Development and Validation of Subject-Specific Finite Element Models for Blunt Trauma Study

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1 Weixin Shen Yuqing Niu SET Division, L-3 Jaycor, 3394 Carmel Mountain Road, San Diego, CA Robert F. Mattrey Department of Radiology, University of California, San Diego, CA Adam Fournier SET Division, L-3 Jaycor, 3394 Carmel Mountain Road, San Diego, CA Jackie Corbeil Yuko Kono Department of Radiology, University of California, San Diego, CA James H. Stuhmiller SET Division, L-3 Jaycor, 3394 Carmel Mountain Road, San Diego, CA Development and Validation of Subject-Specific Finite Element Models for Blunt Trauma Study This study developed and validated finite element (FE) models of swine and human thoraxes and abdomens that had subject-specific anatomies and could accurately and efficiently predict body responses to blunt impacts. Anatomies of the rib cage, torso walls, thoracic, and abdominal organs were reconstructed from X-ray computed tomography (CT) images and extracted into geometries to build FE meshes. The rib cage was modeled as an inhomogeneous beam structure with geometry and bone material parameters determined directly from CT images. Meshes of soft components were generated by mapping structured mesh templates representative of organ topologies onto the geometries. The swine models were developed from and validated by 30 animal tests in which blunt insults were applied to swine subjects and CT images, chest wall motions, lung pressures, and pathological data were acquired. A comparison of the FE calculations of animal responses and experimental measurements showed a good agreement. The s in calculated response time traces were within 10% for most tests. Calculated peak responses showed strong correlations with the experimental values. The stress concentration inside the ribs, lungs, and livers produced by FE simulations also compared favorably to the injury locations. A human FE model was developed from CT images from the Visible Human project and was scaled to simulate historical frontal and side post mortem human subject (PMHS) impact tests. The calculated chest deformation also showed a good agreement with the measurements. The models developed in this study can be of great value for studying blunt thoracic and abdominal trauma and for designing injury prevention techniques, equipments, and devices. DOI: / Keywords: finite element, thorax, abdomen, blunt trauma, human, swine, computed tomography, rib fracture, lung injury, liver injury Manuscript received March 16, 2006; final manuscript received June 11, 2007; published online April 11, Review conducted by Susan Margulies. 1 Introduction Thoracic and abdominal blunt trauma can occur in a number of events. Injuries caused by motor vehicle accidents are common and extensively studied by animal tests and post mortem human subject PMHS tests. Research on body armor showed that while body armor systems were effective in stopping the penetration of bullets or fragments, the subsequent blunt impact could cause significant injuries to the rib cages and soft organs 1 5. Rib fracture, lung contusion, and liver laceration were also observed in law enforcement operations when nonlethal projectiles were used to control a crowd 6. Blunt trauma is the consequence of tissue damage induced by mechanical insults that leads to physiological dysfunctions. The mechanisms leading to tissue damage were examined by a large number of studies and are well summarized When struck by a blunt impact, the body deforms and causes the propagation of stresses and strains inside the body. Depending on geometry, material properties, and loading characteristics, stresses may concentrate inside certain organs, and tissue damage results when the stresses or strains exceed the strength of the tissue due to the formation of shock wave, local shearing, or crushing of tissues. The finite element FE method, with its capability of accounting for complex geometry and material characterization, has become an increasingly powerful tool to calculate tissue stresses and strains. A number of FE models of human thorax and abdomen have been developed over the past few decades. Early thoracic FE models included simplified rib cages as the main loadcarrying structures and used mostly elastic material models. Better anatomies based on commercial data sets Viewpoint Datalabs, Orem, UT or the Visible Human data set 14 and more complex material models were used in more recent thoracic models A few of these models included the abdominal region that was simplified as lumped masses 17,21. The abdomen model developed by Lee 22 had a detailed anatomy of the liver, spleen, and kidney and implemented the viscohyperelastic constitutive relationships for soft tissues. The model was validated against pendulum impact, narrow bar frontal impact, seatbelt loading, and drop tests and was used for vehicle crash simulations. A FE model including both thorax and abdomen was also developed by Roberts et al. 23 and was used to study the body responses to behind-the-body armor ballistic impacts. These modeling efforts not only demonstrated the potential of using FE models to study blunt trauma but also highlighted a few challenging issues related to model development and validation. First, the variation in subject size and anatomy may affect the predicted response and injury outcomes and has to be accounted for. This requires either different models for different subject sizes or a method that allows a base line model to be easily adapted to Journal of Biomechanical Engineering Copyright 2008 by ASME APRIL 2008, Vol. 130 /

