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On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process.

Flegg JA, Menon SN, Maini PK, McElwain DL - Front Physiol (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematical Sciences, Monash University Melbourne, VIC, Australia.

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.

No MeSH data available.


Related in: MedlinePlus

Timeline of major mathematical models of wound healing and of the process of angiogenesis. EC refers to endothelial cells and ECM to extracellular matrix.
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Figure 2: Timeline of major mathematical models of wound healing and of the process of angiogenesis. EC refers to endothelial cells and ECM to extracellular matrix.

Mentions: We now present an overview of a selection of mathematical models that have contributed to the literature on wound healing angiogenesis. These include some that are related to tumor-induced angiogenesis, and others that model the wound healing process without explicitly describing angiogenesis. Figure 2 shows a summary of some of the models discussed in this section, all of which have provided new perspectives on the process of modeling wound healing angiogenesis. While there have been many papers that have made important contributions to this field, it is beyond the scope of this paper to review them all in detail.


On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process.

Flegg JA, Menon SN, Maini PK, McElwain DL - Front Physiol (2015)

Timeline of major mathematical models of wound healing and of the process of angiogenesis. EC refers to endothelial cells and ECM to extracellular matrix.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4588694&req=5

Figure 2: Timeline of major mathematical models of wound healing and of the process of angiogenesis. EC refers to endothelial cells and ECM to extracellular matrix.
Mentions: We now present an overview of a selection of mathematical models that have contributed to the literature on wound healing angiogenesis. These include some that are related to tumor-induced angiogenesis, and others that model the wound healing process without explicitly describing angiogenesis. Figure 2 shows a summary of some of the models discussed in this section, all of which have provided new perspectives on the process of modeling wound healing angiogenesis. While there have been many papers that have made important contributions to this field, it is beyond the scope of this paper to review them all in detail.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematical Sciences, Monash University Melbourne, VIC, Australia.

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.

No MeSH data available.


Related in: MedlinePlus