Reduced-Order Network Models for Biological Scaffolding - Multiscale Modeling in Biomechanics and Mechanobiology - page 106

Chapter 6
Reduced-Order Network Models for Biological
Scaffolding

T.I. Zohdi

6.1 Introduction

Many types of biological soft tissues possess a microstructure comprised of embedded
fibers which, collectively, are load bearing components. A direct simulation of a
continuum model, with a detailed discretization and meshing, for example, using the
Finite Element method, of the fibrous microstructure, would result in literally billions
of numerical degrees of freedom. Furthermore, incorporating damage and rupture
effects at finite strains make such problem difficult for “everyday” use by researchers
in biomechanics, which motivates so-called “reduced-order” models. In this work,
we present a framework for reduced-order models for fiber-laden tissue, that is rel-
atively simple and robust, and which can be implemented with minimal effort by
researchers in the biomechanics community. The advantages of reduced-order fiber
network models are

• the simplicity of the constitutive laws at the fiber level, for example one-dimensional

Fung material laws,

• the ability to easily incorporate effects such as fiber damage and fracture and

•

the amenability of the model to extremely rapid numerical simulation,

The presentation is purposely made to be as transparent and simple as possible.