A stochastic convolution/superposition method with isocenter sampling to evaluate intrafraction motion effects in IMRT

Current methods to calculate dose distributions with organ motion can be broadly classified as "dose convolution" and "fluence convolution" methods. In the former, a static dose distribution is convolved with the probability distribution function (PDF) that characterizes the motion. However, artifacts are produced near the surface and around inhomogeneities because the method assumes shift invariance. Fluence convolution avoids these artifacts by convolving the PDF with the incident fluence instead of the patient dose. In this paper we present an alternative method that improves the accuracy, generality as well as the speed of dose calculation with organ motion. The algorithm starts by sampling an isocenter point from a parametrically defined space curve corresponding to the patient-specific motion trajectory. Then a photon is sampled in the linac head and propagated through the three-dimensional (3-D) collimator structure corresponding to a particular MLC segment chosen randomly from the planned IMRT leaf sequence. The photon is then made to interact at a point in the CT-based simulation phantom. Randomly sampled monoenergetic kernel rays issued from this point are then made to deposit energy in the voxels. Our method explicitly accounts for MLC-specific effects (spectral hardening, tongue-and-groove, head scatter) as well as changes in SSD with isocentric displacement, assuming that the body moves rigidly with the isocenter. Since the positions are randomly sampled from a continuum, there is no motion discretization, and the computation takes no more time than a static calculation. To validate our method, we obtained ten separate film measurements of an IMRT plan delivered on a phantom moving sinusoidally, with each fraction starting with a random phase. For 2 cm motion amplitude, we found that a ten-fraction average of the film measurements gave an agreement with the calculated infinite fraction average to within 2 mm in the isodose curves. The results also corroborate the existing notion that the interfraction dose variability due to the interplay between the MLC motion and breathing motion averages out over typical multifraction treatments. Simulation with motion waveforms more representative of real breathing indicate that the motion can produce penumbral spreading asymmetric about the static dose distributions. Such calculations can help a clinician decide to use, for example, a larger margin in the superior direction than in the inferior direction. In the paper we demonstrate that a 15 min run on a single CPU can readily illustrate the effect of a patient-specific breathing waveform, and can guide the physician in making informed decisions about margin expansion and dose escalation.