Computer modeling of bone's adaptation: the role of normal and shear strains, fluid shear and strain gradients

Abstract

Bone loss is a serious health problem which occurs due to metabolic bone disorders such as osteoporosis or bone/muscle disuse. Bone loss can be noticed in postmenopausal women, bedridden patients and physically challenged individuals, and in astronauts under microgravity environments. This reduces the weight bearing capacity of long bones, and hence promotes bone fracture risks. Several pharmaceutical drugs such as bisphosphonates are available to prevent or inhibit the bone loss; however, their usage over a longer period of time is not recommendable as it may adversely affect the bone remodeling activities. Alternatively, in vivo studies have shown that low-amplitude and cyclic mechanical loading prevents bone loss as loading-induced mechanical environment promotes bone modeling (i.e. new bone formation) at the sites of elevated normal strain magnitude. Thus, normal strain is believed to be the primary stimulus of osteogenesis. However, there are several in vivo studies in the literature where bone formation occurred at sites of minimal normal strain especially near the neutral axis of bending in long bones. Accordingly, most of the in silico studies in the literature assumed normal strain or strain energy density (SED) as a stimulus of osteogenesis, hence, had limited success in modeling osteogenesis at locations of minimal normal strain. Therefore, these computational models fall short in establishing a perfect relationship between mechanical stimulus and site specificity of new bone formation, and thus there is no unifying principle to relate bone modeling to mechanical environment, till present. A few studies have indicated that other/secondary components of mechanical environment such as bending-induced shear strain, canalicular fluid flow and strain gradients may be potential stimuli of osteogenesis near the minimal strain sites; however, their exact role has not been well established. This thesis aims to investigate and establish the role of known mechanical components/stimuli such as normal strain, solid shear strain, canalicular fluid flow and strain gradients in site-specific bone modeling (i.e. new bone formation) using in silico investigations. A computer model of bone adaptation has been developed based on previously reported bone modeling algorithms. The model simulates osteogenesis as a function of mechanical stimuli individually or in their combinations. The model specifically predicts sitespecific new bone distribution for in vivo loading studies carried out in murine models. Based on comparison with experimental data, this work explains osteogenic potential of each mechanical stimulus. The results indicate that normal strain has not adequately explained the new bone formation near sites of minimal normal strain or around the neutral axis; whereas, solid shear strain, canalicular fluid flow and strain gradients predict osteogenesis near the neutral axis. It has also been noticed that various mechanical stimuli act collectively in bone adaptation as the model closely fitted site-specific new bone formation for several in vivo cases when combined osteogenic effects of normal strain with either solid shear strain or fluid shear were considered. It affirms the fact that two or more mechanical stimuli are needed in a computer model for accurate prediction of loading-induced osteogenesis. Nevertheless, solid shear strain consideration may fail to fit new bone formation for four point bending in vivo studies due to absence of shear force, whereas fluid flow estimation requires accurate measurement of permeability constants and poroelastic material properties. This may limit incorporation of solid shear strain and fluid shear as stimuli in computer models. In view of that, this work also investigates the role of strain gradients in new bone formation. The results from this study suggest that strain gradients in circumferential or bone-surface-tangent directions correlate with osteogenesis at the sites of minimal normal strain, whereas gradients in radial or surface-normal directions correlate with osteogenesis at sites of elevated normal strain magnitude. Accordingly, this work proposes a computer model which considers strain gradients as stimuli of osteogenesis to predict loading-induced site-specific new bone formation. This model also incorporates a newly developed relationship between loading parameters such as frequency and cycles, and a bone remodeling parameter, i.e. mineral apposition rate (MAR). The model has been tested and has been found precise in prediction of new bone distribution for an in vivo study. These findings of in silico studies on the relationships between mechanical environment and new bone formation may be further utilized to enhance the osteogenic potential of loading parameters. This will ultimately help in development or improvement of biomechanical interventions such as physical exercises to prevent or cure bone loss. Thus, the research work presented in this thesis has potential applications in clinical orthopedics and associated research fields that focus on bone health improvements.