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Equation-Based Models of Wound Healing and Collective Cell Migration

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Complex Systems and Computational Biology Approaches to Acute Inflammation

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Abstract

Wound healing is a complex process of repair of disrupted connectivity and functionality of a tissue caused by an injury. A wound is considered healed once tissue functionality is restored, often requiring the migration of cells into the wounded region and the proliferation of new cells to re-establish the original density of the tissue. Observations from multiple experimental and clinical wound scenarios have shown that cell migration, proliferation, and overall wound healing time are affected by factors such as wound geometry, tissue type, and cell–cell interactions. Various mathematical models of the mechanisms governing wound healing have been developed to quantify and analyze the effects of these factors on cell migration and proliferation. In this chapter, we review wound healing models based on mathematical equations, including ordinary differential equations and partial differential equations. While these various types of models differ in scope and applicability, the mechanical and mathematical principles underlying all of the models are related and can be used to accomplish three main objectives: to track the cell response and position following the induction of a wound, to understand the role of tissue growth factors in the healing process, and to predict the time required for a wound to heal.

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Abbreviations

ABM:

Agent-based model

ECM:

Extracellular matrix

EGF:

Epidermal growth factor

FGF:

Fibroblast growth factor

GGH:

Glazier–Graner–Hogeweg

IEC-6:

Rat small intestine epithelial cell

KGF:

Keratinocyte growth factor

MAPK:

Mitogen-activated protein kinase

MDCK:

Madin–Darby canine kidney

ODE:

Ordinary differential equation

PDE:

Partial differential equation

ROS:

Reactive oxygen species

TGF:

Transforming growth factor

VEGF:

Vascular endothelial growth factor

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, IN, USA

    Julia Arciero

  2. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA

    David Swigon

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  1. Julia Arciero
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  2. David Swigon
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Correspondence to David Swigon .

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Editors and Affiliations

  1. Department of Surgery, University of Pittsburgh, Pittsburgh, PA, USA

    Yoram Vodovotz

  2. Department of Surgery, University of Vermont, Burlington, VT, USA

    Gary An

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Arciero, J., Swigon, D. (2021). Equation-Based Models of Wound Healing and Collective Cell Migration. In: Vodovotz, Y., An, G. (eds) Complex Systems and Computational Biology Approaches to Acute Inflammation. Springer, Cham. https://doi.org/10.1007/978-3-030-56510-7_11

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