Generalised S-System-Type Equation: Sensitivity of the Deterministic and Stochastic Models for Bone Mechanotransduction

Abstract

The formalism of a bone cell population model is generalised to be of the form of an S-System. This is a system of nonlinear coupled ordinary differential equations (ODEs), each with the same structure: the change in a variable is equal to a difference in the product of a power-law functions with a specific variable. The variables are the densities of a variety of biological populations involved in bone remodelling. They will be specified concretely in the cases of a specific periodically forced system to describe the osteocyte mechanotransduction activities. Previously, such models have only been deterministically simulated causing the populations to form a continuum. Thus, very little is known about how sensitive the model of mechanotransduction is to perturbations in parameters and noise. Here, we revisit this assumption using a Stochastic Simulation Algorithm (SSA), which allows us to directly simulate the discrete nature of the problem and encapsulate the noisy features of individual cell division and death. Critically, these stochastic features are able to cause unforeseen dynamics in the system, as well as completely change the viable parameter region, which produces biologically realistic results.

Keywords

• mathematical model of osteocyte mechanobiology
• external periodic excitation
• mechanotransduction
• bone remodelling
• population model
• autocrine/paracrine signalling