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qMRI Diffuser: Quantitative T1 Mapping of the Brain using a Denoising Diffusion Probabilistic Model

Shishuai Wang, Hua Ma, Juan A. Hernandez-Tamames, Stefan Klein, Dirk H. J. Poot

TL;DR

This work addresses the challenge of extracting reliable quantitative brain MRI parameters by framing qMRI mapping as a conditional generation problem and applying a denoising diffusion probabilistic model (DDPM). The proposed qMRI Diffuser uses the reverse diffusion $p_ heta(x_{t-1}|x_t,y)$ to recover the quantitative maps $x_0$ from noisy intermediates $x_t$, guided by seven weighted images $y$, and trained with the objective $L=\\mathbb{E}_{t,x_0,\\epsilon}ig[\ig\\|\\epsilon-\\\epsilon_ heta(x_t,y,t)\ig\\|^2\ig]$; it further provides voxel-wise uncertainty via repeated inferences. Compared to ResNet and RIM, qMRI Diffuser achieves higher accuracy and precision in T1 mapping, with superior edge preservation and the ability to quantify uncertainty without additional modifications. Trained on synthetic BrainWeb-based data and evaluated on a hardware phantom and an in vivo subject, it generalizes to real scans and holds promise for broader qMRI applications across protocols without requiring differentiable signal-model derivatives.

Abstract

Quantitative MRI (qMRI) offers significant advantages over weighted images by providing objective parameters related to tissue properties. Deep learning-based methods have demonstrated effectiveness in estimating quantitative maps from series of weighted images. In this study, we present qMRI Diffuser, a novel approach to qMRI utilising deep generative models. Specifically, we implemented denoising diffusion probabilistic models (DDPM) for T1 quantification in the brain, framing the estimation of quantitative maps as a conditional generation task. The proposed method is compared with the residual neural network (ResNet) and the recurrent inference machine (RIM) on both phantom and in vivo data. The results indicate that our method achieves improved accuracy and precision in parameter estimation, along with superior visual performance. Moreover, our method inherently incorporates stochasticity, enabling straightforward quantification of uncertainty. Hence, the proposed method holds significant promise for quantitative MR mapping.

qMRI Diffuser: Quantitative T1 Mapping of the Brain using a Denoising Diffusion Probabilistic Model

TL;DR

This work addresses the challenge of extracting reliable quantitative brain MRI parameters by framing qMRI mapping as a conditional generation problem and applying a denoising diffusion probabilistic model (DDPM). The proposed qMRI Diffuser uses the reverse diffusion to recover the quantitative maps from noisy intermediates , guided by seven weighted images , and trained with the objective ; it further provides voxel-wise uncertainty via repeated inferences. Compared to ResNet and RIM, qMRI Diffuser achieves higher accuracy and precision in T1 mapping, with superior edge preservation and the ability to quantify uncertainty without additional modifications. Trained on synthetic BrainWeb-based data and evaluated on a hardware phantom and an in vivo subject, it generalizes to real scans and holds promise for broader qMRI applications across protocols without requiring differentiable signal-model derivatives.

Abstract

Quantitative MRI (qMRI) offers significant advantages over weighted images by providing objective parameters related to tissue properties. Deep learning-based methods have demonstrated effectiveness in estimating quantitative maps from series of weighted images. In this study, we present qMRI Diffuser, a novel approach to qMRI utilising deep generative models. Specifically, we implemented denoising diffusion probabilistic models (DDPM) for T1 quantification in the brain, framing the estimation of quantitative maps as a conditional generation task. The proposed method is compared with the residual neural network (ResNet) and the recurrent inference machine (RIM) on both phantom and in vivo data. The results indicate that our method achieves improved accuracy and precision in parameter estimation, along with superior visual performance. Moreover, our method inherently incorporates stochasticity, enabling straightforward quantification of uncertainty. Hence, the proposed method holds significant promise for quantitative MR mapping.
Paper Structure (12 sections, 3 equations, 3 figures, 1 table)

This paper contains 12 sections, 3 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Method
  3. Experiments
  4. Scanning Protocol
  5. Datasets
  6. Network training
  7. Evaluation
  8. Results
  9. Discussion
  10. Conclusion
  11. Acknowledgments.
  12. Disclosure of Interests.

Figures (3)

  • Figure 1: Illustration of qMRI Diffuser's workflow. A U-Net model is trained to predict the noise added at a given time step. Weighted images acquired at different contrast states are set as the condition for the generation of quantitative maps. The number of channels in $y$ and $x_t$ should correspond to the number of weighted images used and quantitative parameters of interest respectively, and specifically here we set them as 7 and 3.
  • Figure 2: Example of T1 and PD estimation results in the phantom. A slice containing the $NiCl_2$ T1 spheres is presented.
  • Figure 3: Example of T1 and PD estimation results on the in vivo data. The in vivo T1 maps are plotted following the colormap recommendations cmap.