Development of Human Hip Capsule Finite Element Model

The current study focuses on the development of a finite element model of the hip capsule ligament to represent the joint between the femur and the pelvis. The finite element model of the hip capsule is represented as comprising of eight sectors, consisting of the important ligaments in those regions of the capsule. The geometric parameters for the capsule are determined from available literature. A soft tissue material model is used to represent the nonlinear behavior of the capsule ligaments. Available hip distraction test data is used to validate the finite element model. A parametric study is conducted with the isolated capsule sector finite element model to understand the effects of different material parameters on the tensile load-deflection response of the capsule. The material properties for each sector of the hip capsule are systematically estimated to match the corresponding values from isolated capsule sector tensile tests reported in the literature. A verification exercise for the sector hip capsule material properties is carried out by considering a setup comprising an integrated pelvis-hipcapsule-femur finite element model and comparing with data available from hip distraction tests in the literature. The stiffness of the hip capsule finite element model is found to lie within the reported test corridor from hip distraction tests. The developed hip capsule finite element model will be of use in examining the stresses and strains in the joint ligaments. INTRODUCTION The pelvis is one of several human body regions that are susceptible to injury in the event of an automobile impact [Teresinski, 2001, Aekbote et al., 2003, Kuppa and Fessahaie, 2003, Rupp and Schneider, 2004, Sochor and Rupp, 2005]. The simulation and prediction of such injuries requires the use of detailed computer models. One of the challenges of developing such computer models is in the accurate representation of various human body joints in these models. Several contemporary computer models (e.g. Anthropometric Test Device (ATD) Models, ESI's H-Model [Choi et al., 1999], the GM-UVA Human Body Model [Deng, 2007]), intended to simulate the human body in an automobile impact scenario, represent the connection between the pelvis and the femur head by a simplified rigid kinematic joint, with appropriate mechanical properties (joint stiffness in various directions). Such a representation limits injury prediction in the pelvis region on account of the requirement of typical finite element software like LS-DYNA [LS-Dyna, 2006] for the connecting bodies (ilium and femoral head) to be rigid. A natural progression towards accurate representation of the hip capsule is through 1-D elements. Vezin et al. [Vezin and Verriest, 2005] idealized the hip capsular ligament as a set of 1-D elements in the HUMOS model. While this constituted a step forward from the idealized rigid kinematic joint, this model could not be used to perform detailed stress analysis in the capsule region, or to predict phenomena like capsule laxity, ligament tear, etc. [Teresinski, 2001, Philippon and Schenker, 2005]. Stewart and co-workers [Stewart et al., 2004] developed a model of the hip capsular ligament with solid elements and experimentally obtained tissue material properties for simulating total hip arthroplasty (THA) applications. One advantage of representing the hip capsule in the model as soft tissue is the more accurate capture of the load transfer mechanism between the pelvis and the lower extremity in comparison to rigid kinematic joints or 1-D beam representations. This could turn out to be significant for a dynamic load case like pedestrian impact. The hip joint is essentially a ball and socket joint wherein the ligaments and the contact interface between the acetabulum and the femur head constrain the femur head (ball) from slipping out of the acetabulum (socket). The hip capsule is an important part of the hip joint that allows for joint articulation and provides stability. The hip capsule is strengthened by three important ligaments, namely the iliofemoral ligament, the ischiofemoral ligament and the pubo-capsular ligament [Gray and Carter, 1995]. The elastic behavior of the ligament soft tissue allows for flexion, abduction and internal rotation of the lower extremities about the hip joint. Several studies [Wingstrand and Wingstrand, 1997, Scifert et al., 1999] have been carried out to understand hip joint biomechanics, but these have been focused more on sport related injuries and total hip arthroplasty (THA). To date, the availability of hip capsule response data in a dynamic impact scenario is very limited. The availability of relevant material data comprises one of the most significant prerequisites for building accurate finite element (FE models). Until recently, not much data has been published regarding mechanical properties of the hip capsule. Hewitt et al., 2000 performed the first set of tests to understand the material behavior of the important ligaments in the hip capsule. They carried out tensile tests on cadaveric ligament specimens to failure. Several important properties like stress and strain at failure, toe-region and linear region elastic modulus were documented. They also reported the variation of cross -sectional area of the ligaments along the fiber direction (from the acetabulum side to the femoral side). Their study highlighted the mechanical heterogeneity of the hip capsule. It was observed in their tests that the iliofemoral ligament (anterior region of the capsule) was stiffer than the ischiofemoral ligament (posterior region of capsule). However these tests were limited only to key capsule ligaments like the ischiofemoral, iliofemoral and pubofemoral ligaments. This study was also performed at low rates to avoid visco-elastic effects. Stewart et al., 2002 performed more detailed tests on the whole hip capsule instead of a few important hip capsule ligaments. They reported regional material and geometrical properties of the whole human hip capsule ligament. Distraction tests were performed on cadaveric specimens to calculate the stiffness of the whole hip capsule ligament. After each test the whole capsule was cut into several sectors and subjected to tensile load until failure to calculate the stiffness of each sector of the capsule. The sectors were carefully cut so as to not cut across ligament fibers. This study reported several mechanical properties of the capsule like stiffness and failure load of each capsule sector, typical load-deflection curves for the whole capsule and individual sectors for distraction and tensile tests respectively. They also performed tests at various distraction rates but concluded that strain rate effects were insignificant for their load case. However, other studies [Kemper et al., 2007] have reported strain rate effects in testing the iliofemoral and ischiofemoral ligaments. Stewart et al., 2004 used some of their own test data [Stewart et al., 2002] to build finite element models to simulate total hip dislocation. They reported significant improvement in the FE model joint behavior. The focus of the current work is to develop a hip capsule ligament model similar to the one developed in [Stewart et al., 2004], but for eventual application to occupant and pedestrian impact scenarios. The current study focuses on the development of a finite element model of the hip capsule ligaments for a human body model representative of a 50th percentile male. This model is further used to connect the femur to the pelvis. A recently developed material model [LS-DYNA, 2006] for soft tissue, which takes into account viscoelastic effects as well as tissue fiber direction, is used for the ligament model. As a first step, a validated FE model was developed to simulate the individual capsule sector tensile test. Parametric studies were conducted using this model to identify the most important tissue material parameters which influence the capsule stiffness. Subsequently, the material parameters of each sector were estimated. The second step involved the development of a FE model to simulate a hip distraction test. The sectoral material properties obtained in the first step were used to develop a whole hip capsule model to simulate hip distraction test. These FE results verified the estimated material properties of individual capsule sector in the previous step. The integrated hip capsule FE model was further used to conduct a brief parametric study by varying capsule material model parameters. This study provides a glimpse of the influence of material model parameters on overall load-deflection behavior of the hip capsule. METHODS Hip capsule geometry The hip capsule is a dense fibrous tissue with the shape of a cylindrical sleeve. It spans the circumference of the acetabulum rim along the medial end. The other end of the capsule surrounds the neck of the femur. It is attached anteriorly, to the intertrochanteric line, posteriorly to the lower part of the neck closer to lesser trochanter, superiorly and inferiorly to the base of the femur neck [Gray and Carter, 1995]. The thickness of the tissue varies both along the circumference and length of the capsule. The fiber directions vary in different parts of the capsule. There are three dominant dense regions which are identified as the iliofemoral ligament, the ischiofemoral ligament and the pubofemoral ligament. It is very difficult to identify the distinct boundaries of these ligaments and therefore it is better to model the ligaments as a single unified capsule model. The iliofemoral ligament part of the capsule is the thickest and has its fibers run longitudinally. The anterior region is the thinnest and weakest part of the capsule. Stewart et al., 2002 have reported circumferential variation of capsule geometric parameters (length, thickness). They have dissected each of ten cadaveric hip joint specimens into eight sectors and reported the range of these geometric parameters. The average values from this study were taken as the basis for building the FE mesh for the capsule FE model. Variation across the length of the capsule was also considered based on the geometric data provided in Hewitt et al., 2000. The insertion points of various ligaments were obtained from [Gray and Carter, 1995, and Stewart et al., 2002] and were mapped onto a pelvis-femur FE model [Untaroiu et al., 2005, Deng, 2007]. Figure 1 shows the identified insertion points. Figure 2 shows the posterior view of the hip capsule FE model. The eight different sectors as dissected by Stewart et