A 3D COUPLED MATHEMATICAL MODEL FOR THE GROWTH OF AVASCULAR SOLID TUMOR

被引:0
作者
Zhao, Ning [1 ]
Iramina, Keiji [2 ]
Chen, Xian [3 ]
机构
[1] Kyushu Univ, Grad Sch Syst Life Sci, Nishi Ku, Fukuoka 8190395, Japan
[2] Kyushu Univ, Grad Sch Informat Sci & Elect Engn, Dept Informat, Fukuoka 8190395, Japan
[3] Yamaguchi Univ, Grad Sch Med, Dept Biomed Engn, Yamaguchi 7558611, Japan
关键词
Porous medium; tumor micro-environment; avascular tumor growth; convection-diffusion; oxygen transport; BASEMENT-MEMBRANE COLLAGEN; MOLECULAR-MECHANISMS; FEMALE BREAST; INVASION; SIMULATION; TRANSPORT; CELLS; METASTASIS; MOVEMENT; STRESS;
D O I
10.1142/S0219519415500244
中图分类号
Q6 [生物物理学];
学科分类号
071011 ;
摘要
We develop a coupled mathematical model of avascular tumor growth based on porous media mechanics. This comprises of the migration of tumor cells (TCs), the degradation of extracellular matrix (ECM), the transport of matrix-degrading enzymes (MDEs), the seepage of tissue fluid and the supplement and consumption of oxygen. The simulation that a solid tumor grows in the micro-environment composed of the pre-existing capillaries and the surrounding tissues, and the specific property of varying porosity with the growth of TCs in a tumor microenvironment are taken into account. We propose functional coefficients for fluid seepage and oxygen diffusion, and incorporate the convection-diffusion of oxygen and the convection of MDEs. From this modified model the main findings include: first, a solid tumor originating in the inlet region undergoes necrosis in the outlet region because of a low supply of oxygen, while a solid tumor originating in the outlet region undergoes necrosis at the primary site because of overconsumption of oxygen; second, tumors further from capillaries grow faster than tumors close to adjacent capillaries; third, the pre-existing capillaries cause some impact to the transport of those chemical factors involved in tumor growth, and further affect tumor migration and necrosis.
引用
收藏
页数:22
相关论文
共 43 条
  • [31] Solid stress generated by spheroid growth estimated using a linear poroelasticity model
    Roose, T
    Netti, PA
    Munn, LL
    Boucher, Y
    Jain, RK
    [J]. MICROVASCULAR RESEARCH, 2003, 66 (03) : 204 - 212
  • [32] Mathematical models of avascular tumor growth
    Roose, Tiina
    Chapman, S. Jonathan
    Maini, Philip K.
    [J]. SIAM REVIEW, 2007, 49 (02) : 179 - 208
  • [33] A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. I. Theory
    Schuff, M. M.
    Gore, J. P.
    Nauman, E. A.
    [J]. JOURNAL OF MATHEMATICAL BIOLOGY, 2013, 66 (06) : 1179 - 1207
  • [34] A multiphase model for three-dimensional tumor growth
    Sciume, G.
    Shelton, S.
    Gray, W. G.
    Miller, C. T.
    Hussain, F.
    Ferrari, M.
    Decuzzi, P.
    Schrefler, B. A.
    [J]. NEW JOURNAL OF PHYSICS, 2013, 15
  • [35] Sciume G, 2012, Mol Cell Biomech, V9, P193
  • [36] TUMOR-CELL INTERACTIONS WITH THE EXTRACELLULAR-MATRIX DURING INVASION AND METASTASIS
    STETLERSTEVENSON, WG
    AZNAVOORIAN, S
    LIOTTA, LA
    [J]. ANNUAL REVIEW OF CELL BIOLOGY, 1993, 9 : 541 - 573
  • [37] A Novel Method for Simulating the Extracellular Matrix in Models of Tumour Growth
    Toma, Alina
    Mang, Andreas
    Schuetz, Tina A.
    Becker, Stefan
    Buzug, Thorsten M.
    [J]. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE, 2012, 2012
  • [38] Behaviour of a bentonite barrier in the laboratory: Experimental results up to 8 years and numerical simulation
    Villar, M. V.
    Sanchez, M.
    Gens, A.
    [J]. PHYSICS AND CHEMISTRY OF THE EARTH, 2008, 33 : S476 - S485
  • [39] Villar M.V., 2001, P INT S SUCT SWELL P, P259
  • [40] Physical determinants of vascular network remodeling during tumor growth
    Welter, M.
    Rieger, H.
    [J]. EUROPEAN PHYSICAL JOURNAL E, 2010, 33 (02) : 149 - 163