A preliminary iterative 3D meso-scale structural model of the femur was developed, in which bar and shell elements were used to represent trabecular and cortical bone respectively. The cross-sectional areas of the bar elements and the thickness values of the shell elements were adjusted over successive iterations of the model based on a target strain stimulus, resulting in an optimised construct. The predicted trabecular architecture, and cortical thickness distribution showed good agreement with clinical observations, based on the application of a single leg stance load case during gait. The benefit of using a meso-scale structural approach in comparison to micro or macro-scale continuum approaches to predictive bone modelling was achievement of the symbiotic goals of computational efficiency and structural description of the femur.
It has long been observed that the structural composition of the femur (thigh bone), is adapted in response to the mechanical environment that it is subjected to. In cross-section the proximal femur (close to the hip joint), is composed of two distinct types of bone as illustrated in Figure 1, which shows a labelled diagram of a coronal (frontal) slice of the proximal femur. Cortical bone is formed from a layer of low porosity, high stiffness bone, of varying thickness on the outside of the femur. Trabecular bone is formed from a series of struts, giving rise to a structure in which there is a spacial variation of continuum level porosity and directionally dependent stiffness throughout the femur. At a tissue level cortical and trabecular bone can be considered to be the same material, with varying material properties being a result of the architecture. Both the varying thickness of the cortical bone and the structural properties of the trabecular bone are thought to be a result of the forces placed on the femur, which include the joint contact forces at the hip and knee joints, and muscle forces, which act on the cortex (cortical surface) of the femur to facilitate balance and movement. It is generally accepted that the resulting structure of the femur is optimised to withstand the applied forces using a minimal amount of material.
It has been hypothesised that the structure of trabecular bone in particular follows trajectories of compressive and tensile stress, resulting in an optimised structure. This hypothesis originates from observations by Culmann (an engineer) and von Meyer (an anatomist) that the internal structure of a frontally sectioned proximal femur resembled the sketched stress trajectories of a curved (Fairbairn) crane (Culmann 1866, von Meyer 1867). Culmann was a pioneer of graphical methods in engineering, publishing Die graphische Statik (Graphical Statics) in 1866. It is of note that in drawing the trajectory arrangement of trabeculae in the proximal femoral head, von Meyer did not imply that the trajectories were orthogonal. In his work Das Gesetz der Transformation der Knochen (The Law of Bone Remodelling) (Wolff 1986) Wolff criticised von Meyer for this, and produced a trajectory diagram of the proximal femur in which trajectories met at right angles, the implication at a continuum level being that trajectories occur along lines of principal stress. Koch, in his work The Laws of Bone Architecture (Koch 1917) also argues that trabecular trajectories should be orthogonal, based on trajectories following principal stress directions at a continuum level. The reader is directed to Skedros & Baucom (2007) for an in-depth discussion of this assumption. Suffice it to say that under examination trabecular architecture is demonstrated not to be orthotropic throughout the proximal femur. It has been suggested that non-orthogonal trabecular intersections offer increased shear resistance (Pidaparti & Turner 1997), significant if the femoral structure is considered to be optimised for a range of loading scenarios. Wolff’s observations are often now erroneously referred to as ‘Wolff’s law’ in studies investigating bone modelling and remodelling (resorption and apposition of bone). Figure 2 shows diagrams of the representations of the cross-sectional trabecular arrangement in the proximal femur as proposed by von Meyer, Wolff and Koch. 1867) , (b) Wolff (1986) and (c) Koch (1917). Singh et al. (1970) along with others identify five distinct trabeculae groups in the proximal femur. These are described briefly: the principal compressive group carries load from the hip joint, through the femoral head towards the medial (close to the centreline of the body) cortex; the primary tensile group arches from the lateral (distant to the centreline of the body) cortex through to the femoral head; the secondary compressive group spans in a diffuse manner from the medial cortex across the femoral shaft; the secondary tensile group spans in a diffuse manner from the lateral cortex across the medial shaft; the greater trochanter group is thought to be a tensile group running within the greater trochanter. Also noted are the presence of Ward’s triangle, an area of low trabecular density, as well as the femoral canal running between the medial and lateral cortex of the femoral shaft. Frost (2003) introduced the idea of the ‘mechanostat’. The essence of the mechanostat is the notion that bone adapts towards a target strain, similar to a thermostat regulating heating and cooling towards a target temperature. Based on the mechanostat if bone experiences a strain higher than the target strain apposition occurs, causing the strain to revert towards the target strain. While if bone experiences a strain lower than the target strain resorption occurs, again causing the strain to revert towards the target strain. Frost also proposed a lazy zone for the mechanostat, similar to allowing a thermostat to maintain temperature bet
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