In the present study, distortion correction was applied to SE-EPI MRE data to evaluate the effects of geometric distortion on apparent wave parameters and calculated shear stiffness by comparing images before and after correction. For this purpose, we developed a simple custom distortion correction method using a magnitude image with substantially reduced geometric distortion as a reference. The correction process, illustrated in the flowchart in Figure 1, consists of the following three main steps:

(i) Acquisition of Reference Images

Two MR magnitude images were acquired in the absence of any vibrations being induced in the test object. The first magnitude image was acquired using a single-shot fast spin-echo (SSFSE) sequence and the second magnitude image was acquired using the SE-EPI MRE sequence. The SSFSE magnitude image is used as a reference image for calculating distortion in the SE-EPI MRE image. For both magnitude images, multiple equally spaced saturation pulses were applied, producing the so-called tags illustrated in Figure 1(g) and Figure 1(h). The degree of curvature and misalignment of the tags serves as a visual marker of geometric distortion effects, which occur principally in the phase-encoding direction. In particular, the tags are applied in the readout direction and appear as lines in the image, making them well-suited to capturing distortions along the orthogonal phase-encoding direction. A total of six tags, which were available as default options on the MRI system, were applied. Since the geometric distortion of EPI images varies depending on the acquisition parameters that are used, the magnitude images used for the calculation of distortion information were acquired using the same imaging parameters, other than those which refer to the tags, as for the SE-EPI MRE sequence. All MRE images were acquired with the same acquisition parameters in the same orientation and position and with the same field of view (FOV).

Figure 1. Process of elastogram calculation for the standard (uncorrected) method and the distortion correction method. In the uncorrected method, magnitude and phase images (c) (d) are calculated from the output real part and imaginary part images (a), (b). The phase image is converted to a wave image (e), and the elastogram (f) is calculated. In the distortion correction method, two additional magnitude images are acquired by single-shot fast spin-echo (SSFSE) sequence (g) and spin-echo-type echo-planar MR elastography (SE-EPI MRE) sequence (h), with multiple saturation pulses (tags) applied to each. Both magnitude images are compared, and a distortion correction (DC) map (i) of the EPI image is calculated. By applying the DC map to the real part and imaginary part images, distortion-corrected real part and imaginary part images (j), (k) are obtained, from which distortion-corrected magnitude and phase images (l), (m) can be created. Using these corrected images, a more accurate wave image (n) and elastogram (o) with reduced image distortion can be obtained.

(ii) Calculation of Distortion Information

The tagged SE-EPI MRE magnitude image was compared to the tagged SSFSE reference magnitude image, and a distortion correction (DC) map was produced (Figure 1(i)). This DC map was then applied to correct for distortion in images acquired using the SE-EPI MRE sequence, as described below.

(iii) Application of the Distortion Correction

Since SE-EPI MRE images and the tagged SE-EPI MRE magnitude image acquired without vibrations (Figure 1(h)) used for calculation of distortion information were acquired with the same acquisition parameters, except relating specifically to the application of tags, they should have similar geometric distortion. As described by Fehlner et al (2017) [35], the DC map obtained in (ii) must be applied separately to the real and imaginary images (Figure 1(a) and Figure 1(b)), which are then recombined to produce distortion-corrected real and imaginary images (Figure 1(j) and Figure 1(k)). From these, distortion-corrected magnitude and phase images (Figure 1(l) and Figure 1(m)) can be produced. This allows generation of more accurate wave images (Figure 1(n)) and elastograms (Figure 1(o)) with reduced geometric distortion.

All experiments were performed using a SIGNA Premier 3 T MRI system (General Electric Healthcare, Milwaukee, WI, United States) equipped with 60 channel posterior phased-array coil and 30 channel anterior phased-array coil.

