Wound Healing: Multi-Scale Modeling - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 316

Wound Healing: Multi-Scale Modeling

Fred J. Vermolen and Amit Gefen

Abstract This chapter is meant as an overview of our already published work that
we carry out on modeling wound healing on the cellular, colony and tissue scale,
though we detail the description of some stochastic principles that appear in our
models. The relation between the scales is described in terms of the underlying
biological and mathematical concepts. We also present the implications and
applicability of the mathematical models studied.

1 Introduction

Wound healing is a very complicated process with the following partly overlap-
ping phases: inflammation—proliferation—remodeling. During the post-bleeding
inflammatory phase macrophages and white blood cells (leukocytes) enter the
wound site to clear up invading harmful agents and bacteria through the broken
network of capillaries. If a patient suffers from diabetes, then the capillary walls
are suffering from an increased stiffness by which they can break down, and extend
less due to a decreased flexibility, and thereby transport less blood containing
oxygen and indispensable nutrients. Co-agulation of blood occurs to shut-off the
wound. This is followed by angiogenesis, to restore the capillary network, dermal
regeneration,

which involves contraction due to traction forces exerted by

F. J. Vermolen ( & )
Delft Institute of Applied Mathematics, Delft University of Technology,
Mekelweg 4, 2628 Delft, The Netherlands
e-mail: [e-mail]
A. Gefen
Department of Biomedical Engineering, Tel Aviv University, Tel Aviv, Israel
e-mail: [e-mail]