Abstract Book

S1028

ESTRO 37

EP-1898 Smooth animations of the probabilistic analog to worst-case dose distributions N. Wahl 1,2,3 , H.P. Wieser 1,2,4 , L.R. Müller 1,2,3 , P. Hennig 5 , M. Bangert 1,2 1 German Cancer Research Center DKFZ, Medical Physics in Radiation Oncology, Heidelberg, Germany 2 Heidelberg Institute of Radiation Oncology, HIRO, Heidelberg, Germany 3 University of Heidelberg, Department of physics and astronomy, Heidelberg, Germany 4 University of Heidelberg, Medical Faculty, Heidelberg, Germany Purpose or Objective Clinical robustness analysis is rare and usually limited to the re-computation of the treatment plan considering discrete worst case scenarios. To stay within feasible computation times, this analysis has to be based on comparably few random or importance samples, which might not reveal the true variability in dose within a continuous space of possible treatment scenarios. Here, we present an approximate method to generate continuous animations of a dose distribution confidence boundary based on few samples. The resulting visualizations can be interpreted as smooth probabilistic analog to discrete worst case dose distributions. Material and Methods We suggest to approximate the probability distribution over dose by a multivariate Normal distribution whose mean and covariance can be estimated by sampling or analytical methods. Modelling uncertainties in this context with Gaussian densities may not be fully accurate but it is a widely accepted and mathematically convenient practice in radiation therapy. First, it allows that a subset of voxels, i.e. a dose slice or a volume of interest, can be represented by a computationally tractable marginal multivariate Normal distribution. Second, samples can be drawn from this multivariate Normal via a linear transformation of a standard multivariate Normal sample using the mean dose and the Cholesky-decomposition of the covariance matrix. This sampling process can be adapted to explore a continuous subspace of the sample space. To do so, we extend an existing method developed for Gaussian process animations. This method parametrizes a hyper- sphere on the standard multivariate Normal by a randomly chosen radius r , and then "walks" on an orthodrome on this hyper-sphere to generate a set of equiprobable coordinates that can be back-projected, evaluated and displayed one after each other to obtain consecutive and "smooth" samples of the original multivariate Normal. The radius r may also be chosen according to a distinct meaning, e.g. from the quantile function of the χ²-distribution yielding confidence surfaces or by a selected start coordinate. Results We generated a set of visualizations for a carbon plan on the liver case and a proton plan on the prostate case from the open source CORT dataset. 54 importance samples based on combinations of a 2% and 3% range error and 2mm and 3mm setup error where used for the liver and the prostate case, respectively . Since the additional dimension time is needed to present the results, i.e. smooth animations, two animated GIFs showing samples on the 50% confidence ellipsoid (corresponding to ±0.68σ sigma in a single dimension) are provided at https://github.com/becker89/ESTRO2018 . Conclusion We present a method that allows to illustrate the structure of the uncertainties present in a treatment plan based on a continuous animation of equiprobable scenarios. Our technique provides a probabilistic analog 5 Max Planck Institute for Intelligent Systems, Probabilistic Numerics, Tübingen, Germany

datasets each included an easy, medium, and difficult patient, assessed by rectum and target shape and overlap, to allow for developed AP techniques to account for the range of patient variability encountered within the clinic. Once AP techniques were developed, an additional 10 prostate patient datasets were distributed by each centre. Automated treatment planning was performed on all patients by each centre using the developed AP techniques, resulting in a total of 3 plans for 30 patients across three treatment protocols. Plan quality was assessed through DVH analysis and number of protocol compliances. Results The number of deviations for AP techniques from centres A, B, and C were 28 (2 constraint, 1 hard, 12 medium, 13 soft, compliance = 91.5%), 52 (3 constraint, 2 hard, 35 medium, 12 soft, compliance = 87.6%), and 9 (3 constraint, 2 hard, 4 medium, compliance = 96.7%) respectively. Constraint and high priority deviations of host-centre protocols were CTV D99% > 78Gy, rectum V70Gy < 10%, rectum V75Gy < 5% (centre A); rectal wall V75Gy < 10% (centre B); and rectum V74Gy < 1 cc (centre C). Figure 1 shows mean PTV DVH data for AP techniques from centres A (red), B (blue), and C (green) across all datasets. Significantly improved dose distributions for PTV were achieved by centres A and C for centre B patients (dashed), as well as by centre A for centre C patients (dotted). Conversely, figure 2 reveals poorer high dose sparing for rectum due to centre A AP technique.

Figure 1: Mean PTV DVH for all AP techniques across all protocols

Figure 2: Mean rectum DVH for all AP techniques across all protocols Conclusion Automated treatment planning techniques that met each centre’s protocol requirements were successfully developed using a small learning dataset of three patients. Differences in prioritisation of dose objectives affected treatment plan comparison, as centre A techniques produced superior PTV dose coverage, while centre B and C techniques recorded significantly improved high dose sparing for rectum. The study shows that use of AP to implement new protocols across international centres is feasible, and could be utilised to improve plan quality in future clinical trials.