In the phantom MRE experiment, we used a uniform acrylamide phantom that has been developed for the purposes of quality control in MRE imaging (The Japanese Society for Magnetic Resonance in Medicine, Minato-ku, Tokyo, Japan) (Figure 2(a) and Figure 2(b)). MRE was performed using a 2D SE-EPI MRE sequence with repetition time (TR) 1,000 ms, echo time (TE) 60.6 to 86.7 ms, temporal phases 4, matrix 96 × 96, FOV 20 cm × 20 cm, slice thickness 8 mm. External vibrations were generated using a TIT320C-4 12" subwoofer (Dayton Audio, Springboro, OH, United States) as a pneumatic pressure generator and were propagated using vinyl tubing to a pneumatic driver placed under the test object so that waves propagated upward toward the top of the phantom (Figure 2(a)). The pneumatic driver was designed using Rhinoceros 3D 5.0 modeling software (Robert McNeel and Associates, Seattle, WA, United States) and was fabricated using a 3D printer (3D Systems, Rock Hill, SC, United States). The direction perpendicular to the propagating wave was designated as X, and the direction parallel to the propagating wave was designated as Y. To systematically evaluate how the relative orientation between the phase-encoding direction and wave propagation affects apparent wave parameters, acquisitions were performed with the phase-encoding direction oriented either perpendicular (along X) or parallel (along Y) to the principal direction of wave propagation. MEG was consistently applied along the X-axis throughout phantom experiments. For each orientation, three different vibration frequencies (50, 100, and 150 Hz) were used. Imaging was performed in the axial plane (Figure 2(b)). In addition, at each vibration frequency, a reference image to be used in applying the distortion correction (see Section 2.1 (i) above) was acquired using an SSFSE sequence, with TR 1304 ms, TE, 66.8 ms and number of saturation pulses 6 and with the same FOV 20 cm × 20 cm, slice thickness 8 mm and positioning as for MRE imaging.

Figure 2. Phantom MRE experiment setup and region of interest (ROI) setting in elastograms. (a) Setup diagram of phantom MRE experiments. The phantom is cylindrical with a diameter of 180 mm and a height of 145 mm, composed of homogeneous acrylamide. (b) Axial imaging section. (c) Nine ROI locations in the elastogram for measuring shear stiffness.

In liver MRE, three healthy volunteers (all male, age range: 21 - 24 years) were enrolled in this study. All procedures were performed after obtaining informed consent from the participants and receiving approval from the Institutional Ethics Review Board (approval number: 21045). The acquisition parameters for 2D SE-EPI MRE were set according to the conditions described in Quantitative Imaging Biomarkers Alliance (QIBA) guidelines [37] as follows: TR 1,000 ms, TE 61.4 ms, temporal phases 4, matrix 96 × 96, FOV 42 cm × 42 cm, slice thickness 8 mm, vibration frequency 60 Hz. As in the phantom experiment, external vibrations were applied to the liver using a TIT320C-4 12" subwoofer as a pneumatic pressure generator connected to a passive driver from a commercial MRE system (Resoundant, Rochester, MN, United States). Passive driver placement followed QIBA guidelines. The acquisition parameters for the reference images obtained using SSFSE were as follows: TR 1,041 ms, TE 59.7 ms, number of saturation pulses 6, with the same FOV 42 cm × 42 cm, slice thickness 8 mm and positioning as for MRE imaging. The SSFSE reference image and the SE-EPI MRE image were acquired sequentially within the same examination session, each within a single end-expiration breath-hold. Identical breath-hold instructions were provided for both acquisitions to match the respiratory position of the liver and minimize inter-scan displacement.

For distortion correction, the magnitude images produced using the SSFSE and SE-EPI MRE sequences were co-registered using a non-rigid registration method based on B-spline deformation fields [38]-[40] implemented with code written in Python 3.10.9 (Python Software Foundation, Wilmington, DE, United States) and the SimpleITK Ver. 2.2.1 registration framework (Insight Software Consortium, NY, United States). In an iterative approach, the geometric deformation of the SE-EPI MRE image with respect to the SSFSE reference image is computed and corrected by optimizing the spatial correspondence between the two images. Mattes mutual information [41] was adopted as the similarity metric, which quantifies the statistical dependence between images and provides robust similarity evaluation even between images with different contrast characteristics. The Limited-memory Broyden-Fletcher-Goldfarb-Shanno Bounded (L-BFGS-B) algorithm [42][43] was used as the optimization algorithm, achieving efficient optimization through quasi-Newton approximation of the Hessian matrix. The deformation model employed B-spline deformation fields using cubic B-spline basis functions, and local and smooth deformations are produced through linear combinations of basis functions defined on a control point grid. Parameters such as control point spacing and convergence criteria were optimized according to the characteristics of the target images. The initial deformation was set as an identity transformation, and deformation parameters were adjusted stepwise during the optimization process. A multi-level optimization strategy was adopted to improve computational efficiency and convergence stability. At the first level, reduction by a factor of 4 and Gaussian smoothing were applied to roughly estimate global deformations, at the second level, a reduction by a factor of 2 was used to refine moderate deformations, and at the third level, fine deformations were finally adjusted at full resolution. The maximum number of L-BFGS-B iterations was set to 200 per level, and the sampling fraction for mutual information estimation was set to 1%. Linear interpolation was used throughout and the flexibility of B-spline basis functions enables handling of complex local deformations. A full 2D B-spline warp was permitted without explicit constraint to the phase-encoding axis. Inspection of the DC maps confirmed that the resulting deformation was predominantly along the phase-encoding direction, consistent with the directional nature of EPI distortion. Finally, a DC map representing the geometric deformation field was generated. The DC map was then applied to the real and imaginary components of the MRE dataset to produce distortion-corrected magnitude and phase images.

