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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 2D wound domains. Left : Plan view of a rectangular wound that is parallel to the skin surface. Here x = −L1, x = L1, y = −L2, and y = L2 represent the four wound edges. Right: Side view of a rectangular wound that is perpendicular to the skin surface. Here x = −L1 and x = L1 represent the wound extent parallel to the surface, which is located at z = 0, and the wound depth is z = L3.
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Figure 1: Schematic of 2D wound domains. Left : Plan view of a rectangular wound that is parallel to the skin surface. Here x = −L1, x = L1, y = −L2, and y = L2 represent the four wound edges. Right: Side view of a rectangular wound that is perpendicular to the skin surface. Here x = −L1 and x = L1 represent the wound extent parallel to the surface, which is located at z = 0, and the wound depth is z = L3.

Mentions: In order to examine the role that the wound shape or surface extent plays in the healing process, two dimensional (2D) models are often employed. Models of this type could be used to describe wounds with a comparatively larger surface extent, for instance burn wounds, and provide a bird's eye view of the wound surface (Figure 1, left subplot). Examples of 2D models of wound healing angiogenesis include Machado et al., 2011 and Valero et al., 2012. Alternatively, 2D models may be used to describe angiogenesis in healing wounds that extend deep into the dermis, in which case they provide a cross section of wound depth vs. length (Figure 1, right subplot), as in the approaches adopted in Olsen et al. (1997) and Vermolen and Javierre (2011).


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 2D wound domains. Left : Plan view of a rectangular wound that is parallel to the skin surface. Here x = −L1, x = L1, y = −L2, and y = L2 represent the four wound edges. Right: Side view of a rectangular wound that is perpendicular to the skin surface. Here x = −L1 and x = L1 represent the wound extent parallel to the surface, which is located at z = 0, and the wound depth is z = L3.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 1: Schematic of 2D wound domains. Left : Plan view of a rectangular wound that is parallel to the skin surface. Here x = −L1, x = L1, y = −L2, and y = L2 represent the four wound edges. Right: Side view of a rectangular wound that is perpendicular to the skin surface. Here x = −L1 and x = L1 represent the wound extent parallel to the surface, which is located at z = 0, and the wound depth is z = L3.
Mentions: In order to examine the role that the wound shape or surface extent plays in the healing process, two dimensional (2D) models are often employed. Models of this type could be used to describe wounds with a comparatively larger surface extent, for instance burn wounds, and provide a bird's eye view of the wound surface (Figure 1, left subplot). Examples of 2D models of wound healing angiogenesis include Machado et al., 2011 and Valero et al., 2012. Alternatively, 2D models may be used to describe angiogenesis in healing wounds that extend deep into the dermis, in which case they provide a cross section of wound depth vs. length (Figure 1, right subplot), as in the approaches adopted in Olsen et al. (1997) and Vermolen and Javierre (2011).

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