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Simulation of 3D Solid Tumour Angiogenesis Including Arteriole, Capillary and Venule

Jie Wu∗,†, Quan Long, Shixiong Xu*, Anwar R. Padhani§, Yuping Jiang
Department of Mechanics and Engineering Science, Fudan University, Shanghai, China
Brunel Institute for Bioengineering, Brunel University, Uxbridge, Middlesex, UK
Corresponding Author. Brunel Institute for Bioengineering, Brunel University, Uxbridge, Middlese, UB8 3PH, UK. Email:
§ Paul Strickland Scanner Centre, Mount Vernon Hospital, Northwood, Middlesex, UK
Department of neurology, Huashan hospital, Fudan University, Shanghai, China

Molecular & Cellular Biomechanics 2008, 5(4), 217-228.


In this paper, a 3D mathematical model of tumour angiogenesis is developed, to generate a functional tumour vasculature for blood microcirculation. The model follows that of Anderson and Chaplain (1998) [1] with three exceptions: (a) extending the model from 2D to 3D, one arteriole and one venule is induced as two parent vessels to form an intact circulation network for blood flow; (b) generating networks able to penetrate into the tumour interior rather than the exterior only; (c) considering branching generations with different diameters, based on which three groups of vessels, such as arterioles, venules and capillaries are classified. The present study contains four steps: 1. Generation of 3D angiogenic vasculature induced from one arteriole and one venule, with branching generations considered. 2. Examination of vessel connectivity among each other to construct a functional network for blood circulation, investigation of sensitivity of network architectures to changes in some model parameters. 3. Simulation of blood flow in the developed vasculatures. 4. Comparisons of blood flow calculated on the networks induced from an arteriole-venule system and from a single parent vessel.
The networks from simulations could present basic geometric and morphological features of tumour vasculatures. The sensitivity analysis indicates the controllability of the created networks, which could construct architectures of some specific geometric features to suit different types of tumours. The comparisons of blood flow mentioned above demonstrate the validity of the present vasculature, which could be served as a more realistic network structure for research of microcirculation, drug delivery in solid tumors.

Cite This Article

Wu, J., Long, Q., Xu, S., Padhani, A. R., Jiang, Y. (2008). Simulation of 3D Solid Tumour Angiogenesis Including Arteriole, Capillary and Venule. Molecular & Cellular Biomechanics, 5(4), 217–228.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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