2 a subject of specific size. Second, FE simulations are computationally intensive, and both accuracy and efficiency need to be improved for FE models to be useful in practical applications. Third, models have to be validated by experimental data. Complete anatomical, response, and injury data are needed so that developed models can be validated by the measurements acquired from the same subjects. The purpose of this study is to 1 develop a method of generating thoracic and abdominal FE models from computed tomography CT images that features subject-specific anatomies, easy model scaling or morphing, and efficient numerical performance and 2 develop and validate both swine and human FE models using animal and PMHS test data and demonstrate the models applicability in predicting body responses and possible injuries to blunt impacts. 2 Materials and Methods Animal tests were conducted to acquire CT images, animal responses, and pathological data for model development and validation. FE models were developed in a number of steps: 1 anatomical reconstruction of CT images and geometry extraction, 2 development of a rib cage model, 3 meshing of soft organ components and assigning soft tissue material parameters, and 4 model assembly. The developed swine models were calibrated against a subset of the test data to determine optimal model parameters. Model response predictions were then calculated for all tests and compared against the measurements for model validation. The predicted stress/strain concentrations in organs were compared against the observed injury pattern. Similarly, a human FE model was developed from CT images in the Visible Human data set 14 and was validated by the historical PMHS test results 24, Experimental Data. A total of 30 animal tests were conducted to obtain data for developing and validating swine models. The animal protocol was approved by the IACUC of the University of California at San Diego UCSD. During each test, a CT scan was acquired of an anesthetized animal in the supine position in suspended respiration with lungs in expiration using a twin speed scanner four-row detector system twin speed, General Electric, Milwaukee, WI. A continuous helical data set was obtained from the base of the neck through the symphysis pubis acquisition matrix, in-plane resolution= mm 2, slice thickness=2.5 mm. The animal was then subjected to a blunt impact insult delivered by an impactor that was made up of a front impact plate 7.52 cm in diameter and a cylindrical base fixture. The impactor was instrumented with a highshock accelerometer Isotron, 7255A-01 and weighed between 60 g and 80 g. The impact was applied on each animal at the upper chest, lower chest, or abdomen. In a number of tests, two miniaturized pressure catheters Millar instruments, SPR-524, 35 khz natural frequency, mm Hg overpressure were inserted into the lungs through the airway with the assistance of a fluoroscope, with one placed about 1 2 cm below the pleural surfaces underneath the impact location and the other placed inside the airway. The impact acceleration and lung pressures were recorded at 50,000 samples/ s during the impact. A high-speed video camera recorded the impacting action. The time trace measurements were filtered by second order double Butterworth lowpass filter with a cutoff frequency of 15 khz. The impact velocities were not measured due to the difficulty in placing a chronograph in the animal tests. Instead, impact velocities were obtained by integrating the acceleration measurements. After waiting for min to allow soft tissue injuries to develop, another set of CT scans was acquired, following exactly the same matrix to quantify soft tissue injuries. The swine was then euthanized, and a necropsy study was performed, with specific attention paid to the rib cage for fractures, lungs, pleura, heart, mediastinum, liver, and spleen. For developing the human FE model, the CT data set from the Visible Human project was used. The CT image was acquired using a acquisition matrix with an in-plane resolution of 1 1 mm 2 and a slice thickness of 1 mm Anatomical Reconstruction. The CT images were processed by 3D-DOCTOR Able Software to reconstruct the raw anatomies of the rib cage and soft organs. Image segmentation created boundary contours on each CT image that separated different anatomical regions of interest. The boundaries from each image were connected into discrete polygons representing the outer surfaces of the organs. The volume representation of the organs was then obtained as a collection of pixels with coordinates and corresponding attenuation values enclosed by the polygon surfaces Fig. 1 a. Both the polygonal surfaces and volumes were output as IGES files and input into RAPIDFORM INUS Technology, which supports scripting for geometrical modeling Fig. 1 b. For each individual organ, a set of anatomical landmarks and control points that best represented the anatomical features of the organ were identified. A set of curves was created and parametrized against the controlling points. The polygonal surfaces were then decimated and smoothed and fitted by non-uniform rational B-spline NURB surfaces. This procedure allowed the surface representation of the organs to be smoothed. The geometries could also be easily modified or morphed by changing the position of the control points. Special attention was paid to fine tune the parameters so that the geometries of the contacting organs match perfectly. 