Using ordinary differential equations, the authors model the progress of different cell populations in the tumor environment as a continuous process. Within the dynamical system presented by the tumor environment, they apply the theory of optimal controla mathematical optimization methodto design ad-hoc therapies and find an optimal treatment.
The end goal of the control policy is to minimize tumor cells while maximizing effectors, such as immune cells or immune-response chemicals. "The aim is to minimize the tumor concentration while keeping the amount of administered drug below certain thresholds, to avoid toxicity," says Topputo. "In common practice, one searches for effective therapies; in our approach, we look for efficiency and effectiveness."
Elaborating on a prior study where indirect methods used to solve the optimal control problem are not effective, the authors use direct methods that apply algorithms from aerospace engineering to solve the associated optimal control problem in this paper. Optimal protocols are analyzed, and the duration of optimal therapy is determined.
The robustness of the optimal therapies is then assessed. In addition, their applicability toward personalized medicine is discussed, where treatment is customized to each individual based on various factors such as genetic information, family history, social circumstances, environment and lifestyle.
"We have shown that personalized therapy is robust even with uncertain patient conditions. This is relevant as the model coefficients are characterized by uncertainties," Topputo explains. "Further studies would include designing optimal protocols by considering personalized constraints based on individual patient conditions, such as maximum amount of drug, therapy duration, and so on."
Other future directions would be the use of more
|Contact: Karthika Muthukumaraswamy|
Society for Industrial and Applied Mathematics