Optimal treatments for photodynamic therapy

Abstract

Medical applications in operations research have flourished over the last few decades, and one of the most prolific topics has been how to optimally design cancer treatments. The preponderance of this research has considered radiotherapy design, but several new procedures are emerging as alternatives to standard treatments. This paper addresses the developing treatment modality called photodynamic therapy (PDT), which uses the light-harvesting properties of a photosensitizer. The premise is that cells expire due to a toxic reaction caused by exposing a photosensitizer to a specific wavelength of light. The purpose of treatment design is to decide how to best treat the patient, meaning that cancerous tissues are damaged but that surrounding organs are not. This paper has two objectives. First, we develop a model that allows us to explore the design process. In particular, we develop a standard pharmacokinetic model to estimate the absorption and elimination of the photosensitizer. The biological model provides the data to cast the design process as a time dependent linear program. Second, we use the linear program to answer the question of whether or not PDT is a viable treatment for deep tissue cancers with the only drug currently approved in the USA. Our results indicate that even under optimal conditions, the treatments based on the currently approved drug are not capable of targeting tumors without destroying surrounding tissues. However, a treatment’s success significantly increases with the drug’s affinity for cancerous tissues.