On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process.
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.
School of Mathematical Sciences, Monash University Melbourne, VIC, Australia.
Jennifer A
JA
Flegg
The Institute of Mathematical Sciences Chennai, India.
Shakti N
SN
Menon
Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford Oxford, UK.
Philip K
PK
Maini
Institute of Health and Biomedical Innovation and School of Mathematical Sciences, Queensland University of Technology Brisbane, QLD, Australia.
D L Sean
DL
McElwain
mathematical biology; mathematical modeling; reaction-diffusion systems; skin wounds; wound healing