Optimal control of Multiple Myeloma assuming drug evasion and off-target effects

Abstract

Multiple Myeloma (MM) is a plasma cell cancer that occurs in the bone marrow. A leading treatment for MM is the monoclonal antibody Daratumumab, targeting the CD38 receptor, which is highly overexpressed in myeloma cells. In this work we model drug evasion via loss of CD38 expression, which is a proposed mechanism of resistance to Daratumumab treatment. We develop an ODE model that includes drug evasion via two mechanisms: a direct effect in which CD38 expression is lost without cell death in response to Daratumumab, and an indirect effect in which CD38 expression switches on and off in the cancer cells; myeloma cells that do not express CD38 have lower fitness but are shielded from the drug action. The model also incorporates competition with healthy cells, death of healthy cells due to off-target drug effects, and a Michaelis-Menten type immune response. Using optimal control theory, we study the effect of the drug evasion mechanisms and the off-target drug effect on the optimal treatment regime. We identify a general increase in treatment duration and costs, with varying patterns of response for the different controlling parameters. Several distinct optimal treatment regimes are identified within the parameter space. Author summaryIn this work we investigate a model of Multiple Myeloma, a cancer of the bone marrow, and its treatment with the drug Daratumumab. The model incorporates proposed mechanisms by which the cancer evades Daratumumab by reduced expression of the receptor CD38, which is the drug target and normally abundent in the cancer cells. The model includes an off-target effect, meaning that the drug treatment destroys some healthy cells alongside the targeted cancer cells. Both mechanisms can reasonably be expected to reduce the efficacy of the drug. We investigate the model using optimal control methods, which are used to find the drug dose over time which best balances the financial and health costs of treatment against cancer persistence, according to a specified cost function. We show that this drug resistence and off-target effect prolongs the optimal treatment and increase the burden of both the disease and drug. We analyse the distinct effects of the controlling parameters on each of these costs factors as well as the time course, and identify conditions under which extended treatment is required, with either intermittant treatment or a steady reduced dose. Extended treatment may be indefinite or for a fixed period.