Characterization of the Rate-Dependent Mechanical Properties and Failure of Human Knee Ligaments

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1 Characterization of the Rate-Dependent Mechanical Properties and Failure of Human Knee Ligaments J.A.W. van Dommelen *, B.J. Ivarsson, M. Minary Jolandan, S.A. Millington, M. Raut, J.R. Kerrigan, J.R. Crandall Center for Applied Biomechanics, University of Virginia, Charlottesville, USA D.R. Diduch Department of Orthopaedic Surgery, University of Virginia, Charlottesville, USA Copyright 25 SAE International ABSTRACT The structural properties of the four major human knee ligaments were investigated at different loading rates. Bone-ligament-bone specimens of the medial and lateral collateral ligaments and the anterior and posterior cruciate ligaments, obtained from post-mortem human donors, were tested in knee distraction loading in displacement control. All ligaments were tested in the anatomical position corresponding to a fully extended knee. The rate dependence of the structural response of the knee ligaments was investigated by applying loadingunloading cycles at a range of distraction rates. Ramps to failure were applied at knee distraction rates of.16 mm/s,, or 1,6 mm/s. Averages and corridors were constructed for the force response and the failure point of the different ligaments and loading rates. The structural response of the knee ligaments was found to depend on the deformation rate, being both stiffer and more linear at high loading rates. This rate dependence was found to be more pronounced at high loading rates. INTRODUCTION Automobile crashes involving pedestrians are very common, and often lead to severe injuries to the lower extremities. Lower extremity injuries often have longterm effects, and the associated societal cost is high. In a large portion of pedestrian-automobile collisions, knee ligament injuries are sustained. Of 357 fatal pedestrianautomobile collisions surveyed (Teresinski and Madro, 21), 8 % of all pedestrians sustained injuries to knee ligaments and epiphyses, versus 94 % of pedestrians in lateral impacts. Varus-valgus strain has been identified by Teresinski and Madro as the most common mechanism for knee injury in pedestrians hit from the lateral side. The collateral knee ligaments are the most commonly injured ligamentous structures when the knee sustains a varus-valgus strain (Kajzer et al., 199, 1993, 1997, 1999; Bhalla et al., 23; Kerrigan et al., 23a). Automobile manufacturers are currently designing and testing front-end components in anticipation of proposed regulations for injury prevention of lower extremities in pedestrian-automobile collisions. As computational modeling is a powerful tool, several research groups have developed finite element (FE) models of the human lower extremity to evaluate potential pedestrian-injury countermeasures (e.g. Bermond et al., 1993, 1994; Yang et al., 1996; Schuster et al., 2; Takahashi et al., 2, 23; Beillas et al., 21; Maeno et al., 21). Recent advances in computational modeling have made it possible to incorporate increased complexity in the constitutive representations of soft tissues. Since knee ligaments play a central role in knee-joint and lower limb kinematics, their constitutive properties are critical in FE analyses. These constitutive representations must be derived from results obtained in experimental testing. In pedestrian-automobile collisions, accurate descriptions of the collateral ligament behavior are essential for realistic knee-joint kinematics and injury prediction. Structural and material properties of human knee ligaments have been studied extensively, in particular the cruciate ligaments due to their frequent involvement in sports injuries (Trent et al., 1976; Kennedy et al., 1976; Noyes and Grood, 1976; Tremblay et al., 198; Piziali et al., 198; Marinozzi et al., 1983; Butler et al., 1986; Hollis et al., 1988; Rauch et al., 1988; Woo et al., 1991; Jones et al., 1995; Rowden et al., 1997). However, only few studied the human collateral ligaments (Trent et al., 1976; Kennedy et al., 1976; Marinozzi et al., 1983, Kerrigan et al., 23b). Material * Current address: Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.

