Optimization of additive chemotherapy combinations for an in vitro cell cycle model with constant drug exposures
Journal article, 2021

Proliferation of an in vitro population of cancer cells is described by a linear cell cycle model with n states, subject to provocation with m chemotherapeutic compounds. Minimization of a linear combination of constant drug exposures is considered, with stability of the system used as a constraint to ensure a stable or shrinking cell population. The main result concerns the identification of redundant compounds, and an explicit solution formula for the case where all exposures are nonzero. The orthogonal case, where each drug acts on a single and different stage of the cell cycle, leads to a version of the classic inequality between the arithmetic and geometric means. Moreover, it is shown how the general case can be solved by converting it to the orthogonal case using a linear invertible transformation. The results are illustrated with two examples corresponding to combination treatment with two and three compounds, respectively.

Stability analysis

Model-based drug development

Lagrange multipliers

Combination therapy



Tim Cardilin

Fraunhofer-Chalmers Centre

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Torbjörn Lundh

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Mats Jirstrand

Fraunhofer-Chalmers Centre

Mathematical Biosciences

0025-5564 (ISSN)

Vol. 338 108595

Subject Categories

Pharmaceutical Sciences


Pharmacology and Toxicology





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