Application of homogenization theory to the study of trabecular bone mechanics

It is generally accepted that the strength and stiffness of trabecular bone is strongly affected by trabecular microstructure. It has also been hypothesized that stress induced adaptation of trabecular bone is affected by trabecular tissue level stress and/or strain. At this time, however, there is no generally accepted (or easily accomplished) technique for predicting the effect of microstructure on trabecular bone apparent stiffness and strength or estimating tissue level stress or strain. In this paper, a recently developed mechanics theory specifically designed to analyze microstructured materials, called the homogenization theory, is presented and applied to analyze trabecular bone mechanics. Using the homogenization theory it is possible to perform microstructural and continuum analyses separately and then combine them in a systematic manner. Stiffness predictions from two different microstructural models of trabecular bone show reasonable agreement with experimental results, depending on metaphyseal region, (R2>0.5 for proximal humerus specimens, R2 <0.5 for distal femur and proximal tibia specimens). Estimates of both microstructural strain energy density (SED) and apparent SED show that there are large differences (up to 30 times) between apparent SED (as calculated by standard continuum finite element analyses) and the maximum microstructural or tissue SED. Furthermore, a strut and spherical void microstructure gave very different estimates of maximum tissue SED for the same bone volume fraction (BV/TV). The estimates from the spherical void microstructure are between 2 and 20 times greater than the strut microstructure at 10-20% BV/TV.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29647/1/0000736.pd

Spontaneous osteoarthritis in Str/ort mice is unlikely due to greater vulnerability to mechanical trauma

SummaryObjectiveRelative contributions of genetic and mechanical factors to osteoarthritis (OA) remain ill-defined. We have used a joint loading model found to produce focal articular cartilage (AC) lesions, to address whether genetic susceptibility to OA in Str/ort mice is related to AC vulnerability to mechanical trauma and whether joint loading influences spontaneous OA development. We also develop finite element (FE) models to examine whether AC thickness may explain any differential vulnerability to load-induced lesions.MethodsRight knees of 8-week-old Str/ort mice were loaded, AC integrity scored and thickness compared to CBA mice. Mechanical forces engendered in this model and the impact of AC thickness were simulated in C57Bl/6 mice using quasi-static FE modelling.ResultsUnlike joints in non-OA prone CBA mice, Str/ort knees did not exhibit lateral femur (LF) lesions in response to applied loading; but exhibited thicker AC. FE modeling showed increased contact pressure and shear on the lateral femoral surface in loaded joints, and these diminished in joints containing thicker AC. Histological analysis of natural lesions in the tibia of Str/ort joints revealed that applied loading increased OA severity, proteoglycan loss and collagen type II degradation.ConclusionGenetic OA susceptibility in Str/ort mice is not apparently related to greater AC vulnerability to trauma, but joint loading modifies severity of natural OA lesions in the medial tibia. FE modelling suggests that thicker AC in Str/ort mice diminishes tissue stresses and protects against load-induced AC lesions in the LF but that this is unrelated to their genetic susceptibility to OA