Built-in wavelet-induced smoothness to reduce plan complexity in intensity modulated radiation therapy (IMRT)

Abstract

Objective. Reducing plan complexity in intensity modulated radiation therapy (IMRT) to ensure dosimetric accuracy and delivery efficiency of the radiation treatment plans. We propose a novel approach by representing the beamlet intensities using an incomplete wavelet basis that explicitly excludes fluctuating intensity maps from the decision space (explicit hard constraint). This technique provides a built-in wavelet-induced smoothness that improves both dosimetric plan quality and delivery efficiency. Approach. The beamlet intensity maps need to be especially smooth in the leaf travel direction (referred to as the X-direction). We treat the intensity map of each beam as a 2D image and represent it using the wavelets corresponding to low-frequency changes in the X-direction (i.e. approximation and horizontal). The absence of wavelets corresponding to high-frequency changes (i.e. vertical and diagonal) induces built-in smoothness. We still utilize a regularization term in the objective function to promote smoothness in the Y-direction (perpendicular to the X-direction) and further possible smoothness in the X-direction. This technique has been tested on three patient cases of different disease sites (paraspinal, lung, prostate) and all final evaluations and comparisons have been performed on an FDA-approved commercial treatment planning system (Varian EclipseTM). Main results. Wavelet-induced smoothness reduced monitor units by about 10%, 45%, and 14% for paraspinal, lung, and prostate cases, respectively. It also improved organ at risk sparing, especially on the complex paraspinal case where it resulted in about 7%, 13%, and 14% less mean dose to esophagus, lung, and cord, respectively. Moreover, built-in wavelet-induced smoothness desensitizes the results to changing the weight associated to the regularization term, and thereby mitigates the weight fine-tuning difficulty. Significance. Fluence smoothness is often achieved by smoothing the beamlet intensity maps using a proper regularization term in the objective function aiming at disincentivizing fluctuation in the beamlet intensities (implicit soft constraint). This work reports a novel application of wavelets in imposing an explicit smoothness hard constraint in the search space using an incomplete wavelet basis. This idea has been successfully applied to exclude complex and clinically irrelevant radiation plans from the search space. The code and pertained models along with a sample dataset are released on our LowDimRT GitHub (https://github.com/PortPy-Project/LowDimRT).