Accelerated Proton Resonance Frequency-based Magnetic Resonance Thermometry by Optimized Deep Learning Method

TL;DR

This work tackles the challenge of real-time PRF-based MR thermometry for focused ultrasound by introducing training-time optimizations to deep learning reconstructions of undersampled k-space data. The approach combines offline diffusion augmentation, online complex-valued augmentation, knowledge distillation from a teacher model, and an amplitude-phase decoupled loss, applied across multiple base architectures to improve temperature-map reconstruction at $2\times$ and $4\times$ undersampling. Key results show effective acceleration $E_{N=2}\approx 1.9$ and $E_{N=4}\approx 3.7$, with phantom RMSE around $0.888^\circ C$ and ex vivo RMSE around $1.145^\circ C$ for 2× undersampling, plus a Dice score of $0.809$ for the $43^\circ C$ isotherm and Bland-Altman bias of $-0.253^\circ C$ (limits $\pm 2.16^\circ C$); performance declines modestly at $4\times$ undersampling (~10%). These findings demonstrate that deep learning-based reconstruction can significantly speed MR thermometry while preserving temperature accuracy, potentially enabling safer and more effective real-time FUS therapy. The authors provide code and discuss future work toward temporally integrated and reference-free rapid thermometry, with plans to extend validation to in vivo data.

Abstract

Proton resonance frequency (PRF) based MR thermometry is essential for focused ultrasound (FUS) thermal ablation therapies. This work aims to enhance temporal resolution in dynamic MR temperature map reconstruction using an improved deep learning method. The training-optimized methods and five classical neural networks were applied on the 2-fold and 4-fold under-sampling k-space data to reconstruct the temperature maps. The enhanced training modules included offline/online data augmentations, knowledge distillation, and the amplitude-phase decoupling loss function. The heating experiments were performed by a FUS transducer on phantom and ex vivo tissues, respectively. These data were manually under-sampled to imitate acceleration procedures and trained in our method to get the reconstruction model. The additional dozen or so testing datasets were separately obtained for evaluating the real-time performance and temperature accuracy. Acceleration factors of 1.9 and 3.7 were found for 2 times and 4 times k-space under-sampling strategies and the ResUNet-based deep learning reconstruction performed exceptionally well. In 2-fold acceleration scenario, the RMSE of temperature map patches provided the values of 0.888 degree centigrade and 1.145 degree centigrade on phantom and ex vivo testing datasets. The DICE value of temperature areas enclosed by 43 degree centigrade isotherm was 0.809, and the Bland-Altman analysis showed a bias of -0.253 degree centigrade with the apart of plus or minus 2.16 degree centigrade. In 4 times under-sampling case, these evaluating values decreased by approximately 10%. This study demonstrates that deep learning-based reconstruction can significantly enhance the accuracy and efficiency of MR thermometry for clinical FUS thermal therapies.

Figures (6)

• Figure 1: Algorithm Structure Diagram showcasing four optimizing modules: offline diffusion augments (DA), online complex augments (CA), knowledge distillation (KD), and decoupled loss (DL). The DA module employs a trained diffusion model to generate new data samples offline, thereby enhancing data diversity and complexity. The CA module combines augmented amplitude and phase maps of complex data. The KD module extracts knowledge from a larger pretrained teacher model and transfers it to a smaller model, thereby enhancing performance using a compact model. The teacher model is pretrained from FastMRI dataset and fine-tuned on our dataset. The DL module separates the amplitude and phase components of a signal, assigning distinct weights to each, to enhance the reconstruction capability of the phase component. The study incorporates five classical models.
• Figure 2: Schematic diagram of the complex loss function. (a) represents the L1 loss function, which is the sum of the differences in the real part $\Delta x$ and imaginary part $\Delta y$; (b) represents the decoupling loss, which is composed of the absolute error $d$ in magnitude and the difference $l$ in phase (angle). The figure provides an intuitive visualization of the components of the complex loss function.
• Figure 3: Reconstruction results of different methods for phantom and ex vivo datasets under $2\times$ and $4\times$ undersampling rates. Each row presents temperature maps and error maps. The first four rows represent the phantom results, while the subsequent four rows depict the ex vivo results. Different reconstruction methods are displayed in columns 2–10, including ZF (zero-filling), CS, CasNet, CUNet, SwinMR, RUNet, ResUNet, RUNet+all, and ResUNet+all. The first column shows the source temperature maps and under-sampling masks. We zoom in on the central focus area for easier observation. The results illustrate that the proposed optimizing methods for ResUNet, aimed at reconstructing images from various undersampling rates, yield the most favorable outcomes.
• Figure 4: The boxplot shows the average temperature error for each of the nine methods on the phantom test set with $4\times$ undersampling. The y-axis represents the temperature error in degrees Celsius. The box represents the interquartile range (IQR), with the median represented by the horizontal line within the box. The whiskers extend to the minimum and maximum values within 1.5 times the IQR, while any outliers are represented as individual points. The results show that the proposed methods outperform the ZF method, with the ResUNet+all method exhibiting the lowest average temperature error.
• Figure 5: Heat maps of temperature metrics for four reconstruction modules. This figure shows the heat maps of four temperature metrics obtained from pairwise combinations of four reconstruction modules. For each temperature metric, the four modules were pairwise combined to generate 16 combinations, which were evaluated to generate a heat map. The heat maps visually demonstrate the impact of different module combinations on temperature metrics. The values in the heat maps (a), (b), (c), and (d) represent the magnitude of the different temperature metrics; darker colors indicate better reconstruction effects.