Model-based reconstruction framework for correction of signal pile-up and geometric distortions in prostate diffusion MRI

Estimation of undistorted images in brain echo-planar images with distortions using the conjugate gradient method with anatomical regularization

PURPOSE

Although echo-planar imaging (EPI) is widely used for diffusion magnetic resonance (MR) imaging, EPI images suffer from susceptibility-induced geometric distortions. We herein propose a new estimation method for undistorted EPI images using anatomical T₁ -weighted images (T₁ WIs) based on the physics of MR imaging.

METHODS

Our proposed method estimates the undistorted EPI image in the image domain while estimating the magnetic field inhomogeneity map using the conjugate gradient method with anatomical regularization. Our method synthesizes the distorted image to match the measured EPI image containing geometric distortions by alternately updating the undistorted EPI image and the magnetic field inhomogeneity map. We evaluated our proposed method and compared it with a nonrigid registration-based distortion correction method using simulated data and using real data. In the evaluation of the estimation of the magnetic field inhomogeneity map, we used the normalized root-mean-squared error (NRMSE) between the estimated results and the ground truth. In the evaluation of the estimation of undistorted images, we used mutual information (MI) between the undistorted EPI image and the anatomical T₁ WI.

RESULTS

Using the simulated data, the means and standard deviations of the NRMSE values in the nonrigid registration-based method and proposed method were 1.29 ± 0.63 and 0.64 ± 0.30, respectively. The MI values in the proposed method were larger than those in the nonrigid registration-based method in all evaluated slices. For the real data, the proposed method improved the distortion, and the MI values in the proposed method were larger than those in the nonrigid registration-based method. In the estimation of the magnetic field inhomogeneity map, the NRMSE values in our method were smaller than those in the nonrigid registration-based method.

CONCLUSIONS

We demonstrated that our proposed method can estimate the regions with compressed distortions that are not well represented by the nonrigid registration-based methods. The results suggest that the proposed method could be useful in analyses combining EPI images with T₁ WIs.

Image distortion correction for MRI in low field permanent magnet systems with strong B0 inhomogeneity and gradient field nonlinearities

Objective

To correct for image distortions produced by standard Fourier reconstruction techniques on low field permanent magnet MRI systems with strong \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 inhomogeneity and gradient field nonlinearities.

Materials and methods

Conventional image distortion correction algorithms require accurate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta B}_{0}$$\end{document}ΔB0 maps which are not possible to acquire directly when the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 inhomogeneities also produce significant image distortions. Here we use a readout gradient time-shift in a TSE sequence to encode the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 field inhomogeneities in the k-space signals. Using a non-shifted and a shifted acquisition as input, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 maps and images were reconstructed in an iterative manner. In each iteration, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 maps were reconstructed from the phase difference using Tikhonov regularization, while images were reconstructed using either conjugate phase reconstruction (CPR) or model-based (MB) image reconstruction, taking the reconstructed field map into account. MB reconstructions were, furthermore, combined with compressed sensing (CS) to show the flexibility of this approach towards undersampling. These methods were compared to the standard fast Fourier transform (FFT) image reconstruction approach in simulations and measurements. Distortions due to gradient nonlinearities were corrected in CPR and MB using simulated gradient maps.

Results

Simulation results show that for moderate field inhomogeneities and gradient nonlinearities, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 maps and images reconstructed using iterative CPR result in comparable quality to that for iterative MB reconstructions. However, for stronger inhomogeneities, iterative MB reconstruction outperforms iterative CPR in terms of signal intensity correction. Combining MB with CS, similar image and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 map quality can be obtained without a scan time penalty. These findings were confirmed by experimental results.

Discussion

In case of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 inhomogeneities in the order of kHz, iterative MB reconstructions can help to improve both image quality and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 map estimation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10334-021-00907-2.

Characterization of B0-field fluctuations in prostate MRI

Multi-parametric MRI is increasingly used for prostate cancer detection. Improving information from current sequences, such as T2-weighted and diffusion-weighted (DW) imaging, and additional sequences, such as magnetic resonance spectroscopy (MRS) and chemical exchange saturation transfer (CEST), may enhance the performance of multi-parametric MRI. The majority of these techniques are sensitive to B0-field variations and may result in image distortions including signal pile-up and stretching (echo planar imaging (EPI) based DW-MRI) or unwanted shifts in the frequency spectrum (CEST and MRS). Our aim is to temporally and spatially characterize B0-field changes in the prostate. Ten male patients are imaged using dual-echo gradient echo sequences with varying repetitions on a 3 T scanner to evaluate the temporal B0-field changes within the prostate. A phantom is also imaged to consider no physiological motion. The spatial B0-field variations in the prostate are reported as B0-field values (Hz), their spatial gradients (Hz/mm) and the resultant distortions in EPI based DW-MRI images (b-value = 0 s/mm2 and two oppositely phase encoded directions). Over a period of minutes, temporal changes in B0-field values were ≤19 Hz for minimal bowel motion and ≥30 Hz for large motion. Spatially across the prostate, the B0-field values had an interquartile range of ≤18 Hz (minimal motion) and ≤44 Hz (large motion). The B0-field gradients were between -2 and 5 Hz/mm (minimal motion) and 2 and 12 Hz/mm (large motion). Overall, B0-field variations can affect DW, MRS and CEST imaging of the prostate.

