Reducing systematic errors due to deformation of organs at risk in radiotherapy

Abstract

In radiotherapy (RT), the planning CT (pCT) is commonly used to plan the full RT-course. Due to organ deformation and motion, the organ shapes seen at the pCT will not be identical to their shapes during RT. Any difference between the pCT organ shape and the organ's mean shape during RT will cause systematic errors. We propose to use statistical shrinkage estimation to reduce this error using only the pCT and the population mean shape computed from training data. Methods: The method was evaluated for the rectum in a cohort of 37 prostate cancer patients that had a pCT and 7-10 treatment CTs with rectum delineations. Deformable registration was performed both within-patient and between patients, resulting in point-to-point correspondence between all rectum shapes, which enabled us to compute a population mean rectum. Shrinkage estimates were found by combining the pCTs linearly with the population mean. The method was trained and evaluated using leave-one-out cross validation. The shrinkage estimates and the patient mean shapes were compared geometrically using the Dice similarity index (DSI), Hausdorff distance (HD), and bidirectional local distance. Clinical dose/volume histograms, equivalent uniform dose (EUD) and minimum dose to the hottest 5% volume (D5%) were compared for the shrinkage estimate and the pCT. Results: The method resulted in moderate but statistically significant increase in similarity to the patient mean shape over the pCT. On average, the HD was reduced from 15.6 to 13.4 mm, while the DSI was increased from 0.74 to 0.78. Significant reduction in the bias of volume estimates was found in the DVHrange of 52.5-65 Gy, where the bias was reduced from −1.3 to −0.2 percentage points, but no significant improvement was found in EUD or D5%, Conclusions: The results suggest that shrinkage estimation can reduce systematic errors due to organ deformations in RT. The method has potential to increase the accuracy in RT of deformable organs and can improve motion modeling.

An organ deformation model using Bayesian inference to combine population and patient-specific data

“…This correspondence is found using deformable and rigid contour registration both within and between patients. Details are beyond the scope of the current work, but can be found in Rørtveit et al (2021). Due to the random character of the organ shape, a set of shape vectors s 1 , K, s J derived from J scans of a patient is described as J realizations of the random variable s. For all the following methods, the shape coordinates for a specific patient are assumed to follow a multivariate Gaussian distribution:…”

“…When only a single observation for the new patient is available, i. e. J = 1, (22) becomes identical to the shrinkage estimation from Rørtveit et al (2021).…”

“…The parameter κ for the NIW-model was set to 0.25. Using equation (18), we find that, given one input scan, this represents an shrinkage factor of 0.2; i.e the estimated mean is 'shrunk' by a factor 0.2 towards the population mean (Rørtveit et al 2021). The parameter ν, the number of degrees of freedom of the Wishart distribution, was set to 6 for both the NIW and the variational model.…”