Cell Cycle Specific Cancer Chemotherapy for Homogeneous Tumors

Control Theory and Cancer Chemotherapy: How They Interact

“…Mathematically, cancer chemotherapy can be formulated as an optimal control problem. This approach is more relevant than ever today, as testified by recent works (Schättler and Ledzewicz, 2015a , b ; Wang and Schättler, 2016 ; Angaroni et al, 2020 ; Jarrett et al, 2020 ; Sweilam et al, 2020 ). In literature, applications of optimal control theory to mathematical models of cancer biology and role of chemotherapy began to appear in the 1980s and have appeared with regularity in the following years to the present day.…”

“…We consider a multi-compartment and multi-drug model, that according to Ledzewicz and Schättler (Schättler and Ledzewicz, 2015a ) is described by a bilinear system of the form…”

“…Mathematical models for cancer chemotherapy are necessarily cell-cycle specific, because most drugs are active in a specific phase of the cell-cycle as reported in Ledzewicz and Schaettler ( 2004 ), Schättler and Ledzewicz ( 2015a ). The starting point of cell cycle is a growth phase G1 after which the cell enters a phase S where DNA synthesis occurs.…”

“…The molecules of the anticancer drug treatments can be cell-killing agents, but also blocking and recruitment agents. Blocking agents slow down the transitions of the cells through the cell cycle, i.e., they slow down the tumor growth; recruiting agents make cancer cells leave the dormant stage G0 where they are not susceptible to any chemotherapy (Ledzewicz and Schaettler, 2004 ; Schättler and Ledzewicz, 2015a , b ). Usually, in these models the phases of the cell cycle are clustered into compartments with the state representing the average number of cells in each compartment and the control representing the dosages or effects of the various drugs.…”