameters and the input function--in vivo PET data. IEEE Trans Inf Technol Biomed. Mar 2001;5(1): Taylor JS, Tofts PS, Port R, et al. MR Imaging of Tumor Microcirculation: Promise for the New Millenium. Magn Reson Imaging. 1999;10: Giesel FL, Bischoff H, von Tengg-Kobligk H, et al. Dynamic contrast-enhanced MRI of malignant pleural mesothelioma: a feasibility study of noninvasive assessment, therapeutic follow-up, and possible predictor of improved outcome. Chest. Jun 2006;129(6): Jeong AK, Kim JK, Cho KS. Usefulness of a Pharmacokinetic Model Based on Dynamic Contrast-enhanced MRI for the Detection and Localization of Prostate Cancer. J Korean Radiol Soc. 2007;57(2): Dobre MC, Ugurbil K, Marjanska M. Determination of blood longitudinal relaxation time (T1) at high magnetic field strengths. Magn Reson Imaging. Jun 2007;25(5):

48 35. Farahani K, Saxton RE, Yoon HC, De Salles AA, Black KL, Lufkin RB. MRI of thermally denatured blood: methemoglobin formation and relaxation effects. Magn Reson Imaging. Dec 1999;17(10): Lu H, Clingman C, Golay X, van Zijl PC. Determining the longitudinal relaxation time (T1) of blood at 3.0 Tesla. Magn Reson Med. Sep 2004;52(3): Rozijn TH, van der Sanden BP, Heerschap A, Creyghton JH, Bovee WM. Influence of the pharmacokinetic model on the quantification of the Gd-DTPA uptake rate in brain tumours using direct T1 measurements. MAGMA. Aug 1998;6(1): Wedeking P, Eaton S, Covell DG, Nair S, Tweedle MF, Eckelman WC. Pharmacokinetic analysis of blood distribution of intravenously administered 153Gdlabeled Gd(DTPA)2- and 99mTc(DTPA) in rats. Magn Reson Imaging. 1990;8(5): Port RE, Knopp MV, Brix G. Dynamic contrast-enhanced MRI using Gd-DTPA: interindividual variability of the arterial input function and consequences for the assessment of kinetics in tumors. Magn Reson Med. Jun 2001;45(6): Cheng HL. T1 measurement of flowing blood and arterial input function determination for quantitative 3D T1-weighted DCE-MRI. J Magn Reson Imaging. May 2007;25(5): Zierhut ML, Gardner JC, Spilker ME, Sharp JT, Vicini P. Kinetic modeling of contrast-enhanced MRI: an automated technique for assessing inflammation in the rheumatoid arthritis wrist. Ann Biomed Eng. May 2007;35(5): Fritz-Hansen T, Rostrup E, Larsson HB, Sondergaard L, Ring P, Henriksen O. Measurement of the arterial concentration of Gd-DTPA using MRI: a step toward quantitative perfusion imaging. Magn Reson Med. Aug 1996;36(2): McIntyre DJ, Ludwig C, Pasan A, Griffiths JR. A method for interleaved acquisition of a vascular input function for dynamic contrast-enhanced MRI in experimental rat tumours. NMR Biomed. May 2004;17(3): Muzic RF, Jr., Cornelius S. COMKAT: compartment model kinetic analysis tool. J Nucl Med. Apr 2001;42(4): Cohen SD, Hindmarsh AC. CVODE, a stiff/nonstiff ODE solver in C. Computers in Physics. 1996;10(2): Fang YH, Muzic RF, Jr. Spillover and partial-volume correction for imagederived input functions for small-animal 18F-FDG PET studies. J Nucl Med. Apr 2008;49(4):

49 Chapter 2 Spillover and Partial Volume Correction for Image Derived Input Functions for Small Animal 18 F FDG PET Studies 46

50 Accepted by Journal of Nuclear Medicine on 12/20/2007 Manuscript number: JNUMED/2007/ Title Spillover and partial volume correction for image-derived input functions for small animal FDG-PET studies Authors Yu-Hua Dean Fang 1, 3 1, 2, 3 Raymond F. Muzic, Jr. 1 Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio 2 Department of Radiology, University Hospitals of Cleveland, Case Western Reserve University, Cleveland, Ohio 3 Case Center for Imaging Research, Case Western Reserve University, Cleveland, Ohio 47

51 Abstract We present and validate a method to obtain an input function from dynamic image data and zero or one blood sample for small animal FDG-PET studies. The method accounts for spillover and partial volume effects via a physiologic model to yield a modelcorrected input function (MCIF). Methods: Image-derived input functions from heart ventricles and myocardial time-activity curves were obtained from 14 Sprague-Dawley rats and 17 C57BL/6 mice. Each MCIF was expressed as a mathematical equation with seven parameters, which were estimated simultaneously with the myocardial model parameters by fitting the image-derived input functions and myocardium curves to a dualoutput compartment model. Zero or one late blood sample was used in the simultaneous estimation. MCIF was validated by comparison to input measured from blood samples. Validation included computing errors in the areas under the curves (AUCs) and in FDG influx constant Ki in three types of tissue. Results: For the rat data, the AUC error was 5.3±19.0% in the zero-sample MCIF and -2.3±14.8% in the one-sample MCIF. When the MCIF was used to calculate the Ki of the myocardium, brain and muscle, the overall errors were -6.3±27.0% in the zero-sample method (correlation coefficient r=0.967) and 3.1±20.6% in the one-sample method (r=0.970). The t-test failed to detect a significant difference (p>0.05) in the Ki estimates from both the zero-sample and one-sample MCIF. For the mouse data, AUC errors were 4.3±25.5% in the zero-sample MCIF and - 1.7±20.9% in the one-sample MCIF. Ki errors averaged -8.0±27.6% for the zero-sample method (r=0.955) and -2.8±22.7% for the one-sample method (r=0.971). The t-test detected significant differences in the brain and muscle in the Ki for the zero-sample method, but no significant differences with one-sample method. In both rat and mouse, 48

52 zero-sample and one-sample MCIF both showed at least a 10-fold reduction in AUC and Ki errors compared to uncorrected image-derived input functions. Conclusion: MCIF provides a reliable, non-invasive estimate of the input function that can be used to accurately quantify glucose metabolic rate in small-animal FDG-PET studies. Key words: input function, spillover correction, partial volume effect correction, compartment modeling 49

53 INTRODUCTION Positron emission tomography (PET) with 2-[ 18 F]fluoro-2-deoxy-D-glucose (FDG) is widely used to quantify glucose metabolism. This entails compartmental modeling to estimate kinetic rate constants and requires knowledge of the input function, which is the FDG plasma time-activity curve (1, 2). The gold standard to determine the input function is an invasive blood sampling procedure to measure the FDG activity concentration in the arterial blood. For small animal FDG-PET studies, this procedure is challenging because of the small size of blood vessels and the limited blood volume. In addition, blood loss may perturb the physiology and confound the experimental outcome. To avoid these problems, various methods have been proposed to estimate the input function noninvasively. Those methods can be categorized as (i) image-derived input functions, (ii) factor analysis methods, (iii) standardized input functions and (iv) simultaneous estimation. Image-derived input functions (IDIFs) are the time-activity curves obtained by drawing regions over the major vascular structures, such as the ventricular cavity, aorta, or large arteries (3). This method is relatively simple to use in principle. However, in small animal imaging, hearts and arteries are small compared to the scanner spatial resolution. Consequently, vascular radioactivity is blurred into adjacent tissues and vice versa. Also, cardiac and respiratory motion creates additional cross-contamination between vascular structures and surrounding tissues. As a result, curves obtained from regions drawn over the vascular space will be a mixture of the input function and surrounding tissue time- 50

54 activity curves. Some methods have been proposed to correct for the mixing, sometimes called spillover and partial volume effect, for image-derived input functions using a few blood samples in clinical studies (4, 5). For small animal PET imaging, Yee et al. applied the IDIF method to 15 O water studies with correction for partial volume and spillover (6). However, the assumption that the blood tracer concentration achieves equilibrium with that in the tissue makes the method inappropriate for FDG. Green et al. presented an IDIF in mice assuming negligible myocardium contribution to the cavity curve (7). In many circumstances, this assumption is not valid. Factor analysis (FA) methods have been applied to separate the arterial-blood and myocardial tissue components in the dynamic heart images. The heart image is assumed to be a sum of three or more factors, typically: myocardium and blood in the left and right ventricles. Principle component analysis is applied to find these components and therefore obtain an estimate of the input function. FA has been used to extract the input function for rats and mice using just one blood sample (8), showing good correlation between the measured and extracted input functions. FA is described as being robust and requiring few blood samples. However, the ambiguity still exists in this method whether, especially in mice (8), the factors found include the blood curves without spillover and partial volume degradation. Moreover an analysis of the consequence of using FAderived input functions on the FDG influx rate constant has not been reported. Standardized input function methods assume that input functions across animals and experimental conditions have the an identical curve shape that can be used to 51

55 approximate the individual input function by scaling the standard curve to match the concentration measured in one or two blood samples (9). In reality, the input function curve shape varies between subjects based on several factors, such as the injection technique and speed, dietary state of the animal, metabolic status, catheterization site and the animal species. The standard curve therefore lacks the ability to account for the range of curve shapes present, especially in animals with abnormal metabolism. Moreover, the use of standardized input functions has not been validated for mice. Simultaneous estimation was originally proposed to estimate the input function for human brain studies (10). It is assumed that the input function can be described by a mathematical function with multiple parameters that can be estimated simultaneously with the fitting of multiple regions of interest, typically three. Few, usually two, late blood samples are required in the simultaneous estimation process. The main challenge of this method is the large number of parameters (>25) that needs to be estimated, thus making the fitting especially challenging. Moreover, this method has not been validated on small animal PET studies. In this paper we present and validate a method that overcomes the limitations of methods described above. Our method uses simultaneous estimation to correct the spillover and partial volume effect for an image-derived input function. We assume that both the image-derived input function from the heart ventricles and the time-activity curve of myocardium are mixture of the true input function and the myocardium uptake. Using a mathematical equation to express the input function, we can then determine both time- 52

56 activity curves as outputs of a compartment model and simultaneously with the nonvascular tissue parameters. The estimated input is denoted as a model-corrected input function (MCIF) because it is obtained by correcting the spillover and partial volume effects from IDIF by compartment modeling. This method is validated by comparing the MCIF estimated with zero or one blood samples to the input functions measured with blood sampling in rats and mice. We also compared our MCIF to the uncorrected IDIF. 53

57 MATERIALS AND METHODS Rat studies All experiments took place in the Case Center for Imaging Research in Case Western Reserve University and were performed according to a protocol approved by its Institutional Animal Care and Use Committee. A total of twenty data sets were acquired from 14 female Sprague-Dawley rats ranging from 206 to 253 grams. Six of the 14 underwent two studies separated by one week. For each scan, the rat was anesthetized by 2~2.5% isoflurane in oxygen. Each rat was cannulated in tail artery with microrenathanes tubing (0.83mm O.D.) and in tail vein with micro-renathanes tubing (0.63mm O.D.) Each micropet study began with a 10-min transmission scan using a 57 Co source on a micropet R4 scanner (Siemens Medical Solutions USA, Inc.). Following that was a 90-min emission scan in 3-D data acquisition mode commencing with the intravenous bolus injection of approximately 30 MBq FDG. Dynamic image sequences were reconstructed with 12 5-sec, sec, 5 60-sec and sec frames. Fourier rebinning and 2-D filtered back-projection (FBP) algorithm was used for image reconstruction with 256 by 256 by 63 pixels per frame. Pixel spacing was 0.42 x 0.42 x 1.25 mm and field of view included the brain, heart and lung. Correction for radioactive decay, attenuation, scatter and dead-time were performed during the sinogram histogramming and reconstruction. Blood sampling was performed to provide a gold-standard reference. For the first three minutes a continuous automatic blood sampling device, Blood Activity Monitor (BAM), 54

58 was used to acquire data with high sampling rate in order to capture the initial rapid kinetics (11). During this time the blood was continuously drawn from the arterial line using a syringe pump at 0.2 ml/min flow rate and counted by the BAM using contiguous 0.1 sec intervals. After the first three minutes, continuous sampling was discontinued and ten samples were manually taken at 3.5, 4, 4.5, 5, 7, 10, 15, 30, 60 and 90 minutes. For twelve out of the 20 studies, a late venous sample at 92 minutes was taken to compare the activity concentrations in late arterial and venous blood samples. The manual samples were counted with a well counter (Wallac LKB 1282). Sample net weight was measured to obtain the activity concentration from the counts. Input functions from the BAM and manual samples were linearly interpolated to construct a single input function. Shortly after the end of the study, an extra blood sample was taken for determination of hematocrit and plasma activity fraction (plasma FDG over whole-blood FDG). Mouse studies In addition to rat data, our method was tested using mouse data shared on the Internet by Crump Institute of Molecular Imaging, UCLA (12, 13). Seventeen C57BL/6 male mice weighing from 22 to 36 grams were anesthetized by 1.5% to 2% isoflurane in oxygen. Of these, nine were pretreated with insulin. As insulin does not directly affect the spillover and partial volume effects, these data were treated as one group for evaluation of the input function estimation. Into each mouse 9 to 37 MBq FDG was bolus-injected in the tail vein. Input functions were measured using femoral artery blood samples. On average, 15 (range: 5 to 22) samples were collected from each mouse. Eight mice were scanned with micropet Focus-220 scanner and nine with a micropet P4 scanner (both scanners: 55

