The Femur as a Complete Musculo-Skeletal Construct: A Free Boundary Condition Finite Element Approach

Abstract

Previous finite element studies of the femur have made various assumptions with regards to the boundary conditions imposed, with almost all implementing fixed boundary conditions on the femur itself. Several studies have attempted to include the affects of muscle forces acting on the cortex of the femoral bone, by applying muscle forces either at single nodes, or uniformly distributed across muscle attachment areas [1,2], with balanced sets of muscle and joint reaction forces being implemented. Muscle forces are taken from inverse dynamics optimisation studies, and are therefore sensitive to the optimisation criteria used, as well as the omission of passive support structures such as the ligaments.

While it is possible to validate fixed boundary condition numerical models against in-vitro experiments, it remains a matter of debate as to whether either the numerical model or the experiment can be compared to the in-vivo conditions. This study presents a finite element model in which the femur is treated as a complete musculo-skeletal construct, spanning between the hip and knee joints. Linear and non-linear implementations of a free boundary condition modelling approach [3,4] are applied to the bone through the explicit inclusion of muscles and ligaments spanning both the hip joint and the knee joint. The use of these free or soft boundary conditions allows the femur to be modelled without the application of fixed boundary conditions to the cortex. In addition it allows for differing muscle activation levels across muscle origination areas, and does not rely on a pre-defined set of muscle forces found from an inverse dynamics analysis.

Non-linear force regulated, muscle strain based activation strategies were found to result in lower observed principal strains in the cortex of the femur, compared to a linear activation strategy. Non-uniform muscle activation was observed across muscle origination areas for both linear and non-linear models. Future implementations of the model will investigate whether muscle forces may be predicted based on target principal strain values in the femoral bone tissue. Non-linear implementation of the model in particular, was found to produce hip and knee joint reaction forces consistent with in-vivo data from instrumented implants [5,6]. Agreement was also observed with previous joint and muscle force balanced studies.

The development of free boundary condition models is seen to have particular significance with regard to investigating complete musculo-skeletal systems, and can be seen as a complimentary technique to balanced muscle and joint reaction finite element models. The technique has been successfully applied to the femur, and has the potential to be extended to into a model of the entire lower limb.