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Diffusion Schrödinger Bridge Models for High-Quality MR-to-CT Synthesis for Head and Neck Proton Treatment Planning

Muheng Li, Xia Li, Sairos Safai, Damien Weber, Antony Lomax, Ye Zhang

TL;DR

The paper tackles MR-to-CT image synthesis for MR-based proton therapy planning, addressing the need to derive accurate CT-density information from MR scans to compute proton doses. It introduces Diffusion Schrödinger Bridge Models (DSBM) that learn nonlinear diffusion between MR and CT distributions by starting from a learned prior $p_{MR}$ rather than a Gaussian, and by formulating the process with Schrödinger Bridge forward/backward SDEs and an analytic posterior $q(X_t|X_0,X_T)$ with mean $\mu_t$ and covariance $\Sigma_t$. The approach is validated on a head-and-neck dataset of 58 patients, showing image-level improvements ($MAE=72.30\pm8.31$ HU; $Dice_{bone}=83.10\pm3.90\%$) and dosimetric fidelity (mean dose error <$0.01\%$; gamma pass rates around $95.5\%$ to $96.2\%$). Importantly, DSBM achieves these results with few neural function evaluation steps and fast per-volume sampling times (~0.2 s per step), indicating potential for practical MR-based planning and reduced imaging dose. The results support the potential of DSBM to enhance MR-based proton therapy workflows by delivering accurate MR-to-CT synthesis with high dosimetric fidelity at improved efficiency.

Abstract

In recent advancements in proton therapy, MR-based treatment planning is gaining momentum to minimize additional radiation exposure compared to traditional CT-based methods. This transition highlights the critical need for accurate MR-to-CT image synthesis, which is essential for precise proton dose calculations. Our research introduces the Diffusion Schrödinger Bridge Models (DSBM), an innovative approach for high-quality MR-to-CT synthesis. DSBM learns the nonlinear diffusion processes between MR and CT data distributions. This method improves upon traditional diffusion models by initiating synthesis from the prior distribution rather than the Gaussian distribution, enhancing both generation quality and efficiency. We validated the effectiveness of DSBM on a head and neck cancer dataset, demonstrating its superiority over traditional image synthesis methods through both image-level and dosimetric-level evaluations. The effectiveness of DSBM in MR-based proton treatment planning highlights its potential as a valuable tool in various clinical scenarios.

Diffusion Schrödinger Bridge Models for High-Quality MR-to-CT Synthesis for Head and Neck Proton Treatment Planning

TL;DR

The paper tackles MR-to-CT image synthesis for MR-based proton therapy planning, addressing the need to derive accurate CT-density information from MR scans to compute proton doses. It introduces Diffusion Schrödinger Bridge Models (DSBM) that learn nonlinear diffusion between MR and CT distributions by starting from a learned prior rather than a Gaussian, and by formulating the process with Schrödinger Bridge forward/backward SDEs and an analytic posterior with mean and covariance . The approach is validated on a head-and-neck dataset of 58 patients, showing image-level improvements ( HU; ) and dosimetric fidelity (mean dose error <; gamma pass rates around to ). Importantly, DSBM achieves these results with few neural function evaluation steps and fast per-volume sampling times (~0.2 s per step), indicating potential for practical MR-based planning and reduced imaging dose. The results support the potential of DSBM to enhance MR-based proton therapy workflows by delivering accurate MR-to-CT synthesis with high dosimetric fidelity at improved efficiency.

Abstract

In recent advancements in proton therapy, MR-based treatment planning is gaining momentum to minimize additional radiation exposure compared to traditional CT-based methods. This transition highlights the critical need for accurate MR-to-CT image synthesis, which is essential for precise proton dose calculations. Our research introduces the Diffusion Schrödinger Bridge Models (DSBM), an innovative approach for high-quality MR-to-CT synthesis. DSBM learns the nonlinear diffusion processes between MR and CT data distributions. This method improves upon traditional diffusion models by initiating synthesis from the prior distribution rather than the Gaussian distribution, enhancing both generation quality and efficiency. We validated the effectiveness of DSBM on a head and neck cancer dataset, demonstrating its superiority over traditional image synthesis methods through both image-level and dosimetric-level evaluations. The effectiveness of DSBM in MR-based proton treatment planning highlights its potential as a valuable tool in various clinical scenarios.
Paper Structure (9 sections, 4 equations, 3 figures, 3 tables)

This paper contains 9 sections, 4 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Materials and Methods
  3. Diffusion Schrödinger Bridge Models (DSBM)
  4. Dataset and Model Implementations
  5. Image-level Evaluation
  6. Dosimetric-level Evaluation
  7. Results
  8. Discussion
  9. Conclusion

Figures (3)

  • Figure 1: Visual comparisons of sCTs and error histograms from pix2pix and DSBM. Errors are calculated as $|sCT - pCT|$.
  • Figure 2: Dosimetric study of a single case. (Top) Comparison of dose distribution. dDose was calculated as sDose - pDose. (Bottom Left) DVHs, with structures highlighted in the DDVH graph denoted by (*). (Bottom Right) DDVHs. Representation for DVHs and DDVHs: solid lines (---) for pDose, dotted lines (...) for pix2pix model, dashdot (- - -) lines for DSBM (50-step).
  • Figure 3: Comparison of the dosimetric accuracy of the sCTs (N=12), in terms of (upper) differences in typical dose indexes from corresponding DVHs, and (bottom) differences in Vdosediff>3% from corresponding DDVH.