59 Siemens Medical Solutions USA, Inc.) For each PET study, a mouse underwent an x-ray CT scan for attenuation correction and then either a 60-min or 90-min emission scan. Herein only the first 60 minutes of data were used to standardize the data analysis. The image reconstruction method was FBP with 128 by 128 by 95 pixels. Dynamic framing varies slightly among these studies but typically there were sec, 1 2-sec, 1 4-sec, 1 6-sec, 1 15-sec, 3 30-sec, 1 60-sec, sec, sec and sec frames. FDG compartment model The well-established compartment model has been used for estimating the rate constants and the glucose metabolic rate (1, 2). This model entails two tissue compartments: FDG and phosphorylated FDG (FDG-6P) in extravascular tissue, denoted by C e and C m respectively. The state equations are: Eq. 1 Eq. 2 The model output equation is:, Eq. 3 56

60 where m i is the model-predicted activity concentration in the i th frame with the frame beginning at time and ending at time. F v is the fraction of pixel that is vascular space. C p and C a are the plasma and whole-blood time-activity curves, respectively. C p is calculated from C a by:, Eq. 4 where H is the hematocrit and F pa is the fraction of blood activity attributed to that in plasma (plasma activity divided by whole-blood activity.) Although there have been studies showing that the F pa varies with time (14, 15), accounting for this time-variation requires blood sampling. In fact, many studies use whole blood as a surrogate for plasma activity and therefore implicitly assume F pa is constant. Thus, to simplify the procedure and offer the possibility of avoiding blood sampling, we treat F pa as a constant. (We observed F pa to be 0.63±0.07 in rats.) The glucose metabolic rate of glucose is defined by: Eq. 5 LC is the lumped constant between FDG and glucose, and C glu is the glucose concentration in blood. The FDG influx constant Ki equals. Often determination of Ki alone is a sufficient index of glucose metabolism and it can be robustly estimated. In contrast, obtaining precise estimates of k 1 to k 4 is less frequently 57

61 used because of parameter correlation and noise in the time-activity curves. Therefore, our present work focuses on the estimates of Ki in the parameter estimation results. Dual-output cardiac FDG model Ideally, when a ROI is drawn within the cavity of left ventricle, the tissue time-activity curve would equal the whole-blood time-activity curve C a. However, due to spillover and partial volume effects, the model-predicted output of an image-derived input function is more accurately expressed as a mixture of blood and non-vascular tissue activity:, Eq. 6 where is the mixing coefficient from the myocardium to ventricular cavity, and is the mixing coefficient of the input function C a. Similarly, the model output of the surrounding myocardium FDG concentration is:, Eq. 7 where is the mixing coefficient from the tissue FDG uptake, and is the mixing coefficient of the input function C a contribution to myocardium ROI. If there is no spillover and partial volume effect, and would equal one, and and would equal zero. In micropet images, those four mixing coefficients range between 0 and 1, 58

62 with and dominant (closer to 1) and greater than and. In this study, it is assumed that a single set of extravascular compartments (C e, C m ) is adequate to predict both the ventricular ( ) and myocardial ( ) activities because activities measured in these areas reflect a mixture of the same underlying myocardial extravascular and intravascular activities. Simultaneous estimation Typical parameter estimation in compartment modeling assumes that both input and output are known, so that model parameters can be estimated by fitting the model output to experimental data. Simultaneous estimation assumes, however, that the input is unknown but can be described by a model or equation. Then both the parameter sets of the input function and the tracer kinetic model can be estimated simultaneously by fitting model outputs to the experimental data. This entails accounting for the dependence of the model output on the input function parameters. In FDG-PET studies, the input function C a can be approximated by a seven-parameter equation (16): Eq. 8 With Eq. 8 and values for τ, A 1 ~A 3 and L 1 ~L 3, the input function can be approximated and carried into the model for solving the model output in Eq. 6 with a given set of k 1 ~k 4,, and. Model output can be solved in the same way. Model outputs and are then fit to the corresponding measurements: the PET measurement of 59

63 FDG concentration in the ventricular cavity and in the myocardium by minimizing the objective function:, Eq. 9 where p is the parameter vector [τ, A 1, A 2, A 3. L 1, L 2, L 3, k 1, k 2, k 3, k 4,,,, ] to be optimized. n is the total number of frames. w 1 and w 2 are weighting coefficients. If one blood sample is available to incorporate into the estimation process, the objective function can be extended to:, Eq. 10 where b is the blood activity concentration at the sampling time t s. w 3 is the weighting associated with the blood sample. The values of the weights w 1 ~w 3 are estimated simultaneously with all other parameters using an extended least squares (ELS) method described by Muzic and Christian (17). The initial values, lower and upper bounds of all parameters are summarized in Table 1. Once the simultaneous estimation is finished, the estimated values parameters τ, A 1 ~A 3 and L 1 ~L 3 are used in Eq. 8 to calculate the MCIF. VOI and ROI specification 60

64 Heart and myocardium ventricular volumes of interest (VOIs) were drawn for each animal on short-axis slices. When necessary, image volumes were rotated to obtain the short-axis view. A ventricular VOI consisted of two to four 2-D circular ROIs that were placed on the adjacent slices at the center of heart ventricular cavity. Those ROIs were approximately 2.1 mm in diameter for rats and 1.6 mm for mice. A myocardium VOI was made of several 2-D doughnut-like circular ROIs with hollow centers drawn on adjacent slices. The inner diameters of the myocardial ROIs were 4.2 mm for rats and 2.4 mm for mice. The outer diameters were 9.2 mm for rats and 5.2 mm for mice. Fig. 1 shows a ROI on rat images. For validation by comparison of Ki values, brain and skeletal muscle ROIs were drawn for each animal. Software and Computation Environments All numerical analyses were done using MATLAB R2007a (Mathworks, Natick MA). COmpartment Model Kinetic Analysis Tool (COMKAT) (18), a kinetic modeling toolbox free for non-commercial use, was used for implementing the compartment models and fitting of experimental data. The optimization was performed with COMKAT s fitgen function that uses MATLAB function fmincon which is based an interior-reflective Newton method (17, 19). Input function validation How well an estimated input function approximated the measured input function was determined by direct and indirect methods. The direct method compared input functions by calculating the difference in areas under curves (AUCs) and root mean square error 61

65 (RMSE) of estimated input functions. The indirect comparison examined the impact of an estimated input function on the estimated of tissue parameter Ki. Ki values in myocardium, brain and muscle were calculated using a measured input function (Ki mea ) and an MCIF (Ki est ). The error percentage of Ki was calculated as (Ki est -Ki mea )/Ki mea 100% for each region and subject. These percent errors were summarized using mean and standard deviation. Also, the correlation coefficient between Ki mea and Ki est were calculated. A t-test with α=0.05 was used to examine if the Ki mea and Ki est were significantly different in each region. 62

66 RESULTS Results of the direct comparison between measured input functions, IDIF and MCIF are summarized in Table 2. As shown in Fig. 2, an IDIF without any correction is highly biased because of the spillover. Therefore, AUC was highly biased and the RMSE was extremely high for IDIF as seen in Table 2. For example, the magnitude of AUC errors both in rats and mice exceeded 100% meaning the AUC was more than double what it should have been. In contrast, MCIF under all conditions had an AUC error of less than 6% bias for all conditions rats and mice, zero and one blood sample. With inclusion of one blood sample, this error was about 2%. Thus, compared to IDIF, MCIF reduces the AUC error by approximately 20-fold in rats and 100-fold in mice. In terms of RMSE, MCIF achieved values of about 0.04 MBq/ml which were much smaller than the 0.17 to 0.28 MBq/ml values obtained with uncorrected IDIF. To illustrate the input function estimated with zero-sample MCIF compared to the measured input, Fig. 3 shows a representative data set from one rat. The input function is accurately estimated for both the early minutes and the whole study as shown in Fig. 3A and 3B, even when the initial guess of the input function parameters is far from the true values. Fig. 3C demonstrates that the model output fits the IDIF and myocardium data very well. Fig. 4 shows representative fitting results of one set of mouse data, indicating close approximation of the MCIF to the measured input. As the purpose to estimate the input function is for its use in compartment modeling, evaluating how much error is introduced in the estimates of Ki is especially important. 63

67 Table 3 lists the comparison of Ki values obtained from various input functions. When an IDIF without any correction was used in estimating Ki, the estimation of Ki was highly biased compared to the reference Ki values obtained using the measured input. This is due to the IDIF itself being highly biased as shown in the direct comparison described above. In contrast, the MCIF greatly reduced the bias in the Ki estimates. For rats, the overall error percentage of Ki of all three regions averaged 6.3±27.0 for zero-sample MCIF and -3.1±20.6 for one-sample MCIF, with correlation coefficients and 0.970, respectively. The t-test failed to detect a significant difference in all three types of tissue using either zero-sample or one-sample MCIF (p>0.05). Comparing the zero-sample and one-sample MCIF methods, one-sample MCIF methods reduced Ki bias in both the brain and muscle but slightly increased it in the myocardium. The precision was also greatly improved in brain and muscle. Correlation coefficients increased in all three regions with one-sample MCIF. Fig. 5 shows a box plot of the Ki error in zero- and one-sample MCIF. Including one blood sample brought the median value closer to zero and reduced the inter-quartile range. Taken together, these results show that the MCIF performs well in the tasks of estimating the input function and Ki, greatly reducing the error for imagederived input functions. Similar results can be seen in the mouse data as listed in Table 4. Ki was again highly biased when using the IDIF without correction. With the MCIF, the overall error percentage of Ki of all three types of tissue was 8.0±27.6 for zero-sample and 2.8±22.7 for one-sample MCIF method, with correlation coefficients and Considering the individual tissue types, myocardium had the least bias and best precision in Ki 64

68 estimates. Although the correlation was high (r>0.84) in all three types of tissue with zero-sample MCIF, the t-test detected significant biases in Ki estimates in brain and muscle (p<0.05). These biases were resolved by the use of one-sample MCIF: the significant difference was not detected in any of the three regions. Moreover, use of one sample reduced bias and improved precision in brain and muscle, and increased correlation coefficients of all three regions to over 0.9. The advantages of using the blood sample are visually evident in the box plot shown in Fig. 6. In summary, the Ki analysis for MCIF in mice, bias and precision are better than that with IDIF. Inclusion of one blood sample improves MCIF such that no statistically significant bias was detected. As a less-invasive alternative to using one late arterial blood sample, we considered substituting activity concentration in a venous sample as an approximation to that in an arterial sample. In rats, venous activity concentration error averaged -5.8±13.0% compared to the arterial activity concentration. Regression analysis showed a correlation coefficient of (y=0.942 x+0.019, where y is the arterial activity concentration and x and is venous activity concentration), indicating that late venous activity concentration is very close to the arterial concentration. 65

69 DISCUSSION The ability to quantify physiologic function with measurable and testable results in a reliable and practical manner crucial to research. In this regard, compartment modeling has long been regarded as one of the best ways to analyze PET images. However, the blood sampling procedure to measure the input function in small animals has been a major barrier because of its invasive nature, the small size of blood vessels and animals limited blood volume. Although new and advanced devices have been proposed to measure the blood activity such as microfluidic blood-sampling devices (15) and bloodactivity monitors (20), an invasive surgery procedure is required making it difficult for imaging centers to include the technically demanding procedure in the routine PET studies. Obtaining the input function from images using IDIFs or FA is a popular alternative as it can be done without blood sampling. IDIFs have the advantage of simplicity over FA methods but the spillover and partial volume effects makes the IDIF a highly biased estimate. Therefore, we sought to find a practical and robust method to correct for the spillover and partial volume effect for IDIF by using simultaneous estimation to determine and correct the cross-contamination between ventricular and myocardial activities. We compared the estimated input functions from MCIF to the inputs measured from blood samples. Our results show that one-sample MCIF is validated as a reliable method to estimate input functions and Ki constants. Using the extensive blood sampling method as the reference, the AUC error of one-sample MCIF is below 3% on average. Ki bias in 66

70 both rats and mice is less than 10% and correlation coefficients are high. Most importantly, no significant difference was found by the t-test in the one-sample MCIF in both rats and mice, indicating that the one-sample MCIF can be used as a replacement for input functions measured with extensive blood sampling. To use the one-sample MCIF, a late venous sample, which is easy to collect, can be substituted for the arterial blood sample since late arterial and venous concentrations are very similar as our results demonstrate. In addition, as the estimated MCIF is the whole-blood time-activity curve C a, at least one blood sample must be taken to measure the hematocrit and activity fraction for conversion between C p and C a. This could provide the whole-blood concentration used for the simultaneous estimation in MCIF. Therefore, since one blood sample is simple to obtain and necessary for hematocrit determination, we recommend using the one-sample MCIF. On the other hand, although the zero-sample MCIF is not as accurate as one-sample MCIF, its small bias did not reach statistically significance thus it may be applied in rat studies when blood sampling is infeasible or in retrospective analyses of data for which no blood samples were taken. Compared to currently available methods for estimating input functions, MCIF has advantages. First, compared to IDIF, MCIF greatly reduces the bias by correcting for spillover and partial volume effects. Second, compared to simultaneous estimation, MCIF has fewer parameters to estimate. Whereas the simultaneous estimation method first proposed by Wong et al. (10) models each tissue ROI according to an independent set of compartments, the MCIF method assumes that the measured heart ventricle and myocardium curves can be expressed as a weighted sum of the blood activity and the 67

