Effect of Bone Density Alterations on Strain Patterns in the Pelvis: Application of a Validated Finite Element Model

Introduction: Insufficiency fractures of the pelvis occur when normal loads are applied to bone deficient in mineral or elastic resistance [1]. They are most commonly found in the pelvic ring (30.7%) and the sacrum (29.6%) [2]. While reduced bone density in the pelvis is seen as a major risk factor for insufficiency fractures, little is known about the impact of changes in bone density on the strain patterns in the pelvis under normal physiological loading. A better understanding of pelvic mechanics and the effect of changes in the mechanical properties of the bone could lead to improved diagnosis and treatment of insufficiency fractures. Finite element (FE) analysis is a widely used computational modeling technique which has been successfully used to provide information on strain and stress patterns in bony structures given realistic mechanical properties, loading and boundary conditions. The objectives of this study were 1) to develop and validate a 3D FE model of a pelvis under physiological loading using subject-specific estimates of bone geometry and location-dependent trabecular bone material properties, and 2) to analyze the pelvic strain as a function of cortical and trabecular bone density using the validated FE model. Materials and Methods: A 3D volumetric tetrahedral FE mesh was generated from a CT scan of a fresh frozen pelvic specimen, including L5 and bilateral proximal femurs (Amira, MCS Inc). The surface elements representing cortical bone were assigned a uniform elastic modulus (E = 17GPa) while elements in the trabecular bone regions were assigned an elastic modulus based on their CT intensity. CT intensity was calibrated to bone density using a phantom and an empirical relationship was used to convert bone density (g/cm3) to elastic modulus (E = 2017.3ρ2.46, MPa) [3]. In-vitro mechanical testing was conducted on the cadaveric pelvic specimen instrumented with 7 strain gauges per hemipelvis. The specimen was vertically loaded via L5 in a double leg stance position with loads of 0.25, 0.50, 0.75 x Body Weight (500N) applied in a stepwise manner; loading was repeated six times (MTS Bionix 858). The experimental measurements at each strain gauge were used to validate the FE model solved using similar loading and boundary conditions (Abaqus 6.6-1, Abaqus Inc). A response surface was used to analyze the sensitivity of the model to variations in cortical and trabecular bone density characterized by changes in elastic modulus. Cortical and trabecular elastic modulus were analyzed as independent variables representing density increases and decreases of 20% from the baseline validated model. The measured responses were the total maximum and minimum principal strain on the pelvic bone surface at a load of 345N. Elastic modulus was adjusted by ±5%, ±10%, ±15%, and ±20% for (1) trabecular only, (2) cortical only, and (3) both trabecular and cortical to obtain an uniform distribution of runs over the solution space (Design-Expert 7.7-1, Stat-Ease Inc.). Results: A convergence study was performed and the FE mesh density was accepted when the strain at each gauge change by < ±5uE; the resultant mesh was comprised of ~1.3 million tetrahedrons. The strains of the model at gauge locations were well correlated to experimentally obtained values (R2=0.88; y=1.18x-1.76) and agreement improved further when one outlier gauge in a high strain gradient region was removed (R2=0.93; y=1.02-0.17). The highest strain regions of the pelvis under double leg stance loading were the greater sciatic notch, tubercle of pubis and the pelvic rim region closest to the SI joint (Fig 1). The validated FE model effectively simulated density alterations in cortical and trabecular bone via elastic modulus and its effect on strain (Fig. 1). A quadratic regression-fit of the maximum and minimum principal strains as a function of cortical and trabecular bone density was used for the response surface model. In considering the linear terms of the response surface, cortical density had a >60% influence on the maximum and minimum principal strain as compared to trabecular density. Changes of ±20% in cortical and trabecular density changed the principal strains by ~15% and ~9% respectively. There was a significant but small interaction between cortical and trabecular density on strain (<3%). There was also a significant but small non-linear effect of cortical elastic modulus on strain. Changes in elastic modulus had a larger effect on strain at lower densities.