Exploring Mechanisms of Cranial Vault Development using a Coupled Turing‐Biomechanical Model

Abstract

Bones of the mouse cranial vault are formed by differentiation of mesenchymal cells into osteoblasts, a process called intramembranous ossification that is primarily thought to be controlled by a cascade of reactions between extracellular molecules and cells that may be significantly guided by mechanical forces. In this study, we use a computational approach and an extensive experimental database to elucidate the role of biomechanics in morphogenesis of the cranial vault. We assume that the biochemical process can be modeled using Turing's reaction-diffusion model, a mathematical model describing the pattern formation controlled by interacting molecules (activators and inhibitors). In addition, we hypothesize that mechanical stimuli of the cells due to growth of the underlying brain contributes significantly to the process of cell differentiation. We have developed a coupled framework that incorporates these modeling constructs. The mathematical formulation was solved using the finite volume method. The computational domain and model parameters are determined using a large collection of experimental data that provides precise three-dimensional measures of mouse cranial geometry and cranial vault bone formation for specific embryonic time points. The results of this study suggest that mechanical strain contributes information to specific aspects of bone formation. Our mechanobiological model predicts some key features of cranial vault bone formation that were verified by experimental observations in normal case, including the relative location of ossification centers of the individual vault bones, the pattern of cranial vault bone growth over time, and the position of cranial vault sutures. Support or Funding Information Computations for this research were performed on the Pennsylvania State University's Institute for Cyber Science Advanced Cyber Infrastructure (ICS-ACI). This work was supported in part through instrumentation funded by a National Science Foundation grant OCI0821527, a Burroughs-Wellcome Fund 2013 Collaborative Research Travel Grant, Pennsylvania Department of Health using Tobacco Cure Funds, and by the National Institutes of Health grants R01DE022988 and P01HD078233. The model predicts the pattern of cranial vault bone growth. a) Computational prediction of the distribution of differentiating osteoblasts and cranial vault bone formation by embryonic day. b) Observed cranial vault bone formation and growth in embryonic mice. This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.