Cancer is a collection of diseases characterized by an imbalance between proliferation and cell apoptosis resulting from a series of genetic mutations. Common modalities for treating cancer include surgical excision of the tumor mass, local exposure to radiation, or systemic administration of a chemotherapeutic agent. Whenever possible the tumor mass will be removed, but the surgeon cannot be certain that all cancerous cells were excised, particularly if the cancerous mass has already become invasive. Also, by the time of initial tumor mass detection, undetectable metastases may have already spread to other remote body locations, motivating the use of a more systemic treatment. The scheduling of chemotherapeutic treatments, while extensively studied in an empirical fashion, has not been the subject of mathematical evaluation from an optimal scheduling standpoint in the clinical setting. The latter point is especially relevant given that chemotherapeutics also harm healthy proliferating cells, reducing patient quality of life and limiting treatment effectiveness.

Clinical studies focus on determining dose toxicity limits and drug efficacy. Throughout these trials, substantial data are obtained regarding plasma drug concentration, tumor volume progression, and toxicity. This data serves as a basis for constructing pharmacokinetic models for plasma drug distribution, typically through a compartmental approach, while more extensive data collection can motivate the development of complex, physiologically-based pharmacokinetic models. While pharmacodynamic responses are observed, researchers are generally more concerned with the presence of a therapeutic effect rather than accurately modeling the mechanism or magnitude of action. Consequently, treatment schedules are often developed based on previous drugs with similar chemical structures or cellular targets and may not incorporate dynamics associated with drug effect. In addition, most studies collect plasma drug concentrations, but often fail to evaluate tumor drug exposure (i.e., the drug concentration which drives tumor pharmacodynamic response). Pharmacodynamic effects included within tumor models, instead, are typically based on a predicted plasma drug concentration, an assumption that may lead to an over- or under-prediction of the actual drug effect.

Many authors have examined the chemotherapeutic dosing problem in a model-based control framework [1,2], employing constraints on drug delivery (input) or plasma drug concentration (state) to maintain drug administration within toxic limits and a goal of minimizing the tumor volume at a prespecified final time point. These solutions predict a characteristic treatment profile: maximum initial drug delivery, followed by a non-dosing period with the remainder of the drug delivered at the end of the treatment window. Ethically, however, a doctor cannot allow a tumor to grow untreated, thereby invalidating the controller formulation; in addition bulk dosing at the end of the cycle, instead of at the beginning, prohibits immediate future dosing. Dose schedule development, therefore, requires an alternative objective function to obtain clinically useful scheduling results. One possibility is direct inclusion of a toxicity measure within the model. One common toxicity, leukopenia, or a reduction in white blood cell count, is a continuous, quantifiable measure available from patient plasma. Controllers which incorporate models for leukocyte proliferation and drug effect can return drug schedules which minimize patient leukopenia (possibly avoiding other toxicities as well) while simultaneously minimizing overall tumor volume [3,4].

Using pharmacodynamic data from the administration of the chemotherapeutic docetaxel, a linear physiologically-based pharmacokinetic model for drug distribution in mice was developed [5]. This model included explicit outputs for drug concentration in both plasma and tumor along with outputs for liver, spleen, lung, heart, brain, and kidney. Model reduction tools were employed in order to aid subsequent controller calculations. The reduced model was combined with tumor growth models (both lumped and cell cycle) and a model governing circulating white blood cell count. The tumor pharmacodynamic effect was driven by the concentration of drug within the tumor while white blood cell count was influenced by plasma drug concentration. During each cycle, the objective function was set to minimize overall tumor volume subject to dosing limits, toxicity constraints, and the condition of continued treatment following the conclusion of each cycle, resulting in a nonlinear programming problem. In addition, the two typical schedules for docetaxel administration (infusion once every three weeks or infusions once a week for three weeks) were evaluated for efficacy and toxicity as the two schedules have demonstrated significantly different toxicity profiles. Finally, alternative dosing schedules were evaluated to test whether alterations to the present schedules could result in increased anti-tumor effect.

Bibliography

1

R. Martin and K. L. Teo. Optimal Control of Drug Administration in Cancer Chemotherapy. World Scientific, River Edge, NJ, 1994.

2

J. M. Harrold and R. S. Parker. An MILP approach to cancer chemotherapy dose regime design. In Proc. American Control Conf., paper WeM10.5, Boston, MA, 2004.

3

E. K. Afenya. Recovery of normal hemopoiesis in disseminated cancer therapy - a model. Math. Biosci., 172:15-32, 2001.

4

L. E. Friberg, A. Henningson, H. Maas, and et al. Model of chemotherapy-induced myelosuppression with parameter consistency across drugs. Cancer Res., 20:523-7, 2002.

5

J. A. Florian Jr., W. C. Zamboni, J. L. Eiseman, M. D. Krasteva, S. Strychor, E. Joseph, R. A. Parise, M. J. Egorin, and R. S. Parker. A physiologically-based pharmacokinetic model of docetaxel in SCID mice bearing SKOV3 human ovarian xenografts. AACR Annual Meeting, 2006.