A Probabilistic Method to Model Progressive Metatarsal Displacement and Stiffness During Fatigue Testing

To better understand the mechanisms of bone stress injuries (BSI) in metatarsals, we developed an algorithm that adapts finite element (FE) models of metatarsals to simulate fatigue displacements through progressive stiffness loss. Twenty-two human metatarsals were imaged using computed tomography (CT) and then cyclically loaded in uniaxial compression until failure. CT images were used to generate specimen-specific FE models, and a custom program was developed to iteratively simulate cyclic loading and progressive stiffness loss associated with microdamage accumulation. Probability was incorporated into microdamage accumulation through a Weibull distribution. Simulations were able to accurately represent experimental trends in how metatarsal stiffness and displacement changed throughout the mechanical testing. Simulated displacement at failure was not significantly different from experimentally measured displacement. Simulated fatigue life, displacement, and rate of stiffness loss were significantly affected by (1) the Weibull scatter variable, m, and (2) the critical strain value, describing whether damage occurred before or after yielding. These simulations represent a novel alternative method that is significant because it helps us better understand the factors that influence fatigue life and observed mechanical behavior during fatigue testing in whole bones. Advanced adaptive simulations such as the one described here can be leveraged to reduce the reliance on physical testing, generate and test hypotheses regarding damage accumulation in materials, and eventually, be deployed in predictive algorithms with clinical applications.