2 properties of human collateral knee ligaments were reported by Butler et al. (1986) and Quapp and Weiss (1998). Butler et al. (1986) reported data from tests on bone-ligament-bone specimens of the anterior cruciate ligament (ACL), posterior cruciate ligament (PCL) and the lateral collateral ligaments (LCL) averaged together. Quapp and Weiss (1998) tested dog-bone shaped cutouts of the medial collateral ligaments (MCL) by applying a tensile force parallel to either the long axis or the transverse axis of the fibers. Most of the above-mentioned studies were conducted at strain rates at least an order of magnitude below those predicted in car-pedestrian collisions. Therefore, those ligament properties are inadequate for use in FE simulations of car-pedestrian collisions. Unpublished finite element simulations of lateral impact pedestrianautomobile collisions at 4 km/h predict that collateral ligaments are strained at 3-5 s 1. This paper provides new data for the structural behavior and failure of the medial and lateral collateral ligaments and the separate bundles of the anterior and posterior cruciate ligaments at a large range of knee distraction rates. This range of rates includes rates representative for ligament loading in pedestrian-automobile collisions. The results can be employed to validate detailed finite element models of the human lower extremity to be used in the development and evaluation of pedestrian injury countermeasures and to derive constitutive equations for these models. METHODOLOGY Bone-ligament-bone (BLB) specimens were tested to failure in tension by applying displacements to the bony ends of the specimen, with the knee in full extension, see Figure 1. The anatomical distraction orientation is obtained by applying appropriate transverse displacements to one of the bone ends using an xypositioning table. The orientation of the knee joint for ligament tensile tests affects the nature of load application to the ligament. The distraction orientation was chosen because it recruits a significant portion of each ligament s fibers in tension, it initially preserves the anatomical orientation of each ligament, and it is the preferred mode of loading for subsequent FE validations. SPECIMEN PREPARATION Eight male post-mortem human subjects were obtained and used in accordance with local and federal laws, as well as with the ethical guidelines and research protocol approved by the Human Usage Review Panel and a University of Virginia institutional review board. Anthropometric donor information is given in Table 1. The average donor age was 53.4 years, with an average weight of 76. kg. Pretest CT scans verified the absence of bone or joint pathology. All limbs were sectioned prior to thawing and defrosted individually in temperature controlled water for 24 hours prior to ligament specimen preparation. The bone-ligament-bone specimens were extracted and potted by an orthopaedic surgeon (S.A.M.). MCL ACL PCL Figure 1: Schematic representation of the vertical distraction orientation. Table 1: Anthropometric donor information. ID Gender Age (yr) Weight (kg) Height (cm) Race Cause of death 1 male white drowning 2 male white hypertensive cardiovascular disease 3 male white lung cancer 4 male white myocardial infarction 5 male white suicide by hanging 6 male white myocardial infarction 7 male white ETOH complications 8 male white lung cancer average LCL std The average and standard deviation of donor height are based on cadaver 1-7 only. Each lower limb specimen was dissected free of all tissue except for the bones and the major ligaments. For each knee, both collateral ligaments and one cruciate ligament bundle were saved. At this time, the location and orientation of the distal insertion with respect to its proximal insertion for each collateral ligament was recorded so that the in situ orientation could be reproduced during potting and subsequent testing. Also anthropometry measurements were taken from each specimen. The proximal tibiofibular joint was then disarticulated and the fibula was cut off 4-6 cm inferior to the ligament insertion. The proximal MCL and LCL bone plugs were obtained by bisecting the medial and lateral femoral condyles, respectively, in the sagittal plane. The tibia was cut 4-6 cm inferior to the most distal fiber insertion of the MCL and was then split in a sagittal plane. Holes were drilled in the bone plugs and two screws were inserted through each plug. The screws served to fixate the bone plug in the potting material. The specimens were potted in aluminum cups using R1 Fast Cast No. 891 (Goldenwest Mfg; Inc., Cedar Ridge, CA, USA), a fast setting urethane casting resin. Special care was taken to ensure that no resin came in contact with ligamentous tissue and that the bone plugs were cast in the proper anatomical orientation. All ligament

