Exploration of differentiability in a proton computed tomography simulation framework.

Area of Science:

• Medical Physics
• Computational Science
• Software Engineering

Background:

• Algorithmic derivatives enable gradient-based optimization and uncertainty quantification in computer simulations.
• The effectiveness of these derivative-based methods hinges on the 'well-linearizable' nature of the software.
• Proton computed tomography (pCT) simulations are increasingly used, necessitating an evaluation of their suitability for derivative-based analyses.

Approach:

• Numerical experiments were conducted by repeatedly evaluating key computational steps with perturbed input values.
• Debugging techniques and a review of algorithmic steps and arithmetic operations were employed to understand software behavior.
• The study focused on assessing derivative information from a typical pCT scan simulation.

Key Points:

• The model-based iterative reconstruction (MBIR) and Monte Carlo (MC) simulation components were found to be piecewise differentiable.
• High density and magnitude of discontinuities ('jumps') in these components likely hinder meaningful derivative utilization.
• Jumps in MBIR originated from discrete voxel calculations; a 'fuzzy voxels' approach may mitigate this.
• Jumps in MC simulation stemmed from control flow changes affecting random number generation.
• The tracking algorithm addresses an inherently non-differentiable problem.

Conclusions:

• Existing MC and MBIR codes require adaptation for smoother function computation to enable derivative-based applications.
• A method to smooth MBIR functions was presented; further research is needed for MC code adaptation.
• The non-differentiable nature of the tracking algorithm necessitates research into surrogate models.