Incorporating uncertainty in mechanical properties for finite element-based evaluation of bone mechanics

Finite element (FE) models of bone, developed from computed tomography (CT) scan data, are used to evaluate stresses and strains, load transfer and fixation of implants, and potential for fracture. The experimentally derived relationships used to transform CT scan data in Hounsfield unit to modulus and strength contain substantial scatter. The scatter in these relationships has potential to impact the results and conclusions of bone studies. The objectives of this study were to develop a computationally efficient probabilistic FE-based platform capable of incorporating uncertainty in bone property relationships, and to apply the model to a representative analysis; variability in stresses and fracture risk was predicted in five proximal femurs under stance loading conditions. Based on published variability in strength and modulus relationships derived in the proximal femur, the probabilistic analysis predicted the distributions of stress and risk. For the five femurs analyzed, the 1 and 99 percentile bounds varied by an average of 17.3 MPa for stress and by 0.28 for risk. In each femur, the predicted variability in risk was greater than 50% of the mean risk calculated, with obvious implications for clinical assessment. Results using the advanced mean value (AMV) method required only seven analysis trials (1 h) and differed by less than 2% when compared to a 1000-trial Monte-Carlo simulation (400 h). The probabilistic modeling platform developed has broad applicability to bone studies and can be similarly implemented to investigate other loading conditions, structures, sources of uncertainty, or output measures of interest.