71 same underlying extravascular (C e ) and metabolized (C m ) activity concentrations. Consequently, only two VOIs and one set of k 1 ~k 4 needs to be estimated for MCIF with a total number of parameters to estimate of 15 which is 10 fewer than the 25 required by Wong s simultaneous estimation method. We speculate that MCIF will be improved with technological advances. For example, cardiac and respiratory gating could reduce the spillover and partial volume effects in the image-derived input function (21), therefore making MCIF more robust. Similarly, image reconstruction techniques such as maximum a posteriori (MAP) algorithm that accurately model the gamma ray transport can produce images with better resolution, therefore reducing the spillover in the image-derived input function (22). Those methods can be used in combination with MCIF without any conflicts. When MCIF is applied to an IDIF with less spillover and partial volume, MCIF should be able to estimate the input function even more accurately. Although MCIF method is developed and validated using FDG, the methodology should be applicable to other PET tracers. In particular, the output equation of the heart ventricles and myocardium would remain the same and the configuration of the tracer kinetic model and parameter values, including initial values and bounds, would be adjusted. However, for tracers that require precise measurement of metabolites and for which a standard metabolite correction is not available, blood samples are inevitable. Otherwise, for other tracers it would be necessary to validate the adjustments in a study in a limited number of subjects wherein blood samples are collected and used for validation 68

72 as we have done here. Moreover, the MCIF should be applicable to human studies with similar adjustments and validation. 69

73 CONCLUSION Herein we show that the MCIF accurately accounts for spillover and partial volume effect for IDIF and yields an input function suitable for use in quantifying glucose metabolic rate using the FDG model. Specifically, we show that either zero-sample or one-sample MCIF have AUC error, RMSE and Ki estimation errors that are much lower than those obtained using the uncorrected IDIF. Furthermore, the use of one blood sample achieves a bias of Ki estimates to a level that is not statistically significant and that is lower than the uncertainty in the Ki estimates. Therefore, MCIF can be applied to FDG-PET small animal imaging for modeling analysis with minimum blood sampling requirement. The MCIF method is incorporated into the COMKAT toolbox and available online at free for non-commercial research use. ACKNOWLEDGEMENTS This work was supported by National Institute of Health grants R33-CA and R24-CA The authors thank Dr. Henry S.C. Huang and the Crump Institute of Molecular Imaging for the courtesy of sharing mouse data with us. We would also like to thank Chandra Spring Robinson and Deborah Barkauskas for assisting the experiments. 70

74 REFERENCE 1. Huang SC, Phelps ME, Hoffman EJ, Sideris K, Selin CJ, Kuhl DE. Noninvasive determination of local cerebral metabolic rate of glucose in man. Am J Physiol. Jan 1980;238:E Phelps ME, Huang SC, Hoffman EJ, Selin C, Sokoloff L, Kuhl DE. Tomographic measurement of local cerebral glucose metabolic rate in humans with (F-18)2-fluoro-2- deoxy-d-glucose: validation of method. Ann Neurol. 1979;6: van der Weerdt AP, Klein LJ, Boellaard R, Visser CA, Visser FC, Lammertsma AA. Image-derived input functions for determination of MRGlu in cardiac (18)F-FDG PET scans. J Nucl Med. 2001;42: Chen K, Bandy D, Reiman E, et al. Noninvasive quantification of the cerebral metabolic rate for glucose using positron emission tomography, 18 F-fluoro-2- deoxyglucose, the Patlak method, and an image-derived input function. J Cereb Blood Flow Metab. 1998;18: Ohtake T, Kosaka N, Watanabe T, et al. Noninvasive method to obtain input function for measuring tissue glucose utilization of thoracic and abdominal organs. J Nucl Med. 1991;32: Yee SH, Jerabek PA, Fox PT. Non-invasive quantification of cerebral blood flow for rats by micropet imaging of 15 O labelled water: the application of a cardiac timeactivity curve for the tracer arterial input function. Nucl Med Commun. 2005;26: Green LA, Gambhir SS, Srinivasan A, et al. Noninvasive methods for quantitating blood time-activity curves from mouse PET images obtained with fluorine-18- fluorodeoxyglucose. J Nucl Med. 1998;39: Kim J, Herrero P, Sharp T, et al. Minimally invasive method of determining blood input function from PET images in rodents. J Nucl Med. 2006;47: Meyer PT, Circiumaru V, Cardi CA, Thomas DH, Bal H, Acton PD. Simplified quantification of small animal [ 18 F]FDG PET studies using a standard arterial input function. Eur J Nucl Med Mol Imaging. 2006;33: Wong KP, Feng D, Meikle SR, Fulham MJ. Simultaneous estimation of physiological parameters and the input function--in vivo PET data. IEEE Trans Inf Technol Biomed. 2001;5: Salinas CA, Pagel MD, Muzic Jr RF. Measurement of arterial input functions in rats. Paper presented at: 2004 Society for Molecular Imaging Annual Meeting, 2004; St. Louis. 71

75 12. Accessed Dec 7th, Huang SC, Wu HM, Truong D, et al. A Public Domain Dynamic Mouse FDG MicroPET Image Data Set for Evaluation and Validation of Input Function Derivation Methods. Paper presented at: Nuclear Science Symposium Conference Record, IEEE, Weber B, Burger C, Biro P, Buck A. A femoral arteriovenous shunt facilitates arterial whole blood sampling in animals. Eur J Nucl Med Mol Imaging. 2002;29: Wu HM, Sui G, Lee CC, et al. In vivo quantitation of glucose metabolism in mice using small-animal PET and a microfluidic device. J Nucl Med. 2007;48: Feng D, Huang SC, Wang X. Models for computer simulation studies of input functions for tracer kinetic modeling with positron emission tomography. Int J Biomed Comput. 1993;32: Muzic RF, Jr., Christian BT. Evaluation of objective functions for estimation of kinetic parameters. Med Phys. 2006;33: Muzic RF, Jr., Cornelius S. COMKAT: compartment model kinetic analysis tool. J Nucl Med. 2001;42: Coleman TF, Li Y. An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds. SIAM J Optimiz. 1996;6: Convert L, Morin-Brassard G, Cadorette J, Archambault M, Bentourkia M, Lecomte R. A new tool for molecular imaging: the microvolumetric beta blood counter. J Nucl Med. 2007;48: Yang Y, Rendig S, Siegel S, Newport DF, Cherry SR. Cardiac PET imaging in mice with simultaneous cardiac and respiratory gating. Phys Med Biol. 2005;50: Stout D, Kreissl MC, Wu H-M, Schelbert HR, Huang S-C. Left ventricular blood TAC quantitation with micropet imaging in mice using MAP, FBP and blood sampling. Paper presented at: Nuclear Science Symposium Conference Record, 2005 IEEE,

76 TABLES TABLE 1 Initial values and bounds for parameter estimation to obtain the MCIF 73

77 TABLE 2 Direct comparison of estimated input functions 74

78 TABLE 3 Comparison of Ki estimates from measured and estimated input functions from rat data (n=20) 75

79 TABLE 4 Comparison of Ki estimates from measured and estimated input functions from mouse data (n=17) 76

80 FIGURES FIGURE 1. Typical placement of the ventricular and myocardium ROIs. The center ROI is the ventricular one. The area between the other two ROIs denotes myocardium. 77

81 FIGURE 2. The comparison between the measured input function (solid) and the IDIF (dashed) in one rat shows that the IDIF is higher than the measured input, mainly due to the spillover from myocardium FDG activity. 78

82 FIGURE 3. Estimation plots of one rat with zero-sample MCIF estimation. (A) The measured input function (circles) and the estimated input with zero-sample MCIF method (solid) for the first three minutes. (B) The measured input function (circles) and the estimated input with zero-sample MCIF method (solid) for the entire scan duration. (C) Measured and model-predicted time-activity curves for the IDIF and the myocardium uptake. In both A and B the estimated input functions shows a good agreement with the measured one. C shows that the dual output model can fit the data well. 79

83 FIGURE 4. Estimation results of one mouse with zero-sample MCIF estimation. (A) The measured input function (circles) and the estimated input with zero-sample MCIF method (solid) for the first three minutes. (B) The measured input function (circles) and the estimated input with zero-sample MCIF method (solid) for the whole scan duration. (C) Measured and model-predicted time-activity curves for the IDIF and the myocardium uptake. 80

84 FIGURE 5. Box plot of the Ki error percentage of zero-sample and one-sample MCIF estimation for rat data. The box height shows the inter-quartile range (IQR). The median is shown as the line in the box. The whiskers indicate the quartile bounds ± 1.5 x IQR. Outliers that exceed this range are indicated by circles. For visual clarity, results from IDIF are not shown on this plot because the Ki with IDIF has a much higher error magnitude than the MCIF. In general the heights of the boxes of the one-sample MCIF are lower than the zero-sample MCIF. The error median is brought to be closer to zero by the one-sample MCIF. 81

85 FIGURE 6. Box plot of the Ki error percentage of zero-sample and one-sample estimation for mouse data. See Figure 4 caption for description of what the box height, center line and whiskers indicate. Notice the significant reduction of inter-quartile range in one-sample MCIF. Error median is closer to zero in the one-sample MCIF, too. 82

86 Chapter 3 Simultaneous Measurement of the Arterial Input Function and Tissue Uptake of Gd DTPA with Single Frame Inversion Recovery turboflash Sequences for Kinetic Modeling Analysis 83

87 Intended journal for submission: Magnetic Resonance in Medicine Expected submission date: April 2009 Title Simultaneous measurement of the arterial input function and tissue uptake of Gd DTPA with single frame inversion recovery turboflash sequences for kinetic modeling analysis Authors Yu Hua Dean Fang 1,2, Chris Flash 2,3, Jack Jesberger 2,3, and Raymond F. Muzic, Jr. 1,2,3 1 Department of Biomedical Engineering, Case Western Reserve University, Cleveland OH 2 Case Center for Imaging Research, Case Western Reserve University, Cleveland OH 3 Department of Radiology, Case Western Reserve University, Cleveland OH 84

88 Abstract A new kinetic modeling method is proposed for estimating tissue permeability to contrast agents with small animal DCE MRI studies. Without the typical conversion between signal intensity to T1 and concentration, the signal intensity measured from single frame, inversion recovery turboflash sequences is modeled as a function of Gd DTPA concentration. By incorporating the partial inversion and time of flight effects of flowing blood, arterial input functions and tissue kinetic parameters (Ktrans and ve) can be measured by fitting the experimental intensity curves without requiring cardiac gating or specific slice orientations. Methods. Intensity equations were derived for tissue and flowing blood as weighted summation of different components of signal sources into functions of [Gd], relaxivity and pre contrast T1. [Gd] in arterial blood and extra cellular, extra vascular spaces (EES) can be modeled by mathematical equations. Physiologic parameters were estimated by non linear optimization algorithms via direct curve fitting to the time intensity curves. Simulation studies were used to evaluate the imaging protocol in terms of sampling rate, parameter estimation sensitivities to noises and identifiability of input function and tumor parameters. Six data sets from normal Sprague Dawley rats ~220g were acquired to evaluate the parameter estimation for input functions and brain Ktrans, ve and fraction of vasculature Fv. Each study was divided into two parts of scans. The preparation scans were used to measure pre contrast T1, effective flip angle and inversion power of a region of interest (ROI). The contrast enhanced scans entailed repeated, single slice and single frame, inversion recovery turboflash scans. Intensity curves obtained from internal carotid arteries and brain ROIs were fitted 85

89 directly to the kinetic model and intensity equations to estimate parameters of both the input and tissue. Results. Simulation studies showed that our method was capable of accurate estimation of both the input function and the tumor parameters with low bias and high precision under presence of noises. Input functions estimated from animal data were compared to literature values and showed good consistency with them while providing individually estimated curve shapes. The estimated Ktrans and Fv also corresponded to brain physiology well. Conclusion. With the proposed protocol and novel modeling techniques, tissue permeability can be quantified by kinetic modeling analysis with DCE MRI using an individually estimated arterial input function. 86

90 INTRODUCTION Dynamic contrast enhanced (DCE) MRI has been widely applied in both clinical and pre clinical studies to evaluate functional changes of lesions. Gd DTPA is one of the most popular contrast agents used in DCE MRI. Its molecular size and properties allow it to enter the extravascular extracellular spaces (ESS). Therefore, Gd DTPA has become a standard clinical contrast agent to study vascular permeability, especially in oncology studies (1 3). This method has profound applications in preclinical imaging studies as an indication for therapy and treatment evaluation for the tumor physiology (4, 5). In order to quantify the in vivo perfusion with DCE MRI data, kinetic models of Gd DTPA uptake and clearance have been developed to estimate capillary permeability parameters. The Tofts model, which is a single compartment model with wash in and wash out transports, is well established and widely accepted for such analysis (6 8). This model describes the relationship between the arterial input function and the tissue concentration time course. In order to apply this kinetic model for curve fitting of experimental data, image data must first be converted to T1 values and then to concentration units. With a measured arterial input function, an optimization algorithm can be utilized to adjust the kinetic parameters until the model predicted output function best fits the experimental curve. The estimated parameters, typically denoted as Ktrans and kep, have been shown to be valuable in 87

