Exploration of differentiability in a proton computed tomography simulation framework

  • Objective. Gradient-based optimization using algorithmic derivatives can be a useful technique to improve engineering designs with respect to a computer-implemented objective function. Likewise, uncertainty quantification through computer simulations can be carried out by means of derivatives of the computer simulation. However, the effectiveness of these techniques depends on how 'well-linearizable' the software is. In this study, we assess how promising derivative information of a typical proton computed tomography (pCT) scan computer simulation is for the aforementioned applications. Approach. This study is mainly based on numerical experiments, in which we repeatedly evaluate three representative computational steps with perturbed input values. We support our observations with a review of the algorithmic steps and arithmetic operations performed by the software, using debugging techniques. Main results. The model-based iterative reconstruction (MBIR) subprocedure (at the end of the software pipeline) and the Monte Carlo (MC) simulation (at the beginning) were piecewise differentiable. However, the observed high density and magnitude of jumps was likely to preclude most meaningful uses of the derivatives. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path, and could be reduced in magnitude by a 'fuzzy voxels' approach. The investigated jumps in the MC function arose from local changes in the control flow that affected the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem. Significance. Besides the technical challenges of merely applying AD to existing software projects, the MC and MBIR codes must be adapted to compute smoother functions. For the MBIR code, we presented one possible approach for this while for the MC code, this will be subject to further research. For the tracking subprocedure, further research on surrogate models is necessary.

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Author:Max AehleORCiD, Johan Alme, Gergely Gábor Banaföldi, Johannes BlühdornORCiD, Tea Bodova, Vyacheslav Borshchov, Anthony van den Brink, Viljar Eikeland, Gregory Feofilov, Christoph Garth, Nicolas R. Gauger, Ola Grøttvik, Håvard Helstrup, Sergey Igolkin, Ralf Keidel, Chinorat Kobdaj, Tobias KortusORCiD, Lisa Kusch, Viktor Leonhardt, Shruti Mehendale, Raju Ningappa Mulawade, Odd Harald Odland, Georg O'Neill, Gábor Papp, Thomas Peitzmann, Helge Egil Seime PettersenORCiD, Pierluigi Piersimoni, Rohit Pochampalli, Maksym Protsenko, Max Rauch, Attiq Ur Rehman, Matthias Richter, Dieter Röhrich, Max Sagebaum, Joshua Santana, Alexander SchillingORCiD, Joao Seco, Arnon Songmoolnak, Ákos SudárORCiD, Ganesh Tambave, Ihor Tymchuk, Kjetil Ullaland, Monika Varga-Kofarago, Lennart VolzORCiD, Boris Wagner, Steffen Wendzel, Alexander WiebelORCiD, Ren Zheng Xiao, Shiming Yang, Sebastian Zillien
Parent Title (English):Physics in Medicine & Biology
Document Type:Article
Language of publication:English
Date of Publication (online):2024/04/30
Year of first Publication:2023
Publishing Institution:Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
Date of the Publication (Server):2024/04/30
Page Number:18
Faculties / Organisational entities:Kaiserslautern - Fachbereich Informatik
DDC-Cassification:0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik
Licence (German):Zweitveröffentlichung