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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

Illustration of the angiogenesis process at a discrete cell level, modified from Cotran et al. (1999).
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Figure 5: Illustration of the angiogenesis process at a discrete cell level, modified from Cotran et al. (1999).

Mentions: Historically, progress in the mathematical modeling of wound healing angiogenesis has been made by drawing on work done in the mathematical modeling of tumor-induced angiogenesis. There remain numerous insights and techniques from the tumor literature that could be utilized to develop better models of wound healing angiogenesis. To date, while there has only been a single model of wound healing angiogenesis that treats cells as discrete, i.e., Machado et al., 2011 where ECs are governed by a random walk, there have been a variety of models have been published on multi-scale models of tumor angiogenesis, investigating important aspects of vessel rheology, diameter, and adaption (Alarcón et al., 2005, 2006b; Owen et al., 2009). Indeed, the decisions of individual cells play an important role in wound healing angiogenesis: the basement membrane that surrounds the blood vessels must be degraded to allow ECs to migrate through the walls of the parent vessel (Figure 5).


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)

Illustration of the angiogenesis process at a discrete cell level, modified from Cotran et al. (1999).
© Copyright Policy
Related In: Results  -  Collection

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

Figure 5: Illustration of the angiogenesis process at a discrete cell level, modified from Cotran et al. (1999).
Mentions: Historically, progress in the mathematical modeling of wound healing angiogenesis has been made by drawing on work done in the mathematical modeling of tumor-induced angiogenesis. There remain numerous insights and techniques from the tumor literature that could be utilized to develop better models of wound healing angiogenesis. To date, while there has only been a single model of wound healing angiogenesis that treats cells as discrete, i.e., Machado et al., 2011 where ECs are governed by a random walk, there have been a variety of models have been published on multi-scale models of tumor angiogenesis, investigating important aspects of vessel rheology, diameter, and adaption (Alarcón et al., 2005, 2006b; Owen et al., 2009). Indeed, the decisions of individual cells play an important role in wound healing angiogenesis: the basement membrane that surrounds the blood vessels must be degraded to allow ECs to migrate through the walls of the parent vessel (Figure 5).

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