91 evaluating perfusion and capillary permeability in both clinical and pre clinical evaluations (4, 5, 9). Although it has been widely applied in various types of imaging studies, this process to quantify perfusion has several challenges that limit such quantification to become more a routine procedure. First, measurement of the arterial input function (AIF) is challenging in DCE MRI studies. AIF is difficult to measure from blood samples because T1 measured from blood samples could vary significantly from in vivo blood T1 due to the changes in oxygen level and blood protein denaturing (10 12). In addition, small blood volumes of rodents limit the amount that can be withdrawn in a study and makes the blood sampling procedure difficult to perform. As a result, in DCE MRI studies with kinetic modeling requirements the input function is usually measured from images. However, measuring the AIF is still difficult in most pulse sequences because of the flowing blood that experience different excitation history (13, 14). Different methods have been proposed to measure the arterial input functions in small animal DCE MRI studies. One approach is to image the left ventricle or the aorta with cardiac gating using TOMROP sequences (15 17). This method has been shown to be capable of fast sampling and accurate measurement of the arterial input function. However, accurate cardiac gating is required and could become a challenge, as the heart rates in small rodents are fairly high. In addition, multi slice or interleaved acquisition must be used if the tissue or organ to be imaged is on a different slice than the heart. Other than measuring the AIF from the left ventricle, the alternative is to measure the AIF from arteries. A few different methods have been proposed. Cheng proposed to use saturation recovery methods 88

92 with a slice oriented on the same direction as the iliac artery in rabbits (18). However, in rodents it might not be as easy to place such a slice right along the artery. The curvature of the arteries often increases the difficulty to orient slices over arteries. In addition the slice orientation, preferably to be determined by the optimal view of the lesion, must be decided by the artery in this method. Other groups have reported using customized surface coils to measure the AIF from the tail artery or tail vein (19, 20). But this method requires additional hardware so may not be applied in all imaging groups. To avoid the challenges in measuring the input functions from images, an alternative method is to approximate the AIF by a bi or tri exponential input function that has fixed curve shape. Such AIF is sometimes denoted as a standard arterial input function (SAIF). Its parameter values have been reported in rats (21, 22) and applied in several reports for tumor studies (4, 23). This method is easy to use by only requiring the exact magnitude to be adjusted by the actual dose injected normalized to the standard 0.1 mmol/kg dose. The limitation of this method is that the curve shape is not determined individually. Port et al. reported that the individual difference in curve shape, determined by the renal clearance and circulations, does affect accuracy of parameter estimation in Gd DTPA kinetic modeling (24). In addition, dose residuals within the syringe and catheter can be a significant source of errors when the individual magnitude of SAIF is adjusted by the net injection dose. Therefore, the AIF should be measured individually for both the curve shape and magnitude in order to achieve good accuracy in parameter estimation. 89

93 In this report we also introduce a modeling method that directly fits the experimental intensity curve without having to convert between intensity, T1 and concentration. By formulating the relationship of intensity as a function of T1 and T1 as a function of concentration, time intensity curves can be modeled as a function of physiologic parameters and fitted directly without having to be converted to T1 and concentration. This approach can prevent the possible noise propagation that could happen during data transformation. Also, this approach can represent the data more properly when the ROI contains vasculature and this fraction of vasculature needs to be estimated precisely. The efficacy of this method is demonstrated with simulation studies and animal data from normal rats. Our goal is to develop an imaging protocol that is easy to operate, does not require cardiac gating and adopts common slice orientations. With the developed imaging protocol, methods for measuring the input function and capillary permeability are proposed in this report using the direct curve fitting to the timeintensity curves. Our results of input function measurement are compared to the reported SAIF from literature by evaluating the curve shapes and magnitudes. This measured input function is then applied in the kinetic modeling analysis of brain intensity data. Ktrans, ve and Fv of brain tissues are estimated and compared to previously reported values or description from literature for data validation. 90

94 METHODS AND MATERIALS Definition of quantities and symbols The nomenclature suggested by Tofts et al. is used for standardizing the physiological quantities and symbols in DCE MRI kinetic modeling (8). To help readers clarify those parameters, Table 1 summaries all imaging and physiologic parameters that appear in this report with their definitions, units. Table 1 also shows whether a parameter is pre determined or estimated and how its estimation was achieved. Kinetic model of Gd DTPA The Gd DTPA kinetic model has been well accepted as a one compartment model. The plasma input function, Cp, is the Gd DTPA molar concentration in plasma of arterial blood. After leaking from the capillaries, Gd DTPA enters the ESS by the rate constant Ktrans and gets cleared by the rate constant kep. The relationship between the concentration in tissue (Ct) and Cp can be represented by:. Eq. 1 It has been widely recognized that Gd DTPA is a permeability limited contrast agent which leads to the interpretation of Ktrans as: 91

95 , Eq. 2 where PS is the permeability surface area and ρ is the tissue density. And kep is related to Ktrans by:. Eq. 3 Since it is usually difficult to measure density in vivo in tissues, Ktrans and kep have long been used directly to evaluate tissue permeability to Gd DTPA. The analytical solution to Eq. 1 can be represented as a convolution integral as:, Eq. 4 where denotes the convolution operator. Based on previous studies for the AIF clearance, it has been shown that the AIF can be accurately described by a triexponential function (22): Eq. 5 With Eq. 4 and Eq. 5, Ct can be solved analytically as: e L 1t e k ept C t = K trans A 1 k ep L 1 + A 2 e k ept k ep L 2 + A 3 e L 2t e k ept k ep L 3 e L 3t Eq. 6 T1 reduction by Gd DTPA The paramagnetic property of Gd DTPA is known to reduce T1 by: 92

96 Eq. 7 where T1,pre and T1,post are the time constants for longitudinal relaxation before and after the contrast agent injection (25). r1 is the T1 relaxivity which is dependent on temperature and field strength. The relaxivity is found to be 3.2 (s 1 mm 1 ) from calibration studies on our 9.4T Bruker Biospin system. This value is similar to the values reported by other groups in the same field strength (26, 27). Intensity measured from an IR turboflash image With a perfect, non selective 180 degree inversion preparation and a fast train of α pulses with short TR and TE, the intensity of an IR turboflash image can be represented by the measured transverse magnetization at the center of k space (15): n 1 1 E SI = A[(1 2e TI /T1 )E n 1 + (1 e TR/T1 )( 1 E )]sinα * nom e TE /T 2, Eq. 8 where A is the scale factor that depends on the proton density, receiver gain and characteristics of the scanner systems. n is the number of phase encoding steps at the center of k space. For a total phase encoding steps of NP, n = NP/2. is the nominal flip angle. E is defined as: Eq. 9 93

97 With SI and E defined, the intensity is denoted as I in this report by taking the magnitude of SI. Assuming that the T2* effect can be negligible with the 0.1 mmol/kg dose (28, 29), magnitude intensity I can be calculated from Eq. 8 as:, Eq. 10 where AI is a lumped scaling constant that is composed of the system scaling, proton density, sinα and the transverse relaxation terms. In practice, neither the inversion pulse nor the excitation pulse is perfect because of the slice profile variation. Therefore, Eq. 9 and Eq. 10 should be modified as: Eq. 11, Eq. 12 where is the effective excitation flip angle at the specific location on the slice. λ is defined as the actual inversion power. For a perfect 180 inversion and 90 saturation, λ corresponds to 2 and 1 respectively. Considering the contrast enhancement by Gd DPTA, the pre contrast and postcontrast intensity can be both expressed as an intensity concentration function (ICF) which is dependent on T1,pre and [Gd] by: 94

98 , Eq. 13 where E is determined as: Eq. 14 With Eq. 13 and 14, pre contrast intensity can be calculated with [Gd]=0 and the post contrast intensity is calculated by the [Gd] concentration at a specific time and location. It is important to carefully address the signal intensity contributed by different components within a ROI. Within a volume of tissue, there are cells, capillaries and the EES. All three components contribute to the signal intensity. However, since the amount of intracellular Gd DTPA is often negligible, the signal intensity from cells is fixed regardless of the injection. The measured intensity of a ROI can be expressed as a weighted sum of the intensity from all three components of the tissue: I ROI = v e SI EES + Fv SI vasculature + (1 v e Fv) SI cells = v e ICF(T 1, pre,c e ) + Fv ICF(T 1, pre,c a ) + (1 v e Fv) ICF(T 1, pre,[gd] = 0), Eq. 15 where Ce is the concentration in EES and Ca is the concentration is the arterial blood. They are related to Ct and Cp by: Eq. 16, Eq

99 where Hct is the hematocrit. Intensity of arterial blood measured with IR turboflash It is important to note that Eq. 8 and 10 are only valid when the spins are stationary and all of them have experienced NP/2 excitation pulses (NP is the number of phase encoding steps) at the center of k space. Since the arterial blood is flowing and the effective receiving area (~10cm) of the receiver coil does not cover the entire body of a rat, the blood within the receiving coil has actually experienced different number of α pulses. Therefore, the intensity of the flowing blood must be modeled to account for this difference in α pulse excitations in order to accurately estimate the concentration of Gd DTPA in blood. An approach described by Gao and Gore is taken to express the overall intensity as a weighted summation of plugs of blood that has experienced different numbers of excitations (30, 31). The other confounding factor is that, because the coil range is limited, the non selective inversion pulse would only affect certain fraction of entire blood volume of an animal. Therefore, in the blood intensity, signal comes from both the inverted blood and non inverted blood experiencing different history of excitation pulses. Derivation of signal intensity equations is explained as follows. First, with Eq. 15 the magnitude intensity of flowing blood as a summation of signals from plasma and blood cells can be expressed as: 96

100 I blood = (1 Hct) SI plasma + Hct SI cells = (1 Hct) BICF(T 1, pre,c p ) + Hct BICF(T 1, pre,[gd] = 0), Eq. 18 where BICF represents the intensity as a function of T1,pre and [Gd] concentration in blood. It is assumed that, within each TR, the fraction of fresh blood that enters the effective region of a coil is denoted by Fflow. With the method described by Gao and Gore (30, 31), this fraction can be calculated by the flow velocity and coil length for a specific artery. However, in this study this fraction is hard to calculate directly from velocity at a single blood vessel. This fraction in the equation intensity is simply used as it is as its value is estimated during fitting the arterial intensity curve. Therefore, fraction of blood Fn that has experienced exactly n α pulses can be expressed as: Eq. 19 and the overall intensity is expressed as a weighted summation of the intensities of each slot of blood with individual excitation history: Eq. 20, 97

101 where BICF denotes the blood intensity concentration function. Furthermore, if there are some flowing spins that did not experience the inversion preparation, their intensity can be represented as: Eq. 21 In summary, the total magnitude intensity of arterial blood can be expressed by the magnitude taken from weighted summation of respective signal sources as: Eq. 22 In Eq. 15 and Eq. 22, the signal intensity has been formulated as a function of contrast agent concentration for both flowing blood and tissues. Consider a study in which there are repeated acquisition of an inversion prepared turboflash image with fixed TI, TR, TE, flip angle and receiver gain. If there is no contrast agent injected, the signal intensity curve should remain at the baseline value. During those repeated scans, at some time point the contrast agent is injected. Since the timeintensity cuves have been shown to be functions of contrast agent concentration, non linear curve fitting methods can be used to estimate parameters that lead to the best fit of experimental data. 98

102 Simulation studies Simulation studies are first used to examine the proposed imaging protocol and parameter estimation methods. The intensity curves are simulated versus T1 values for three different situations: stationary spins, flowing spins with perfect inversion and flowing spins with only some fraction being inverted. Then the intensity equations are used to simulate the intensity curves for flowing blood and tumors. The parameters reported by Wedeking et al. are used as the parameters of reference input function in this study (22). For tumor parameters, the values reported by Ferrier et al. are used in this report as Ktrans = (min 1 ), ve = and Fv = 2.8% (2). Finv and Fflow are assumed to be 0.9 and respectively. With the arterial and tumor intensity curves simulated, the ratio of the maximum enhancement is calculated by finding the ratio of maximal intensity versus the baseline signal intensity in order to access the degree of enhancement if applied in a DCE tumor study. We then performed five different simulations to evaluate the bias and precision of our method for estimating the input function and tissue parameters. The same set of parameter for a SAIF and tumor perfusion used to simulate intensity curves as described in the previous paragraph was used again for the simulation studies. Each simulation was repeated with realizations, each with independently sampled Gaussian white noise with 0.2 as the noise level which is defined as the standard deviation divided by mean value in the baseline intensities. This noise level is 99

103 approximated based on preliminary animal data. These five simulations are described as follows: 1. Simulation for tumor parameter estimation: Since the purpose of the proposed methods is mainly targeted at the DCE MRI studies for studying tumor permeability, we first want to evaluate if the true input function is known, how accurate the parameter estimation is when noise is present in the tumor intensity curves. The tumor intensity curves are simulated with the SAIF and then added with noise. Following that, SAIF is used as the input function for parameter estimation of Ktrans, ve and Fv. The estimated tumor parameters are then compared to the true values to calculate the bias and precision as the mean and SD respectively of the difference between the estimated and true values. 2. Simulation for input function estimation: We would like to know whether the input function could be accurately estimated from the noisy intensity curves of blood. Therefore, the SAIF is used as the reference input function to simulate both the blood and tumor intensity curves. Simulated random noise is included at a level of 0.2. Then it is assumed that the true input function is unknown and an input function could be estimated from a noisy arterial intensity curve. The initial guesses of the input function parameters are: Finv = 0.7, Fflow = , A1~L3 equaled to true value times 30%. Once the input function parameters are estimated, the estimated parameter values are evaluated to determine bias and precision. This estimated input is then used 100

