A simple mechanistic model of sprout spacing in tumour-associated angiogenesis

Addison-Smith, Beth; McElwain, D. L. S.; Maini, Philip K.

doi:10.1016/j.jtbi.2007.08.030

Cited by 23 publications

(22 citation statements)

References 26 publications

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“…Addison-Smith et al [3] focus on a different issue related to tumour-induced angiogenesis, namely the mechanisms of sprout formation. In the previous models, the initial site of the sprout on the existing capillary was either given a priori or determined stochastically.…”

Section: Cell-based Models Of Angiogenesismentioning

confidence: 99%

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A review of mathematical models for the formation of vascular networks

Scianna

Bell

Preziosi

2013

Journal of Theoretical Biology

151

139

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Two major mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former term describes the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter term describes the sprouting of new vessels from an existing capillary or post-capillary venule. Similar mechanisms are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis. A number of mathematical approaches have been used to analyze these phenomena. In this paper, we review the different types of models, with special emphasis on their ability to reproduce different biological systems and to predict measurable quantities which describe the overall processes. Finally, we highlight the advantages specific to each of the different modelling approaches.

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Section: Cell-based Models Of Angiogenesismentioning

confidence: 99%

“…In the previous models, the initial site of the sprout on the existing capillary was either given a priori or determined stochastically. In [3], the authors have developed instead a simple mathematical model to determine the probable locations of sprouts and the relative distance between them.…”

Section: Cell-based Models Of Angiogenesismentioning

confidence: 99%

A review of mathematical models for the formation of vascular networks

Scianna

Bell

Preziosi

2013

Journal of Theoretical Biology

151

139

View full text Add to dashboard Cite

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“…The flux of the EC is then assumed to be proportional to the tip flux, where the rate constant is the number of EC that makes up an average capillary tip. More recently, Schugart et al developed a seven species model of acute wound healing angiogenesis [25], using a similar approach to Gaffney et al [24] in their treatment of the EC flux, while Addison-Smith et al used a simple mechanistic model for the sprouting of vessels during tumour-induced angiogenesis [26]. Mantzaris et al provides an excellent review of continuum models of angiogenesis and concludes that continuum models are important for providing significant insight into the relative importance of different processes [27].…”

Section: Introductionmentioning

confidence: 99%

A Three Species Model to Simulate Application of Hyperbaric Oxygen Therapy to Chronic Wounds

et al. 2009

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Chronic wounds are a significant socioeconomic problem for governments worldwide. Approximately 15% of people who suffer from diabetes will experience a lower-limb ulcer at some stage of their lives, and 24% of these wounds will ultimately result in amputation of the lower limb. Hyperbaric Oxygen Therapy (HBOT) has been shown to aid the healing of chronic wounds; however, the causal reasons for the improved healing remain unclear and hence current HBOT protocols remain empirical. Here we develop a three-species mathematical model of wound healing that is used to simulate the application of hyperbaric oxygen therapy in the treatment of wounds. Based on our modelling, we predict that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds. Furthermore, treatment should continue until healing is complete, and HBOT will not stimulate healing under all circumstances, leading us to conclude that finding the right protocol for an individual patient is crucial if HBOT is to be effective. We provide constraints that depend on the model parameters for the range of HBOT protocols that will stimulate healing. More specifically, we predict that patients with a poor arterial supply of oxygen, high consumption of oxygen by the wound tissue, chronically hypoxic wounds, and/or a dysfunctional endothelial cell response to oxygen are at risk of nonresponsiveness to HBOT. The work of this paper can, in some way, highlight which patients are most likely to respond well to HBOT (for example, those with a good arterial supply), and thus has the potential to assist in improving both the success rate and hence the cost-effectiveness of this therapy.

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“…In the typical reaction-transport model of wound healing angiogenesis (see for example, Pettet et al, 1996a ; Schugart et al, 2008 ), new capillary tips ( n ) can develop from existing vessels ( b ), regulated by a chemical ( a ), modeled by a term such as λ ab . The budding of new capillaries from existing ones is known to be tightly spatially regulated (Asahara et al, 1998 ; Addison-Smith et al, 2008 ) and this needs to be taken into consideration in mathematical models of wound healing angiogenesis, especially in 2D or higher dimensions.…”

Section: Open Problemsmentioning

confidence: 99%

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

et al. 2015

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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.

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A simple mechanistic model of sprout spacing in tumour-associated angiogenesis

Cited by 23 publications

References 26 publications

A review of mathematical models for the formation of vascular networks

A review of mathematical models for the formation of vascular networks

A Three Species Model to Simulate Application of Hyperbaric Oxygen Therapy to Chronic Wounds

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

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