3 specimens were kept moist during the extraction and subsequent potting using physiological.9 % saline. After the potting, the specimens were wrapped in saline soaked gauze and refrozen. TEST METHOD Twelve to twenty-four hours prior to each test, the test specimen was allowed to thaw at 2 ºC in a refrigerator. Before testing, the specimen was removed from the refrigerator and submerged in saline (at room temperature) for a minimum of 15 minutes. The ligament length was then measured using digital calipers. The length was defined as the shortest distance between insertions, parallel to the long-axis of the ligament. The specimen was mounted in a test fixture that was attached to the cross head of the actuator of an Instron 88 servo hydraulic biaxial test machine (Instron, Canton, MA, USA), see Figure 2(a). order not to produce any macro- or micro-failures. The relative elongation ε of the ligament is defined as the ratio between the elongation and the anatomical length of the ligament: ε =, (1) where is the anatomical length (defined as the shortest distance between insertions) and is the elongation of the ligament in the ligament direction. The vertical displacement d required to produce a relative ligament elongation ε in a structure of length with an initial elevation angle ϕ (see Figure 2(b)) can be shown to be: 2 d = sin( ϕ ) + sin ϕ + ε( ε + 2). (2) mounting cup bone plugs mounting cup (a) actuator ligament loadcell xy-table Figure 2: Schematic illustration of (a) test setup and (b) mounted ligament. An accelerometer was mounted on the actuator to record its acceleration during the high rate (~1,6 mm/s) tests. A Denton 6-axis load cell (Robert A. Denton, Inc., Rochester Hills, MI, USA) was mounted between an xytable and the bottom plate to measure all components of the ligament force vector. An accelerometer was mounted on the bottom plate to record any vibrations of the load cell and bottom fixture. Once the specimen was mounted, the relative transverse displacement (defining the distraction orientation), as measured by the orthopaedic surgeon during specimen preparation, was applied to the distal bone cup. The ligament was kept moist by applying gauze soaked with room temperature physiological (.9 %) saline every 5-15 minutes during testing. The unpreconditioned zero strain position was determined by lowering the actuator until there was no load on the ligament, and then raising the actuator until the vertical tensile load through the ligament measured 2 N (Funk et al., 2). The ligament was then preconditioned by applying 24 cycles of a sinusoidal displacement at 8 Hz and a distraction amplitude leading to a relative ligament elongation of 8 %. The preconditioning amplitude was limited to this value in ϕ (b) After preconditioning, the ligament was allowed to recover for a minimum of 1, seconds in a slacked position. A new zero strain position (preconditioned zero strain) was then determined by again applying a 2 N preload. This zero strain position was maintained throughout the remaining of the test battery. The ligament was subjected to four (approximate) separate step-functions of relative ligament elongations of 8 %, 6.4 %, 4.8 %, and 3.2 %, respectively (see Figure 3), to measure force-relaxation. Each step was applied with a constant distraction rate of 1 mm/s. After each displacement step, the actuator position was held for 5 seconds during which the relaxation of the ligament force was measured. Data was acquired at a sample rate of 2, Hz during the first 5 seconds after the application of the step displacement, 2 Hz during the next 55 seconds and 2 Hz for the remaining time of the step. The ligament was allowed to recover at zero-strain for a minimum of 1, seconds after each step. Following these steps, three loading-unloading cycles to the preconditioning-amplitude were applied at a constant distraction rate of 1 mm/s, 1 mm/s, and 1 mm/s, respectively. Data was acquired at a sample rate of 1, Hz. After each cycle, the specimen was allowed to recover for 1, seconds at zero strain. displacement precond. step and hold loading unloading cycles time Figure 3: Schematic illustration of the test sequence: preconditioning, a series of step-and-hold tests with decreasing amplitude, and three loading-unloading cycles with increasing distraction rate. This test sequence was followed by a ramp to failure.

4 Following the series of tests, during which the displacement amplitude never exceeded the preconditioning amplitude, each ligament was subjected to a distraction ramp to failure, at a constant distraction rate of.16 mm/s,, or 1,6 mm/s. All cruciate ligaments were subjected to high rate loading (1,6 mm/s). During the tests, data was acquired at a rate of 2 Hz for the slow (.16 mm/s) and medium () rate tests and at 2, Hz for the high rate tests. Since it was desired to have the load applied to the ligament at constant actuator velocity, before the highest rate tests (1,6 mm/s), the actuator was lowered to put slack in the ligament. Slacking the ligament as much as possible allowed the actuator to accelerate to constant velocity before any load was applied to the ligament. The force at the zero strain position was used as the zero