104 to estimate the tumor parameters to evaluate its effect on the tumor parameters. Again bias and precision is evaluated for parameter estimation results. 3. Simulation for evaluating the sampling rate: Using inversion recovery methods, we have to wait for five times the longest T1 between each inversion to allow full recovery of longitudinal magnetization (32). Therefore, in this study a sampling rate of one scan every 15 seconds is used. Previous reports have suggested sampling rates ranging from once a second (33) to once 10 seconds (34). It should be evaluated whether our sampling rate is going to affect the accuracy of parameter estimation if the peak of the arterial intensity is missed because of down sampling. Therefore, the SAIF is again used as reference input but on purpose shifted it by 7.5 seconds to make the maximal effect of down sampling. Simulated intensity curves for arterial blood with noise added are then fitted by estimating the input function parameters. These are used in estimating the tumor parameters. Results of these two estimation processes are compared to the true values. 4. Simulation for different input function shapes: This simulation serves as the test for the effect of using standard versus customized input functions for the estimation of tumor parameters. In this simulation, the SAIF is modified by multiplying A1, A2 and A3 by 1.2, 0.9 and 0.8 respectively. This input function is denoted as the modified input function and used as the reference input. The blood and tumor intensity curves are simulated with this modified input 101

105 function and added with noise. Then the SAIF is used without modification to estimate the tumor parameters for comparison with the true parameters. 5. Simulation for estimating the input function for modified inputs: Following the description of simulation 4, the simulated blood intensity curve is fitted to estimate input function parameters. This estimated input function is used to estimate the tumor parameters. Both input and tumor parameters are analyzed in terms of bias and precision. Animal model Six data sets were acquired from three female Sprague Dawley rats with average weight of grams. Animals were anesthetized with 2% isoflurane in oxygen. Before being placed in the scanner, each animal received tail vein cannulation with an MRE 025 microrenathane tubing (0.63 mm outer diameter) that is used for i.v. injection of Gd DTPA. After the cannulation, the animal would then be placed on an animal bed within the coil of the MRI system. Animal breathing rates and temperatures were monitored with physiologic monitoring systems. Throughout the entire imaging study, body temperature of the animal was maintained using a feedback control system. Neither the cardiac not the respiration gating was used during the study. The animal study protocol was approved by the IACUC of Case Western Reserve University. 102

106 Preparation scans In this study, the pre contrast scans were used to measure the (1) pre contrast T1, (2) excitation flip angle at a specific spatial location on the slice, and (3) the inversion power at the spatial location. Under anesthesia, rats were scanned with a 9.4T Bruker Biospec MRI system. Each animal was placed in a head first, supine position with the neck approximately at the center of coil FOV. Scanner host software (ParaVision 3.0.2) was used for data acquisition. For each animal, an axial slice was acquired in the brain area with a turboflash sequence with non selective inversion preparation (TR/TE = 8.54/3 ms; FOV = 3.5 cm; matrix = 64 x 64; NP = 64; nominal flip angle = 10 degrees; slice thickness = 2 mm). This scan was repeated with different TI values, which were the time delays between the 180 degree inversion pulse and the first excitation pulse. TI was used as 100, 150, 200, 300, 400, 500, 750, 1000, 2000, 5000, ms, and each choice of TI was repeated twice to reduce the noise effect on curve fitting. In addition to those scans, a FLASH scan was acquired with long TR (12 seconds) and without the inversion preparation. The receiver gain was fixed for all scans described above for individual rats. To identify the internal carotid artery within the image, a FLASH image was acquired with TR/TE = 100/3 ms, flip angle = 30 degrees, NP = 128 and matrix = 128 by 128. Contrast enhanced scans The same FLASH sequence with non selective inversion preparation described in the preparation scans was used with modification of TI = 300 ms, NP = 128 and 103

107 matrix = 128 by 128. Such scan was repeated every 15 seconds to ensure the full recovery of longitudinal magnetization back to equilibrium (5 times the longest T1) between each scan. Total scan duration was 70 minutes. Immediately before the 41 st scan 0.1 mmol/kg of Gd DTPA (undiluted Magnivist, Berlex, Germany) was injected as a fast bolus. Syringe weight before and after injection was measured for calculating the net injection dose. Actual injected dose for the six data sets was found to average as ± mmol/kg. Data processing and curve fitting procedures The images of scans previous described were reconstructed as magnitude images with ParaVision and then transferred to a Macintosh MacBookPro for data processing under MATLAB R2008a (Mathworks, Natick MA). MATLAB functions were made to read the absolute intensity from each pixel within a manually drawn ROI and then calculate the mean intensity. For each data set, a ROI was placed on the internal carotid artery and another placed in the brain. Such ROIs were then applied to the preparation scans and contrast enhanced scans to obtain the corresponding intensity curves. Following that, three curve fitting steps were used to estimate all necessary parameters. These three steps included (1) curve fitting for preparation scans for blood and brain to estimate pre contrast T1, effective flip angle, and inversion power, (2) curve fitting of the intensity curve from contrast enhanced scans of arterial blood to estimate the AIF; and (3) curve fitting of the brain intensity 104

108 curve from contrast enhanced scans to estimate Ktrans, ve and Fv. Detailed curve fitting methods were described as follows. For the preparation scans, each rat was scanned 23 times, including 22 inversionprepared and one long TR, non inverted FLASH scans. For the brain ROI, those 23 data points were fitted with a non linear least square (NLLS) optimization algorithm as a four parameter estimation problem (overall scaling, pre contrast T1, effective flip angle and inversion power). Eq. 11 and 12 were used to calculate the intensity with n=32. For the arterial ROI, a slightly different approach was taken. Because of the flowing blood, scans with long TI and long TR might not be valid for calculating intensity with Eq. 12. Therefore, a ROI was first drawn adjacent to the arterial ROI and used to estimate the effective flip angle and inversion power. Then the flip angle and inversion power were fixed for the arterial ROI to fit the data points of TI between 100 and 750 ms for estimating the pre contrast T1 of arterial blood. After the pre contrast T1, flip angle and inversion power were determined for the arterial blood and brain, curve fitting of the contrast enhanced intensity curves was performed. First, the arterial blood intensity curve was fitted with the NLLS algorithm for estimating the Cp(t) parameters (A1, A2, A3, L1, L2, L3), Finv and Fflow by the intensity calculated by Eq. 22 with n = 64. Initial values and constrain bounds are summarized in Table 2. Overall scaling was not estimated but calculated by the known pre contrast T1 and average pre injection signal intensity. For the AIF curve shape and magnitude, whether the overall tendency falls within the reasonable range and whether there is individual difference in them were 105

109 evaluated. To do so, the SAIF by Wedeking et al. (22) was used again as a reference and compared our results to it. First, mean and standard deviation of A1~A3, L1~L3 were calculated and compared to those reported in the SAIF. Second, all AIFs estimated were adjusted in magnitude to the standard dose of 0.1 mmol/kg. Average AIF concentration of Gd DTPA was calculated as well as the standard deviation. These statistics were compared to the SAIF on plots. With the AIF estimated, the contrast enhanced brain intensity curve was fitted with the intensity calculated from Eq. 15 for estimating the Ktrans, ve and Fv. Note that kep = Ktrans/ve so only ve had to be estimated. Since the blood in capillary has a low flow velocity, intensity of the blood in capillaries was calculated in Eq. 15 by assuming it was stationary. The calculation of T1 was separated for EES and blood with their individual pre contrast T1 values and Gd DTPA concentration functions. Intensity curves of EES and capillary blood were calculated separately and used to calculate the weighted summation of overall ROI intensity within Eq

110 RESULTS Simulation studies We used the proposed imaging protocol, kinetic model and the intensity equations to simulate the intensity curves. First, the intensity values of different T1 was calculated and plotted in Figure 1 with Eq. 15 for stationary spins and Eq. 22 for flowing spins. For flowing spins, both the fully inverted and partially inverted conditions were simulated as shown in Figure 1. The signal intensities had high amplitude at low T1s and a zero crossing point around 1700 to 1800 ms. Therefore, for baseline scans, images would be of fairly low signal intensities and SNR was rather low. However, simulation showed that once the contrast agent was injected, significant contrast was produced for tissues with high permeability. The SAIF and tumor parameters were used to simulate both the blood and tumor intensity curves as shown in Figure 2. In tumor, maximal enhancement was found to be 6.8 times after 2.5 minutes post injection. Five simulation studies were performed to examine the accuracy of input function and tumor parameter estimation. The summary of them is listed in Table 2 as mean and SD of error percentage. Under the assumption that the true input function was known for a noisy intensity curve of tumor ROI, simulation 1 showed a low bias (error mean < 2%) and good precision (error SD < 10%) in tumor parameters 107

111 indicating that noise only had a minor effect on the accuracy of estimating the tumor parameters. In simulation 2, 3, and 5, the input function was estimated based on the simulated blood intensities with noise present in them. In simulation 2 and 5, our method has shown a good accuracy in estimating the input functions under two different curve shapes. Except for Fflow, most input function parameters in simulation 2 and 5 had less than 5% bias and about 10% in error SD. The over estimation of Fflow did not actually affect the estimation of A1~L3. Therefore, the estimated input functions were very close to the reference input and accordingly, when used for estimating tumor parameters, similar bias and precision was achieved in simulation 2 and 5 compared to simulation 1. Simulation 3 was used to evaluate the effect of potential down sampling of our protocol. In our simulation, when a delay of 7.5 was used to shift the peak of intensity curve, the sampled peak was about 10% lower than the actual peak magnitude. All parameters in simulation 3 had similar values of error % except for A1 and Ktrans. A1 was affected by the down sampling and showed a bias of 9.8%. This under estimation was within acceptable margins as a 10% bias is typically regarded as rather low in parameter estimation of Ktrans. Other than the Ktrans bias, all other statistics of Ktrans, ve and Fv showed similar tendency as in simulation 2 and 5. In simulation 4, reference input function was modified by changing both the magnitude and curve shape of the SAIF to evaluate if a SAIF was still suitable for estimating the tumor parameters. As shown in Table 2, all Ktrans, ve and Fv were 108

112 found to be significantly biased because the input function was effective a wrong one. On the other hand, in simulation 5 an estimated input function with our method was able to properly approximate the reference input function and gave good estimation of tumor parameters. Animal studies The proposed animal study included two parts of scans: preparation scans and contrast enhanced scans. The purpose of preparation scans was to find the precontrast T1, effective flip angle and inversion power. With the six data sets collected, arterial blood T1,pre averaged ± ms while was 8.8 ± 2.0 degrees and λ was 1.7 ± 0.1 (Mean ± SD). For the brain ROI, average T1,pre was ± ms with = 9.6 ± 1.5 degrees and λ = 1.9 ± 0.1. The blood and brain T1 values were consistent with previous reported values on high field scanners (35). The intensity curve and curve fitting result of a brain ROI for the preparation scans of one rat was plotted in Fig. 3. Contrast enhanced images of one data set were shown in Figure 4. Figure 4A showed the regular FLASH image before the injection of contrast agent. Figure 4B showed the averaged image from the pre contrast scans with inversion preparation and turboflash sequence. Figure 4C to 4J are images at different times with respect to injection as displayed by the absolute intensity. In Figure 4D and 4E, the blood 109

113 vessels showed rapid enhancement because of the high concentration in arterial blood. By drawing ROI in the arteries and brain, intensity curves of them were calculated from the contrast enhanced scans. Intensity curves were shown in Figure 5 to 7 for two representative data sets. In the data set shown in Figure 5, the arterial intensity curve (dotted) was successfully fitted by model equations (solid line) (Figure 5A) and the estimated input function was similar to the SAIF (Figure 5B). On the other hand, in the data set in Figure 6, the intensity curve was also fitted well but the estimated input function had a different curve shape than the SAIF. The brain intensity and fitted curves were plotted in Figure 7A while Figure 7B showed the estimated Ce. Because normal blood brain barrier restricted the leakage of Gd DTPA from entering the EES, the maximum concentration Ce was fairly low as less than 0.01 mm. The parameter estimation results of all six data sets were summarized in Table 3. Again since the BBB functions normally in our data, very low Ktrans was estimated from our data, averaging min 1. The blood volume fraction Fv averaged as 1.7 % which accurately falls within the previously reported values (36). In Figure 6 the mean and standard deviation of all six estimated Cp was plotted with a SAIF reported by Wedeking et al. (22). The mean Cp corresponded to the standard input very well in the overall magnitude. However, the curve shape and standard deviation showed that the estimated input function varies individually, indicating that our method provides individual estimation of the AIF with difference in the curve shapes and magnitude. 110

114 DISCUSSION In the recent years as technologies advance in high field scanners dedicated for small animal imaging, DCE MRI becomes more and more popular in studying tumor physiological in pre clinical research applications. One challenge remains to be the adequate quantification with absolute measurement of the physiology in analyzing the perfusion or permeability with DCE MRI image data. Among different indices calculated to evaluate the physiology, kinetic modeling has been regarded as the most quantitative way based on a solid theory of molecular transports. Effort has been spent on establishing the standard nomenclature and model definition for modeling different types of contrast agents (8). However, some challenges still exist and need to be addressed especially in small animal imaging. The first challenge is the transformation of data required to convert the intensity to T1 and T1 to concentration before applying the data for kinetic modeling analysis. This conversion process can be problematic in two ways. First, if within the ROI there are two types of tissues such as blood and cells, the measured effective T1 might not give accurate calculation of concentration because it s the R 1 that is linear to concentration, instead of the. This effect might be more problematic if these two tissues relax at fairly different T1s. With a single value of T1 derived from ROI, careful considerations must be taken to evaluate whether the T1 measurement method provides accurate estimation of concentrations especially when the blood 111

