A Computational Analysis of Bone Formation in the Cranial Vault Using a Coupled Reaction–diffusion-Strain Model

Abstract

Bones of the murine cranial vault are formed by differentiation of mesenchymal cells into osteoblasts, a process that is primarily understood to be controlled by a cascade of reactions between extracellular molecules and cells. We assume that the process can be modeled using Turing’s reaction-diffusion equations, a mathematical model describing the pattern formation controlled by two interacting molecules (activator and inhibitor). In addition to the processes modeled by reaction-diffusion equations, we hypothesize that mechanical stimuli of the cells due to growth of the underlying brain contribute significantly to the process of cell differentiation in cranial vault development. Structural analysis of the surface of the brain was conducted to explore the effects of the mechanical strain on bone formation. We propose a mechanobiological model for the formation of cranial vault bones by coupling the reaction-diffusion model with structural mechanics. 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 provide precise three dimensional (3D) measures of murine 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 including the relative location of ossification centers of individual vault bones, the pattern of cranial vault bone growth over time, and the position of cranial vault sutures.

Midface and upper airway dysgenesis in FGFR2-craniosynostosis involves multiple tissue-specific and cell cycle effects

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Craniofacial skeletal response to encephalization: How do we know what we think we know?

“…While the number of experiments one can conduct with animal models is limited, computational modeling provides infinite ways to explore the role of biomechanics of brain growth in the differentiation of cells destined to form cranial vault bones and the sutures that form between them. Lee and coworkers proposed a mechanobiological model for the formation of cranial vault bones and sutures, coupling structural mechanics of changing embryonic brain morphology with reaction–diffusion equations (Turing, 1952) that describe the interaction of two molecules (an activator and an inhibitor) supervising the differentiation of osteoblasts (Lee, 2018; Lee, Richtsmeier, & Kraft, 2017). The mechanobiological model predicts some key features of cranial vault bone formation, including the relative location of ossification centers of the individual vault bones, the pattern of cranial vault bone growth over time, and the location of cranial vault sutures (Lee, 2018).…”

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