  Over the past decade, several targeted therapies (e.g. imatinib, dasatinib,
nilotinib) have been developed to treat Chronic Myeloid Leukemia (CML). Despite
an initial response to therapy, drug resistance remains a problem for some CML
patients. Recent studies have shown that resistance mutations that preexist
treatment can be detected in a substan- tial number of patients, and that this
may be associated with eventual treatment failure. One proposed method to
extend treatment efficacy is to use a combination of multiple targeted
therapies. However, the design of such combination therapies (timing, sequence,
etc.) remains an open challenge. In this work we mathematically model the
dynamics of CML response to combination therapy and analyze the impact of
combination treatment schedules on treatment efficacy in patients with
preexisting resistance. We then propose an optimization problem to find the
best schedule of multiple therapies based on the evolution of CML according to
our ordinary differential equation model. This resulting optimiza- tion problem
is nontrivial due to the presence of ordinary different equation constraints
and integer variables. Our model also incorporates realistic drug toxicity
constraints by tracking the dynamics of patient neutrophil counts in response
to therapy. Using realis- tic parameter estimates, we determine optimal
combination strategies that maximize time until treatment failure.