115 fraction is not negligible. Also, probable noise propagation in the conversion steps might also cause additional errors in the parameter estimation. A preferred approach in parameter estimation in general is to fit the raw data directly with modeling approaches. In this report we have proposed a complete process including the imaging protocol for animal studies, careful description of relating intensity to concentration and detailed steps for estimating the input function and use the estimated input to estimate tissue parameters. In Eq. 15 and 2, it is obvious that this approach has an advantage of being very general and applicable on different types of tissues even when they are highly heterogeneous. The rationale is that the intensity from a ROI can be calculated from taking the absolute value of a weighted sum of signals from different components in the tissue. But this linearity might not be valid for T1 based on the T1 mapping method. Therefore, Eq. 15 is suitable for relating the concentration to intensity and for estimating the tissue parameters with good accuracy as shown in the simulations. Realizing that the arterial blood will not follow the same equation as stationary tissue for intensities, we have modeled the signal intensity carefully by considering fraction of perfectly inverted spins, fraction of spins that flows within the coil and the hematocrit. Although there are many parameters (total of 8) to estimate for each input function, our simulation studies have shown these parameters are properly identifiable even when the initial guess is relatively far from the true values and there is noise present in the intensity curves. Furthermore, we have shown in our 112

116 simulation that the estimated input functions are reliable when they are applied to estimate the tissue parameters. As the direct measurement of the concentration from blood samples is quite difficult and may be inaccurate compared to the blood in vivo, we validated the accuracy of input function estimation indirectly by simulation studies and comparing estimated input function parameters to literature values. In the simulation study, it has been shown that our method is capable to estimate the input for different curve shapes (simulation 2 and 5). Our results also showed that the sampling rate of once each 15s, although causing about 10% bias in Ktrans estimation, is sufficient to give satisfactory estimation of tissue parameters (simulation 4). With the animal data, that the overall magnitude is found to fall within the right range in our estimated input functions compared to the reference SAIF. On the other hand, individual input function curve shape can be estimated. When those estimated input functions were used to estimate the tissue parameters, results were consistent with expected physiology of BBB as Ktrans is fairly low and the Fv estimated is consistent with those previously reported. Therefore, it can be concluded that by carefully modeling the intensity equation considering most details and direct fitting the intensity curves, the proposed method can be used to accurately estimate the input function for kinetic modeling of DCE MRI data. Compared to existing methods for input function estimation, our method has its advantages and weakness. It is simple to perform as the inversion recovery turboflash sequence is very common and can often be applied without 113

117 modification for the protocol proposed in this report. No physiologic gating is required, and the artery acquired on the same slice of tissue of interest can be used for estimating the input function. It does not require special surface coils as required in some methods (19, 20) or a specific slice orientation (18). The individual curve shape can be estimated as suggested to be preferable over SAIF (24, 33). On the other hand, this method has a sampling rate of 0.25 Hz which is lower than methods with cardiac gating applied (15 17). In addition, since there are many parameters involved in the whole estimation process such as effective flip angle and degree of inversion, individual accuracy for measurement must be within acceptable margins in order to accurately estimate the input function and tissue parameters. In this study we proposed the use of a single frame inversion recovery turboflash sequence. The advantage of this method over the multi frame IRTF, or Look Locker method, is the significant reduction of alpha pulses applied. By reducing the number of pulses, we are able to use a higher angle to increase SNR and more phase encoding steps to improve spatial resolution. However, Look Locker method has the advantage of being less sensitive to the effective flip angle variation and actual inversion power (32). To further improve the proposed pulse sequence, optimization of the protocol is necessary by determining the optimal flip angle, pulse shape, inversion delay and other scanning parameters specifically for targeted tissue and field strength. Other methods for measuring the slice profile may be considered to make the measurement of effective flip angle more accurate (37). 114

118 We speculate the methods proposed in this report, including the direct fitting and input function estimation, can be further applied in two different directions. First, the application on mice studies is expected to be probable. In fact, since the whole body of a 25 gram mouse can often be covered completely by the homogeneous region of the coil, the blood flowing effect will be close to negligible because all blood will experience the inversion pulse and the same alpha excitation history. Therefore, estimation of input functions will be an easier task to perform. On the other hand, the proposed methods of direct data fitting and input function estimation are expected to be appropriate for saturation recovery pulses. Although inversion recovery methods generally have greater dynamic range which in theory reduces the noise effect, the summation of magnetization at different signs near zero crossing points can lead to potential errors for calculating the signal intensities. Compared with that, saturation recovery has the advantage of the longitudinal magnetization mostly being positive. Therefore, the derivation of intensity equations might be easier with saturation recovery methods. Also, saturation recovery methods are not limited by the requirement of 5 T1 for full recovery of longitudinal magnetization and may help to increase the sampling rate of data acquisition. 115

119 CONCLUSION We have proposed a new framework for acquiring and analyzing DCE MRI data for kinetic modeling in small animals. A single frame IRTF pulse sequence is used to allow acquisition of both blood and tissue intensity curves without cardiac gating. By carefully modeling the intensity equation as function of blood and tissue concentrations, the input function can be estimated by directly fitting the intensity curves without having to convert between T1 and concentrations. With simulation and animal studies, results showed the usefulness and accuracy of our estimated input functions and the application of them on estimating the tissue kinetic parameters. Being simple to operate, reliable and robust, this method is suitable for estimating perfusion for routine DCE MRI studies in small animals. 116

120 ACKNOWLEDGEMENTS The work described in this study was supported by National Cancer Institute Grants CA and CA and by the Case Center for Imaging Research. The authors would like to thank Dr. Mark Griswold for valuable inputs for experiment design. We also express our gratitude to Hsuan Ming Huang and the research staff of Case Center for Imaging Research for assisting our animal studies and data acquisition. 117

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125 TABLES TABLE 1 Quantities and symbols Quantity Definition Unit Determined from Value MR specific quantities r1 T1 relaxivity constant ms 1 mm 1 Calibration study TR Repetition time for excitation in FLASH ms Chosen for protocol 8.54 TE Echo time in FLASH Ms Chosen for protocol 3 TI Time delay between the inversion pulse ms Chosen for protocol 300 and the first α pulse Nominal flip angle degree Chosen for protocol 10 Effective flip angle degree Estimated from preparation scans λ Effective inversion power No Unit Estimated from preparation scans NP Number of phase encoding steps No Unit Chose for protocol 128 n Phase encoding steps to the center of k No Unit Chosen for protocol 64 space SI Signal intensity before taking the Arbitrary Obtained from a ROI on the images magnitude units I Magnitude intensity of ROI by taking the Arbitrary Obtained from a ROI on the images absolute value of SI units AI Scaling factor for signal intensity Arbitrary Estimated from preparation scans units D Length of effective region of receiver coil cm Scanner specifications 10 Physiologic quantities Cp(t) Plasma concentration of Gd DTPA mm Arterial intensity curve fitting Ct(t) Tissue concentration of Gd DTPA mm Tissue intensity curve fitting Ktrans Transfer constant from blood to EES min 1 Tissue intensity curve fitting EES volume fraction No Unit Tissue intensity curve fitting kep Transfer constant from EES to blood min 1 Calculated from Ktrans/ A1~A3 Scaling constants of Cp(t) mm Arterial intensity curve fitting ~L3 Time constants of Cp(t) 1/min Arterial intensity curve fitting T1,pre Pre contrast longitudinal relaxation time ms Estimated from preparation scans T1,post Post contrast longitudinal relaxation time ms Modeled by equations Fv Tissue vasculature volume fraction No Unit Tissue intensity curve fitting Hct Hematocrit No Unit Taken from literature 0.4 Finv Fraction of blood that was inverted No Unit Arterial intensity curve fitting Fflow Fraction of blood that enters coil within each TR No Unit Arterial intensity curve fitting 122

126 TABLE 2 Simulation results Simulation number Reference input Input for tissue SAIF SAIF Shifted SAIF Modified SAIF Modified SAIF SAIF EAIF EAIF SAIF EAIF K trans 0.01 ± ± ± ± ± 3.95 v e 0.01 ± ± ± ± ± 1.90 Fv 0.18 ± ± ± ± ± F inv 4.45 ± ± ± 3.67 F flow ± ± ± A ± ± ± 6.23 A ± ± ± 8.76 A ± ± ± L ± ± ± 7.98 L ± ± ± L ± ± ± (Values are expressed as mean ± SD) 123

127 TABLE 3 Parameter estimation settings and statistics of estimated values for animal data. (n=6) Parame ter Initial value Lower bound Upper bound Estimate d mean Estimate d SD Estimate d min Estimate d max F inv F flow A 1 (mm) A 2 (mm) A 3 (mm) L 1 (min 1) L 2 (min 1) L 3 (min 1) K trans (min 1 ) v e Fv

128 FIGURES FIGURE 1. Simulated intensity versus T1 for stationary (dashed), flowing spins (solid) and partially inverted flowing spins (dotted) based on the proposed imaging protocol of inversion prepared turboflash. In this simulation, it is assumed that α equals 10 degrees and the inversion pulse is a perfect 180 degree inversion. In the partially inverted spins, spins are divided into two groups: Perfectly inverted (fraction: 0.9) and non inverted (fraction: 0.1). 125

129 FIGURE 2. Simulated intensity curves for (A) flowing blood and (B) tumors as noisefree (dashed) and noisy (dotted) data. 126

130 FIGURE 3. Curve fitting results for intensities of a brain ROI from preparation scans. In this data set, the fitted T1 = ms, effective flip angle = 8.27, and effective inversion power =

131 FIGURE 4. Images of a rat study. Intensities of the inversion prepared turboflash images are shown by the absolute measurement with the same units. 128

132 FIGURE 5. Arterial intensity data and curve fitting results of one rat. In this data set, the estimated input function is similar to the SAIF. 129

133 FIGURE 6. Arterial intensity data and curve fitting results. Estimate input function in this data set has a significantly different curve shape than the SAIF. 130

134 FIGURE 7. Brain intensity data and curve fitting results. 131

135 FIGURE 8. Comparison of estimated input function to a standard input function. The estimated AIF (solid) is plotted as the mean with horizontal bars representing the standard deviations based on all six data sets. 132

136 Chapter 4 Integrated software environment based on COMKAT for analyzing tracer pharmacokinetics with molecular imaging 133

137 Intended journal for submission: Journal of Nuclear Medicine Expected submission date: April, 2009 Title Integrated software environment based on COMKAT for analyzing tracer pharmacokinetics with molecular imaging Authors Yu Hua Dean Fang 1,2, Pravesh Asthana 3, Christian Salinas 4, Hsuan Ming Huang 1,2 and Raymond F. Muzic, Jr. 1,2,5 1 Department of Biomedical Engineering, Case Western Reserve University, Cleveland OH 2 Case Center for Imaging Research, Case Western Reserve University, Cleveland OH 3 Crossrate Technology, Windham, Maine 4 GSK Clinical Imaging Centre, Imperial College, London, United Kingdom 5 Department of Radiology, Case Western Reserve University, Cleveland OH 134

138 ABSTRACT An integrated software package, COmparment Model Kinetic Analysis Tool (COMKAT) is presented in this report. COMKAT is open source, free for academic research use, and provides a well integrated, user friendly, and powerful software package for molecular imaging research. COMKAT is intended for pharmacokinetic analysis in molecular imaging. Including both command line and graphical user interfaces, COMKAT is specifically designed to connect kinetic modeling and image analysis with extensive functionality and flexibility. With COMKAT, users may load and display images, draw regions of interest (ROIs), load input functions, select kinetic models from a pre defined list, or create a novel model and perform parameter estimation all without having to write any computer code. For imaging analysis, COMKAT Image Tool supports multiple image file formats including the DICOM standard. Image contrast, zoom, re slicing, display color table, and frame summation can be adjusted in COMKAT Image Tool. It also displays and automatically registers images from two modalities. Parametric imaging capability is provided and this can be combined with the distributed computing support to enhance computation speeds. COMKAT has been compiled into a standalone executable file for users without MATLAB licenses. Extensive documentation, examples, and COMKAT itself are available on its wiki based website Users are encouraged to contribute sharing their experience, examples, and extensions to COMKAT. 135

139 INTRODUCTION With advanced molecular imaging technologies, in vivo physiology and metabolism can be quantified noninvasively. In PET imaging, kinetic models or compartment models can be used to describe the pharmacokinetics of tracers and quantify physiology. For example, the two compartment kinetic model of 18 F FDG has been well studied and extensively used for measuring the glucose metabolic rate (1, 2). It has been shown that kinetic modeling has several advantages for measuring the physiologic functions than semi quantitative methods, such as standard uptake values (SUV). Kinetic modeling has a more solid theoretic basis that helps interpret data with physiological relevance (3). In addition, results from kinetic modeling are less dependent on modality, instrument, institution, and protocol compared to results from qualitative and semi quantitative methods (4). However, one challenge for applying kinetic modeling in image quantification is the lack of availability of software designed specifically for kinetic modeling analysis in molecular imaging research. There are quite a few sophisticated kinetic modeling software packages that are publicly available, including RFit (5), Pk Fit (6), and SAAM II (7). Their drawback nevertheless is that they are not specifically designed for image analysis and therefore lack the functionality for image processing. On the other hand, many software packages provided by scanner vendors have image processing but not kinetic modeling capabilities. Alternative solutions with imaging and modeling capability include commercial products such as PMOD (8) which requires licensing 136