al., 2002 and corresponding fiber directions are also shown in Figure 2. The thickness variation of capsule along the circumference is also captured in the FE model. In general it can be observed that sector 1 represents the pubofemoral ligament, sectors 2-4 represent the femoral arcuate and posterior regions of capsule, sectors 5-6 represent the ischiofemoral ligament, sector 7 is the superior iliofemoral ligament and sector 8 is the inferior iliofemoral ligament. Figure 1: Insertion Points – anterior view Figure 2: Whole Hip Capsule – posterior view Capsule material model Accurate capture of the ligament mechanics necessitates the use of appropriate material models for the capsule model. As reported in earlier studies [Hewitt et al., 2002, Stewart et al., 2002] the hip capsule tissue behaves in a highly nonlinear manner. A recently developed advanced tissue material model is used in LSDYNA® to represent the capsule. The material model (MAT_SOFT_TISSUE_VISCO [LS-DYNA, 2006]) is based on a viscoelastic model proposed by Puso and Weiss [Puso and Weiss, 1998], and is a transversely isotropic (stiffer in the fiber direction) hyperelastic model for representing biological soft tissues like the capsule ligament. The constitutive model provides an isotropic Mooney-Rivlin mix reinforced by fibers. The overall strain energy (W) is uncoupled and includes two isotropic deviatoric ground substance (matrix) terms, a fiber term (F), and a bulk term as given below in Equation 1 [Puso and Weiss, 1998]. Here I1, I2 are the deviatoric invariants of the right Cauchy deformation tensor, λ is the deviatoric part of the stretch along the current fiber direction, and J is the volume ratio. The material coefficients C1, C2 are the Mooney-Rivlin coefficients and K is the effective bulk modulus. The derivatives of the fiber term F are defined as a function of fiber stretch to capture the behavior of crimped collagen as given below in equation 2.The fibers are assumed to be unable to resist compressive loading when λ is less than 1. An exponential function describes the straightening of the fibers, while a linear function describes the behavior of the fibers once they are straightened past a critical fiber stretch. The parameter C3 scales the exponential stress, C4 specifies the rate at which collagen straightens, C5 is the modulus of straightened fibers, and λ* is the critical fiber stretch at which the fibers are straightened. C6 is determined to ensure stress continuity at λ*. Apart from these parameters the LS-DYNA material model also allows co-ordinate system input for defining the fiber direction in each element. This is very important considering the different fiber directions in different sectors of the capsule as shown in Figure 2. Figure 3 shows typical load-deflection responses from tensile tests on a capsule tissue sector reported by Stewart et al., 2002 and Hewitt et al, 2002. The curves are initially flat (toe region) followed by exponential rise in stiffness and eventually have a linear slope region. The material model described above is therefore well suited to model the capsule tissue behavior. It can also be seen in the figure that different parts of the capsule have different stiffness. The curves corresponding to the superior and inferior iliofemoral ligament, the ischiofemoral ligament and the femoral arcuate ligament from Hewitt et al., 2002 have two major differentiators: the slope of the linear portion of the curve and the initiation point for exponential rise in stiffness. The heterogeneity of capsule tissue is more evident in Figure 4; it shows the variation in tangent structural stiffness of each sector across the ten capsule specimens as reported by Stewart et al., 2002. Figure 3: Load Deflection Curves for ligament tensile test from [Stewart et al., 2002 and Hewitt et al., 2002] Figure 4: Spatial Distribution of Capsule Material Properties (A – Tangent Structural Stiffness, B – Ultimate Load at Failure) [Stewart et al., 2002] In the current study, the capsule material properties are estimated and verified in two separate stages. In the first stage the material properties for each of eight individual sectors of the capsule were estimated using isolated sector tensile test data (Stewart et al., 2002) and verified in the next stage using hip distraction test data (Stewart et al., 2002). Isolated sector material properties A FE model was developed to simulate an isolated sector tensile test conducted by Stewart et al., 2002. The dimensions of the representative capsule sector specimen are 45mm x 15mm x 5mm. All finite element simulations were carried out using LS-DYNA® (LS-DYNA, 2006) with hexahedral elements. A convergence study was carried out to obtain the requisite mesh densities for the test setup, and the final mesh consisted of 400 elements and 700 nodes. The tissue was clamped at both ends to rigid blocks. The bottom rigid block was constrained in all directions and a unidirectional tensile load was applied at a rate of 4mm/s to the top end. This FE model represents the tensile tests carried out by Stewart et al., 2002 on all the sectors of the capsule. Table 1: Initial Material Properties Bulk Modulus (GPa) C1 (GPa) C1 (GPa) C1 (GPa) C1 C1 (GPa) λ* 4.315 6.2e-5 0 4.2e-03 158.9 0.2793 1.06 Table 2: Material Parameter Variation