Mathematical modeling of solid cancer growth with angiogenesis

Mathematical Modeling of Interleukin-35 Promoting Tumor Growth and Angiogenesis

Interleukin-35 (IL-35), a cytokine from the Interleukin-12 cytokine family, has been considered as an anti-inflammatory cytokine which promotes tumor progression and tumor immune evasion. It has also been demonstrated that IL-35 is secreted by regulatory T cells. Recent mouse experiments have shown that IL-35 produced by cancer cells promotes tumor growth via enhancing myeloid cell accumulation...

Mathematical modeling of tumor-induced angiogenesis.

Angiogenesis, the growth of a network of blood vessels, is a crucial component of solid tumor growth, linking the relatively harmless avascular and the potentially fatal vascular growth phases of the tumor. As a process, angiogenesis is a well-orchestrated sequence of events involving endothelial cell migration and proliferation; degradation of tissue; new capillary vessel formation; loop forma...

Othmer Mathematical modeling of tumor - induced angiogenesis

Mathematical Modeling of the Temperature-Dependent Growth of Living Systems

In this investigation a non-equilibrium thermodynamic model of the temperature dependent biological growth of a living systems has been analyzed. The results are derived on the basis of Gompertzian growth equation. In this model, we have considered the temperature dependent growth rate and development parameter. The non-equilibrium thermodynamic model is also considered for exploring the variat...

Two Dimensional Mathematical Model of Tumor Angiogenesis: Coupling of Avascular Growth and Vascularization

Introduction As a tumor grows, the demand for oxygen and nutrients increases and it grows further if acquires the ability to induce angiogenesis. In this study, we aimed to present a two-dimensional continuous mathematical model for avascular tumor growth, coupled with a discrete model of angiogenesis. Materials and Methods In the avascular growth model, tumor is considered as a single mass, wh...