Diffusion Schrödinger bridge models for high-quality MR-to-CT synthesis for proton treatment planning

In recent advancements in proton therapy, magnetic resonance (MR)-based treatment planning is gaining momentum due to its excellent soft tissue contrast and high potential to minimize extra radiation exposure compared to traditional computed tomography (CT)-based methods. This transition underscores the critical need for accurate MR-to-CT image synthesis, which is essential for precise proton dose calculations.

This study aims to introduce and evaluate the diffusion Schrödinger bridge models (DSBM), an innovative approach for high-quality and efficient MR-to-CT synthesis, in order to improve both the quality and speed of synthetic CT (sCT) image generation.

The DSBM learns the nonlinear diffusion processes between MR and CT data distributions. Unlike traditional diffusion models (DMs), which start synthesis from a Gaussian distribution, DSBM starts from the prior distribution, enabling more direct and efficient synthesis. The model was trained on 46 head-and-neck (HN) MR-CT pairs and 77 brain tumor MR-CT pairs, with 8 and 10 scans used for testing, respectively. Comprehensive evaluations were conducted at both image and dosimetric levels, using metrics such as mean absolute error (MAE), Dice score, voxel-wise proton dose differences, gamma pass rates of clinical plans, and typical dose indices.

For the HN dataset, DSBM achieved a lower MAE of 72.42 $\pm$ 9.78 Hounsfield unit (HU) compared to 77.72 $\pm$ 9.11 HU with the best baseline approach, and a higher Dice score for bone of 83.32 $\pm$ 3.25% compared to 82.55 $\pm$ 3.62%, indicating superior anatomical accuracy. Dosimetric evaluations showed a 1%/1 mm gamma pass rate of 95.85 $\pm$ 2.99%, surpassing the 95.25 $\pm$ 3.09% achieved by the baseline model. For the brain tumor dataset, DSBM outperformed the baseline with an MAE of 91.73 $\pm$ 6.86 HU compared to 103.25 $\pm$ 9.58 HU, and a Dice score for bone of 82.85 $\pm$ 3.88% compared to 81.27 $\pm$ 4.59%. DSBM also demonstrated a higher 1%/1 mm gamma pass rate of 97.93 $\pm$ 1.82%, confirming its robustness across different anatomical regions. Notably, DSBM achieved these results with very few number of neural function evaluation steps, significantly improving computational efficiency compared to standard DMs.

The DSBM demonstrates superior performance over traditional image synthesis methods in MR-based proton treatment planning. Its ability to generate high-quality sCT images with enhanced speed and accuracy highlights its potential as a valuable and efficient tool in various radiotherapy clinical scenarios.