(509d) An Algorithm for Patient-Specific Cancer Chemotherapy Scheduling

The annual U.S. cancer care expenditure is projected to reach $147 billion in 2013 [1]. An improvement in cancer understanding and treatment is needed to ease the economic burden and improve patient outcomes. Advances have been made in developing new cancer treatments such as targeted therapies and immunotherapy.  However, a systemic treatment is needed when tumors are not surgically resectable or when tumors reach a detectable size (small mestatasis to remote sites is assumed) [2]. Chemotherapy remains the most common method used for systemic cancer treatment [3].  Chemotherapy affects both healthy and diseased tissues. A balance between successful killing of cancer cells and minimizing the toxicity to the host remains a challenge for clinicians in deploying chemotherapy treatments.

The balance between efficacy and toxicity creates a challenging and interesting problem for chemotherapy scheduling optimization. The objective is to minimize the tumor volume within pharmacokinetic, toxicity, and logistical constraints related to the chemotherapy regimen for a particular drug/tumor pair.  Here we present a clinically-relevant formulation of the multiple input chemotherapy scheduling problem using the billion-dollar (sales) per year agent docetaxel ($1.2 billion in 2012) coupled with granulocyte-colony stimulating factor (G-CSF), which mitigates the primary toxicity associated with docetaxel administration.

Docetaxel is a widely used chemotherapeutic for the treatment of breast cancer, non-small cell lung cancer, prostate cancer, and head and neck cancer. However, the primary adverse effect of docetaxel is myleosuppression, or neutropenia, a low absolute neutrophil count (ANC) in the plasma (Grade 1: ANC >1.5x10⁶ cells/ml; Grade 2: 1.0x10⁶ cells/ml ≤ ANC  < 1.5x10 cells/ml; Grade 3: 0.5x10 cells/ml ≤ ANC <10⁶  cells/ml; Grade 4: ANC < 0.5x10⁶ cells/ml) [4]. Depending on the administration schedule, a patient treated with docetaxel may suffer severe neutropenia, especially, at higher doses of docetaxel (e.g., 100 mg/m² infusion every three weeks) [5, 6]. Other studies have shown decreased neutropenia at a dose level of 35 mg/m²delivered weekly for 6 weeks (followed by two weeks off). Interestingly, anti-tumor efficacy was unchanged [7,8].

 Granulocyte-colony stimulating factor (G-CSF) is a protein that induces the production of neutrophil progenitors, leading to an increase in white blood cell counts. In patients with low neutrophil counts, G-CSF has been shown to reduce neutropenia when injected into patients from day 2-12 after a docetaxel injection on day 1 [9]. G-CSF injection therefore provides an additional actuator to blunt the severe neutropenic response induced by some chemotherapies.  

 The chemotherapy scheduling problem that we pose and solve will be model-based; hence we require models of drug pharmacokinetics (PK), pharmacodynamic (PD) effect, and toxicity. We use a rigorously-derived reduced-order form of our previously developed physiologically-based model of docetaxel PK [10] to drive a novel reduced-order version of our docetaxel neutropenia model [11], which includes G-CSF PK and PD.  We subsequently synthesize the tumor growth and antitumor efficacy model specific to docetaxel and prostate cancer.   The problem objective is to minimize tumor volume at the end of every 6 week cycle with manageable toxicity.

 The optimization problem is subject to dynamics constraints via mathematical models of docetaxel PK, PD efficacy, and toxicity.  Clinically-relevant logistical constraints include: (i) the number of permissible drug doses per week (5); (ii) maximum docetaxel dose (240mg/m² per 6 week cycle); (iii) maximum infusion duration (4 hours); (iv) and G-CSF usage only in the cases of most severe neutropenia (Grade 4 toxicity).  Model-predicted week to week ANC above Grade 3 neutropenia is also considered in the docetaxel scheduling problem. The nonlinearities in the toxicity model, the tumor growth model, and drug efficacy model in combination with integer variables associated with toxicity and logistical constraints result in the docetaxel scheduling problem formulating as a mixed-integer nonlinear programming (MINLP). Using variable transformation, linearization, and piecewise continuous linear approximation, the MINLP will be reformulated with reduced complexity and solved using GAMS/CPLEX or Pyomo. Building on the results of [12], we will compare the single-cycle results with a receding horizon formulation where multiple cycles are synthesized simultaneously, with recalculation when data (tumor measurements, ANC, etc.) becomes available.  The overall objective is to provide clinicians with a model-based tool to assist in improving treatment efficiency and ultimately patient treatment outcome and survival.

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