On the dynamics of the growth plate in primary ossification

Abstract

In this work a mathematical model for the interaction of two key signalling molecules in rat tibia ossification is presented and discussed. The molecules under consideration are Indian hedgehog (Ihh) and parathyroid hormone-related peptide (PTHrP). These are known to be major agents in the dynamics of the so-called Growth Plate, where transition from pristine cartilage to advancing bone takes place. Our model consists in a steady-state linear approximation to a Reaction-Diffusion system where only diffusion and absorption mechanisms are retained. Estimates on some system parameters are given, on the basis of the knowledge of a few measurable quantities. This allows for explicitly solving our model, whereupon a discussion on robustness and regulatory properties thereof is provided. In particular, we show that the size of the Proliferative Zone in the Growth Plate is rather insensitive to variations in the flux coefficients for Ihh and PTHrP at their boundaries. Besides, we also show that the model is also insensitive to large changes in the (comparatively small) critical value of the PTHrP concentration which marks the transition form Proliferative to Hyperthropic Regions within the Growth Plate. These results hold irrespective of the particular diffusivities selected for Ihh and PTHrP.

An Emerging Paradigm in Tissue Engineering: From Chemical Engineering to Developmental Engineering for Bioartificial Tissue Formation through a Series of Unit Operations that Simulate the In Vivo Successive Developmental Stages†

“…Such a model for the interaction of two key signaling molecules, Indian hedgehog (Ihh) and parathyroid hormone-related peptide (PTHrP), has been developed. 249 The model is a steady-state linear approximation to a reaction-diffusion system where only diffusion and absorption mechanisms are considered. The authors predicted the robustness of the growth plate.…”

“…Specifically, for our subject of growth plate control, mathematical models have also appeared in the literature and can be further developed and modified for the particular experimental settings. Such a model for the interaction of two key signaling molecules, Indian hedgehog (Ihh) and parathyroid hormone-related peptide (PTHrP), has been developed . The model is a steady-state linear approximation to a reaction-diffusion system where only diffusion and absorption mechanisms are considered.…”

The effect of electric fields on hyaline cartilage: an in vitro and in silico study

“…Endochondral ossification is a complex process that is regulated by specific molecules and mechanical stimuli such as tension, compression, shear and hydrostatic pressures [99]- [102], [105], [106].…”

“…For instance, the mathematical models implemented have simulated the effect of mechanical loading on the endochondral ossification, examining formation of the secondary center [113], [114], growth plate progression [115], and growth plate zone size [103], [104], and development of bone deformities [116]. Our group has previously used computational models based on the reaction-diffusion equations to explain how biochemical factors affect long bone formation, including the Ihh/PTHrP-negative loop and VEGF stimulator within the growth plate and bone rudiment [28], [105], [117], [118], the spongiosa primary development [104], [119], the growth pattern of the secondary ossification center [104], [117], [120], and the formation of cartilaginous canals in the epiphysis [121]. Previous mathematical models of endochondral ossification have studied the mechanical and biochemical factors involved in bone development separately.…”

Analysis of the biological implications of the mechanical environment within the growth plate during bone development in physiological and pathological scenarios

“…Poliferative-hypertrophy transitions have also been studied using in silico approaches through mathematical modelling. Such models describe endochondral ossification progress within growth plate, focusing on either ossification front advance as either a function of biochemical or mechanical parameters, or using a macroscopic point of view, that measure bone size as indicative of ossification process [280,282,284,287,[352][353][354]. However, most of the published works do not specify the effect of such parameters on cellular processes such as chondrocyte proliferation, and hypertrophy, as well as mineralization within the growth plate, limiting their capacity to analyze growth plate cellular behavior.…”