140 fees or Internet based applications such as KIS (9). However, to date there is not a software package that is specifically designed for both modeling and imaging, publicly available with open source distribution and capable of specifying new kinetic models with graphical user interfaces (GUIs). To address this unmet need, we have developed COmpartment Model Kinetic Analysis Tool (COMKAT) (10) as an integrated software environment for model based analysis and physiologic interpretation of biomedical image data. In this report we describe our implementation and the availability of the COMKAT software package. First developed as a toolbox for kinetic modeling under MATLAB and published in 2001 (10), COMKAT has been a powerful package for kinetic modeling with many unique features including intuitive command line functions for building and solving kinetic models, parameter estimation for fitting experimental data, a GUI based model creation tool, and a free, open sourced distribution for academic research use. Since 2001, COMKAT has been significantly improved in order to make COMKAT more useful to a larger user base. First, user friendly GUIs have been implemented for both kinetic modeling and image processing. COMKAT now has GUIs that allow users to specify kinetic models, load input functions and experimental data, and perform model solving and parameter estimation without having to write computer programs themselves. Second, the image processing GUI has been designed to load, display, and fuse images from two modalities with various functions to adjust the display. Third, COMKAT now provides functions to generate parametric images based on pixel wise parameter estimation. To accelerate such computation, COMKAT supports distributed computing when multi 137

141 core/multi CPU systems or a cluster is available. Lastly, the COMKAT website is now based on wiki with extensive examples and instructions on how to use COMKAT. With all the improvements and enhancement of capabilities, COMKAT continues to be shared and distributed as a free and open source software package for academic research use. Moreover, COMKAT users may now choose to obtain a compiled version of COMKAT that can run independent of a MATLAB license. With these powerful features, COMKAT has been made even more attractive and useful for users to analyze molecular images with kinetic modeling. 138

142 MATERIALS AND METHODS Framework of COMKAT The functions and GUIs of COMKAT can be categorized into several components, including the COMKAT GUI, COMKAT Image Tool, COMKAT Input Function GUI, COMKAT Command line Functions, and miscellaneous analytic tools as illustrated as in Fig. 1. When COMKAT is opened, users first enter the central COMKAT GUI, the graphical user interface for kinetic modeling of image data. COMKAT GUI is linked to the COMKAT Input Function GUI and COMKAT Image Tool, for users to specify input functions and experimental data from ROIs or VOIs on the images. The underlying support for setting up, solving, and fitting kinetic models to experimental data is provided through COMKAT Command line Functions. For COMKAT functions and GUIs, a brief summary of their features and functionality is listed in Table 1. In the following sections, the functionality of each component of COMKAT will be reviewed in detail. COMKAT GUI The COMKAT GUI serves as the front end interface for people who wish to use COMKAT without writing MATLAB code. In the COMKAT GUI, an input function and a kinetic model are required. Experimental data is required when data are to be fit by a model. Users may specify input functions with the COMKAT Input Function GUI, 139

143 which is described below. To specify the kinetic model, COMKAT GUI allows users to either choose from a list of pre programmed model templates or create their own kinetic model in a GUI. The template model list includes the most commonly used kinetic models such as a FDG two compartment model, a perfusion singlecompartment model, and a saturable receptor model (11). Users may also use the model creation GUI to design their own model and add it to the template list. Once the COMKAT GUI has a model and input function specified, COMKAT GUI solves for the model output immediately using the default initial guesses for the parameter values. Users may then adjust values of initial guess and the plot is updated essentially instantaneously. Parameter estimation or data fitting is performed similarly. Users must specify the experimental data in one of two ways, either from regional time activity curves from COMKAT Image Tool or from previously calculated curves that have been stored in files. Supported file formats are listed in Table 2. Multiple curves can be loaded at the same time with individual curves identified by ROI name.. With the experimental data specified and plotted in the COMKAT GUI, users may adjust the initial guesses for each ROI as described above. For the values of each parameter COMKAT GUI supports separate initial guesses, upper and lower bounds for each ROI. Users may then initiate fitting in which case COMKAT sequences through each ROI and estimates its parameter values by minimizing a (e.g. weighted least squares) similarity measure. The final estimated values are stored separately. Fitted curves are then plotted on the output panel so that users can visually assess the fit. Goodness of fit can also be evaluated by sum of square errors and runs test that can 140

144 be accessed from COMKAT GUI. If necessary, the user may adjust initial guesses or bounds and redo the estimation until a satisfactory fit is achieved. Input Function GUI Input functions are essential for kinetic modeling and therefore there are provisions for handling them within the software. In COMKAT, there is an Input Function GUI specifically developed for loading input functions from data stored in a variety of file formats as listed in Table 2. In addition to the activities of blood samples, users also have to specify the radionuclide, specific activity, hematocrit, and the fraction of blood activity attributed to unmetabolized radiopharmaceutical in plasma. COMKAT Input Function GUI also allows users to specify a time varying function for activity fraction as it may vary over time for some radiopharmaceutical. Based on the data specified in previous steps, COMKAT Input Function GUI calculates the plasma and the blood time activity curves. Equations for this are described in detail elsewhere (11). When users complete all steps for specifying the input function, the COMKAT Input Function GUI returns the input functions back to the COMKAT GUI with both the plasma and whole blood input functions. The plasma input function is used as input to the kinetic model, and the whole blood input function is used to calculate the contribution of vascular activity to the pixel value if the contribution is included in the model specification.comkat Input Function GUI can also correct spillover and partial volumes for an image derived input function for small animals based on 141

145 methods described by Fang and Muzic (12) to minimize and even eliminate the need for invasive blood sampling. COMKAT Image Tool COMKAT Image Tool is implemented as the front end GUI for image processing in COMKAT. Image reading functions are written for number of file formats. Table 2 lists the formats currently supported. With the images loaded and displayed on COMKAT Image Tool, users may adjust contrast, color look up table and zoom for better visualization. Users may also easily view images of different slices or temporal frames with slide bars in GUI and triangulate to view any location in the volume by clicking at the desired location in any of the orthogonal views. In addition to the default views of axial, coronal and sagital axes, COMKAT Image Tool also supports arbitrary slice orientations by allowing users to rotate image volumes. To smooth noisy images, COMKAT Image Tool provides user with functionality of spatial filtering and frame summation to improve visual display. To display multimodality images, COMKAT Image Tool is capable of loading and displaying two different image data sets as fused slices. COMKAT Image Tool automatically processes the information about image orientation, resolution and pixel spacing for both data sets so that they will be displayed with the same magnification and, if relevant information is available, the same positioning of the subject. Otherwise, an automatic image registration method is provided in COMKAT Image Tool by using 142

146 the mutual information similarity criterion (13, 14) to help users co register the image volumes. Once the tissue or organ of interest is displayed, a user can draw ROIs on any view, slice or frame on the images. For each ROI, COMKAT Image Tool calculates the average pixel value and automatically converts that to the calibrated value in, for example, activity concentration or Hounsfield units. Users may also create volumes of interest (VOIs) in COMKAT Image Tool by drawing multiple ROIs and grouping them. COMKAT Image Tool allows users to specify multiple ROIs or VOIs for the same data set and the associated time activity curves will be returned back to the COMKAT GUI for model analysis. Optionally, the time activity curves may be saved in text or spreadsheet compatible files. Distributed computing functionality To perform the pixel wise estimation of parameters for generating a parametric image, a function of COMKAT GUI is designed to perform the computation. From the user s perspective, the GUI for computing parametric images uses the kinetic model specified in COMKAT GUI, prompts users for estimation settings, and determines the parameter values for each pixel. To reduce the amount of time required for computation, a masking functionality is used. For each pixel, its estimated parameters values are used to construct a new image data which is called a parametric image. A new volume will be created and saved for each parameter after the computation is completed. 143

147 Since it is a pixel wise operation, the generation of parametric images may be especially computation intensive. One method to accelerate this, when processing of pixels may be done independently, is to divide the calculation into subsets and assigning each to a worker process which may be run on a selected core, CPU, or computer. Therefore, the parametric imaging function in COMKAT GUI is implemented to support distributed computing to enable users to make use of computational resources spanning from two cores in a notebook computer s CPU to multiple cores of multiple CPU computers in a cluster. The MATLAB function parfor under the Parallel Computing Toolbox is used in COMKAT GUI to distribute the pixel wise computation over workers. Once the computation on all workers is complete, results are returned back to the user s computer and consolidated. COMKAT GUI then converts those returned matrices to DICOM images with a MATLAB DICOM writer of its Image Processing Toolbox. COMKAT Command line functions In addition to the development of GUIs and parametric imaging functions described above, considerable improvement have been made to the underlying COMKAT command line functions since they were first published in First, to speed up solving the differential equations, a mex function has been created that implements the differential equations that define the model. This function uses CVODES (15) to solve the differential equations and returns the model solution, and optionally, the derivatives of the solution with respect to parameter values, to the MATLAB 144

148 environment. The mex function uses a number of strategies (e.g. caching results of intermediate calculations, re using memory, and reducing the number of function calls back into MATLAB) to achieve high efficiency. This is especially important when parameter estimation is required because the model is solved using many different values of the parameters. This mex file has been compiled on XXXXXX platforms. For maximum portability across computer platforms, a non compiled solver is also available. Second, COMKAT now supports a number of different builtin kinetic rules (e.g. diffusion, receptor ligand saturable binding, and Mechaelis Menten) to describe compartmental exchange. In addition, the user can define a customized kinetic rule by providing a MATLAB function that returns the value of a concentration or time dependent rate constant. Third, COMKAT now supports several weighting mechanism including weighted least squares, penalized weighted least squares, iterative reweighted least squares, and extended least squares criteria for fitting data under different noise models (16). Validation and performance evaluation for COMKAT The validation of COMKAT is done for both its command line functions and the COMKAT GUI. This is particularly useful to confirm that COMKAT is functioning correctly after installation. To validate the command line functions, users may use COMKAT Validation Suite that solves for the model output analytically, when possible, or numerically using the COMKAT.. At completion, an html report is created and displayed on the screen. The report includes plots of COMKAT and 145

149 reference solutions obtained on the user s computer and the same obtained on the developer s computers. The accuracy of COMKAT command line function on developer s computers has been confirmed against prior publications (10). The performance of COMKAT command line functions is evaluated by its speed for solving model equations for the output and sensitivity equations. As previously described, COMKAT now uses a mex function that is compiled and linked to CVODES for solving model output. This compiled solver is compared to the MATLAB built in ODE solver ode15s. Both solvers are used to calculated an FDG model output for 500 times on a Intel dual core Core2 desktop computer operating at 2.4GHz. COMKAT GUI is tested with input function and image data from small animal PET studies to evaluate whether results from COMKAT GUI equal to those obtained from scripts implemented with COMKAT command line functions. The animal study protocol was approved by the Institutional Animal Care and Use Committee (IACUC) of Case Western Reserve University. To evaluate the speed and accuracy of COMKAT GUI, data from one female, 236 gram Sprague Dawley rat were used. It was injected with 832 µci of FDG intravenously and scanned with a Concorde micropet R4 system (17). Tail arterial blood activity was determined at a 10 Hz sampling rate using a syringe pump to continuously draw blood through a catheter and past a BGO detector for the first 1.5 minutes following FDG injection. Subsequently, arterial blood was manually sampled 9 times over the balance of a 90 minute scan. A dynamic image sequence was reconstructed with a filtered back projection algorithm. A standard two compartment FDG kinetic model was used to generate model predicted output and to fit experimental data (1). Parameters were first 146

150 estimated for a brain ROI and a myocardium ROI COMKAT GUI. Then the timeactivity curves of these two ROIs were fitted for parameter estimation again with a MATLAB script that uses COMKAT command line functions. Results from COMKAT GUI and a script were compared. This data set is available on the COMKAT website for users to download and test within COMKAT. Some of the major functions are tested for speed in the COMKAT GUI and COMKAT Image Tool. For COMKAT GUI, the time required for initializing it, loading a kinetic model from the templates, solving and plotting model output, and parameter estimation. Average time required is calculated from ten runs. In the COMKAT Image Tool, speed is evaluated for loading the test data set of micropet images, frame summation, and refreshing the displayed image each time a display adjustment is made. This part of evaluation for function speed in GUIs does not include the time required for user input such as selecting the files to open or specify which parameters to estimate. The performance advantage of distributed computing is evaluated for the parametric imaging. This evaluation is done by comparing the time required under local computation with one worker vs. that obtained with distributed computing in the task of estimating the FDG kinetic rate constants pixel wise in volume with 128 by 128 by 63 pixels by 44 frames from a micropet study. Computation is done by either the local computation or using distributed computing with two, four, eight, 16 and 31 workers on a mini cluster. (The maximum number of workers available for is 31 because the MATLAB built in scheduler will use one of the 32 available 147

151 licenses.) The hardware used for this test is a mini cluster consisting of four Dell PowerEdge 1950 III servers running Windows Server Each server has two quad core Intel Xeon 2.5GHz CPUs (32 cores total) and 9 GB of RAM. The speed up ratio is calculated by: Time required for n workers Speed-up ratio(n)= Eq. 1 Time required for local computation, where n denotes the number of workers (one per core) used in a specific test under distributed computing mode. Each test of a specific number of workers and local processing was executed five times and the result averaged. 148

