Modelling the Impact of Pericyte Migration and Coverage of Vessels on the Efficacy of Vascular Disrupting Agents

Abstract

Abstract. Over the past decade or so, there have been a large number of modelling approaches aimed at elucidating the most important mechanisms affecting the formation of new capillaries from parent blood vessels -a process known as angiogenesis. Most studies have focussed upon the way in which capillary sprouts are initiated and migrate in response to diffusible chemical stimuli supplied by hypoxic stromal cells and leukocytes in the contexts of solid tumour growth and wound healing. However, relatively few studies have examined the important role played by blood perfusion during angiogenesis and fewer still have explored the ways in which a dynamically evolving vascular bed architecture can affect the distribution of flow within it. From the perspective of solid tumour growth and, perhaps more importantly, its treatment (e.g. chemotherapy), it would clearly be of some benefit to understand this coupling between vascular structure and perfusion more fully. This paper focuses on the implications of such a coupling upon chemotherapeutic, anti-angiogenic, and anti-vascular treatments.In an extension to previous work by the authors, the issue of pericyte recruitment during vessel maturation is considered in order to study the effects of different anti-vascular and anti-angiogenic therapies from a more rigorous modelling standpoint. Pericytes are a prime target for new vascular disrupting agents (VDAs) currently in clinical trials. However, different compounds attack different components of the vascular network and the implications of targeting only certain elements of the capillary bed are not immediately clear. In light of these uncertainties, the effects of anti-angiogenic and anti-vascular drugs are re-examined by using an extended model that includes an interdependency between vessel remodelling potential and local pericyte density. Two-and three-dimensional simulation results are presented and suggest that it may be possible to identify a VDA-specific "plasticity window" (a time period corresponding to low pericyte density), within * Corresponding author. E-mail: chaplain@maths.dundee.ac. Impact of pericytes on blood vessel Networks which a given VDA would be most effective.

On the importance of the submicrovascular network in a computational model of tumour growth

“…The interested reader is referred to this study for details. This function has been extensively used in mathematical models and is also detailed in the following contributions (Alarcòn et al, 2003;McDougall et al, 2006McDougall et al, , 2010Owen et al, 2009;Stéphanou et al, 2006;Wu et al, 2009). …”

“…The matrix is degraded by the enzyme with rate γ. The enzyme diffuses in the tissue with diffusion coefficient D and decays with rate ν (details on this model can be found in Stéphanou et al (2006) and McDougall et al (2010)). The initial distribution of matrix fibres forming the tissue, that is before angiogenesis starts, is assumed to be homogeneous with concentration value f(x, y, 0) = f 0 .…”

A Computational Framework to Assess the Efficacy of Cytotoxic Molecules and Vascular Disrupting Agents against Solid Tumours

“…5). We note that this model of vascular tumour growth and adaptation to rheological constraints was subsequently developed in the following contributions [23,21,24].…”

“…The current models are able to describe the tumour evolution from avascular to vascular growth. They integrate blood flow and vascular adaptation due to rheological constraints [1,41,23,24]. They integrate vascular remodelling in connection with the tumour mass evolution and allow to take into account the effects of treatment [14].…”

Biology is the new physics

“…“This began with a paper in 1998 featuring a mathematical modelling technique to capture the growth of new blood‐vessels,” he said (Anderson & Chaplain, 1998). Since then, the field has advanced in various ways to model changes in the dynamics of the blood system as the tumour grows, and to include delivery of drugs in the models (McDougall et al , 2010).…”