The MRE data before and after distortion correction were further processed using MRE-rTool (Keio University Hospital, Shinjuku-ku, Tokyo, Japan) [44]. Elastograms were generated using local frequency estimation (LFE), a method in which shear stiffness is calculated based on local wavelengths [44]-[46]. This approach is particularly sensitive to distortion-induced alterations in apparent wavelength, making it well-suited for evaluating the impact of geometric distortion on shear stiffness quantification.

The acrylamide phantom has a uniform internal structure with homogeneous mechanical properties. In the absence of geometric distortion, propagating waves should exhibit consistent wavelength, resulting in a uniform elastogram. However, geometric distortion can alter the apparent wave characteristics and lead to artificial variations in calculated shear stiffness. To evaluate this effect, nine circular ROIs (each approximately 440 mm²) were placed on the elastogram in a 3 × 3 grid pattern, positioned at least 10 mm from the phantom edge to avoid wave reflection and interference artifacts (Figure 2(c)). ROI placement was performed manually by a single operator (Y.I.) on both the uncorrected and corrected elastograms, with ROIs positioned at spatially corresponding locations within the phantom. The coefficient of variation (CV) of the measurements obtained for the nine ROIs was calculated before and after application of the distortion correction, and compared. The Brown-Forsythe test was used to assess whether the variance of shear stiffness values across the nine ROIs differed significantly between the uncorrected and corrected conditions. This test was selected because the principal effect of geometric distortion in a homogeneous phantom is to introduce spatial non-uniformity (i.e., increased variance across ROIs) rather than a systematic shift in mean stiffness. Accordingly, the reported p-values correspond to differences in variance (spatial uniformity), not differences in mean stiffness. Statistical significance was set at p < 0.05. Because no independent stiffness reference was obtained for the phantom, the phantom endpoint reflects distortion-related spatial non-uniformity rather than absolute accuracy against a ground-truth value.

For liver MRE, a single freeform ROI was manually drawn within the right hepatic lobe on both the uncorrected and corrected elastograms by a single operator (Y.I.), avoiding large vessels, biliary structures, and the liver edge, following QIBA recommendations [37], with ROIs positioned at anatomically corresponding regions. Given the small sample size (n = 3), formal statistical hypothesis testing was not performed. Instead, descriptive statistics and 95% confidence intervals for stiffness changes (corrected minus uncorrected values) were calculated using the t-distribution, with results interpreted descriptively in comparison with phantom study findings.

Tagged EPI magnitude images, wave images, and elastograms before and after distortion correction at vibration frequencies of 50 Hz, 100 Hz, and 150 Hz are shown in Figure 3(a)-(c), respectively. Mean Shear stiffness values and CV values across the nine ROIs for both phase-encoding directions are presented in Table 1. Figure 4 shows stiffness values before and after distortion correction when the phase-encoding direction was perpendicular (a)-(c) and parallel (d)-(f) to the wave propagation direction at each frequency (50 Hz, 100 Hz, and 150 Hz).

Considering first the data acquired at a vibration frequency of 50 Hz, when phase-encoding was applied perpendicular to the direction of wave propagation, obvious distortion was present in the tagged magnitude images (Figure 3(a), left panel, row 2). This distortion was removed by distortion correction (right column). However, because the distortion occurred perpendicular to the direction of wave propagation, it did not affect the apparent wavelength of the propagating waves (row 3). Accordingly, uniformity was comparable in the elastograms obtained before and after distortion correction (row 4), and the CV values were comparable before and after distortion correction. There was no significant difference in the shear stiffness values within the nine ROIs before and after distortion correction (Figure 4(a); p = 0.56).

