Modelling Cyclic Walking in Femurs With Metastatic Lesions: Femur-Specific Accumulation of Plasticity

Introduction Clinical fracture risk assessment in metastatic bone disease is extremely difficult, but subject-specific finite element (FE) modelling may improve these assessments in the future [Derikx, 2015]. By coupling to musculoskeletal modelling, realistic loading conditions can be implemented in FE analysis. However, it is unknown whether such analyses require complex elastic-plastic material models, or whether a linear elastic calculation already provides a reasonable prediction of fracture. Moreover, plastic deformation may accumulate over time, which is ignored by linear elastic calculations. In this study we compared linear and non-linear fracture predictions under realistic loading conditions in two patients with metastatic bone disease. Methods Two patients (P1, P2) with lytic lesions were included. Patient-specific femoral geometry and bone density were retrieved from quantitative CT-scans; the latter was used for implementing element-specific material behaviour [Keyak, 2005]. Muscle forces and hip contact forces acting on the femur during walking were calculated using musculoskeletal modelling (one typical case, adapted from [Wesseling, 2014]), and subsequently normalized to the patient’s body weight. Muscle forces were applied to attachment points that were morphed onto the patient femurs. Hip contact forces were applied to a cup mimicking the acetabulum, via a control node in the hip joint centre. Two simulations were run for each patient: a linear elastic analysis simulating a single walk cycle and a non-linear elastic-plastic analysis simulating 10 subsequent walk cycles. The safety factor (SF; yield stress/Von Mises stress) and plasticity were studied as measures of femoral failure in the linear and non-linear simulations, respectively, and compared between patients. Results The volume of elements with SF<1 (Figure 1A) as well as the volume of elements that underwent plastic deformation (Figure 1B) was highest in the femur of P1. In P1 the volume of plastic deformation increased over the loading cycles and eventually exceeded the peak volume of elements with SF<1 in the linear analysis. In P2, the volume of plasticity more or less stabilized after two loading cycles, and eventually resembled the volume of elements with SF<1 in the linear analysis. Discussion These preliminary results suggest that accumulation of plasticity under cyclic loading is femur-specific. Due to the variable and local weakening of the bone strength by metastatic lesions, relatively small changes in magnitude or direction of loading may initiate local failure and catalyze progressive failure in subsequent loading cycles. Hence, in some cases a linear analysis is sufficient, while in others it is not. Non-linear material behaviour and cyclic loading conditions are therefore required to capture these phenomena.