Model analogies between pattern formation in deforming engineering materials & morphogenesis in ageing human brains

Abstract

Mathematical models developed within the material mechanics and material physics communities have been routinely adapted to interpret and further understand physiological and biological processes. The field of biomechanics, in particular, has emerged from a direct application of elasticity and fluid mechanics theories to model cell and tissue behavior, as well as bone fracture and blood flow. On the other hand, Turing’s reaction-diffusion model of morphogenesis for biochemical systems has been adapted to interpret pattern formation in deforming materials. An important aspect, however, that has not been sufficiently examined is to investigate the role of an externally applied or internally developed stress. Another, equally interesting issue that has not been adequately explored, concerns the development of a common effective methodology to analyze signals and images for both humanmade and naturemade systems, especially when differential equations are not available to use for this purpose. The article is an initial modest effort to discuss such common features between nonliving and living materials. It focuses, in particular, to modeling analogies between pattern formation of defects in deforming engineering materials under application of external stress and morphogenesis of cellular structures in ageing brain tissue under development of internal stress.

Keywords

• pattern formation/morphogenesis
• nanomaterials/brain
• alzheimer