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**Mathematical modelling of flow in 2D and 3D vascular networks: Applications to anti-angiogenic and chemotherapeutic drug strategies.**
*(English)*
Zbl 1080.92050

Summary: The aim of this paper is to investigate the conditions required to optimize the amount of chemotherapeutic drug absorbed by a solid tumour through a network of blood vessels. This work is based on a study of vascular networks generated from a discrete mathematical model of tumour angiogenesis, which describes the formation of a capillary network in response to chemical stimuli released by a solid tumour. Simulations of blood flow in the vasculature connecting the parent vessel to the solid tumour are then performed by adapting modelling techniques from the field of petroleum engineering to this biomedical application.

We begin with a qualitative, comparative study relating to the efficiency of drug delivery in 2D and 3D tumour-induced vasculatures and evaluate the influence of key parameters (mean capillary radius, blood viscosity and delivery regime) upon uptake by the tumour. We then go on to examine the impact of the vascular architecture upon nutrient (e.g., oxygen) and drug delivery by comparing the efficiency of three vasculatures characterized by different spatial distributions of branching order and anastomosis density (i.e., the number of fused loops or connections). We identify the main criteria required of a tumour-induced vascular network for optimized delivery of nutrients and/or cytotoxic agents.

We conclude by focusing on a particular vascular network and investigate how “capillary pruning” (i.e., network re-modelling) modifies the network connectivity and associated blood flow distribution. We demonstrate how random removal of vessels may lead to a significant increase in the amount of drug delivered to the tumour. Selective removal of vessels characterized by low flow is seen to speed up delivery, whilst the targeting of high flow capillaries leads to a rapid shut down of the entire capillary bed. These results allow us to propose the possibility of optimized cancer treatment therapies, based upon a coupled anti-angiogenic/chemotherapy strategy. The anti-angiogenesis treatment would be used to optimize network efficiency, thereby maximizing drug uptake during subsequent chemotherapy treatments.

We begin with a qualitative, comparative study relating to the efficiency of drug delivery in 2D and 3D tumour-induced vasculatures and evaluate the influence of key parameters (mean capillary radius, blood viscosity and delivery regime) upon uptake by the tumour. We then go on to examine the impact of the vascular architecture upon nutrient (e.g., oxygen) and drug delivery by comparing the efficiency of three vasculatures characterized by different spatial distributions of branching order and anastomosis density (i.e., the number of fused loops or connections). We identify the main criteria required of a tumour-induced vascular network for optimized delivery of nutrients and/or cytotoxic agents.

We conclude by focusing on a particular vascular network and investigate how “capillary pruning” (i.e., network re-modelling) modifies the network connectivity and associated blood flow distribution. We demonstrate how random removal of vessels may lead to a significant increase in the amount of drug delivered to the tumour. Selective removal of vessels characterized by low flow is seen to speed up delivery, whilst the targeting of high flow capillaries leads to a rapid shut down of the entire capillary bed. These results allow us to propose the possibility of optimized cancer treatment therapies, based upon a coupled anti-angiogenic/chemotherapy strategy. The anti-angiogenesis treatment would be used to optimize network efficiency, thereby maximizing drug uptake during subsequent chemotherapy treatments.

### MSC:

92C50 | Medical applications (general) |

92C35 | Physiological flow |

35Q92 | PDEs in connection with biology, chemistry and other natural sciences |

### Keywords:

Angiogenesis; Vascular networks; Flow distribution; Branching coefficients; Chemotherapy treatments; Capillary blood flow
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\textit{A. Stéphanou} et al., Math. Comput. Modelling 41, No. 10, 1137--1156 (2005; Zbl 1080.92050)

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