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Accelerated Diffusion Tensor Imaging using A Diffusion Generative Deep Learning Model

Phillip Andrew Martin^1,2, Brian Toner^2,3, Maria Altbach^2,4, and Ali Bilgin^1,2,3,4
¹Electrical and Computer Engineering, University of Arizona, Tucson, AZ, United States, ²Medical Imaging, University of Arizona, Tucson, AZ, United States, ³Applied Mathematics, University of Arizona, Tucson, AZ, United States, ⁴Biomedical Engineering, University of Arizona, Tucson, AZ, United States

Synopsis

Keywords: AI Diffusion Models, Diffusion Tensor Imaging

Motivation: High-quality diffusion tensor imaging involves fitting a large number of diffusion-encoded images to a tensor model. This challenging process requires long scans and is vulnerable to motion artifacts. There’s a need for accelerated acquisitions while preserving robust diffusion tensor estimates.

Goal(s): To develop a generative diffusion model that produces high-quality tensor metrics using a few diffusion-encoded images.

Approach: The proposed generative model was trained using 300 randomly selected subjects from the Human Connectome Project Dataset and tested on 20 subjects.

Results: Our model demonstrates the ability to generate high-quality tensor metrics for as few as 3 DWIs.

Impact: This study demonstrates that a generative diffusion model can produce high-quality tensor metrics with significant reduction in scan time, potentially eliminating image distortions and artifacts.

Introduction

Diffusion-weighted magnetic resonance imaging (dMRI) is a prominent technique, for qualitatively and quantitatively assessing microstructural characteristics of tissues. dMRI techniques such as Diffusion Tensor Imaging (DTI)¹ have been utilized to study a wide range of structural and pathological processes such as neuronal connectivity², ischemia³, tumor growth and response to therapy⁴. One of the major challenges of dMRI is the long data acquisition times required to obtain a large number of diffusion-weighted images (DWIs) for accurate estimation of various diffusion metrics. Recently, deep learning (DL) techniques were proposed to accelerate dMRI^5,6,7,8,9. In this work, we present a novel generative diffusion DL model which produces robust and high-quality DTI metrics given an accelerated acquisition of DWIs and bypasses the need for diffusion tensor fitting.

Methods

DWI datasets were acquired from the Human Connectome Project (HCP) database¹⁰. 300 randomly selected datasets were used for training/validation and 20 for testing. HCP data consists of 270 DWIs (90 each at b = 1000, 2000, 3000 s/mm²) combined with 18 b =0 images. These data were fitted to a tensor model (Fig1a), acquiring fractional anisotropy (FA), axial diffusivity (AD), and radial diffusivity (RD) maps using MRtrix.¹¹ Our proposed method (Fig1b) is a conditional diffusion model¹² built to generate DTI metrics conditioned on a small set of noisy DWIs. Let y denote the desired DTI metric and x the set of acquired DWIs combined with one b=0 image. Our overarching goal is to learn the empirical data distribution p(y|x) through a training procedure. The forward diffusion process is modeled as a Markovian process over T iterations. Gaussian noise is iteratively added to an initial data point $$${y_{0}}$$$, such that at iteration t = T, the noisy image $$${y_{T}}$$$ is well approximated by a standard Gaussian distribution. During training, given an initial data point $$${y_{0}}$$$ a noise level $$$\gamma$$$, and a noise sample $$$\epsilon \sim \mathcal{N}(0, I)$$$, a noisy image is created as $$$\widetilde{y}$$$ = $$$\sqrt{\gamma} y_0 + \sqrt{1 - \gamma} \epsilon$$$ and is used to train a model $$$f_{\theta}(x, \widetilde{y}, \gamma)$$$. The network is trained to predict the noise sample $$$\epsilon$$$ given $$$x$$$, $$$\widetilde{y}, \gamma$$$. During inference, samples from a standard Gaussian distribution are converted to samples from p(y|x) using the trained model. Our model was implemented in PyTorch and trained over 500 epochs using a linear noise schedule with 1000 timesteps, and batch size = 8. A UNet was used for denoising, which comprised three convolutional levels with 4 residual blocks each. Images were zero-padded to 192 x 192. Experiments were conducted using different number of conditioning DWIs (k=3,4, and 6 DWIs + 1 b = 0 image). For comparison, DTI metrics were obtained using Marcenko-Pastur Principle Component Analysis (MP PCA)¹³ and conventional DTI results for k=6 DWIs, in addition to the reference metrics which used all available data (k=270 DWIs + 18 b=0 images).