2.3 Modeling of the Rib Cage. A three-dimensional 3D modeling of a bony structure is computationally expensive because the combination of a high elastic modulus of bone and small element sizes leads to very small time steps in a transient dynamic analysis. Shen et al. 26 developed a specialized method that modeled ribs and cartilages as inhomogeneous beams and main load-carrying structures enclosed by shell elements for better geometry and contact treatment Fig. 1 c. An iterative procedure processed the volumetric data and created the centerlines and outer surfaces of ribs. The beam elements were generated along the centerlines, and shell elements were added along the chest wall surface. The equivalent beam properties in terms of line density, cross-section area, homogenized tensile stiffness, flexural stiffness, and tensional stiffness were calculated for each beam node using a generalized classical beam formulation based on the material distribution inside rib cross sections. The bone densities were estimated from CT values as eff =AHu+1000 kg/m 3 27,28. The elastic moduli of bones were estimated from bone apparent density 29. The average elastic moduli were assigned to the shell elements. Simulations of a benchmark problem showed that this approach accurately reconstructed the geometrical features of rib and cartilages and accurately and efficiently predicted the rib motions, stresses, and strains due to impact 30. The spine was represented by a series of linear beam elements, each representing a motion segment with nodes at the vertebral body centroids 31,32. Additional beam elements were added to transfer the forces and moments to the motion segments through the vertebral processes and the rib attachment points with properties determined from geometry and approximate stiffness 33. The sternum was modeled as linear elastic 3D solid elements assigned with the average density and Young s modulus estimated from CT images. The costovertebral joints and sternochondral joints were modeled as short beams with stiffness values obtained by Chen et al. 12, Closkey et al. 34, and Lee et al Modeling of Soft Organs and Base Line Material Parameters. Most soft components, including skin, muscles, lungs, heart, liver, spleen, and stomach, were modeled as homogeneous solids with hyperviscoelastic material properties. Pleural surfaces enclosing the lungs and the diaphragm were modeled as / Vol. 130, APRIL 2008 Transactions of the ASME

3 Fig. 1 Demonstration of procedures for the model development and validation. a Raw anatomies of rib cage, torso walls, and soft organs were reconstructed from CT images. b Geometrical modeling of raw anatomies produced smoothed geometries that matched together and can easily be modified. c FE modeling of rib cage treated the rib as inhomogeneous composite beam/shell structure with bone material properties directly calculated from CT number. d FE meshes of soft organs, such as a lung, were generated by mapping a carefully constructed mesh template onto NURB surfaces. e Human and swine models were assembled for simulating animal and PMHS tests Journal of Biomechanical Engineering APRIL 2008, Vol. 130 /

4 Table 1 Summary of model components and material parameters Part Element kg/m 3 K GPa i s Gi kpa Reference Ribs Beam Shell, E were determined from rib beam structures with equivalent mechanical properties of 3D ribs Spine Beam Average CT number was used to calculate and E 31,32 Sternum Solid =1600; E=10 GPa Muscle Solid ;1;0.1;0.01; ;120;360;480; Skin Solid ;1;0.1;0.01; ;240;360;480;690 Lungs Solid =200; K=100 kpa; C/ =592 Pa; =5.85; = 3.21; C 1 / =19.3 Pa; 19 C 2 =2.71 Heart Solid =1000; K=2 MPa; C 1 =1085; B 1 =24.26; B 2 =40.52; B 3 =1.63 Diaphragm Membrane; h=2 mm =1000; E=3 MPa 19 Liver Solid ;1; ;200; Spleen Solid ;1; ;200;300 Stomach Solid ;1; ;200;300 Other abdomen Solid =1000; E=500 kpa; Poisson s ratio: 0.45 membrane elements. Structured hexahedral meshes that gave better numerical performance in a transient dynamical analysis were generated by Truegrid XYZ Scientific Applications for each soft organ. Structured mesh templates that were based on geometry control points used in the geometrical extraction to represent the topology of the organs were manually created. The mesh templates were then mapped on NURB outer surfaces of the organs. The quality of mesh in terms of mesh fineness, element Jacobi, and volume uniformness 36,37 was examined, and necessary changes were made by adjusting the controlling points and number of elements along the mesh template, both saved as parameters in