| Issue |
Math. Model. Nat. Phenom.
Volume 9, Number 4, 2014
Optimal control
|
|
|---|---|---|
| Page(s) | 131 - 152 | |
| DOI | https://doi.org/10.1051/mmnp/20149409 | |
| Published online | 20 June 2014 | |
A Review of Optimal Chemotherapy Protocols: From MTD towards Metronomic Therapy
1
Dept. of Mathematics and Statistics, Southern Illinois University
Edwardsville, Edwardsville, Illinois, 62026-1653, USA
2
Dept. of Electrical and Systems Engr., Washington
University, St.
Louis, Missouri,
63130-4899,
USA
⋆
Corresponding author. E-mail: uledzew@siue.edu
We review mathematical results about the qualitative structure of chemotherapy protocols that were obtained with the methods of optimal control. As increasingly more complex features are incorporated into the mathematical model—progressing from models for homogeneous, chemotherapeutically sensitive tumor cell populations to models for heterogeneous agglomerations of subpopulations of various sensitivities to models that include tumor immune-system interactions—the structures of optimal controls change from bang-bang solutions (which correspond to maximum dose rate chemotherapy with restperiods) to solutions that favor singular controls (representing reduced dose rates). Medically, this corresponds to a transition from standard MTD (maximum tolerated dose) type protocols to chemo-switch strategies towards metronomic dosing.
Mathematics Subject Classification: 92C50 / 49K15
Key words: optimal control / cancer chemotherapy / homogeneous and heterogeneous tumor populations / tumor immune system interactions
© EDP Sciences, 2014
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