Designing combination therapies using multiple optimal controls

Jesse A Sharp; Alexander P Browning; Tarunendu Mapder; Christopher M Baker; Kevin Burrage; Matthew J Simpson

doi:10.1016/j.jtbi.2020.110277

Designing combination therapies using multiple optimal controls

J Theor Biol. 2020 Jul 21:497:110277. doi: 10.1016/j.jtbi.2020.110277. Epub 2020 Apr 13.

Authors

Jesse A Sharp¹, Alexander P Browning², Tarunendu Mapder², Christopher M Baker³, Kevin Burrage⁴, Matthew J Simpson⁵

Affiliations

¹ School of Mathematical Sciences, Queensland University of Technology (QUT), Australia; ARC Centre of Excellence for Mathematical and Statistical Frontiers, QUT, Australia. Electronic address: jesse.sharp@hdr.qut.edu.au.
² School of Mathematical Sciences, Queensland University of Technology (QUT), Australia; ARC Centre of Excellence for Mathematical and Statistical Frontiers, QUT, Australia.
³ School of Mathematical Sciences, Queensland University of Technology (QUT), Australia; ARC Centre of Excellence for Mathematical and Statistical Frontiers, QUT, Australia; School of Mathematics and Statistics, The University of Melbourne, Australia.
⁴ School of Mathematical Sciences, Queensland University of Technology (QUT), Australia; ARC Centre of Excellence for Mathematical and Statistical Frontiers, QUT, Australia; Department of Computer Science, University of Oxford, UK (Visiting Professor).
⁵ School of Mathematical Sciences, Queensland University of Technology (QUT), Australia.

PMID: 32294472
DOI: 10.1016/j.jtbi.2020.110277

Abstract

Strategic management of populations of interacting biological species routinely requires interventions combining multiple treatments or therapies. This is important in key research areas such as ecology, epidemiology, wound healing and oncology. Despite the well developed theory and techniques for determining single optimal controls, there is limited practical guidance supporting implementation of combination therapies. In this work we use optimal control theory to calculate optimal strategies for applying combination therapies to a model of acute myeloid leukaemia. We present a versatile framework to systematically explore the trade-offs that arise in designing combination therapy protocols using optimal control. We consider various combinations of continuous and bang-bang (discrete) controls, and we investigate how the control dynamics interact and respond to changes in the weighting and form of the pay-off characterising optimality. We demonstrate that the optimal controls respond non-linearly to treatment strength and control parameters, due to the interactions between species. We discuss challenges in appropriately characterising optimality in a multiple control setting and provide practical guidance for applying multiple optimal controls. Code used in this work to implement multiple optimal controls is available on GitHub.

Keywords: Acute myeloid leukaemia (AML); Chemotherapy; Combination therapy; Leukaemia; Optimal control; Stem cells.

Publication types

Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

Combined Modality Therapy
Ecology
Humans
Leukemia, Myeloid, Acute*