Cell Cycle as an Object of Control

Optimal control for a mathematical model for chemotherapy with pharmacometrics

“…Optimal control for mathematical models of cancer chemotherapy has a long history dating back to the 1970s and 1980s and the fundamental work by Eisen [5], Swierniak and Kimmel [10,40] and Swan [36,37]. This work continued throughout the 1990s (e.g., see the monograph by Martin and Teo [27] or [41]), and revitalized in the 2000s when novel approaches to cancer therapy such as angiogenic treatments (e.g., [18]) or immunotherapies (e.g., [28]) became available. This research continues strongly into the present time as the numerous references in [32] attest to.…”

On the Role of the Objective in the Optimization of Compartmental Models for Biomedical Therapies

“…Transition terms model the exchanges between populations. For example, in cell-cycle specific models for cancer chemotherapy [ 8 ], quiescent and proliferating cells are distinguished and proliferating cells move through growth phases, synthesis and mitosis, all represented by different coordinates of the state vector x . Similarly, in models including drug resistance , random changes from sensitive to resistant cells occur which, in cases of cancer chemotherapy, also may be reversible.…”

“…It has found numerous applications in the sciences and has become a staple of engineering design, but applications to biomedical problems are less well known. Yet, optimal control as a tool in the analysis of mathematical models of cancer chemotherapy dates back to the 1970s and 1980s (e.g., see [1][2][3][4][5][6]), and these efforts have continued actively throughout the years to the present day (e.g., see [7][8][9][10][11][12][13][14] and the many references in [15]).…”

Sufficient optimality conditions for extremal controls based on functional increment formulas

“…In particular, Problem (P 2 ) models the process of curing of malignant tumors (the chemotherapy) by stoppage of development of cancerous cells at a certain stage [10].…”