Finite element (FE) modelling has been widely used to create and assess musculoskeletal models. However to achieve a high degree of resolution in describing the structure, significant computational power and time are required. The objective of this study was to introduce a complimentary approach to FE modelling using structural beam theory. This requires far less computational power and models can be analyzed in a fraction of a second, offering quick, intuitive results for engineers and surgeons.

Beam theory was first introduced as a method for analyzing the stresses in long bones in 1917. It was used as the de facto method for several decades. The introduction of FE modelling offered great advances; beam theory calculations were considered laborious and less accurate. However with the advances in computational power so too comes the ability to create modern automated beam theory models.

A study was conducted using the commercially available general structural analysis software Oasys GSA. A synthetic biomechanical femur was CT scanned and the solid model constructed. This model was sectioned into approximately seventy sections in the regions of the shaft and condyles, thirty in the neck and thirty in the head. Line plots of the shape of each of the sections, for both cortical and trabecular parts, were then imported into Oasys GSA. The centroid, area, second moments of area and torsion constant were calculated for each section. The sections were plotted at the position of the cortical centroid and parallel axis theorem was used to plot the trabecular section in the same position. A force representing the hip joint reaction force was applied to a node corresponding to the centre of the femoral head. Muscular forces were applied to stiff radial elements according to those active at the point of peak joint contact force during gait.

Oasys GSA produced instant results showing moment and deflection characteristics of the femur. This data was then used to predict strain plots, which were directly compared to FE results. Initial results compare favourably.

This study has demonstrated an updated fast, efficient and intuitive alternative to finite element modelling.

Finite element models of the musculoskeletal system have the possibility of describing the in vivo situation to a greater extent than a single in vitro experimental study ever could. However these models and the assumptions made must be validated before they can be considered truly useful. The object of this study was to validate, using digital image correlation (DIC) and strain gauging, a novel free boundary condition finite element model of the femur.

The femur was treated as a complete musculoskeletal construct without specific fixed restraint acting on the bone. Spring elements with defined force-displacement relationships were used to characterize all muscles and ligaments crossing the hip and knee joints. This model was subjected to a loading condition representing single leg stance. From the developed model muscle, ligament and joint reaction forces were extracted as well as displacement and strain plots. The muscles with the most influence were selected to be represented in the simplified experimental setup.

To validate the finite element model a balanced in vitro experimental set up was designed. The femur was loaded proximally through a construct representative of the pelvis and balanced distally on a construct representing the tibio-femoral joint. Muscles were represented using a cabling system with glued attachments. Strains were recorded using DIC and strain gauging. DIC is an image analysis technique that enables non-contact measurement of strains across surfaces. The resulting strain distributions were compared to the finite element model.

The finite element model produced hip and knee joint reaction forces comparable to in vivo data from instrumented implants. The experimental models produced strain data from both DIC and strain gauging; these were in good agreement with the finite element models. The DIC process was also shown to be a viable method for measuring strain on the surface of the specimen.

In conclusion a novel approach to finite element modeling of the femur was validated, allowing greater confidence for the model to be further developed and used in clinical settings.