Figure 3. Phantom MRE results: EPI magnitude images with tags, DC maps, wave images, and elastograms at 50 Hz (a), 100 Hz (b), and 150 Hz (c). Left and right panels show phase-encoding gradients applied perpendicular and parallel to the wave propagation direction, respectively. Left and right columns show the results before and after distortion correction. Each panel displays DC maps (row 1, right column only), tagged SE-EPI images (row 2), wave images (row 3), and elastograms (row 4).

When phase-encoding was in the direction parallel to wave propagation, at first glance the tagged magnitude images appeared comparable before and after distortion correction (Figure 3(a), right panel, row 2). However, detailed examination (including analysis of profiles, not illustrated) revealed alterations in tag spacing in the non-corrected data, with compression in the upper portion and expansion in the lower portion of the phantom. Because this distortion occurred in the direction of wave propagation, it altered the apparent wavelength, resulting in reduced apparent wavelength in the upper portion and increased apparent wavelength in the lower portion of the image (row 3), producing non-uniform elastograms (row 4). Distortion correction successfully restored equal tag spacing (right column, row 2), consistent apparent wavelength (right column, row 3), and uniform elastograms (right column, row 4). The CV values were lower for the distortion-corrected elastograms, indicating greater improvement compared to when the phase-encoding direction was perpendicular to the direction of wave propagation. There was a significant difference in the variance of shear stiffness values across the nine ROIs before and after distortion correction (Figure 4(d); p < 0.01), indicating a reduction in distortion-related spatial non-uniformity.

With regard to the effect of increasing vibration frequency to 100 Hz and then to 150 Hz, when phase-encoding was perpendicular to the direction of wave propagation, there were no apparent differences in the uniformity of the elastograms before and after distortion correction (Figure 3(b) and Figure 3(c), left panels). The CV values remained largely unchanged, and there was no significant difference in the stiffness values before and after distortion correction (Figure 4(b); 100 Hz, p = 0.94 and Figure 4(c); 150 Hz, p = 0.11). However, when the phase-encoding direction was parallel to the direction of wave propagation, non-uniformity increased with increasing vibration frequency (i.e., with shortening wavelength) in the non-corrected wave images (Figure 3(b) and Figure 3(c), right panels, row 3) and elastograms (row 4), and the CV values also increased. Distortion correction successfully restored consistent apparent wavelength (Figure 3(b) and Figure 3(c), right panels, row 3, right column) and uniform elastograms (row 4, right column) regardless of vibration frequency, with lower CV values. There were significant differences in the variance of shear stiffness values before and after distortion correction (Figure 4(e); 100 Hz, p < 0.001 and Figure 4(f); 150 Hz, p < 0.01), reflecting reduced spatial non-uniformity after correction.

Table 1. Mean shear stiffness and coefficient of variation (CV) before and after distortion correction in the phantom experiment.

Figure 4. Phantom MRE results: comparison of stiffness values before and after distortion correction. Phase-encoding direction perpendicular (a)-(c) and parallel (d)-(f) to wave propagation direction at 50 Hz (a) (d), 100 Hz (b) (e), and 150 Hz (c) (f). ns, not significant; **, p < 0.01; ***, p < 0.001. Brown-Forsythe test for equality of variance across the nine ROIs.

Tagged EPI magnitude images, wave images, and elastograms for all participants before and after distortion correction are shown in Figure 5. Shear stiffness values for each volunteer are presented in Table 2. The shear stiffness values showed small changes following distortion correction across all three volunteers. The mean difference in stiffness values (corrected minus uncorrected) was 0.10 ± 0.15 kPa, with a 95% confidence interval of [−0.28, 0.48] kPa. Although this confidence interval included zero, the limited sample size precludes firm conclusions regarding the statistical significance of distortion correction effects in vivo.

Figure 5. Liver MRE results: EPI magnitude images with tags, wave images, and elastograms of all participants before and after distortion correction. Wave images and elastograms are overlaid on the magnitude images for individual volunteers.

Table 2. Shear stiffness of the ROI for all participants in the liver MRE experiment. 95% CI, 95% confidence interval.