force level. High-speed video images (1, frames/s) were taken during the failure tests at the highest rate. High resolution digital photographs were taken approximately every second during the medium speed () tests. During the lowest speed failure tests (.16 mm/s) a photograph of the ligament was taken at 1 minute intervals. After the test, the ligament failure mode was documented. The structural response of a ligament is the result of the interplay between the material properties of ligamentous tissue and the geometry of the ligament. In this study, it was chosen to report structural properties only. All force levels reported represent the magnitude of the total force vector. The relative ligament elongation is defined as the elongation relative to its anatomical length, which is measured as the shortest distance between insertions. RESULTS RATE-DEPENDENCE Four steps in knee distraction were applied to the ligament at different levels of relative ligament elongation. The response to the step-and-hold tests are given in Figure 4 for a lateral collateral ligament. The initial (t < 1 s) relaxation behavior is independent of the applied deformation, i.e. time-deformation separability is applicable in this time range. The structural response of a lateral collateral ligament to the following three loadingunloading cycles at different rates of knee distraction is displayed in Figure % 6.4 % 4.8 % 3.2 % time [s] Figure 4: Response to step-and-hold tests for a lateral collateral ligament (LCL, donor 3). TEST MATRIX The cruciate ligaments were split into their functional bundles: the antero-medial part of the ACL (aacl), the postero-lateral bundle of the ACL (pacl), the anterolateral part of the PCL (apcl) and the postero-medial part of the PCL (ppcl). A total of 32 bone-ligament-bone (BLB) specimens were tested in tension to failure. The test matrix for the failure tests on these specimens is shown in Table mm/s 1 mm/s 1 mm/s Table 2: Test matrix for failure tests. The number of tests at each distraction rate by ligament type is given in each entry of the table. 1,6 mm/s.16 mm/s Total MCL LCL aacl pacl apcl ppcl Total Figure 5: Response to loading-unloading cycles at different rates of knee distraction for a lateral collateral ligament (LCL, donor 8). A clear rate-dependence can be observed in this figure. A similar response was obtained for all bone-ligament bone specimens. The force level during loading at a relative ligament elongation of.4 was determined for each cycle. The rate-dependence of this force level per specimen is shown in Figure 6 for each ligament type.

5 mm/s 1 mm/s 1 mm/s 1 mm/s.1 mm/s.1 mm/s log(rate) (a) MCL (a) MCL ε =.6 ε =.5 ε =.4 ε =.3 ε = log(rate) (b) LCL log(rate) (b) MCL aacl pacl apcl ppcl Figure 7: Response of a medial collateral ligament (donor 2) to loading-unloading cycles. (a) Force-elongation curves at different rates and (b) force level at various levels of relative ligament elongation vs. distraction rate log(rate) (c) cruciate ligaments Figure 6: Rate-dependence of the force at a relative ligament elongation of.4, for (a) 8 medial collateral ligaments, (b) 8 lateral collateral ligaments, and (c) 8 cruciate ligaments. The lines connect responses per specimen. For a number of ligaments, tests were performed at a larger range of knee distraction rates. These specimens were subjected to loading-unloading cycles to 8 % relative ligament elongation (i.e. the preconditioning level) at distraction rates ranging from.1 mm/s to 1, mm/s. The force-elongation responses are shown in Figures 7(a) and 8(a). Furthermore, Figure 7(b) and 8(b) show the force measures during loading at various levels of relative ligament elongation versus the applied loading rate. The dependence of these force levels on the loading rate is found to increase with the rate of distraction. FAILURE After subjecting the specimens to a sequence of preconditioning, step-and-hold tests and loadingunloading cycles, each bone-ligament-bone specimen was subjected to a ramp to failure at a constant rate of knee distraction. In four high rate tests for the medial collateral ligaments and two for the lateral collateral ligaments, failures were observed in either bone pieces (away from the insertion) or potting material. All cruciate specimens showed ligament failures. In Figure 9, individual failure curves are displayed for each type of ligaments. For specimens with non-ligament failures, dashed lines are used. In Figure 1, the relative ligament elongation is shown versus the time, multiplied by the chosen knee distraction rate (i.e..16 mm/s,, or 1,6 mm/s). The actual ligament elongation rate is, besides the chosen distraction rate, dependent on the ligament size and elevation angle and therefore differs between specimens. The average relative ligament elongation rates (in the region of constant distraction rate) are given in Table 3. The average relative elongation rate of the high rate tests is representative for ligament loading during pedestrian-automobile collisions.

