Blind Multi-Channel Estimation of Arterial Input Function in Dynamic Contrast-Enhanced MRI

Transcription

1 Blind Multi-Channel Estimation of Ateial Input Function in Dynamic Contast-Enhanced MRI Jiřík R 1,2, Batoš M 2, Standaa M 3, Taxt T 4 1 Institute of Scientific Instuments of the Academy of Sciences of the Czech Republic, 2 Dept. of Biomedical Eng., Bno Univ. of Technology, Czech Republic, 3 Masayk Memoial Cance Institute, Bno, Czech Republic, 4 Dept. of Biomedicine, Univesity of Begen, Noway jiik@feec.vutb.cz Abstact. This pape studies dynamic contast-enhanced magnetic esonance imaging, a technique to estimate maps of physiological paametes descibing tissue pefusion at the capillay level. One of the most challenging poblems of this imaging method is the measuement of the ateial input function. One possibility to estimate the ateial input function is based on multi-channel blind deconvolution applied to signals measued in seveal tissue egions. An extension to the published methods is pesented. A new egulaization tem is intoduced and a moe complex model of the tissue esidual function is used. Tests on synthetic and clinical data demonstate the eliability of the method. 1 Intoduction Dynamic contast-enhanced magnetic esonance imaging (DCE-MRI) is an imaging modality used fo estimation of tissue pefusion paametes at the capillay level, such as factional blood volume, factional volume of the extacellula extavascula space, blood flow, pemeability-suface aea, etc. [1]. These paametes ae impotant in diagnosis and theapy-monitoing, especially in cance imaging, but also imaging of othe diseases changing vascula physiology can benefit fom such a close insight into functional status of tissues. DCE-MRI is cuently widely used in eseach and vey likely just one step befoe clinical use. In DCE-MRI, image data fom an aea of inteest ae acquied fo seveal minutes following application of a contast agent bolus. Fo each egion of inteest (ROI, ideally a voxel), a time-cuve of the contast agent concentation is then deived fom the image data and analyzed to estimate the pefusion paametes. Fo quantitative pefusion analysis, the contast agent concentation time couse in a feeding atey, the so called ateial input function (AIF), has to be deived fom the image data too. This is one of the main poblems fo eliability and epoducibility of the method, mainly due to patial volume effect, flow atifacts, dispesion of the AIF between the measuement site and the tissue-roi site and due to nonlineaity between the measued quantity (1/T1) and the contast agent concentation fo highe concentations [1]. One possibility to solve this poblem is to estimate the AIF fom the tissue cuves (contast agent concentation in the tissue ROI vesus time) of seveal ROIs in tissues adjacent to aeas of inteest. Each tissue cuve can be modeled as a convolution of the tissue impulse esponse, R( Φ, t), (a model-based tissue specific function of pefusion paametes Φ and time t) and the AIF, C a (t), which is assumed to be the same fo all ROIs. This leads to a multi-channel blind deconvolution whee C a (t) is estimated simultaneously with the pefusion paametes Φ. This contibution is an extension of the appoaches in [2, 3]. A new egulaization tem is included in the deconvolution to povide bette obustness with espect to the measuement noise. In addition, a moe complex model of R( Φ, t), distibuted-capillay adiabatic tissue homogeneity (DCATH) model [4], is used instead of the simple widely used Tofts model [1]. ISSN X 373 Analysis of Biomedical Signals and Images; 2:

2 This allows moe degees of feedom of R( Φ, t) and may lead to a moe accuate AIF estimates. 2 Methods The poposed multi-channel blind deconvolution is fomulated as minimization of the following function with espect to C a [n] and Φ : 2 [ C Φ, ] +, (1) t (, Ca ( R( λ D( Ca ( n whee, is the ROI index, n is the time index, is convolution, C t (, is the contastagent concentation cuve in the -th tissue ROI, C a ( is the AIF, R( Φ, is the impulse esponse of the -th ROI, Φ is a vecto of pefusion paametes fo the -th ROI, λ is the egulaization weight and D( is the 2 nd -ode diffeence opeato impulse esponse. While the fist tem epesents the fidelity of the measued signal to the model, the second tem is a new egulaization tem, imposing piece-wise linea shape to the AIF estimate (inducing spase chaacte of the 2 nd -ode diffeence). The egulaization tem pevents amplification of noise typical fo maximum-likelihood deconvolution (optimization of the 1 st tem of Eq. (1) only) and, at the same time, allows steep edges of the AIF cuve. In blind deconvolution, the multiplicative factos of the functions in convolution can not be estimated without futhe containts. Hence, the integal of the AIF was set to a fixed value. Fo synthetic data this value was known fom the efeence AIF and fo clinical data the value was set to the integal of the measued AIF. The optimization was implemented as altenating between optimization with espect to C a ( and Φ, using the Active Set Algoithm (Matlab Optimization Toolbox). Although convegence to the global optimum is not theoetically guaanteed, the simulation esults indicate a good convegence. 3 Results 3.1 Simulated data Fo simulated data, AIF was measued fom a clinical ecoding of heat as the mean pixel value within a ROI inside the left venticle. The fist-pass pat of the AIF was low compaed to a typical AIF shape due to flow atifacts and nonlineaity of the elationship between R1 and the contast agent concentation. Hence, the measued AIF was squaed to appoach a moe ealistic shape (Fig. 2). Then, this AIF was convolved with impulse esponse functions R( Φ,, = 1,2,3, to poduce thee tissue cuves. The pefusion paamete sets Φ wee set to physiologically valid tissue paametes. Finally, white Gaussian noise was added to each tissue cuve. The signal-to-noise atio (SNR) was 3dB which appoximately coesponds to the SNR fo ROIs in ou clinical ecodings. An example of thee synthetic tissue cuves simulating thee ROIs in diffeent tissues is given in Fig. 1. The poposed AIF estimation method was applied to the synthetic data 5 times, fo diffeent noise ealizations. The estimated AIF in tems of mean ± standad deviation ae given in Fig. 2. The achieved elative eo was 13,8 %. The same pocedue was tested with othe egulaization tems, used mainly in image estoation: Tikhonov [5] and total vaiance [6] egulaization tems. The coesponding elative eos wee 16.7 % and 14.6 %, espectively. The main deviation fom the efeence AIF was in the ovesmoothed fist-pass pat of the AIF. This pat was shapest fo the poposed egulaization. The egulaization weight facto was chosen expeimentally fo all egulaization types. n ISSN X 374 Analysis of Biomedical Signals and Images; 2:

