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Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (10): 1237-1246.doi: https://doi.org/10.1007/s10483-013-1741-9

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Hybrid discrete-continuum model of tumor growth considering capillary points

 LYU Jie1, XU Shi-Xiong2, YAO Wei2, ZHOU Yu3, LONG Quan4   

  1. 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.
  • Received:2012-06-17 Revised:2013-04-01 Online:2013-09-29 Published:2013-09-29

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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 matrixconcentration in the microenvironment with respect to time are shown by graphs. The relationships between different oxygenated environments and the numbers of surviving, dead, proliferative, and quiescent tumor cells are also investigated.

Key words: null, mathematical model, capillary point, tumor growth, oxygen

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