Computational morphogenesis of embryonic bone development: past, present, and future

Mesenchymal stem cell differentiation into osteoblasts is an important developmental process in the production of embryonic bone. Recent research in the field of mechanobiology suggests that cell differentiation, bone formation, and bone remodeling are dependent on mechanical stimuli. Reaction-diffusion systems are frequently used in the field of theoretic biology to computationally predict embryonic bone growth. Patterning in a reaction-diffusion system results from the activation and inhibition of chemical morphogens. We theorize by way of new findings and results that some growth solutions predicted using reaction-diffusion systems are dependent on domain mesh, domain geometry, and initial concentration. These findings complicate solution reproducibility within the computational biology community and limit the advancement of reaction-diffusion models. Mesh-dependent reaction-diffusion growth solutions share a unique similarity to phenotypic variation and individual variation. We propose a reaction-diffusion system with imbedded mechanical strain for predicting embryonic development of the cranial vault. Tensile strain on the developing cranial vault results from the rapid growth of the underlying brain. The model, which is solved using the finite volume method, was used to predict cranial growth in Mus musculus, the most commonly used experimental animal model. The predicted cranial morphology aligns well with in vivo mouse cranial morphology. Growth predictions were validated by linking model parameters to genetic mutations and replicating the resulting developmental abnormalities in the cranial vault.