New insights into vascular collapse and growth dynamics in solid tumors.

The experimentally-observed phenomenon of vascular collapse in tumors represents a significant barrier to the delivery of blood-borne therapeutic drugs, and has been attributed to the elevated tissue stresses resulting from confined proliferation of tumor cells. This paper presents a mathematical framework which describes the evolution of growth-induced stresses in tumors and gives new insights into both vascular collapse and tumor growth dynamics. The linear-elastic description of anisotropic growth adopted here provides the mechanical model with a realistic constitutive basis, incorporating both the solid and stress-relaxation characteristics of soft biological tissues. A particular distribution of spatially non-uniform growth is proposed which is considered representative of a vascular tumor. The stress distribution associated with this growth pattern predicts the onset of vascular collapse, producing the well-defined regions observed in vascular collapse experiments: a peripheral layer with open blood vessels adjacent to a region of vascular collapse, enclosing an inner region where the vessels are open. The model also highlights the roles of various tissue properties in inducing vascular collapse. Moreover, the tumor growth rates predicted by this model reflect experimental observations, with exponential growth taking place immediately following vascularization, followed by a period of exponential retardation.