Truegrid. This procedure generated high-quality predominantly hexahedral meshes Fig. 1 d and reduced s along organ interfaces since meshes of individual organs were created from matching geometries. Material constitutive models and parameters for soft tissues were mostly based on literature values. CT numbers were also used to help estimate material densities. Skin, muscles, and abdominal organs were modeled as nearly incompressible, hyperelastic, and viscoelastic. The main parameters such as bulk modulus K and shear modulus G were determined by fitting the material model against test data 38. Viscoelasticity used a shear stress relaxation function represented by six terms of Prony s series as g t = 6 i=1 G i e it, where G i are shear moduli and i are decaying constants that were obtained by best matching the available relaxation data 39 and maintaining a nearly constant hysteresis over the frequency ranges of interest 40. The lung material used the hyperelastic model with the strain energy function by Fung et al. 41 and Vawter 42, the parameters obtained by Deng and Chang 19, and a linear equation of state p= p 0 1 / 0 that relates lung pressure p to density, initial density 0, and ambient pressure p The hyperelastic model by McCulloch and Omens 44 was used to model the passive behavior of heart muscles. The parameters were obtained by Gucciione and McCulloch 45 from the biaxial testing of a cadaver heart specimen. The rib cage ribs, sternum, and spine and diaphragm were modeled as elastic since a sensitivity study showed that the strain rate dependent component had little effects on the responses. A base line range of material parameters were first established from the literature data. These parameters were then fine tuned so that the FE calculation of body responses best matched the measurements from the first five animal tests. The calibrated material parameters Table 1 were then used for simulating all the tests. 2.5 Model Assembly and Simulation. Model components were assembled using two types of interfaces. Tied interfaces among the skin, muscles, diaphragm, and rib cage allowed neither penetration nor sliding. Contacting surfaces were defined between the rib cage and organs, between the diaphragm and organs, and among thoracic and abdominal organs to allow sliding along the interfaces. A FE model of the impactor was also assembled into the model to simulate a specific test Fig. 1 e, with contact surfaces defined between the front plate of the impactor and the body surface. The impactor was oriented toward the impact spot by a tilt angle estimated from the experiment. The initial velocity was assigned to be the impact velocity estimated from experimental measurements. Simulations were conducted using the LS-DYNA3D explicit dynamics solver Livermore Software Technology Corp. on a cluster system with ten 2.0 GHz CPUs running the Linux operating system. 3 Results 3.1 Subject-Specific Swine and Human FE Models. 30 FE models were developed from acquired CT images of the animal subjects, and another FE model was developed for humans from the Visible Human CT images. A swine FE model on average had about 75,000 nodes, 2500 beam elements, 15,000 shell elements, 49,000 solid elements, and 400,000 total degrees of freedom DOFs. The hexahedral elements account for about 90% of all solid elements, with the remaining being wedge or tetrahedral elements. A typical simulation of a test with impact duration lasting 3 ms took about 8 h. The time marching steps were on the order of s, which were determined by the beam elements of the ribs. The human model had about 77,000 nodes, 3000 beam elements, 18,000 shell elements, 47,000 solid elements, and 450,000 total DOFs. The hexahedral elements also accounted for about 90% of all solid elements, with the remaining being wedge or tetrahedral elements. 3.2 Comparison of Measured and Calculated Responses. The experimental velocity and deformation time histories at the impact locations were obtained by integrating measured accelerations. The accelerometer sensor drifting was corrected by using the free flight distance between takeoff and impact as a displacement constraint point in the calculation. The drag from the wire also caused a slight tilting of the impactor during flight. It was also accounted for by estimating the tilt angels from the highspeed video recordings. Based on 20 laboratory tests in which chronographs were used to measure the actual impact velocities, the method led to less than 2 m/s or about 4% in the estimated impact velocity. The impact force equaled the multiplica / Vol. 130, APRIL 2008 Transactions of the ASME

