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

Apostolos C Tsolakis,George Petsos,Olga Kapetanou,Elias C Aifantis,Ioannis N Nikolaidis

doi:10.1515/jmbm-2019-0012

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

Apostolos C Tsolakis, George Petsos + Show 3 more

Open Access

https://doi.org/10.1515/jmbm-2019-0012

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Abstract

AbstractMathematical 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.

Highlights

Mathematical models developed within the material mechanics and material physics communities have been routinely adapted to interpret and further understand physiological and biological processes
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
A new continuum mechanics framework that has been formulated for modeling material behavior across the scale spectrum is Aifantis gradient theory for deformation and diffusion processes in the presence of evolving micro/nano structures [1–5]

Summary

Introduction

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 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. A new continuum mechanics framework that has been formulated for modeling material behavior across the scale spectrum is Aifantis gradient theory for deformation and diffusion processes in the presence of evolving micro/nano structures [1–5]. It is based on the introduction of extra Laplacian terms in the classical constitutive equations (e.g. Hooke’s and Fick’s laws) to incorporate nonlocality and deterministic scale effects.

Pattern formation of material defects during deformation

Self-organization of brain cells during neurodegeneration