Predicting Cortical Bone Resorption in Disuse Condition Caused by Transient Muscle Paralysis

Abstract

Load removal from the load-bearing bone, such as in the case of extended space travel and prolonged bed rest, harms bone health and leads to severe bone loss. However, the constitutive idea relating the quantity of bone loss to the absence of physiological loading is poorly understood. This work attempts to develop a mathematical model that predicts cortical bone loss at three sections: ‘distal’, ‘mid-section’, and ‘proximal’ along the length of a mouse tibia. Load-induced interstitial fluid flow-based dissipation energy density has been adopted as a stimulus to trigger mechanotransduction. The developed model takes the loss of stimulus due to the disuse of bone as an input and predicts the quantity of bone loss with spatial accuracy.In the loaded bone, the fluid velocity is found to be maximum at the endocortical surface and negligible at the periosteal surface due to the permeable and impermeable boundary conditions, respectively, at the two surfaces. In case of disuse of bone, there is no fluid flow, which leads to a more significant loss of fluid flow at the endocortical surface. This loss of fluid flow coincides with the botulinum toxin (Botox)-induced endocortical bone loss data in the literature. Motivated by this fact, we hypothesized that the bone loss site would be the site of maximum stimulus loss due to disuse.To test the hypothesis, we calculated stimulus loss, i.e., loss of dissipation energy density due to bone disuse, based on the poroelastic analysis of the bone using a finite element method. A novel mathematical model has been then developed that successfully relates this loss of stimulus to the in-vivo bone loss data in the literature. According to the developed model, the site-specific mineral rate is found to be proportional to the square root of the loss of dissipation energy density. To the author’s best knowledge, this model is the first of its kind to compute site-specific bone loss. The developed model can be extended to predict bone loss due to other disuse conditions such as long space travel, prolonged bed rest, etc.