5 Fig. 2 Comparison of the FE calculation of time traces of deformation, velocity, delivered energy, and lung pressure with experimental measurements obtained in test 14 tion of the acceleration and the impactor mass. Integrating the impact force multiplied by velocity over time gave the energy delivered to the subjects. FE simulations, on the other hand, directly output the velocity and deformation time. Energy delivered to the body was estimated from the difference between the initial and the instantaneous kinetic energy of the impactor based on the FE output of impactor velocity. For tests where lung transient pressures were also measured, the locations of the pressure catheter 50 khz near the impact location, usually 1 2 cm below the pleural surface, were estimated from CT images. The lung pressures at the corresponding elements in FE were also output from the FE simulations and compared against the measurements. Figure 2 gives the results from one of the tests test 14. The weight of the impactor was 76 g, and the impact velocity was estimated to be 51 m/s. The locations of the pressure catheters were determined from CT images and confirmed during necropsy by carefully cutting open the airways following the catheter lead. One pressure catheter continued to the sixth bronchiole and terminated approximately 5 cm reaching into the hemorrhaged area 1 2 cm from the pleural surface under the impact location. The pressure measurement from this catheter was given in Fig. 2. Both postimpact CT images and necropsy showed that the placement of the sensor caused lung damage, primarily due to the small size of the catheter 3 Fg in diameter. Since the tip of the catheter is larger than the alveolar size, the pressure measurement from the catheter inside the lung parenchyma represented the average pressure of local lung tissues around the catheter tip. The catheter inside the bronchiole was used to give the far-field reference pressure trace. The measurements, plotted as black dashed lines, indicated that the impact lasted about 1.5 ms compression and rebounding phases and the main impact loading phase lasted about ms when the impact velocity decreased to zero. The total energy delivered to the body was around 106 Js. Lung pressure measurement indicated a fast-rising near shock wave inside the lung parenchyma near the impact location that reached a peak of about 350 kpa in 0.4 ms. The total duration of the pressure wave lasted around 1.5 ms, about the same as the impact duration. To quantify the overall difference between calculated and experiment time traces in all tests, an measurement was defined as Error= c m / m, where c and m were calculated and experimental time traces during the loading period, respectively, and c was the Frobenius norm of time trace c. A comparison of FE results and experimental measurements of each test, including duration, peak values, and s in time traces, is given in Table 2. The impact duration lasted for ms in most tests. The s in the calculated chest wall motion and delivered energy time histories were less than 10%. The s in calculated lung pressure time histories were 5 25%. The average in peak deformation was about 6.42%. FE calculations of peak deformation, impact durations, maximum delivered energy, and lung pres- Journal of Biomechanical Engineering APRIL 2008, Vol. 130 /

6 / Vol. 130, APRIL 2008 Transactions of the ASME ID Subject weight kg Impact mass g Table 2 Comparison of FE calculated response time traces with experimental results Velocity ms Duration ms Deformation cm Delivered energy J Lung pressure kpa Initial Velocity Trace Expt. FE Error Expt. peak FE peak Peak Trace Expt. peak FE peak Peak Trace Expt. peak FE peak Peak Trace

7 Fig. 3 Comparison of FE calculation of peak response values with experimental values sure showed strong correlations with the measurements with correlation coefficient, r 2 =0.9716, , , and , respectively. The comparison of experiment and calculated values open circle are plotted in Fig. 3 against the perfect fitting line measurement equals prediction that has a correlation coefficient r 2 =1. The data points follow closely with the perfect fitting line, suggesting that calculated values were not statistically very different from the experiment data. Notice that calculated peak energy that was delivered to the body matched almost perfectly with experiment values since the initial velocity of the impactor and, thus, the impact energy were prescribed to drive the simulations. 3.3 Comparison of the FE Calculation of Stress Distribution With Observed Injuries. The main tissue damages observed from post-ct images and necropsy studies included fractures of ribs, lung contusions, and lacerations of liver. Stress distributions inside the corresponding organs were obtained from FE simulations and were compared against the observed tissue damages. Most fractures of ribs occurred at or very close to the impact location and started from the side of the rib posterior to the impact, indicating that they were localized fractures caused by the excessive bending stresses. Since the rib cage was modeled as a beam structure, the stresses were determined from the cross section of the rib and the beam internal forces and moments output from FE simulations. The maximum bending stresses were largest in the posterior sections of ribs directly underneath the impact and decreased away from the impact location Fig. 4 a. Comparing the peak bending stresses at the likely fracture locations with the actual occurrences of fracture yes or no suggested that tensile stress values corresponding to a 50% chance of rib fracture were between 120 MPa and 160 MPa. The value was consistent with those from a previous study of rib fracture due to high-speed impacts 53 and within the range of bone strength data reported