3 C t [a.u.] ROI 1 ROI 2 ROI BIOSIGNAL 21 Fig 1. Example synthetic contast-agent concentation cuves fo thee tissue ROIs. 15 AIF [a.u.] Fig 2. Synthetic data efeence AIF (black solid) and mean estimated AIF ± standad deviation (ed dotted) fo 5 AIF estimations fo vaious andom noise ealizations. 3.2 Clinical data The pocedue of AIF estimation was also tested on clinical ecodings and compaed with the measued AIFs. Fig. 3 shows an AIF measued fom a clinical ecoding (solid line) and estimated fom 3 ROIs in the same ecoding (dotted line). A 1.5T MRI Siemens Avanto scanne was used with a 2D FLASH sequence, TR/TE = 6.4/2.7 ms. All legal issues wee fulfilled, including a witten consent of the patients and the ethical-committee appoval. An example coonal-section image of abdomen (Fig. 4a) shows a kidney cance metastasis in the left lumba quadate muscle (cicula-shape stuctue in the ight image potio. The AIF estimated by the poposed method, using thee tissue ROIs, had a shape fist-pass peak compaed to the AIF measued in the left-side lumba atey pesumably feeding the tumo, which illustates the atifacts in the AIF measuements. The egulaization weighting facto λ was chosen expeimentally. Examples of the pefusion-paamete maps obtained fom the same patient using deconvolution and the DCATH model of the tissue impulse esponse (complete pocedue descibed in [7]) ae given in Fig. 4. The inceased blood plasma flow, Fplasma, and blood plasma volume, v p, in the tumo im coelate with highly vasculaized polifeating tumo tissue. The inceased volume of the extacellula extavascula space, v e, inside the tumo and also in the adjacent muscle coelate pobably with cental necosis and eactive edema. These obsevations show, that the method povides clinically elevant and expected data which indicates the coectness of this appoach. ISSN X 375 Analysis of Biomedical Signals and Images; 2:

4 AIF [a.u.] Fig 3. Measued (solid) and estimated (dotted) AIF based on clinical data. (a) (b) (c) (d) Fig 4. Clinical data. (a) Coonal section abdominal image with kidney cance metastasis. (b) Map of blood plasma flow. (c) Map of extacellula-extavascula volume. (d) Map of blood plasma volume. ISSN X 376 Analysis of Biomedical Signals and Images; 2:

5 4 Discussion and Conclusions An extension to available methods fo blind multi-channel AIF estimation is pesented. It enables pefusion imaging in expeiments whee the AIF is not measuable. In a clinical setting this situation is vey common especially in non-bain applications. The lack of a eliable AIF measuement has been a seious baie to wide use of clinical DCE-MRI imaging. Faily good fit was achieved fo tests on synthetic and clinical data. Howeve, equiements fo estimation accuacy still need to be specified. Acknowledgement This wok has been suppoted by the poject of the Czech Science Foundation no. GA12/9/16 and by the institutional eseach fame no. MSM sponsoed by the Ministy of Education of the Czech Republic. The clinical pat of the study has been facilitated by the eseach fame no. MZMOU25 FUNDIN sponsoed by the Ministy of Health of the Czech Republic. Refeences [1] Jackson A, Buckley DL, Pake M. Dynamic Contast-Enhanced Magnetic Resonance Imaging in Oncology. Belin: Spinge; 25. [2] Yang C, Kaczma GS, Medved M, Stadle WM. Multiple efeence tissue method fo contast agent ateial input function estimation. Magnetic Resonance in Medicine 27; 58: [3] Riabkov DY, Di Bella EVR. Estimation of kinetic paametes without input functions: Analysis of thee methods fo multichannel blind identification. IEEE Tansactions on Biomedical Engineeing 22; 49: [4] Koh TS, Zeman V, Dako J, Lee TY, Milosevic MF, Haide M, et al. The inclusion of capillay distibution in the adiabatic tissue homogeneity model of blood flow. Physics in Medicine and Biology 21; 46: [5] Taantola A. Invese Poblem Theoy. Philadelphia: Society fo Industial and Applied Mathematics, 24. [6] Rudin LI, Oshe S, Fatemi E. Nonlinea total vaiation based noise emoval algoithms. Phys D 1992; 6: [7] Batoš M, Keunen O, Jiřík R, Bjekvig R, Taxt T. Pefusion Analysis of DCE-MRI Images Using a Fully Continuous Tissue Homogeneity Model with Mean Tansit Time Dispesion and Fequency Domain Estimation of the Signal Delay. In Poceedings of 2th Intenational EURASIP Confeence BIOSIGNAL 21. Bno: Vutium, 21. In pint. ISSN X 377 Analysis of Biomedical Signals and Images; 2: