Biomechanical response of the pubic symphysis in lateral pelvic impacts: A finite element study

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Journal of Biomechanics 40 (2007) 2758–2766 www.elsevier.com/locate/jbiomech www.JBiomech.com

Biomechanical response of the pubic symphysis in lateral pelvic impacts: A finite element study Zuoping Lia, Jong-Eun Kimb, James S. Davidsonc, Brandon S. Etheridged, Jorge E. Alonsoe, Alan W. Eberhardtf, a Department of Biomedical Engineering, University of Alabama at Birmingham, Hoehn 361, 1075 13th St. S., Birmingham, AL 35294, USA Department of Mechanical Engineering, University of Alabama at Birmingham, Hoehn 330A, 1075 13th St. S., Birmingham, AL 35294, USA c Department of Civil and Environmental Engineering, University of Alabama at Birmingham, Hoehn 331 B, 1530 3rd Ave S., Birmingham, AL 35294, USA d Department of Biomedical Engineering, University of Alabama at Birmingham, Hoehn 260, 1075 13th St. S., Birmingham, AL 35294, USA e Division of Orthopedic Surgery, University of Alabama at Birmingham, FOT 960, 20th St. S., Birmingham, AL, USA f Department of Biomedical Engineering, University of Alabama at Birmingham, Hoehn 368, 1075 13th St. S., Birmingham, AL 35294, USA b

Accepted 31 January 2007

Abstract Automotive side impacts are a leading cause of injuries to the pubic symphysis, yet the mechanisms of those injuries have not been clearly established. Previous mechanical testing of isolated symphyses revealed increased joint laxity following drop tower lateral impacts to isolated pelvic bone structures, which suggested that the joints were damaged by excessive stresses and/or deformations during the impact tests. In the present study, a finite element (FE) model of a female pelvis including a previously validated symphysis sub-model was developed from computed tomography data. The full pelvis model was validated against measured force–time impact responses from drop tower experiments and then used to study the biomechanical response of the symphysis during the experimental impacts. The FE models predicted that the joint underwent a combination of lateral compression, posterior bending, anterior/posterior and superior/ inferior shear that exceeded normal physiological levels prior to the onset of bony fractures. Large strains occurred concurrently within the pubic ligaments. Removal of the contralateral constraints to better approximate the boundary conditions of a seated motor vehicle occupant reduced cortical stresses and deformations of the pubic symphysis; however, ligament strains, compressive and shear stresses in the interpubic disc, as well as posterior bending of the joint structure remained as potential sources of joint damage during automotive side impacts. r 2007 Elsevier Ltd. All rights reserved. Keywords: Side impact; Pubic symphysis; Pelvis; Finite element

1. Introduction The pubic symphysis is a non-synovial joint that connects the anterior portion of the two pelvic coxal bones. Local soft tissues include an interpubic fibrocartilaginous disc as well as anterior, posterior, inferior, and superior ligaments (Pick and Howden, 1977). The pubic symphysis maintains the structural integrity of the pelvis Corresponding author. Tel.: +1 205 934 8464; fax: +1 205 996 6946.

E-mail addresses: [email protected] (Z. Li), [email protected] (J.-E. Kim), [email protected] (J.S. Davidson), [email protected] (B.S. Etheridge), [email protected] (J.E. Alonso), [email protected] (A.W. Eberhardt). 0021-9290/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2007.01.023

and provides joint stability by neutralizing shear and tensile stresses (Gamble et al., 1986). The primary physiological movements of the symphysis include superior/inferior shear during single-legged stance and anterior/ posterior rotation of the pubic rami during walking (Walheim and Selvik, 1984). Near-side automotive impacts (where the vehicle strikes the occupant side) are the number one cause of pelvic injuries (Gokcen et al., 1994; Samaha and Elliott, 2003). Pelvic bone fractures are associated with high mortality and morbidity rates (Levine and Crampton, 1963; Parreira et al., 2000; Starr et al., 2002), as well as substantial economic costs (Thomas and Frampton, 1999). Side

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impact conditions tend to produce lateral compression fractures of the pelvic ring that involve the pubic rami, sacrum and acetabulum, and with increased severity, separation at the pubic symphysis and sacroiliac joints (Grattan and Hobbs, 1969; Schmidtke et al., 1995; Siegel et al., 1993; States and States, 1968; Tile and Hearn, 1995). Chronic symphyseal pain is one of the major complications related to symphysis injury (Mkandawire et al., 2002; Weber et al., 1999). Fracture tolerances and mechanistic descriptions of pelvic fractures for male and female pelves have been provided through experimental side impact studies using isolated pelves (Beason et al., 2003; Etheridge et al., 2005; Guillemot et al., 1998; Molz et al., 1997) as well as whole cadavers (Bouquet et al., 1998; Cavanaugh et al., 1990; Cesari and Ramet, 1982; Nusholtz et al., 1982; Viano et al., 1989; Zhu et al., 1993). These studies mainly focused on bony fractures of the pelvis and their relations to impact parameters such as force, time, pelvic compression, acceleration, energy, and viscous criteria. Little data exist with regard to the structural response of the pubic symphysis and injury mechanisms of the associated soft tissues during side impacts to the pelvis. Previous experiments conducted in our lab demonstrated that pubic symphyses harvested from pelves that had been laterally impacted in drop tower experiments exhibited increased joint laxity as compared to non-impacted controls (Dakin et al., 2001). Reductions in symphysis stiffness following the lateral compression experiments were conjectured to be the result of excessive compression and posterior bending of the joint structure prior to bony fracture. The actual structural response of the pubic symphysis, however, was not measured during those tests. Clearer understanding of the biomechanics of the pubic symphysis in side impacts may serve to elucidate the mechanisms of joint laxity. Several finite element (FE) studies have examined pelvic responses in side impacts (Dawson et al., 1999; Majumder et al., 2004; Plummer et al., 1998; Renaudin et al., 1993), emphasizing the structural response and stresses within the pelvic bones. In each of these studies, the geometry and soft tissue properties of the pubic symphysis were greatly simplified and the biomechanical response of the symphysis was not emphasized. The objective of the present study was to develop FE models with a more biofidelic symphysis to investigate the deformations and stresses experienced by the pubic ligaments and interpubic disc under side impact conditions simulating both drop tower experiments and automotive side impacts. 2. Materials and methods 2.1. FE model development The geometry for the current pelvis model was developed from CT data (Philips Brilliance 16P, Philips Medical Systems, Eindhoven, the Netherlands, 512  512 acquisition matrix, 1.25 mm slice thickness and increment, 205 slices, bone algorithm) of a human female pelvis (age 53, height 160 cm, weight 58.6 kg) with proximal femurs, using Amira software

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(Computer Mercury System, Inc., Chelmsford, MA). Semi-automatic segmentation was employed to extract the cortical/trabecular bone contours and soft tissue volumes. For regions of thin cortices (o0.7 mm), overestimation of cortical thickness by the CT scanner is unavoidable (Anderson et al., 2005; Prevrhal et al., 1999); therefore, following mesh generation, cortical thicknesses were confirmed against anatomic measures of the original pelvis at the selected sections of the pubic rami, acetabular wall, and iliac wing. Sacroiliac cartilage was created by filling the spaces between the sacral and iliac bone surfaces from the CT data. Similarly, a layer of acetabular cartilage was created by filling the space between femoral head and the subchondral bone of the acetabulum. The interpubic disc filled the space between the pubic bones and the four pubic ligaments surrounding the disc were manually segmented as four discrete solid bands, based on the CT data with reference to real symphysis specimens. Volumetric hexahedral grids of these segmented components were generated from tetrahedral grids using an indirect hex meshing method in Amira. Hypermesh software (Altair Engineering Inc., Troy, MI) was employed to create the remaining FE models, including a drop-mass impactor, and to apply the loading and boundary conditions that simulated previous drop tower experiments (Fig. 1a; Beason et al., 2003). Thirty-two discrete elastic truss elements were used to represent the sacroiliac ligaments with a total cross-sectional area of 320 mm2 (Bakland and Hansen, 1984; Bechtel, 2001). Hip capsular ligaments were modeled by 30 discrete truss elements with a total cross-sectional area of 300 mm2 (Hewitt et al., 2001), and hip intracapsular ligaments were simulated by 10 discrete truss elements that connected the femoral head and the acetabular fossa. The impactor (mass ¼ 13.4 kg) was given an initial velocity, V0 ¼ 4.5 m/s, made to impact the right greater trochanter of the pelvis, as in the experiments. The right femur was positioned at approximately 01 abduction and 901 flexion, consistent with the ‘‘seated’’ posture of the pelvis in the experiments. Surface-to-surface contact was enforced between the impactor and greater trochanter, and between the femoral head and acetabular cartilage layer. A rigid wall was employed to simulate frictional and normal support of the ischial tuberosities, with a friction coefficient of 0.15 (Molz et al., 1997). The contralateral (left) iliac wing and greater trochanter were fully constrained. A compressive preload (65% body weight) was applied along the longitudinal axis of the vertebral column (Walker, 1977). Models with varying mesh densities were tested to determine the level of mesh refinement necessary to obtain convergent cortical bone stresses and strains (within 5%). The resulting FE model (Fig. 1b) contained approximately 260,000 hexahedral elements and 72 discrete truss elements.

2.2. Material properties Cortical and trabecular bone, ligaments spanning the hip and sacroiliac joints, and the impact mass were all assumed to be isotropic and linearly elastic materials. Young’s modulus and Poisson’s ratio were assigned as follows: E ¼ 17 GPa and n ¼ 0.29 for cortical bone; E ¼ 70 MPa and n ¼ 0.2 for trabecular bone (Dalstra and Huiskes, 1995); n ¼ 0.4 and E ¼ 181 MPa for the hip ligaments (Hewitt et al., 2001) and n ¼ 0.4 and E ¼ 250 MPa for sacroiliac ligaments (Yamada, 1970). Articular cartilage of the acetabulum and sacroiliac joints were represented as two-parameter Mooney–Rivlin materials with C1 ¼ 4.1 MPa and C2 ¼ 0.41 MPa (Little et al., 1986). The impactor was assumed to be steel (E ¼ 207 GPa, n ¼ 0.3; Bauld, 1986). The hyperelastic material properties of the interpubic disc and ligaments in the symphysis sub-model were estimated using a heuristic, inverse FE material identification method (To¨nu¨k and Silver-Thorn, 2004). Details were presented in our previous study (Li et al., 2006) and are summarized below. A three-parameter Mooney–Rivlin model was used to represent the interpubic fibrocartilaginous disc, W ¼ C 10 ðI 1  3Þ þ C 01 ðI 2  3Þ þ C 11 ðI 1  3ÞðI 2  3Þ.

(1)

The constants C10, C01 and C11 (Table 1) were determined using the average experimental data of female symphysis obtained in compression tests (Dakin et al., 2001).

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Fig. 1. (a) Illustration of experimental drop tower side impact apparatus (modified from Beason et al., 2003); (b) side impact FE model of the female pelvis illustrating boundary conditions, compressive pre-load (P) and impactor; and (c) impact force–time history predicted from FE model (solid line), which lies within the range of experimental curves (Beason et al., 2003) indicated by the gray envelope. The pubic ligaments were represented by a transversely isotropic hyperelastic model with the following strain energy function (Gardiner and Weiss, 2003): 

W ¼ F 1 ðI 1 Þ þ F 2 ðlÞ þ

K ðInðJÞÞ2 . 2

(2)

Constants (C1–C6) and fiber stretch, l , are not known for the pubic ligaments; therefore we assumed the same C1 value as the ground substance matrix of the medial collateral ligament in the literature (Gardiner and Weiss, 2003). C3, C4, C5 and l were estimated using average values from tensile tests on female symphyses (Dakin et al., 2001). The y-intercept of the linear region, C6, was automatically determined in the FE code to ensure C0 stress continuity at l ¼ l . Incompressibility of the pubic ligaments in the third term (Eq. (2)) was enforced by assigning the bulk modulus, K, to be two orders of magnitude greater than C1 (Quapp and Weiss, 1998). The resulting coefficients are listed in Table 1. In addition, viscoelastic constants were found by curve-fitting the overall creep response of the pubic symphysis (Li et al., 2006). These Prony series constants (Table 1) were implemented in the interpubic disc and pubic ligament models in the present study to simulate the rate-dependent behavior of the symphysis joint.

2.3. FE analyses To validate the model, impact response parameters (peak impact force, Fmax, dissipated energy, Epeak, time to reach peak load, tpeak) were output from FE model simulations under drop tower side impact conditions and compared with average data recorded from six experimental impacts (Beason et al., 2003). Following model validation, sensitivity studies were conducted to quantify the model response to variations in the material constants of cortical and trabecular bone, as well as the soft tissues of the symphysis sub-model. Finally, the contralateral constraints were removed allowing the pelvis to translate along the impact (x) direction (hereafter referred to as the ‘‘free contralateral BC’’), which may more closely approximate conditions of a pelvis in an automobile side impact. Additional y and z constraints were applied to the second and third sacral vertebra to maintain the ‘‘seated’’ posture of the pelvic structure during the impact simulations. The FE models were analyzed using the explicit code in LS-DYNA software (LSTC, Livermore, CA) on a 2.4 GHz Linux cluster in the Enabling Technology Lab at the University of Alabama at Birmingham. The FE implementation of the material models for the interpubic disc (Type 77) and pubic ligaments (Type 91) in LS-DYNA was detailed in our

ARTICLE IN PRESS Z. Li et al. / Journal of Biomechanics 40 (2007) 2758–2766 Table 1 Material properties for the interpubic disc and pubic ligaments used in the FE model. Mooney-Rivlin hyperelastic material Interpubic disc

C10 (MPa)

C01 (MPa)

0.1

0.45

Table 2 Pelvic impact response parameters: FE predictions and drop tower side impact results (Beason et al., 2003) for FE model validation

C11 (Mpa)

Data

Fmax (kN)

Epeak (J)

tpeak (ms)

0.6

Experiment FE

4.0571.34 4.5

75.0733.4 68

13.073.58 13

Transversely isotropic hyperelastic material Pubic ligaments

C1(MPa)

C3(MPa)

C4

C5 (MPa)

l*

1.44

0.19

35.5

155.0

1.055

Prony series constants for the disc and pubic ligaments Relaxation constants

a1

a2

t1(s)

t2 (s)

0.25

1.34

32.25

0.015

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previous study (Li et al., 2006). CPU time for running the FE model was approximately 60 h using eight processors. The model-predicted von Mises stresses of cortical bone in the highly stressed regions (superior and inferior rami) were compared to strain-rate dependent yield strengths of cortical bone reported in the literature (Wright and Hayes, 1976) to define individual element failure. Bone fracture was assumed to initiate at locations where the von Mises stresses in 15 or more contiguous elements exceeded the corresponding bone yield strength (Keyak et al., 1998).

450 Experiment FE data

3. Results 3.1. Validation and sensitivity study

Load (N)

150

The present FE model (pelvis+proximal femurs) containing the symphysis sub-model was found to provide reasonable agreement with average experimental data (Beason et al., 2003) for the impact response parameters under the drop tower side impact conditions (Table 2), supporting the validity of the modeling approach. For example, the peak impact forces predicted by the models were 4.5 kN, which was within the range of the experimental recordings (4.0571.34 kN). The impact force–time history predicted by the FE model was within the range of the experimental curves of six tested pelves (Fig. 1c), providing further confidence in the model. Beason and coworkers concluded that load-spike artifacts occurred in unpadded impacts, prior to the true impacts (the small light gray regions at the start of the experimental impacts in Fig. 1c). The FE model did not predict such load spikes. Following the start of true impact event (at roughly 4 ms), the model-predicted curve (solid line) lies inside the experimental envelope. The pubic symphysis sub-model (Fig. 2a) was validated previously (Li et al., 2006) against average experimental data (Dakin et al., 2001) from four female pubic symphysis. Loaded and unloaded to 70.8 mm at a rate of 1 mm/s, the symphysis revealed average stiffness values of 543777 N/ mm in tension and 11587337 N/mm in compression. Based on these results, the tension–compression curve of

-0.8

-0.4 .

0

0.4

0.8

-150

-450 Displacement (mm)

Fig. 2. (a) FE sub-model of pubic symphysis with pubic bones (gray), interpubic disc (yellow) and pubic ligaments (blue), (b) load–displacement curves obtained from tension–compression experiments on female pubic symphyses (Dakin et al., 2001) and the present FE sub-model (Li et al., 2006), at displacements of 70.8 mm and a loading rate of 1 mm/s.

one specimen (tensile stiffness: 547.19 N/mm; compressive stiffness: 1136.10 N/mm) was selected for curve-fitting material constants in the present symphysis sub-model. The total sum of the normalized error in tension and compression between experiments and FE prediction was within 10%, supporting the validity of the symphysis submodel (Fig. 2b). At a higher loading rate of 100 mm/s

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(similar to the present side impact loading rate), the symphysis sub-model predictions correlated reasonably well with corresponding experimental curves (Li et al., 2006), indicating the applicability of the model in the highrate impact simulations. The sensitivity study under drop tower impact conditions indicated that a 10% increase in elastic modulus of cortical bone (E ¼ 18.6 GPa) in the FE model increased cortical bone stresses by as much as 13%. A 100% increase in trabecular bone modulus (E ¼ 140 MPa) increased cortical stresses less than 10%, however, demonstrating that cortical bone stresses were more sensitive to alterations in cortical modulus, as seen previously (Anderson et al., 2005). Two-fold increases in material properties of hip and sacroiliac ligaments, acetabular and sacroiliac cartilage changed model-predicted cortical stresses by less than 5%. Deformations of the pubic symphysis were insensitive to these variations in the properties of bone and soft tissues (o2% variation). Doubling the magnitude of the material constants in the interpubic disc model and pubic ligament model simultaneously decreased the magnitude of disc deformations by only 16%, suggesting that the symphysis properties determined previously were acceptable for use in the present study.

3.2. Bone stress and symphysis response The drop tower model predicted that bone fracture occurred in the superior ramus, contralateral to the impact at tfrac ¼ 11 ms, based on the following results. According to FE model predictions, stresses exceeded 150 MPa in 15 cortical elements with a total volume over 350 mm3. A cortical bone strain rate of 0.4 s1 was calculated according to the peak strain divided by tfrac. The yield strength of cortical bone at this strain rate was previously reported as 150 MPa (Wright and Hayes, 1976). Fig. 3a shows the model-predicted von Mises stress contours at tfrac, indicating that the highest stress (163 MPa) occurred in the contralateral superior ramus (Fig. 3b). Peak stresses less than yield were predicted in the superior ramus (136 MPa, impact side), the contralateral inferior ramus (86 MPa), and the inferior rami (73 MPa, impact side); therefore, fractures were not predicted in these regions. The time of fracture, tfrac ¼ 11 ms, was used to computationally predict the deformation characteristics of the pubic symphysis that would be expected prior to bony fractures in the drop tower simulations. The relative motion between the surfaces of the two pubic bones (points A and B, Fig. 4) demonstrated that the deformations

Von Mises Stress [MPa] 1.6E+02 1.4E+02 1.2E+02 1.1E+02 8.9E+01 7.1E+01 5.3E+01 3.6E+01 1.8E+01 0.0E+00 Fixed

Free

von Mises stress (MPa)

200 Contra. sup. ramus Impact sup. ramus Contra. inf. ramus Impact inf. ramus

150

100

50

0 Fixed

Free

Fig. 3. (a) von Mises stress contours predicted by the FE models showing peak values in the superior rami with the fixed and free contralateral boundary conditions, at tfrac ¼ 11 ms and tpeak ¼ 6 ms, respectively and (b) Corresponding peak von Mises stress values in the superior and inferior pubic rami.

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Relative displacement (mm)

2.5 X-component Y-component Z-component

2

1.5

1

0.5

0 Fixed

Free

Fig. 5. Peak relative displacement between the left and right pubic bones connected to the interpubic disc under the side impact simulations with the fixed and free contralateral boundary conditions.

experienced by the interpubic disc were a combination of disc compression in the lateral (x) direction, and shear in the anterior–posterior (y) and superior–inferior (z) directions. The maximum deformations (ui) of the disc were ux ¼ 1.9 mm, uy ¼ 2.3 mm and uz ¼ 1.5 mm (the maximum value for uy actually occurred at t ¼ 6 ms), as shown in Fig. 5. The pubic bone on the impacted side rotated internally up to 61 in the transverse plane relative to the contralateral pubic bone, indicative of posterior bending of the pubic symphysis (Fig. 4d). The peak principal compressive stress (10.1 MPa) and the maximum shear stress (8.3 MPa) occurred at the centroid of the disc. Compression between the surfaces of the pubic bones caused the interpubic disc to expand outwardly (Poisson effect), which was accompanied by large deformations of the pubic ligaments. Under the drop tower conditions, peak values of the Green–Lagrange maximum principal strains (EI) and maximum shear strains (Ems) predicted by the FE models for the four pubic ligaments are shown in Table 3. At tfrac ¼ 11 ms, maximum strains in the posterior ligament were EI ¼ 0.36 and Ems ¼ 0.31. The corresponding peak shear (Cauchy) stresses (Fig. 6) reached 1.6, 2.3, 1.0 and 1.8 MPa for the anterior, posterior, superior and inferior ligaments, respectively. For the free contralateral BC, peak stresses occurred at tpeak ¼ 6 ms. The maximum von Mises stress in the superior and inferior rami decreased substantially to values well below the 150 MPa yield strength (Figs. 3a and b).

Ligament

Anterior

Posterior

Superior

Inferior

BCs

Fixed

Free

Fixed

Free

Fixed

Free

Fixed

Free

EI Ems

0.22 0.19

0.2 0.18

0.36 0.31

0.25 0.23

0.2 0.2

0.16 0.16

0.22 0.21

0.18 0.18

3

Max shear stress (MPa)

Fig. 4. Deformation characteristics of the pubic symphysis during side impact simulation with fixed contralateral boundary condition: undeformed front (a) and top views (b) along with deformed front (c) and top views (d), which illustrate disc compression, sagittal and vertical shear as well as posterior bending of the symphysis (scale factor ¼ 2).

Table 3 Green strains predicted by FE models for the anterior, posterior, superior and inferior ligaments for side impacts with fixed and free contralateral boundary conditions (BCs)

Anterior Posterior Superior Inferior

2

1

0 Fixed

Free

Fig. 6. Maximum shear stress predictions for the anterior, posterior, superior and inferior ligaments for the side impact simulations with the fixed and free contralateral boundary conditions.

Thus, the model predicted that the pelvis would not fracture under the same impact loading conditions following removal of the contralateral constraints. The corresponding deformations of the interpubic disc were reduced

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to ux ¼ 1.4 mm, uy ¼ 1.7 mm and uz ¼ 1.3 mm (Fig. 5). The posterior bending angle reached 4.51. The maximum principal compressive stress in the disc decreased to 7.6 MPa, while the maximum shear stress was reduced to 6.1 MPa. The peak Green strains for the pubic ligaments were reduced to EI ¼ 0.25 and Ems ¼ 0.23 (Table 3), while peak shear stresses in the anterior, posterior, superior and inferior ligaments were 1.0, 1.4, 0.8 and 1.4 MPa, respectively (Fig. 6). 4. Discussion In the present study, FE model geometries were developed by segmenting CT scans of a 53-year-old female cadaver pelvis with proximal femurs. The models included a previously validated sub-model of a pubic symphysis with non-linear hyperviscoelastic descriptions of the interpubic disc and ligaments (Li et al., 2006). The purpose was to study the biomechanical response of the symphysis under conditions where an impact force was applied to the greater trochanter of the pelvis/femur structure in a seated posture. Novel data regarding the deformation characteristics and stress distributions within the interpubic disc and ligaments were obtained that would be technically difficult or impossible to measure during experiments. Results from drop tower simulations agreed with measurements of the force–time response observed at the impact site during previous drop tower experiments. In these experiments, the contralateral (non-impact) side of the pelvis was rigidly fixed. The models indicated that the symphysis was subject to a combination of lateral compression and posterior bending, as well as anterior–posterior and superior–inferior shear in the sagittal plane, prior to fracture of the pelvic bones. Peak values of relative symphyseal mobility (between the pubic bones) during single-legged stance and walking have been measured as ux ¼ 1.3 mm, uy ¼ 2.6 mm, uz ¼ 1 mm (recall Fig. 4 for reference coordinates), and anterior–posterior bending of 31 (Walheim and Selvik, 1984). Injury criteria for the pubic ligaments and disc have not yet been established; therefore, we chose to consider these data presently as functional limits, beyond which some form of tissue damage could be assumed. Under the drop tower conditions, the models predicted relative displacements exceeded these values by a factor of almost two in compression and posterior bending, and by 40% in superior/inferior shear. The compressive strength of the interpubic disc is not known; however, the average compressive strength of the human intervertebral disc has been measured (11.0 MPa, Adams and Hutton, 1988), which is a fibrocartilaginous structure similar to the interpubic disc. The compressive stresses (10.1 MPa) in the modeled disc at tfrac approached this value. Principal strains for the pubic ligaments were over 30% in tension and shear, prior to the predicted onset of bone fracture. These results suggest potential modes of damage to the interpubic disc and ligaments, which may have resulted in

the joint laxity measured in symphyses following drop tower experiments (Dakin et al., 2001). With the contralateral constraints removed to better approximate conditions of a seated vehicle occupant (the ‘‘free contralateral BC’’), model predictions of compressive disc stresses, tensile and shear ligament strains, and cortical bone stresses were all substantially reduced. Relative displacements between the pubic bones (ux ¼ 1.4 mm and uz ¼ 1.3 mm) along with the peak posterior bending angle (4.51) remained higher than the values reported in Walheim and Selvik (1984). Peak compressive stress (7.6 MPa) in the disc was reduced to well below the compressive strength of the intervertebral disc. Green’s strains for the pubic ligaments decreased to 0.25 for peak maximum principal strains and 0.23 for peak maximum shear strain. While no formal conclusions may be reached regarding the potential for injury, compression, superior–inferior shear and posterior bending remain as likely candidates. The results further demonstrate that the contralateral boundary conditions played an important role in the FE predictions. The present model, which included geometrically accurate pelvic bone structures and a validated pubic symphysis, represents a more complex and biofidelic model than previous FE models used to study the biomechanical response of the pelvis in side impacts (Dawson et al., 1999; Majumder et al., 2004; Plummer et al., 1998; Renaudin et al., 1993). The drop tower model predictions agreed with experimental data from the previous experiments in terms of impact force–time history curves and stress patterns leading to fractures of the pubic rami (Beason et al., 2003). One notable result was the contralateral (non-impact) superior ramus experiencing the highest stress magnitudes and greatest propensity for fracture. This outcome appears to be the result of the boundary conditions where the contralateral greater trochanter and iliac wing were fully constrained in cement during the impact event. With the contralateral constraints released, the maximum stress occurred on the impact side, which is more consistent with fractures occurring in actual automotive side impacts (Grattan and Hobbs, 1969; Schmidtke et al., 1995; Siegel et al., 1993; States and States, 1968; Tile and Hearn, 1995). The present model revealed the highest probability of fracture in the superior pubic rami, followed by the inferior rami and the acetabulum, consistent with the findings in previous side impact studies on isolated pelves (Etheridge et al., 2005; Guillemot et al., 1998) and whole cadavers (Bouquet et al., 1998; Cavanaugh et al., 1990; Cesari and Ramet, 1982; Nusholtz et al., 1982; Viano et al., 1989; Zhu et al., 1993). The present model could not simulate bony fractures; therefore, model output was considered as valid only until the time at which bone fracture was predicted, as in the contralateral superior ramus in the drop tower simulation. Other limitations may have affected the present computational results. The FE model was developed using CT data from one specific pelvis of an average-sized female, which was not one of the pelvis specimens used in the

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experiments. Individual physiological differences between pelvic specimens may affect model predictions. In addition, soft tissues surrounding the pelvis (skin, muscles and fat) were not included, which have been shown previously to increase fracture forces (Etheridge et al., 2005), serving as a cushion that lowers abbreviated injury scores for the pelvis and abdomen in vehicle collisions (Arbabi et al., 2003; Wang et al., 2003). A novel feature of this study was the use of strain ratedependent bone strength. The yield strength of bone has been reported to vary from 80 to 270 MPa, for strain rates ranging from 0.0001 to 1000 s1 (Wright and Hayes, 1976). From those data, the current value of 150 MPa was obtained and used to predict bony fracture in the present simulations where the strain rate was approximately 0.4 s1. No effort was made presently to confirm this strength in separate tests on pelvic bones. The four pubic ligaments were approximated as discrete solid bands with a unique (axial) fiber stretch direction. In real ligaments, these fiber orientations may differ. Previous studies have shown that ligaments exhibit direction-dependent properties in response to external loads with longitudinal tensile strength and tangent modulus one order of magnitude higher than those in the transverse direction (Quapp and Weiss, 1998). Principal elongations of the pubic ligaments did not occur along the assumed fiber directions in the present models, suggesting that shear loading during side impacts may damage these structures that primarily resist tensile forces in vivo. Efforts to improve occupant protection in future vehicles are likely to involve new side airbag designs and interior door structures that contain novel energy absorbing materials. Such efforts may benefit from sophisticated computer models of the human pelvis, such as the one used presently. The long term aim of preventing bone fractures and soft tissue injuries in vehicle occupants during automobile side impacts remains important. FE models based on CT scans, constructed using automatic or semiautomatic segmentation and meshing schemes, and containing advanced constitutive models of soft tissues, are likely to play an ever increasing role in the study of the biomechanical response of the human body during vehicle collisions. The present FE simulations employed these modern techniques to study injury of the pubic symphysis. We uncovered potential sources of injury and subsequent joint laxity, as well as a clear reminder of the importance of accurate boundary conditions in FE modeling.

Acknowledgment Financial support from the Center for Injury Sciences, the Injury Control Research Center, the Southern Consortium of Injury Biomechanics, the Department of Biomedical Engineering, and the Department of Mechanical Engineering at the University of Alabama at Birmingham is gratefully acknowledged.

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