Optimization of combination therapy for chronic myeloid leukemia with dosing constraints

J Math Biol. 2018 Nov;77(5):1533-1561. doi: 10.1007/s00285-018-1262-6. Epub 2018 Jul 10.


In this work, we demonstrate a mathematical technique for optimizing combination regimens with constraints. We apply the technique to a mathematical model for treatment of patients with chronic myeloid leukemia. The in-host model includes leukemic cell and immune system dynamics during treatment with tyrosine kinase inhibitors and immunomodulatory compounds. The model is minimal (semi-mechanistic) with just enough detail that all relevant therapeutic effects can be represented. The regimens are optimized to yield the highest possible reduction in disease burden, taking into account dosing constraints and side effect risks due to drug exposure. We compare the following three types of regimens: (1) regimens that are restricted to certain discrete dose levels, which can only change every three months; (2) optimal regimens determined using optimal control; and (3) regimens that are piecewise-constant like the first type of regimen, but are obtained as approximations to the optimal control regimens. All three types of regimens result in similar outcomes, but the last one is easy to compute in addition to being clinically feasible.

Keywords: Chronic myeloid leukemia (CML); Combination therapy; Constrained optimization; Immunotherapy; Optimal control; Tyrosine kinase inhibitors (TKIs).

MeSH terms

  • Antineoplastic Agents / administration & dosage
  • Antineoplastic Agents, Immunological / administration & dosage
  • Antineoplastic Combined Chemotherapy Protocols / administration & dosage*
  • Computer Simulation
  • Fusion Proteins, bcr-abl / antagonists & inhibitors
  • Humans
  • Immunologic Factors / administration & dosage
  • Immunotherapy / methods
  • Immunotherapy / statistics & numerical data
  • Leukemia, Myelogenous, Chronic, BCR-ABL Positive / drug therapy*
  • Leukemia, Myelogenous, Chronic, BCR-ABL Positive / therapy
  • Mathematical Concepts
  • Models, Biological*
  • Protein Kinase Inhibitors / administration & dosage


  • Antineoplastic Agents
  • Antineoplastic Agents, Immunological
  • BCR-ABL1 fusion protein, human
  • Immunologic Factors
  • Protein Kinase Inhibitors
  • Fusion Proteins, bcr-abl