Exploration of Differentiability in a Proton Computed Tomography Simulation Framework

TL;DR

This study evaluates the differentiability of a proton computed tomography simulation framework, identifying which components are suitable for algorithmic differentiation to optimize and quantify uncertainties in the process.

Contribution

It provides a detailed analysis of the differentiability of key simulation components, guiding the integration of algorithmic differentiation in pCT software.

Findings

MBIR and MC simulation components are piecewise differentiable.

Jumps caused by discrete voxel calculations and control flow changes.

Tracking algorithm is inherently non-differentiable.

Abstract

Objective. Algorithmic differentiation (AD) can be a useful technique to numerically optimize design and algorithmic parameters by, and quantify uncertainties in, computer simulations. However, the effectiveness of AD 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. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path. Jumps in the MC function likely arose from changes in the control flow that affect the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem. Significance. The MC and MBIR codes are ready for the integration of AD, and further research on surrogate models for the tracking subprocedure is necessary.