Conference Paper

# Cancer disease: integrative modelling approaches

Sch. of Math. Sci., Nottingham Univ.

DOI: 10.1109/ISBI.2006.1625040 Conference: Biomedical Imaging: Nano to Macro, 2006. 3rd IEEE International Symposium on Source: DBLP

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- Multiscale Model. and Simul. 01/2010; 3(2):440.
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**ABSTRACT:**A hybrid cellular automaton model is described and used to simulate early tumor growth and examine the roles of host tissue vascular density and tumor metabolism in the ability of a small number of monoclonal transformed cells to develop into an invasive tumor. The model incorporates normal cells, tumor cells, necrotic or empty space, and a random network of native microvessels as components of a cellular automaton state vector. Diffusion of glucose and H+ions (the latter largely resulting from the tumor's excessive reliance on anaerobic metabolism) to and from the microvessels, and their utilization or production by cells, is modeled through the solution of differential equations. In this way, the cells and microvessels affect the extracellular concentrations of glucose and H+which, in turn, affect the evolution of the automaton. Simulations of the model demonstrate that: (i) high tumor H+ion production is favorable for tumor growth and invasion; however for every H+ion production rate, there exists a range of optimal microvessel densities (leading to a local pH favorable to tumor but not to normal cells) for which growth and invasion is most effective, (ii) at vascular densities below this range, both tumor and normal cells die due to excessively low pH, (iii) for vascular densities above the optimal range the microvessel network is highly efficient at removing acid and therefore the tumor cells lose their advantage over normal cells gained by high local H+concentration. While significant spatial gradients of glucose formed, no regions of detrimentally poor glucose perfusion (for either cell type) were observed, regardless of microvessel density. Depending on metabolic phenotype, a variety of tumor morphologies similar to those clinically observed were realized in the simulations. Lastly, a sharp transition (analogous to that of the adenoma–carcinoma sequence) between states of initial tumor confinement and efficient invasiveness was observed when H+production reached a critical value.Journal of Theoretical Biology 01/2002; 213(3):315-331. · 2.35 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A theoretical model was developed to simulate long-term changes of vessel diameters during structural adaptation of microvascular networks in response to tissue needs. The diameter of each vascular segment was assumed to change with time in response to four local stimuli: endothelial wall shear stress (tauw), intravascular pressure (P), a flow-dependent metabolic stimulus (M), and a stimulus conducted from distal to proximal segments along vascular walls (C). Increases in tauw, M, or C or decreases in P were assumed to stimulate diameter increases. Hemodynamic quantities were estimated using a mathematical model of network flow. Simulations were continued until equilibrium states were reached in which the stimuli were in balance. Predictions were compared with data from intravital microscopy of the rat mesentery, including topological position, diameter, length, and flow velocity for each segment of complete networks. Stable equilibrium states, with realistic distributions of velocities and diameters, were achieved only when all four stimuli were included. According to the model, responses to tauw and P ensure that diameters are smaller in peripheral than in proximal segments and are larger in venules than in corresponding arterioles, whereas M prevents collapse of networks to single pathways and C suppresses generation of large proximal shunts.The American journal of physiology 09/1998; 275(2 Pt 2):H349-60. · 3.28 Impact Factor

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