Results and Discussion

A qualitative assessment of tensor metrics FA, AD, and RD produced by the proposed method for k = 6 DWIs is shown in Fig2. All maps produced by the proposed method closely resemble the maps obtained using the full 288 image reference. Fig3 demonstrates FA maps obtained using the proposed method using k=3, 4, and 6 DWIs. It is shown that these maps can delineate structural features even using as few as 3 DWIs, which is beyond the theoretical limit of DTI modeling. Fig4 shows correlation histograms of the predicted FA, AD, and RD metrics of each method relative to the reference values over the test cohort. While the MP PCA and DTI methods show significant bias and prediction variance, the proposed DL framework predictions remain tightly distributed around the reference values. Table1 evaluates quantitative performance of our diffusion framework in calculating MAE, PSNR, and PCCs over all computational pipelines. The proposed diffusion method demonstrates superior performance over all metrics. Overall, the results indicate that our proposed model accurately predicts superior tensor metrics, even when dealing with significantly accelerated data acquisition. Additionally, it's worth noting that the proposed approach exhibits adaptability and has the potential for future expansion to encompass various MRI diffusion models. Such an extension would involve addressing the challenge of resolving crossing fibers, thereby enhancing its utility in delineating microstructural features within white matter.

Conclusion

We produced an innovative generative diffusion method that possesses the capability to predict superior tensor metrics when presented with highly accelerated DWI acquisitions. Importantly, this technique bypasses the diffusion tensor fitting process. The framework opens up the exciting potential to obtain high-quality DTI metrics while drastically reducing the overall scan duration.

Acknowledgements

We would like to acknowledge grant support from the Arizona Biomedical Research Commission (CTR056039), Arizona Alzheimer’s Consortium, and the Technology and Research Initiative Fund Technology and Research Initiative Fund (TRIF).

References

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Figures

Figure 1: The proposed diffusion DL pipeline: (a) For training, 288 DWIs across b = 0, 1000, 2000, 3000 s/mm² are fit to a tensor model. The resulting tensors are used to obtain tensor metrics, FA, AD, and RD. (b) A separate DL model is trained for each DTI metric. Given a set of noisy DWIs x, the model is trained to produce a clean DTI metric y. During inference, a sample from the standard Gaussian distribution is combined with the noisy DWIs x to produce the predicted DTI metric.

Figure 2: Tensor Metrics FA, AD, and RD maps obtained using accelerated acquisitions of 6 DWIs for b = 1000 s/mm². Our Diffusion DTI DL framework shows higher-quality maps across different metrics compared to DTI and MP PCA.

Figure 3: FA maps obtained by the proposed method using different number of conditioning DWIs (k=3, 4, and 6) compared to other methods. Absolute prediction errors for each method are also shown. Diffusion DTI DL framework produces high-quality FA maps even for very high acceleration factors.

Figure 4: (a) Two-dimensional correlation histograms comparing predicted FA, AD, and RD values for each computational framework to the corresponding reference values over the entire test cohort of n=20 subjects (k=6 DWIs). (b) Two-dimensional correlation histograms of FA values produced by the proposed method for k=3, 4, and 6. Overall, the metrics produced by the proposed model are more tightly distributed about the reference values than DTI and MP PCA.

Figure 5: (a) Quantitative performance comparison of different methods using Mean Absolute Error (MAE), Peak Signal-to-Noise Ratio (PSNR), and Pearson Correlation Coefficients (PCCs) for k=6 DWIs. (b) MAE, PSNR, and PCC metrics obtained by the proposed method for FA using k=3, 4, and 6 DWIs. The proposed model achieves the best performance across all metrics.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

1749

DOI: https://doi.org/10.58530/2024/1749