6 22.16 mm/s 16 mm/s 2 1 mm/s 316 mm/s 1 mm/s 1 mm/s 1 mm/s.1 mm/s.1 mm/s (a) MCL.9 (a) LCL 7 ε =.6 ε =.5 ε =.4 ε =.3 ε = mm/s 16 mm/s log(rate) (b) LCL (b) LCL Figure 8: Response of a lateral collateral ligament (donor 3) to loading-unloading cycles. (a) Force-elongation curves at different rates and (b) force level at various levels of relative ligament elongation vs. distraction rate. aacl pacl apcl ppcl Table 3: Average relative ligament elongation rates and the corresponding standard deviations. MCL LCL aacl pacl apcl ppcl 1,6 mm/s -1 [s ] -3-1 [1 s ].16 mm/s -5-1 [1 s ] 45 ± ± ± ± ± ± ± ± ± ± 6.1 Due to the limited number of specimens, the (average - minimum) value is given instead of the standard deviation (c) cruciate ligaments Figure 9: Force responses during failure tests for (a) medial collateral ligaments, (b) lateral collateral ligaments, and (c) cruciate ligaments. Solid lines represent ligament failures, whereas dashed lines represent either non-ligament failures or unrecorded (denoted by *) failure points.

7 mm/s 16 mm/s responses and averaged failure points are shown in Figure 11. The failure point is defined as the location on the force-elongation curve corresponding to the force maximum mm/s 16 mm/s time*rate [mm] (a) MCL mm/s 16 mm/s mm/s 16 mm/s (a) MCL time*rate [mm] (b) LCL aacl pacl apcl ppcl aacl pacl apcl ppcl (b) LCL time*rate [mm] (c) cruciate ligaments Figure 1: Relative ligament elongation versus the time, multiplied by the (programmed) distraction rate for (a) medial collateral ligaments, (b) lateral collateral ligaments, and (c) cruciate ligaments. For a number of specimens, the application of slack prior to the high rate ramp was geometrically not possible, hence the smaller elongation rate in the early region (c) cruciate ligaments The averaged ligament response, as well as a standard deviation bandwidth was constructed for each ligament type and loading rate. To increase the number of specimens in the averaging process, also previously obtained data, partly published in Kerrigan et al. (23b), was included (see Table 4). Also the pre-failure response of specimens exhibiting non-ligament failure has been included in the averaging procedure. Averaged Figure 11: Averaged responses and averaged failure points for (a) medial collateral ligaments, (b) lateral collateral ligaments, and (c) cruciate ligaments. Solid lines represent averages of three or more curves and a one standard deviation bandwidth. Dashed lines represent averages of two curves and the minimum and maximum range.

8 Table 4: The total number of specimens used for response averaging (obtained by combining the newly obtained data with previously reported data (Kerrigan et al., 23b)). 1,6 mm/s.16 mm/s Total MCL LCL aacl pacl apcl ppcl Total For the collateral ligaments, which were tested at a large range of distraction rates, a rate-dependence is observed, with the high rate response being stiffer and more linear. The averaged responses indicate no large differences between either the antero-medial and the postero-lateral bundle of the ACL or the antero-lateral bundle and the postero-medial bundle of the PCL. The averaged failure points are summarized in Table 5. The average ligament elongation at failure is found to be considerably larger for the MCLs than for the other ligaments tested in this study. This can be partly attributed to the definition of ligament elongation used. This definition is based on the measured shortest length between insertions. However, the lower insertion of the medial collateral ligament extents well below the tibial condyle. This lower part is also a part of the load-bearing and straining structure. The average ratio of largest ligament length (based on lower insertion) / shortest ligament length (based on upper insertion) of the medial collateral ligaments was 2.9. Table 5: Average and standard deviation of failure points for data combined with Kerrigan et al. (23b) tests. rate f [kn] [-] [mm/s ] MCL ±.34.4 ± ± ±.51 1,6 1.4 ± ±.86 LCL ± ± ±.78.2 ±.55 1,6.54 ± ±.16 aacl 1,6.99 ± ±.28 pacl 1,6 1. ± ±.3 apcl 1,6.65 ± ±.23 ppcl 1,6.29 ± ±.14 Since only two curves are available, the (average - minimum) bandwidth is given instead of the standard deviation. where f is the magnitude of the force vector and ε denotes the relative ligament elongation, is fitted to the averaged failure curves. The obtained parameters are given in Table 6. Again, the force response is found to be more linear for high loading rates. Table 6: Parameters of a power law fit to the averaged failure curves. 1,6 mm/s.16 mm/s C [kn] n [-] C [kn] n [-] C [kn] n [-] MCL LCL aacl pacl apcl ppcl Typically observed failure modes are given in Table 7. The typical failure mode appeared to be dependent on the loading rate (although this is inconclusive due to the limited number of specimens). Typical post-failure images are shown in Figure 12. Table 7: Typical failure modes for bone-ligament-bone specimens in distraction loading. 1,6 mm/s.16 mm/s MCL tibial insertion tibial insertion midsubstance/ fem. ins. LCL femoral insertion fibular insertion fibular insertion cruc. lig. femoral insertion (a) MCL (b) MCL (c) LCL Figure 12: Typical failure modes; (a), (b) medial collateral ligaments, (c) lateral collateral ligament. The force-elongation curves of the bone-ligament-bone specimens have a strongly nonlinear shape. A two parameter power law, which can be written as: f n = Cε, (3)

