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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

Schematic of capillary network formation. Sprouts branch and join to form a closed network of capillaries, modified from Gaffney et al. (2002).
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Figure 4: Schematic of capillary network formation. Sprouts branch and join to form a closed network of capillaries, modified from Gaffney et al. (2002).

Mentions: The formation of a capillary network in a healing wound occurs by capillary tip extension from a parent vessel, maturation of capillary tips into capillary sprouts, anastomosis of sprouts to sprouts and sprouts to tips and further branching (Figure 4). The process of anastomosis in wound healing angiogenesis reaction-transport models is typically modeled with very simple terms, such as λnb for when a capillary tip (n) meets a vessel (b) or λn2 when two tips meet, where λ is a positive constant. This approach is overly simplified as it does not include any mechanism by which the two tips, or the tip and vessel, seek each other out and eventually meet. It is difficult to generate new insights on anastomosis from such a model. A complication in extending current models to higher dimensions is that, while a capillary tip and vessel will almost always meet in 2D, in 3D they will almost never meet.


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)

Schematic of capillary network formation. Sprouts branch and join to form a closed network of capillaries, modified from Gaffney et al. (2002).
© Copyright Policy
Related In: Results  -  Collection

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

Figure 4: Schematic of capillary network formation. Sprouts branch and join to form a closed network of capillaries, modified from Gaffney et al. (2002).
Mentions: The formation of a capillary network in a healing wound occurs by capillary tip extension from a parent vessel, maturation of capillary tips into capillary sprouts, anastomosis of sprouts to sprouts and sprouts to tips and further branching (Figure 4). The process of anastomosis in wound healing angiogenesis reaction-transport models is typically modeled with very simple terms, such as λnb for when a capillary tip (n) meets a vessel (b) or λn2 when two tips meet, where λ is a positive constant. This approach is overly simplified as it does not include any mechanism by which the two tips, or the tip and vessel, seek each other out and eventually meet. It is difficult to generate new insights on anastomosis from such a model. A complication in extending current models to higher dimensions is that, while a capillary tip and vessel will almost always meet in 2D, in 3D they will almost never meet.

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