Injury Risk Functions Based on Responses of Population-Based Finite Element Models: Application to Femurs under Dynamic Loading

A fundamental purpose of biomechanical testing and the field of injury biomechanics is the development of injury risk functions (IRFs). Up to the present, IRFs have usually been developed in a “top-down” approach by relating injury outcomes in cadaveric tests to dummy measures in matched crash conditions. While IRFs developed in the top-down approach have been commonly used in the automobile safety field, future initiatives for the development of IRFs may need to address 1) the limited number of cadaveric specimens available for testing and 2) the limited ability of scaling techniques to capture the complexity of the human body.
The central idea of this study is that population-based finite element (FE) models, whose input distributions are based on subject-specific finite element (SS-FE) and statistical modeling approaches, may hold the key to overcoming the challenges facing the development of IRFs. SS-FE models, incorporating specific skeletal geometry of specimens into the models, help researchers verify the predictive capability of FE models with given material properties and their parameter distributions by minimizing the geometric error between cadaveric specimens and the models. If accurate subject-specific modeling technique can be developed and validated, this may facilitate the development of statistical models that can analyze geometric variations across the population. In the end, assigning probabilistic distributions as input variables instead of a single value allows generation of population-based FE models which captures variabilities across the population. Among other applications, these population-based FE models could be utilized to develop IRFs whose range of variabilities are informed by observations from the population-based FE model responses. In other words, the population-based FE modeling approach allows us to develop the IRFs in a “bottom-up” manner rather using the current “top-down” approach.
The goal of this dissertation was to explore a framework for developing IRFs in a “bottom-up” approach based on the responses of parametrically-variable finite element (FE) models representing exemplar populations. To illustrate the process, first, subject-specific FE models of human femurs were developed and validated. Next, principal component analysis and regression were used to identify parametric geometric descriptors of the human femur and the distribution of those factors for three target occupant sizes (5th, 50th, and 95th percentile males). Also, distributions of material parameters of cortical bone were obtained using regression analysis based on the literature for three target occupant ages (25, 50, and 75 years). A Monte-Carlo method was then implemented to generate populations of FE models of the femur for target occupant sizes and ages. In total, 100 femur models incorporating the variation in the population of interest were generated for each target occupant and simulations were conducted with each of these models under three-point dynamic (1.5m/s) bending. In the end, model-based IRFs were developed using logistic regression analysis, based on the 500,000 observations (each 100 femur models with 5,000 ultimate strains) of moment-at-fracture in the population-simulation dataset for each target occupant. In addition, to exemplify an application of the proposed framework, this dissertation developed a closed-form of model-based IRFs for the human femur under a frontal oblique car crash test, whose loading conditions were analyzed from the publicly-available NHTSA crash test database, using survival analysis with a multivariate logistic model based on 27 million observations of moment-at-fracture in the population-simulation dataset.
The framework proposed in this dissertation would be beneficial for developing IRFs in a bottom-up manner, whose range of variabilities are informed by the observations of moment-at-fracture in population-based FE model responses. This method would be able to address challenges facing the current development procedure of IRFs for diverse or specialized populations: specifically, this method mitigates the uncertainties in applying empirical scaling and may improve IRF fidelity when a limited number of experimental specimens are available.