in literature under various loading conditions 28, Most animals incurred a contusion in the lung parenchyma near the point of impact and developed hemorrhage or edema. The contused lung therefore had a much higher density than normal lung tissue, and contusion was evident in postimpact CT images. A threshold density of 1.0 g/cm 3, indicating the complete infusion of blood or fluid into alveoli, was used to segment the contused lung volumes. Since studies have linked the occurrence of lung contusion to the peak pressure inside lung tissues 7, pressure time traces and then peak pressure values were calculated from FE simulations for each lung element and compared to observed lung contusion. Figure 4 b compares the contusion observed from necropsy and post-ct imaging in one of the tests to the distribution of peak pressure inside the lungs. Lung contusion occurred on the lower right lobe, and the center of the contused volume was estimated from CT images to be about 1.5 from the sixth bronchiole extended toward the pleural surface. The contused volume was 130 cm 3 or about 10% of the total volume of the right lung 1 h after the impact. The total lung volume was determined by counting all the volumes enclosed by the lung pleural surfaces at the end of expiration and, therefore, represented the functional residual capacity plus volume of dead space. Since lungs deformed significantly in preimpact CT images from which FE models were developed in postimpact CT images when the Journal of Biomechanical Engineering APRIL 2008, Vol. 130 /

8 Fig. 4 Comparison of injuries observed in tests with FE calculation of stresses. a Ribs fracture versus FE calculation of tensile stress distribution. b Lung contusion from necropsy and reconstructed postimpact CT images versus FE calculation of pressure distribution. c Liver injury versus FE calculation of compressive stress distribution. injuries were observed, a series of landmark points were used to identify the same points in post-ct images and the FE model. The maximum pressure value from FE simulations was found on the pleural surface and near the point directly extended from the sixth bronchiole. It was within 1 cm to the estimated center of the contused area. Using a threshold value of 81 kpa to segment the stress fringe plots gave an estimated damaged volume of 9.6%, about the same as that determined from post-ct images. Repeating the same process, thresholds that best matched contused lung volumes in each tests were found to be between 70 kpa and 100 kpa, consistent with the values reported in other studies 50. The lacerations of liver were mostly found in the small pigs impacted on the lower thorax or abdominal region and occurred on the surfaces of liver directly underneath the impact. The lacerations varied in severity from a single small laceration less than 1 cm to multiple lacerations as large as 4 5 cm. In FE simulations, maximum normal stresses also occurred on liver surfaces directly underneath the impact and had higher values in tests where more liver damage occurred. Past studies of liver tissue strength under impact loadings reported ultimate strains of 43.8% 4.0% or ultimate stresses of kpa for liver 7,51. By comparing FE calculated stresses with injury outcomes yes or no liver injuries in all the tests, the stress value corresponding to a 50% chance of liver laceration was found be about 180 kpa, which was within the reported values. 3.4 Qualitative Validation of Human Model. The chest deformations of PMHS acquired in frontal 24 and side impact tests 25 were used to validate the human FE model. The weight of the Visible Man was 91.1 kg, about the same as that of a 95% male. To account for different sizes of PMHS subjects, the FE model was scaled in dimension by the cubic root of the ratio between the subject weight and the weight of the Visible Man. Two human sizes, a standard 5% male of 60.1 kg and a 50% male of 73.4 kg 52, were used in the FE simulations. The comparison of peak deformations Table 3 is therefore qualitative in nature. FE simulations, however, did produce chest deformations that were compatible with the measurements. Using a threshold stress value of 150 MPa corresponding to about 50% chance of rib fracture 53, the predicted numbers of fractured ribs were also consistent with the reported numbers. 4 Discussion Geometrical representation of anatomy. The anatomies used to create FE meshes were reconstructed from fine CT images at mm spacing. The organ geometries were also processed carefully to minimize numerical s associated with misfitting of contact surfaces. Creating FE meshes from mesh templates with adjustable control points significantly simplified the generation of high-quality FE mesh and reduced the model development time from months to days. The mesh fineness of each organ component or the whole model can also be controlled to satisfy different levels of accuracy requirement. Numerical efficiency. The specialized method that modeled the rib cage as a composite structure of inhomogeneous beams and / Vol. 130, APRIL 2008 Transactions of the ASME

