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Hybrid discrete-continuum model of tumor growth considering capillary points.pdf

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Hybrid discrete-continuum model of tumor growth considering capillary points.pdf

Appl. Math. Mech. -Engl. Ed., 34(10), 1237–1246 (2013) Applied Mathematics DOI 10.1007/s10483-013-1741-9 and Mechanics c Shanghai University and Springer-Verlag Berlin Heidelberg 2013 (English Edition) Hybrid discrete-continuum model of tumor growth considering capillary points∗ 1 2 2 Jie LYU ( ) , Shi-xiong XU () , Wei YAO ( ) , 3 4 Yu ZHOU ( ) , Quan LONG ( ) (1. Department of Medical Instrumentation Engineering, Shanghai Medical Instrumentation College, Shanghai 200093, P. R. China; 2. Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, P. R. China; 3. Neusoft Medical System, Shenyang 110179, P. R. China; 4. Brunel Institute for Bioengineering, School of Engineering and Design, Brunel University, Uxbridge, Middlesex UB8 3PH, U. K.) Abstract A hybrid discrete-continuum model of tumor growth in the avascular phase considering capillary points is established. The inﬂuence of the position of capillary points on tumor growth is also studied by simulation. The results of the dynamic tumor growth and the distribution of oxygen, matrix-degrading enzymes, and extracellular matrix- concentration in the microenvironment with respect to time are shown by graphs. The relationships between diﬀerent oxygenated environments and the numbers