Radiopharmaceuticals are pharmaceuticals with which radioisotopes have been chelated. Upon ingestion or injection, these radiopharmaceuticals bind with cancer cells in a patient’s body delivering a targeted dose of radiation to the tumor. Current treatment protocols are limited to the use of one radiopharmaceutical at a time. However, a conceptual framework established by by David Bushnell, MD (Radiology-University of Iowa) and Mark Madsen, Ph.D. (Physics/Radiology-University of Iowa) suggests that the use of two (or more) radiopharmaceuticals in tandem may allow for increased delivery of radiation to the tumor without exceeding critical thresholds for healthy organs.
Determining the combination of doses leading to maximal radiation delivery involves the modeling of drug uptake by relevant tissues, as well as the implementation of methods to solve constrained optimization problems. The two papers emerging from work in which I was involved focused on simple linear models, and thus only utilized mathematical methods related to linear programming. However, in their senior capstone projects, two of my students began the process of refining these models to account for possible nonlinearities in drug uptake and radiation delivery.