Author: Hector Andrade-Loarca, Ines Butz, Chiara Gianoli, Prof. Gitta Kutyniok, Jianfei Li, Katia Parodi, Prof. Vincenzo Patera, Angelo Schiavi, Prof. Ozan Öktem 👨🔬
Affiliation: Sapienza University of Rome, Department of Mathematics, Royal Institute of Technology, School of Computation, Information and Technology, Technische Universitaet Muenchen, Department of Medical Physics, Ludwig-Maximilians-Universität München (LMU Munich), Department of Mathematics, Ludwig-Maximilians-Universität (LMU) München, Department of Medical Physics, Ludwig-Maximilians-Universität (LMU) München 🌍
Purpose: To explore and demonstrate the feasibility of accurate and fast prediction of the water equivalent thickness (WET) distribution of tissue traversed by a proton imaging pencil beam, aiming at improving the Hounsfield Unit (HU) to Relative (to water) Stopping Power calibration (RSP) in treatment planning based on sparse proton radiographies (pRads). We propose a data-driven model to replace the conventional, approximative forward-projector for direct optimization on detector-space data as our previous work on end-to-end learned calibration using convolutional networks is in its current implementation limited by information loss in projection image formation.
Methods: In idealized-data experiments, the impact of reaching full consistency between forward-projector and pRads on the ill-posed calibration problem is quantified by comparing optimization performances on analytically generated, model-conformal pRads vs. realistic Monte-Carlo (MC) simulated pRads. Next, the data-driven forward-projector is trained on a dataset of ~6400 pencil beams generated in a MC-simulated proton imaging setup emulating an integration-mode range-telescope. WET distributions were scored at small steps throughout the CT volume to provide transport physics information during model training. A modified version of the DoTa architecture is used, representing the sequential nature of proton transmission through matter. It is trained for 1000 epochs, minimizing the Kullback-Leibler divergence between predicted and MC-simulated WET distributions.
Results: By virtually removing the model error from the optimization based on two pRads, the mean relative calibration error is reduced from ~3.2% to ~1.1% for a piecewise-linear calibration curve with 10 data points. Preliminary testing of the data-driven model shows some accurately predicted WET distributions, but enhancement of the dataset and further hyperparameter tuning are required.
Conclusion: Reducing, or ideally removing model errors from the forward-projector improves the HU to RSP calibration optimization for the integration-mode detector. Other detectors will be investigated. The transformer model is a promising candidate for learned, approximation-free forward-projection.