Abstract
Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.
Highlights
The process of successful skin wound healing involves highly complex coordinated interactions of many different cell types, tissues and biochemical mediators (Martin, 1997)
We present an overview of a selection of mathematical models that have contributed to the literature on wound healing angiogenesis
Over the last 30 years, considerable effort has gone into developing mathematical models of the wound healing process
Summary
The process of successful skin wound healing involves highly complex coordinated interactions of many different cell types, tissues and biochemical mediators (Martin, 1997). The development of theoretical models that describe the components of wound repair, together with their synergistic or antagonistic interactions, can provide a means to identify elements of the process that can be manipulated in a rational, mechanism-based strategy for improved clinical management Such models can give insight into the relative importance of the interlinked, underlying processes, aiding in the enhancement of treatment methodologies (McDougall et al, 2006). To our knowledge, there are no published reviews on the seminal continuum models that describe wound healing angiogenesis as a reaction-transport mechanism In this pedagogical review, we detail the mathematical principles involved in developing such models, in a way accessible to researchers who are unfamiliar with these techniques. Further progress can be made in the areas of discrete, hybrid and multiphase modeling of wound healing angiogenesis by drawing on the existing literature for tumor-induced angiogenesis
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