9 In Figure 13, various stages of the failure process of a medial collateral ligament are displayed. The ligament is loaded at a knee distraction rate of 1,6 mm/s. For this ligament, failure occurs at the tibial insertion. bundles in this study as well as combined maximum force of the two PCL bundles lie within the range of forces reported in literature, although it is noted that the loading rate of the present study is considerably larger than most previously published studies. Moreover, the applied distraction orientation (the anatomical orientation corresponding to the fully extended knee) deviates from the orientation used in most other studies. CONCLUSION (a) ms (b) 7 ms (c) 14 ms (d) 21 ms (e) 28 ms (f) 35 ms Figure 13: Various stages of failure of a medial collateral ligament at a distraction rate of 1,6 mm/s. For the lateral collateral ligaments, the average maximum force observed in this study is in agreement with the range of 377 to 425 N reported in literature (Trent et al., 1976; Marinozzi et al., 1983). However, the average maximum force found for the medial collateral ligaments is considerably larger than reported in several other studies (Trent et al., 1976; Kennedy et al., 1976; Marinozzi et al., 1983). In the latter studies, the maximum force ranges from 465 to 665 N for loading rates comparable to the medium distraction rate of this study. The maximum force for the cruciate ligaments as found in literature varies widely (e.g. Trent et al., 1976; Kennedy et al., 1976; Noyes and Grood 1976; Tremblay et al., 198; Piziali et al., 198; Marinozzi et al., 1983; Butler et al., 1986; Hollis et al., 1988; Rauch et al., 1988; Woo et al., 1991; Jones et al., 1995; Rowden et al., 1997). For the ACL, maximum forces ranging from 335 to 2,195 N can be found in the above-mentioned studies, whereas the PCL maximum force ranges from 258 to 1,627 N. The combined maximum force of the two ACL In this study, the structural response to tensile loading at different rates was investigated for the four major human knee ligaments. Bone-ligament-bone specimens were tested in knee distraction loading. The anatomical orientation of the tested ligaments corresponded to the fully extended knee. A clear rate-dependence was observed when the same ligaments were loaded to nondamaging strain levels at different loading rates. The rate dependence was found to be stronger at high loading rates. The viscoelastic structural behavior of knee ligaments will be further discussed in Van Dommelen et al., 25a, 25b) The ligaments were loaded to failure in displacement control at knee distraction rates of.16 mm/s, 1.6 mm/s, and 1,6 mm/s. Averages and standard deviation corridors for the force response were reported, as well as for the failure point and loading rates. Again, the structural response of the knee ligaments was found to be affected by the deformation rate. The ligaments were both stiffer and the response was more linear at high loading rates. No large differences were observed between the averaged responses of either the anteromedial and the postero-lateral bundle of the ACL or between the averaged curves of the antero-lateral and the postero-medial bundle of the PCL. The maximum force levels observed in the medial collateral ligaments were considerably larger than those of the lateral collateral ligaments. Moreover, also the average ligament elongation at failure was found to be significantly larger for the MCLs than for the other ligaments tested. The latter was attributed to the definition of relative ligament elongation used in combination with the complicated geometry of the MCL. REFERENCES 1. Beillas, P., Begeman, P.C., Yang, K.H., King, A.I., Arnoux, P-J., Kang, H-S., Kayvantash, K., Brunte, C., Cavallero, C., and Prasad, P. Lower limb: advanced FE model and new experimental data. Stapp Car Crash Journal, pp , Bermond, F., Ramet, M., Bouquet, R., and Cesari, D. A finite element model of the pedestrian knee-joint in lateral impact. International Conference on the Biomechanics of Impacts (IRCOBI), 1993.

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