Researchers at North Carolina State University have developed a mathematical model for computing radiation therapy treatments that could substantially reduce patient side effects while delivering the same results as conventional radiation therapy.
Cancer patients who receive radiotherapy to destroy their tumors are given a total dose of radiation split into multiple equal treatments delivered over days or weeks. This is due to something called the fractionation effect: radiation-induced cell damage is lower if the same physical dose is delivered in multiple fractions, because it allows healthy cells to recover between treatments. Current clinical protocols stipulate that patients receive the same dose in each treatment session, every day.
But do the doses have to be the same each day? “Different doses, carefully planned to minimize side effects, can be just as effective,” says Dávid Papp, assistant professor of mathematics at NC State University. “However, the extent of this benefit has never been assessed. The algorithms we use now to determine the best personalized treatments don’t work when computing treatments with different dose distributions in different fractions.”
Papp set out to develop and test a so-called “spatiotemporal fractionation” approach that would reduce the radiation dose to healthy tissue while maintaining effectiveness against the tumor. In a proof-of-concept study, Papp tested the plan against model slices of five different liver tumors, each representing a unique tumor size or location to allow comparisons with actual clinical treatments.
“We wanted to see what the quantitative benefits of such a new protocol would be,” says Papp. “How much can you reduce the radiation’s effect on the liver while making sure that the tumor receives a consistent and effective dose? A reduction of 20 percent would reduce side effects enough to warrant a change in everyday clinical practice.”
Papp’s model reduced the liver dose by 13 to 35 percent without compromising other clinical goals. He has begun work on refining the model to make it more robust, with a view toward in vivo testing.
“Conventional radiation treatments don’t necessarily achieve maximum benefit,” Papp says. “Our protocol, by delivering a high single-fraction dose to parts of the tumor during each fraction and a consistent lower dose to the liver and other healthy tissue, could reduce patient side effects substantially while maintaining the same effectiveness as conventional treatments.”
The research appears in Physics in Medicine and Biology. Papp is corresponding author. Graduate student Melissa Gaddy, postdoctoral researcher Sercan Yildiz from the Statistical and Applied Mathematical Sciences Institute (SAMSI), and Jan Unkelbach, radiation oncologist at University Hospital Zürich, contributed to the work.
Note to editors: An abstract follows.
“Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit”
Authors: Dávid Papp, Melissa Gaddy, North Carolina State University; Sercan Yildiz, Statistical and Applied Mathematical Sciences Institute; Jan Unkelbach, University of Zürich, Switzerland
Published: Physics in Medicine and Biology
Spatiotemporal fractionation schemes, that is, treatments delivering different dose distributions in different fractions, can potentially lower treatment side effects without compromising tumor control. This can be achieved by hypofractionating parts of the tumor while delivering approximately uniformly fractionated doses to the surrounding tissue. Plan optimization for such treatments is based on biologically effective dose (BED); however, this leads to computationally
challenging nonconvex optimization problems. Optimization methods that are in current use yield only locally optimal solutions, and it has hitherto been unclear whether these plans are close to the global optimum. We present an optimization framework to compute rigorous bounds on the maximum achievable normal tissue BED reduction for spatiotemporal plans. The approach is demonstrated on liver tumors, where the primary goal is to reduce mean liver BED without compromising any other treatment objective. The BED-based treatment plan optimization problems are formulated as quadratically constrained quadratic programming (QCQP) problems. First, a conventional, uniformly fractionated reference plan is computed using convex optimization. Then, a second, nonconvex, QCQP model is solved to local optimality to compute a spatiotemporally fractionated plan that minimizes mean liver BED, subject to the constraints that the plan is no worse than the reference plan with respect to all other planning goals. Finally, we derive a convex relaxation of the second model in the form of a semidefinite programming (SDP) problem, which provides a rigorous lower bound on the lowest achievable mean liver BED. The method is presented on 5 cases with distinct geometries. The computed spatiotemporal plans achieve 12-35 percent mean liver BED reduction over the optimal uniformly fractionated plans. This reduction corresponds to 79-97 percent of the gap between the mean liver BED of the uniform reference plans and our lower bounds on the lowest achievable mean liver BED. The results indicate that spatiotemporal treatments can achieve substantial reductions in normal tissue dose and BED, and that local optimization techniques provide high-quality plans that are close to realizing the maximum potential normal tissue dose reduction.