Abstract Book

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ESTRO 37

deviation of RBExD. The covariance matrix allows to model arbitrary physical and biological uncertainty patterns. This in turn allows closed form probabilistic optimization based on the expectation value of the standard piece-wise quadratic objective function. Our approach is evaluated on a 1D artificial case treated with opposing fields. We assume a prescribed dose of 3GyE and a biological system with alpha x =0.1 Gy -1 and beta x =0.05 Gy -2 . Linear quadratic model parameter of carbon ions are obtained using the local effect model IV. We model 3.5% range uncertainty and a depth dependent uncertainty in α c and β c (25% at Bragg peak, less before and after).

Conclusion Our results suggest that in PBS proton therapy Range Shifter need to be used with extreme caution when planning the treatment with an analytical algorithm due to potentially great discrepancies between the planned dose and the dose delivered to the patients, also in case of brain tumours where this issue could be underestimated. Our results also suggest that a MC evaluation of the dose has to be performed every time the RS is used and, mostly, when it is used with large air gaps and beam directions tangential to the patient surface. OC-0088 Simultaneous consideration of biologyical and physical uncertainties in robust ion therapy planning H.P. Wieser 1,2,3 , N. Wahl 1,3,4 , P. Hennig 5 , M. Bangert 1,3 1 German Cancer Research Center DKFZ, Medical Physics in Radiation Oncology, Heidelberg, Germany 2 University of Heidelberg, Medical Faculty, Heidelberg, Germany 3 Heidelberg Institute of Radiation Oncology, HIRO, Heidelberg, Germany 4 University of Heidelberg, Physics Faculty, Heidelberg, Germany Purpose or Objective Particle therapy is particularly prone to uncertainties. While this issue is commonly addressed for range and setup errors with robust optimization, uncertainties in the relative biological effectiveness (RBE) models are usually not considered. Especially for carbon ion therapy, where RBE induces pronounced non-linear modulation within the RBE-weighted dose (RBExD), biological uncertainties may be of particular importance. Here, we present a computational pipeline that combines physical and biological uncertainties simultaneously into a joint probabilistic optimization process. Our work builds upon analytical probabilistic modeling (APM) that uses closed form expressions for the computation of the expectation value of the RBExD and its standard deviation. Material and Methods APM builds upon a Gaussian parameterization of the RBExD calculation directly operating on α x dose (shown in figure 1) and sqrt(β) x dose (not shown) profiles. With such a formulation, uncertainties in range and setup can be modeled as positional uncertainties in the individual Gaussian components (range uncertainties are indicated by horizontal error bars in figure 1 (setup uncertainties are not shown). Uncertainties in the biological model, i.e., uncertainties in depth dependent dose averaged α c and β c can be modeled as uncertainty in the weight (i.e. the height) of the individual Gaussian components (indicated by vertical error bars in figure 1). Assuming a joint Gaussian probability distribution over component uncertainties in position and weight enables analytical calculation of the expectation value and standard 5 Max Planck Institute for Intelligent Systems, Probabilistic Numerics, Tuebingen, Germany

Results Figure 2 shows a maximal deviation between APM (solid lines) and 5000 random samples (crosses) of 1.28% for the expectation value and 14.5% for the standard deviation. In comparison to conventional optimization neglecting uncertainties (figure 2 (a)), a probabilistic optimization considering biological and physical uncertainties with APM reduces the mean σ[RBExD] in the target from 0.42 to 0.23 GyE through automatic margin generation and RBE homogenization.