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Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis. (English) Zbl 1406.92049
Summary: We extend the diffuse interface model developed in Part I [S. M. Wise et al., ibid. 253, No. 3, 524–543 (2008; Zbl 1398.92135)] to study nonlinear tumor growth in 3-D. Extensions include the tracking of multiple viable cell species populations through a continuum diffuse-interface method, onset and aging of discrete tumor vessels through angiogenesis, and incorporation of individual cell movement using a hybrid continuum-discrete approach. We investigate disease progression as a function of cellular-scale parameters such as proliferation and oxygen/nutrient uptake rates. We find that heterogeneity in the physiologically complex tumor microenvironment, caused by non-uniform distribution of oxygen, cell nutrients, and metabolites, as well as phenotypic changes affecting cellular-scale parameters, can be quantitatively linked to the tumor macro-scale as a mechanism that promotes morphological instability. This instability leads to invasion through tumor infiltration of surrounding healthy tissue. Models that employ a biologically founded, multiscale approach, as illustrated in this work, could help to quantitatively link the critical effect of heterogeneity in the tumor microenvironment with clinically observed tumor growth and invasion. Using patient tumor-specific parameter values, this may provide a predictive tool to characterize the complex in vivo tumor physiological characteristics and clinical response, and thus lead to improved treatment modalities and prognosis.

MSC:
92C15 Developmental biology, pattern formation
92C17 Cell movement (chemotaxis, etc.)
92C50 Medical applications (general)
92C37 Cell biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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