152 RESULTS Implementation and validation for COMKAT Figure 2 shows a sreen snapshot of the COMKAT GUI window before data are loaded or a model is specified.. It is ivided into four panels that display the input function, output function, model illustration and parameter settings, respectively. The input function data were loaded with COMKAT Input Function GUI as shown in Fig. 3. COMKAT Input Function GUI then returned the whole blood and plasma timeactivity curves, in the form of first order piecewise polynomial (ie. for linear interpolation), back to COMKAT GUI wherein the two compartment FDG model was selected from a drop down list. With the kinetic model and input function specified, model simulated output was automatically calculated using default values for the model parameters and plotted on the Output Function panel. Subsequently, the values of the parameters may be changed interactively and the plot is updated instantaneously. To specify experimental data for parameter estimation, COMKAT Image Tool was opened from COMKAT GUI to specify experimental data. Fig. 4 shows the appearance of COMKAT Image Tool in which a set of micropet R4 image data was loaded and displayed. To achieve better viewing, it showed an image that was summed through frames. On the screen three default views were displayed as axial, coronal and sagital planes. Two ROIs were drawn on the brain and myocardium as shown in Fig. 4. Corresponding time activity curves were automatically calculated from the images and returned back to the COMKAT GUI. 149

153 After the tissue time activity curves were returned back to COMKAT GUI, parameters for both ROIs were estimated. These two ROIs were processed sequentially and independently, with the estimation results stored and displayed separately. Optionally these results were then stored as a report in a spreadsheet file and could be used for further analysis. Accuracy of COMKAT command line functions and COMKAT GUI were validated separately. Command line functions were validated with the COMKAT Validation Suite. The model output and sensitivity functions were calculated first by analytic solution and then by the numeric solver with COMKAT. As expected, results were found to be within 0.01% agreement. After the command line functions were validated, parameter estimation results obtained from the COMKAT GUI were compared to those obtained using COMKAT command line functions. Parameter estimation results were found to be identical between the GUI based and commandline implementation. Performance evaluation The speed evaluation of the major functions in command line functions, COMKAT GUI and COMKAT Image Tool is summarized in Table 3. The speed of COMKAT command line functions was evaluated for solving the FDG model output with both the compiled and built in solvers. Average time required to complete some major functions of COMKAT GUI and COMAKT Image Tool was measured to evaluate the performance. Performance of the application of distributed computing in the pixel 150

154 wise parameter estimation for parametric images was evaluated. Results of the computation for parametric images were summarized in Table 4. Software distribution COMKAT was packaged into a compressed file for users to download from the website ( as an open source project with free licenses for academic research use. COMKAT has been supported and tested on multiple operating systems including Microsoft Windows XP (32 and 64 bit), Linux (32 and 64 bit) and MacOS X. The COMKAT GUI was compiled into a standalone executable file with the MATLAB Compiler. This standalone executable file also contained the compiled COMKAT Image Tool and COMKAT Input Function GUI. Being available to download on the COMKAT website, this compiled COMKAT distribution does not require users to have MATLAB installed; however, it does require users to install MATLAB Compiler Runtime (MCR), which is redistributable without licensing fees. The comparison between the standard and compiled distribution of COMKAT was summarized in Table 1. Software documentation More details for using COMKAT can be found at the COMKAT website and this information is updated frequently. The COMKAT website is the primary source for documentation. The website includes the user manuals and examples. These 151

155 examples cover a wide range of applications from parameter estimation tasks using COMKAT GUI to complicated modeling analysis in MATLAB scripting with COMKAT command line functions. For example, new users wishing to learn the command line interface might begin with a description and the commands needed to implement the standard FDG model. A slightly more complicated model would be one which includes Michaelis Menten kinetics. At the higher end of complexity is a model that accounts for competition between endogenous neurotransmitter and radioligand (ntpet) (18). Because the COMKAT website is now running on a wiki server software, many pages of the documentation are editable by users. In fact, users are encouraged to share their experience with others through discussion, feedback, and posting of new examples. 152

156 DISCUSSION Kinetic modeling has long been used in quantifying in vivo biochemistry (19, 20). In molecular imaging, numerous reports have proven the value of using kinetic modeling to absolutely quantify physiology (1, 21 23). However, lack of software that is specifically designed for applying kinetic modeling to image data has been an impediment for researchers and particularly those without a computer programming background. In this report, the software package COMKAT is described that we believe will be useful for many researchers for their needs in image quantification. COMKAT has several unique features. First, COMKAT is shared online without licensing costs for academic, non profit research applications. Users without MATLAB licenses may download a COMKAT package that runs as a compiled, standalone executable application. Although some functionality might be limited in the compiled release as shown in Table 1, most fundamental capabilities in the compiled COMKAT GUI function just the same as running under MATLAB. Second, we share COMKAT as an open source project to maximize transparency, extensibility, and collaboration. For example, users may trace program bugs or add new functionalities to COMKAT for their specific needs in image analysis and quantification. Third, COMKAT is developed as a user friendly application with various GUIs. For users that do not have any experience in MATLAB programming, they can refer to our documentation that explains in detail how to use COMKAT in the graphical interfaces and quickly learn how to adopt COMKAT for their data 153

157 analysis. As for data compatibility, COMKAT supports various image and data formats including DICOM. Finally, COMKAT allows users to easily design novel kinetic models with either a GUI or command line functions. For users that wish to evaluate different kinetic models, COMKAT can help streamline and simplify model development, output solving and analysis for sensitivity functions. COMKAT is also shown to be a very fast software package in kinetic modeling. As described previously, COMKAT is linked to a compiled solver that solves the differential equations faster than the built in MATLAB solvers. Results in Table 3 show that the compiled solver is more than 40 times faster compared to the ode15s. This improvement is important because during the iterations within parameter estimation, model output and sensitivity functions will be solved many times before the convergence. Based on the fast speed from this compiled solver, COMKAT GUI can solve for model output and refresh the plot within 0.2 second each time a parameter value is changed. This fast computation speed in GUI is helpful for users so they can quickly simulate model output or find appropriate initial guesses for parameter estimation. Other major functions of COMKAT GUI and COMKAT Image Tools have also been evaluated and found to be satisfactory in terms of speed. For example, loading image data is intrinsically a time consuming computation. With COMKAT Image Tool it takes as little as 8.1 seconds to load a 63 slice, 44 frame 128 by 128 pixels data set, which is fairly fast speed for loading a XXXX MB data set. Display adjustment is also done quickly, < 0.2 second. In summary, the speed in COMKAT for both command line and GUI functions is fast and will help users to increase throughput in image quantification using kinetic modeling. 154

158 Another unique and useful feature for COMKAT is the capability to generate parametric images with support for distributed computing. It has been demonstrated that distributed computing can be applied to accelerate the pixel wise estimation by using computation power of a cluster system or multi core computers. Results showed that, by using 31 workers COMKAT GUI achieved approximately 25 fold acceleration and reduced time requirement from minutes to 6 minutes. This represents an efficiency of 25/31 or 80%. Since the speed up ratio has an approximately linear dependence on the number of workers, further speed enhancement can be expected if more workers are used. Such capabilities have been implemented as part of COMKAT GUI functionality that can be easily executed. Although COMKAT is first designed for PET images and still uses activity concentrations as default units, it can be applied to other modalities and units of data. For example in dynamic contrast enhanced (DCE) MRI studies, perfusion or capillary permeability can be measured with kinetic modeling using contrast agents such as Gd DTPA (24). If the user may obtain pre and post injection T1 values of a specific tissue, contrast agent concentration can be calculated as units of molar concentrations. Similarly, input function concentration can be measured with image derived methods (25 27). Users may then save those input functions and ROI experimental data into text files or spreadsheets, load them into COMKAT GUI and perform kinetic modeling. Detailed unit conversion is documented in our online manual. Meanwhile, one future development of COMKAT is to improve its support in parameter estimation for DCE MRI studies. This would entail plans to provide more 155

159 extensive support for MR images, conversion between intensity and contrast agent concentration, and standardization of DCE MRI imaging protocols. COMKAT is an ongoing project and will plan to continue to maintain and enhance it. Beyond the plans to extend support for parametric imaging and DCE MRI studies as previously described, COMKAT will be expanded by adding more kinetic models, improving computation speed, and becoming less dependent on MATLAB. Meanwhile, documentations are continuing to be added to COMKAT website especially for examples of specific research applications. Users are encouraged to try COMKAT, provide feedback and even participate in COMKAT development. We hope to see more and more users benefit from using COMKAT in image quantification, as COMKAT serves as a powerful and user friendly software environment for molecular imaging research. 156

160 CONCLUSION COMKAT is an integrated software package that is capable of analyzing molecular images with kinetic modeling methods. COMKAT has numerous, including seamless connection between imaging and modeling GUIs, support for user defined kinetic models and experimental data, parameter estimation, parametric imaging functionality and no licensing fees for academic research use. With these powerful functions, COMKAT is suitable for a wide spectrum of data analysis tasks including quantifying physiology, kinetic model development, image processing and data simulation. To download COMKAT please visit our website at ACKNOWLEDGEMENTS The work was supported by NIH grant R33 CA and R24 CA

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164 TABLES TABLE 1 Summary and comparison of functionalities of COMKAT distributions. Functions COMKAT GUI COMKAT on MATLAB COMKAT stand alone application Loading input functions from files Simulating model output Creating new kinetic models Parameter estimation Loading tissue time activity curves from files Loading tissue time activity curves from COMKAT Image Tool Calculating parametric images Distributed computing for parametric imaging * COMKAT Image Tool Supporting multiple image formats (see Table 2) Image display and contrast adjustments Frame summation Spatial filtering 161

165 Draw ROI or VOI Image co registration Image translation and rotation Image re slicing in arbitrary orientations MATLAB scripting with COMKAT command line functions Available for Windows, Linux and MacOS X COMKAT licensing MATLAB licensing Free for academic research use Requires computers with MATLAB installation and licenses Free for academic research use Requires computers with MATLAB Compiler Runtime (no licensing fees) * Requires MATLAB licenses for MATAB Distributed Computing Server and Parallel Computing Toolbox 162

166 TABLE 2 Data formats supported by COMKAT GUI and COMKAT Image Tool Data type Input function Output function (time activity curves) Supported file formats in COMKAT Text files (.txt), Comma Separated Value files (.csv), Excel spreadsheets (.xls), MATLAB binary files (.mat) Text files (.txt), Comma Separated Value files (.csv), Excel spreadsheets (.xls), MATLAB binary files (.mat) DICOM (part 10), NIFTI, Analyze, Siemens micropet (ASIPro), Image Files Siemems ECAT Exact (ECAT7), Philips Allegro and Gemini (ImageIO), Bruker Biospin 163

167 TABLE 3 Summary of computation speed for major functions in COMKAT. COMKAT Command line Functions COMKAT GUI COMKAT Image Tool Output solving Task Compiled solver Built in solver Initialization Model loading Output solving and plotting Parameter estimation Reading and displaying images Frame summation Refreshing display (ode15s) Time Mean (ms) Time SD (ms) The computation is based on an FDG kinetic model of a micropet rat study. For COMKAT command line functions runs = 500, otherwise runs =

168 TABLE 4 Summary of computation speed for parametric imaging Number of workers Time Mean (min) Local Time SD (min) Speed up ratio Efficiency (%) Time required for computation was calculated from five runs. The local computation was used as reference for calculating the speed up ratios by estimating parameters pixel wise on one core of one CPU without distributed computing. Efficiency was calculated as (speed up ratio/number of workers). With regression analysis, a linear relationship was found in speed up ration (y) versus number of workers (x) as y = x with r =

169 FIGURES COMKAT Image Tool COMKAT GUI COMKAT Input function GUI Analysis tools Model solving and parameter estimation COMKAT Command Line Functions FIGURE 1 Framework of COMKAT software. For most users, COMKAT GUI serves as the front page of the software. It calls several other GUIs of COMKAT to import data and kinetic models. The user may also perform several different types of model analysis with the analysis tools. Behind the scenes, COMKAT GUI calls COMKAT command line functions to calculate model output and perform parameter estimation. 166

170 FIGURE 2 Screen capture of the layout of COMKAT GUI when initialized. The interface is composed by four panels: input and output function, compartment model illustration and the model parameter values. From this GUI, users may then begin to load input and output data and specify kinetic model to use. 167

171 FIGURE 3 Screen capture of the COMKAT Input Function GUI. It allows users to read multiple files and combine all data. The input function shown here is from the testing data of a rat FDG micropet study. It contains the input function data from automatic counting for the first two minutes and the manual samples afterwards. Linear interpolation is used to fit the data. Once the specification is completed, the Input Function GUI returns the input function specified back to the COMKAT GUI with plasma and whole blood time activity curves. 168

172 FIGURE 4 The appearance of COMKAT Image Tool when micropet images are loaded. With COMKAT Image Tool, users may adjust image display and draw ROIs or VOIs. In this figure two ROIs are drawn. On the sagital view a ROI is drawn on the brain area. On the axial view a ROI is drawn on the myocardium area. Corresponding time activity curves are shown on the plot. Once users finish drawing ROIs and click the Return to main GUI button, COMKAT Image Tool returns the ROI information and time activity curves back to COMKAT GUI. 169

173 FIGURE 5 COMKAT GUI with all necessary information specified. On the screen, both the model and data are successfully loaded. Users may click buttons next to parameter values or enter their numbers to refresh the model simulated output curves. Once a good guess of initial value is done, users can estimate parameter values by clicking Estimate button. Parameter values will be estimated and the fitted curve will be plotted on the output function figure. 170