9 Table 3 Comparison of FE estimates of human deformation with PMHS test measurements Test/FE Subject weight kg Impact mass kg Impact velocity ms Peak deformation cm Fractured ribs Frontal impact on thorax Side impact on thorax Side impact on abdomen Test FE FE Test FE FE Test FE FE Test FE FE Test FE FE Test FE FE Test FE FE Test FE FE shells contributed to the numerical efficiency of the models. A simple benchmark problem showed that this method was not only efficient but was also as accurate as a very finely meshed 3D FE model of rib cage for impact simulations 30. A typical FE model developed in this study had about 19,000 nodes, 2900 beam, and 15,700 shell elements to model the whole rib cage. It took around 8 h to run an impact simulation of 3 ms on a single 2.0 GHz CPU. A fully 3D rib cage FE model at a compatible resolution, on the other hand, would have at least 235,000 nodes and 200,000 elements and would be very costly computationally. Effects of material properties. The selection of constitutive relationships and material parameters of soft tissue was a big concern due to both the complexity of soft tissue material characterization and the lack of material test data of soft tissues at high strain rate. The FE simulations, using material models and base line parameters from literature and calibrated by the first five animal tests, nevertheless gave very consistent predictions of chest wall motion and energy delivered to the body. It was most likely due to the fact that body responses to these high-speed impacts at ms were dominated by the inertia effects and slight variations in material parameters and did not significantly affect the results. To test the hypothesis, a sensitivity study in which material parameters were adjusted from the base line values by 50% 25% was conducted. Their effects on response values were examined. The sensitivity of a parameter was defined as the ratio between the percentage of change in the response value and the percentage of change in the parameter. The percentage of change in the response value was calculated by V 1 V 0 / V 0, where V 0 and V 1 were response values calculated from FE simulations using base line material parameters or parameters adjusted by 25%, respectively, and indicated a Frobenius norm. The material parameters studied in the sensitivity analysis included the densities, bulk moduli K, shear moduli G, and viscoelastic parameters Gi, i of the skin and muscle. The sensitivity study Table 4 showed that within the range of parameters selected, impact duration, deformation, and energy delivered were mostly sensitive to the densities of the chest muscles and skin, confirming that the impact responses were dominated by inertia effects. Pressures in the lung were significantly affected by the bulk properties,k implicitly described by the equation of state. The contributions from the deviatoric components G and viscoelastic terms Gi, i were negligible. Lung pressures were also affected by material damping that was indicative of the dissipation of the transient pressure wave over space. A comparison of FE simulation results and test measurements indicated that the damping coefficient of the lung was about 4000 rad/ min. Accuracy in estimating responses and predicting injuries. Results in Fig. 4 and Table 2 show that the FE calculations of body responses, especially motion and energy responses, matched reasonably well with experiment measurements. The s in impact duration, peak deformation, and maximum delivered energy were smaller than 5% on average. The s in time traces of velocity, deformation, and energy delivery were slightly larger, but were all below 8% on average. Good agreements in lung pressures were also obtained for most tests in which pressures in the lung were measured. FE models were able to predict the timing of both the fast rising and decaying portions of the pressure waves. The s Table 4 Sensitivity of FE calculation of body response to material parameters Impact duration Deformation Energy delivered Lung pressure skin, muscle 11% 11% 12% 10% K skin, muscle 1% 1% 1% 2% G skin, muscle 3% 2% 2% 3% Gi, I skin, muscle 3% 2% 2% 3% lung 1% 1% 1% 20% K lung 1% 1% 1% 45% G lung 1% 1% 1% 5% Gi, I lung 1% 2% 2% 5% Damping lung 3% 3% 3% 10% Journal of Biomechanical Engineering APRIL 2008, Vol. 130 /

10 Table 5 Comparison of calculated responses from three FE models with experimental values Measured data Case 1 Case 2 Case 3 Maximum deformation cm Error in displacement trace ms Impact duration ms Error in velocity trace Error in delivered energy trace Maximum delivered energy J Maximum lung pressure kpa Error in lung pressure trace in peak lung pressures were less than 6% on average. However, s in peak pressures were large 11 22% in a couple of tests. The locations where pressure traces were calculated in the FE model were estimated from CT images and might not match the exact locations of catheters during the tests since the animal subjects were held in slightly different positions during CT imaging and impact tests. Based on FE simulations, a 1 cm in estimating the position of the catheter could lead to an in the peak pressure of 10 20%. It was also noticed that the s in pressure traces were above 15% for most tests. This was mostly due to the fact that the measured and the calculated traces were not perfectly synchronized in