Distortion correction of diffusion weighted MRI without reverse phase-encoding scans or field-maps

Diffusion magnetic resonance images may suffer from geometric distortions due to susceptibility induced off resonance fields, which cause geometric mismatch with anatomical images and ultimately affect subsequent quantification of microstructural or connectivity indices. State-of-the art diffusion distortion correction methods typically require data acquired with reverse phase encoding directions, resulting in varying magnitudes and orientations of distortion, which allow estimation of an undistorted volume. Alternatively, additional field maps acquisitions can be used along with sequence information to determine warping fields. However, not all imaging protocols include these additional scans and cannot take advantage of state-of-the art distortion correction. To avoid additional acquisitions, structural MRI (undistorted scans) can be used as registration targets for intensity driven correction. In this study, we aim to (1) enable susceptibility distortion correction with historical and/or limited diffusion datasets that do not include specific sequences for distortion correction and (2) avoid the computationally intensive registration procedure typically required for distortion correction using structural scans. To achieve these aims, we use deep learning (3D U-nets) to synthesize an undistorted b0 image that matches geometry of structural T1w images and intensity contrasts from diffusion images. Importantly, the training dataset is heterogenous, consisting of varying acquisitions of both structural and diffusion. We apply our approach to a withheld test set and show that distortions are successfully corrected after processing. We quantitatively evaluate the proposed distortion correction and intensity-based registration against state-of-the-art distortion correction (FSL topup). The results illustrate that the proposed pipeline results in b0 images that are geometrically similar to non-distorted structural images, and more closely match state-of-the-art correction with additional acquisitions. In addition, we show generalizability of the proposed approach to datasets that were not in the original training / validation / testing datasets. These datasets included varying populations, contrasts, resolutions, and magnitudes and orientations of distortion and show efficacious distortion correction. The method is available as a Singularity container, source code, and an executable trained model to facilitate evaluation.

Joint B0 and image estimation integrated with model based reconstruction for field map update and distortion correction in prostate diffusion MRI

In prostate Diffusion Weighted MRI, differences in susceptibility values exist at the interface between the prostate and rectal-air. This can result in off-resonance magnetic field leading to geometric distortions including signal stretching and signal pile-up in the reconstructed images. Using a set of EPI data acquired with blip-up and blip-down phase encoding gradient directions, model based reconstruction has recently been proposed that can correct these distortions by using a B0 field estimated from a separate B0 scan. However, change in the size of the rectal air region across time can occur that can result in a mismatch of the B0 field to the EPI scan. Also, the measured B0 field itself can be erroneous in regions of low Signal to Noise ratio around the prostate rectal air interface. In this work, using a set of single shot EPI data acquired with blip-up and blip-down phase encoding gradient directions, a novel joint model based reconstruction is proposed that can account for changes in the off resonance effects between the B0 and EPI scans. For ten prostate patients, using a measured B0 field as an initial B0 estimate, on a 5-point scale (1-5) image quality scores evaluated by an experienced radiologist, the proposed framework achieved scores of 3.50 ± 0.85 and 3.40 ± 0.51 for b-values of 0 and 500 s/mm2, respectively compared to 3.40 ± 0.70 and 3.30 ± 0.67 for model based reconstruction. The proposed framework is also capable of estimating a distortion corrected EPI image even without an initial B0 field estimate in situations where a separate B0 scan cannot be obtained due to time constraint.

Model-based reconstruction framework for correction of signal pile-up and geometric distortions in prostate diffusion MRI

PURPOSE

Prostate diffusion-weighted MRI scans can suffer from geometric distortions, signal pileup, and signal dropout attributed to differences in tissue susceptibility values at the interface between the prostate and rectal air. The aim of this work is to present and validate a novel model based reconstruction method that can correct for these distortions.

METHODS

In regions of severe signal pileup, standard techniques for distortion correction have difficulty recovering the underlying true signal. Furthermore, because of drifts and inaccuracies in the determination of center frequency, echo planar imaging (EPI) scans can be shifted in the phase-encoding direction. In this work, using a B0 field map and a set of EPI data acquired with blip-up and blip-down phase encoding gradients, we model the distortion correction problem linking the distortion-free image to the acquired raw corrupted k-space data and solve it in a manner analogous to the sensitivity encoding method. Both a quantitative and qualitative assessment of the proposed method is performed in vivo in 10 patients.

RESULTS

Without distortion correction, mean Dice similarity scores between a reference T2W and the uncorrected EPI images were 0.64 and 0.60 for b-values of 0 and 500 s/mm2 , respectively. Compared to the Topup (distortion correction method commonly used for neuro imaging), the proposed method achieved Dice scores (0.87 and 0.85 versus 0.82 and 0.80) and better qualitative results in patients where signal pileup was present because of high rectal gas residue.

CONCLUSION

Model-based reconstruction can be used for distortion correction in prostate diffusion MRI.