Dynamically Reorganising Vascular Networks Modelled Using Cellular Automata Approach
We present the model of tumour induced angiogenesis that apart from predominating phenomena, as influence of VEGF, includes newly discovered factors such as Dll4/Notch signalling and remodelling processes. The Cellular Automata approach is employed to mod
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Abstract. We present the model of tumour induced angiogenesis that apart from predominating phenomena, as influence of VEGF, includes newly discovered factors such as Dll4/Notch signalling and remodelling processes. The Cellular Automata approach is employed to model cellular and intracellular processes that occur in cancer tissue and surroundings. Vascular system is modelled by using the Graph of Cellular Automata, which combines graph theory with the Cellular Automata paradigm. Additionally, an outline of model verification method which uses graph descriptors is presented and exemplified.
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Introduction
Angiogenesis is the process of blood vessels formation [1]. The cells influenced by the stresses (e.g., low O2 , low pH), synthesise angiogenic stimulators (most of all VEGF — Vascular Endothelial Growth Factor) [1]. Stimulators diffuse towards the nearest blood vessels and activate the endothelial cells (ECs) that lines the vessel walls. In the response the endothelial cells start to proliferate and migrate being attracted by the gradient of VEGF. The wall of parent blood vessel becomes degraded and a lumen of a new capillary is formed. The process of angiogenesis has a crucial role in solid tumour growth. Clusters of growing tumour cells are short of oxygen and nutrients. The ”starving” tumour cells produce VEGF and other angiogenic stimulators (Tumour Angiogenesis Factors — TAFs) that activate neighbouring vessels. Tumour induced angiogenesis is a very promising target in anti-cancer therapy [3]. Inhibition of angiogenesis or regression of existing vasculature may suppress tumour development. Treatment targeted on improving vasculature around tumour can be helpful for drug delivery during chemotherapy. The computer models of angiogenesis employ continuous or discrete approaches [2]. The continuous models base on differential equations and as a result we obtain distributions of endothelial cells in the tissue. The main disadvantage of the continuous approach is the lack of information about the structure of vascular network. In contrast, the discrete models are able to produce vascular network of a given topology [2]. These models mostly base on the Cellular Automata (CA) paradigm and assume that modelled species (endothelial cells, angiogenic factors H. Umeo et al. (Eds): ACRI 2008, LNCS 5191, pp. 494–499, 2008. c Springer-Verlag Berlin Heidelberg 2008
Dynamically Reorganising Vascular Networks Modelled
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etc.) are treated individually. In [6], Anderson and Chaplain assumed that growth of a single sprout is governed by move of the endothelial cell located at its tip. It moves across regular, rectangular network of CA according to predefined rules. At each step of simulation the tip cell moves in one out of four directions or waits with a certain probability. The probabilities are calculated by using diffusion equation with terms reflecting VEGF and fibronectin influence [6]. Additional rules that model vessels branching and anastomosing were also defined. In [8] we proposed a new framework for modelling multiscal
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