Optimal control of multiple myeloma assuming drug resistance and off-target effects

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 resistance via loss of CD38 expression, which is a proposed mechanism of resistance to Daratumumab treatment. We develop an ODE model that includes drug resistance 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 resistance mechanisms and the off-target drug effect on the optimal treatment regime. We identify a general increase in the duration and costs of optimal treatment, as a result of these added mechanisms. Several distinct optimal treatment regimes are identified within the parameter space.