LQR tracking of a delay differential equation model for the study of nanoparticle dosing strategies for cancer therapy

Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a “guess and check” method with no way of predicting the effects of the drugs based on the actual bioavailability to the patient's body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do no routinely attempt to quantifiably explain this discrepancy. In this work, mathematical modeling and analysis techniques are joined together with experimentation to gain further insight into the challenges of nanoparticle delivery to tumor sites. There exists a commonly accepted model of drug clearance in the pharmacokinetics community, and it is demonstrated here that this model provides an accurate reflection of reality, as observed in experiment for delivery of gold-coated nanorods. This model is then utilized in a state space feedback control framework to regulate the nanoparticle concentration in the bloodstream. An equal time delay is also introduced in both the state and control input for the purpose of studying alternate dosing strategies. This study will aid in the prediction of the effects of the drugs in a patient's body, thus leading to better models for drug regimen and administration.