Mathematical analysis to the variation of tumor cells density according to recovery of five organs: Kidney, liver, heart, spleen, and lung

Abstract

Background and objectiveHarmonious interactions of five representative organs: kidney, liver, heart, spleen, and lung, improve metastasis and cell divisions, and abnormal cell division causes cancer cell development. The research is processed through a mathematical approach based on win-win principle of five organs to generate medicine in blood vessel. The variations of solute medicine amount in blood vessel with respect to the flow rates of injected drugs are interpreted. The alterations of tumor cells density and tumor angiogenesis factor concentration are described according to the recovery of five organs’ functions. MethodsA compartmental analysis is applied to obtain medicine concentration in blood vessel by the functional recovery of five organs considering time level ti, the reaction rate coefficient Rj, and the medicine flow rate α. Random motility and chemotaxis in response to tumor angiogenesis factor gradients are comprised to derive mathematical governing equations for tumor cells motion and a finite volume method with time-changing is adopted to obtain numerical solutions due to the complexity of the governing equations. ResultsDrug concentration in blood vessel grows as heart reaction rate increases, and the medicine made through the functional enhancements of five representative organs is highly influential to restrain the activity of tumor angiogenesis factor. With the growth of medicine concentration in blood vessel according to the decline of reaction rate and medicine flow rate, tumor cells reacts hypersensitively at the moment of medicines injection and the density of tumor cells approached to zero. ConclusionsConsequently, reaction rate, time level, and medicine flow rate are crucial factors in the determination of medicine amount in blood vessel and to control tumor angiogenesis factor concentration, and harmonious balanced functions among five organs based on win-win principle contribute to control the activity of tumor cells.