time and should not be interpreted as a lack of accuracy in model calculations. For example, for test 14, Fig. 2 shows a good agreement in the timing of the rising and decaying portions of the pressure wave as well as the peak value 3.92%. The in the time trace, however, was still at 19%. The results in Sec. 3.3 indicate that the FE models produced higher stress concentrations at places where tissue damage occurred. Using bending stress, pressure, and compressive stress as predictors for rib fracture, lung contusion, and liver lacerations, respectively, and injury outcomes yes and no, threshold values of the stress predictors that were likely to cause these injuries were found to be in ranges of tissue strength data reported in the literature. However, it should be noted that this effort alone was not sufficient to produce correlations with good statistical confidence to predict the extent and severity of lung and liver injuries due to the difficulty in the accurate quantification of soft tissue injuries and, more importantly, the limited number of injuries produced in the tests. Another limitation to the study was that the validation of human FE models was qualitative in nature. Without complete data sets that included both CT images and response measurements from the same test subjects, the validation was conducted by scaling the Fig. 5 Comparison of calculated response time histories from three FE models. 1 Subject-specific model with optimized mesh. 2 Non-subject-specific model. 3 Subject-specific model with reduced mesh / Vol. 130, APRIL 2008 Transactions of the ASME

11 Fig. 6 Comparison of calculated rib, lung, and liver stress distribution from the three FE models. a Peak rib stress, b Lung pressure, and c liver compressive stress from model 1 left, model 2 middle, and model 3 right. human FE model and comparing calculated peak deformations and measurements from historical frontal and side impact tests. While the results showed that calculations fell in the range of measurements, a more accurate and conclusive validation requires using PMHS tests to acquire anatomical, impact response, and pathology data. It should also be noted that the validation of the swine FE models was limited to high-speed impact lasting about 2 3 ms when body responses were dominated by the inertia effects. The application of the models for low-speed impacts may need further calibration and validation since the effects of material parameters may become more important over the longer loading duration. Subject specificity and mesh fineness of the model. Most research that studied blunt injuries using FE models did not use subject-specific models with very fine meshes. Instead, the models were based on a generic or simplified anatomical representation with rather coarse FE meshes. When combined with a sufficient amount of test data, some models were successfully used to predict blunt injuries. The subject-specific models developed in this effort could help examine the effects of subject specificity, in terms of the variation in subject anatomy, mesh fineness on calculated responses, and predicted injury likelihoods and possibly help develop or verify simplified generic FE models. Results were obtained from using three different FE models to simulate test 14: Model 1 was the subject-specific model with optimized mesh fineness 78,168 nodes, 49,716 solids, 14,934 shells, and 2451 beams ; model 2 had about the same mesh size but was scaled from a generic anatomy to have the same weight as subject 14; model 3 reduced the mesh of model 1 to about half the size 39,778 nodes, 26,678 solids, 6386 shells, and 1369 beams. The calculated key body responses were compared to experiments and are given in Table 5 and Fig. 5. Reducing either subject specificity or mesh fineness only caused slightly larger s in predicted motion and energy responses. However, it led to significantly larger s in stress responses. The calculated peak lung pressure values were only one-third of the measured value if subject specificity were not accounted for or if an optimized mesh was not used. The comparison of calculated maximum bending stress in ribs, peak pressures in lungs, and peak compressive stress in liver from Journal of Biomechanical Engineering APRIL 2008, Vol. 130 /

12 three models is given in Fig. 6. The locations where the stresses concentrated were not affected, but the values of the stresses changed significantly if a subject-specific anatomy or a fine mesh was not used. It suggests that generic FE models with coarse mesh might be used to study blunt injuries, but the threshold values to determine injuries have to be consistent with the models used and have to be calibrated by injury tests. It should be noted that these results merely showed that subject specificity and mesh fineness could significantly affect FE model calculations of body responses, and the results are by no means conclusive. The models developed in this effort, however, could be used for a more detailed analysis. In summary, a method for developing subject-specific thoracic and abdominal FE models was shown to predict body responses to high-speed blunt impact reasonably well. 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