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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

Numerical simulation of the 6-species Pettet et al. model, showing the spatial distribution of the species within the wound at a certain time for a given set of parameter values. The wound healing unit moves through the wound space, from wound edge to wound center.
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Figure 3: Numerical simulation of the 6-species Pettet et al. model, showing the spatial distribution of the species within the wound at a certain time for a given set of parameter values. The wound healing unit moves through the wound space, from wound edge to wound center.

Mentions: This 6-species angiogenesis model made several important contributions to the literature: many of the important interactions of chemical and cell species were modeled for the first time, including oxygen mediation of chemoattractant production, oxygen-dependent fibroblast proliferation and ECM dependent tip movement. Moreover, clinical insight was gained by numerical simulations that illustrate both healing and stalled wound situations, for distinct sets of parameter values. The model successfully captured the propagation of a wound healing unit through the wound space and an elevated blood vessel density prior to vascular remodeling (Figure 3), both of which are observed experimentally. In this model, chemoattractant is produced in regions where the oxygen concentration is known to promote the release of pro-angiogenic factors (between a lower and upper threshold of the oxygen concentration). The chemoattractant then attracts fibroblasts to migrate into the wound space, laying down ECM as they move. This newly-laid ECM allows capillary tips to migrate further into the wound, toward the high level of chemoattractant. As they move, these capillary tips lay down capillary sprouts according to the snail-trail model. This laying down of sprouts in turn allows more oxygen to be supplied to the wound, which subsequently moves the wound healing unit further into the wound space. As the wound healing unit moves through the wound, the capillary tips behind the wound healing unit are lost due to anastomosis (see Figure 3).


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)

Numerical simulation of the 6-species Pettet et al. model, showing the spatial distribution of the species within the wound at a certain time for a given set of parameter values. The wound healing unit moves through the wound space, from wound edge to wound center.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 3: Numerical simulation of the 6-species Pettet et al. model, showing the spatial distribution of the species within the wound at a certain time for a given set of parameter values. The wound healing unit moves through the wound space, from wound edge to wound center.
Mentions: This 6-species angiogenesis model made several important contributions to the literature: many of the important interactions of chemical and cell species were modeled for the first time, including oxygen mediation of chemoattractant production, oxygen-dependent fibroblast proliferation and ECM dependent tip movement. Moreover, clinical insight was gained by numerical simulations that illustrate both healing and stalled wound situations, for distinct sets of parameter values. The model successfully captured the propagation of a wound healing unit through the wound space and an elevated blood vessel density prior to vascular remodeling (Figure 3), both of which are observed experimentally. In this model, chemoattractant is produced in regions where the oxygen concentration is known to promote the release of pro-angiogenic factors (between a lower and upper threshold of the oxygen concentration). The chemoattractant then attracts fibroblasts to migrate into the wound space, laying down ECM as they move. This newly-laid ECM allows capillary tips to migrate further into the wound, toward the high level of chemoattractant. As they move, these capillary tips lay down capillary sprouts according to the snail-trail model. This laying down of sprouts in turn allows more oxygen to be supplied to the wound, which subsequently moves the wound healing unit further into the wound space. As the wound healing unit moves through the wound, the capillary tips behind the wound healing unit are lost due to anastomosis (see Figure 3).

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