Spatio-temporal structure of cell distribution in cortical Bone Multicellular Units: a mathematical model

TL;DR

This paper introduces a mathematical model that simulates the spatio-temporal dynamics of bone cell distribution within cortical Bone Multicellular Units, enhancing understanding of bone remodelling processes.

Contribution

It presents a novel continuum model integrating key biochemical pathways to reproduce and analyze the structured cell distribution in BMUs.

Findings

Model reproduces experimentally observed cell distributions.

Travelling-wave solutions correspond to BMU progression.

Model links spatial profiles to cellular differentiation and apoptosis rates.

Abstract

Bone remodelling maintains the functionality of skeletal tissue by locally coordinating bone-resorbing cells (osteoclasts) and bone-forming cells (osteoblasts) in the form of Bone Multicellular Units (BMUs). Understanding the emergence of such structured units out of the complex network of biochemical interactions between bone cells is essential to extend our fundamental knowledge of normal bone physiology and its disorders. To this end, we propose a spatio-temporal continuum model that integrates some of the most important interaction pathways currently known to exist between cells of the osteoblastic and osteoclastic lineage. This mathematical model allows us to test the significance and completeness of these pathways based on their ability to reproduce the spatio-temporal dynamics of individual BMUs. We show that under suitable conditions, the experimentally-observed structured cell distribution of cortical BMUs is retrieved. The proposed model admits travelling-wave-like solutions for the cell densities with tightly organised profiles, corresponding to the progression of a single remodelling BMU. The shapes of these spatial profiles within the travelling structure can be linked to the intrinsic parameters of the model such as differentiation and apoptosis rates for bone cells. In addition to the cell distribution, the spatial distribution of regulatory factors can also be calculated. This provides new insights on how different regulatory factors exert their action on bone cells leading to cellular spatial and temporal segregation, and functional coordination.