“Cross-Correlation-Based Misregistration Correction for Super Resolution T2-Weighted Spin-Echo Images: Application to Prostate”

Abstract

Purpose

The purpose is to develop a retrospective correction for subtle slice-to-slice positional inconsistencies that can occur when overlapped slices are acquired for super resolution in T2-weighted spin-echo multi-slice imaging.

Methods

Spin-echo acquisition of overlapped slices is typically done using multiple passes. After the passes are assembled into the final slice set, consecutive slices are correlated due to their overlap. Cross correlation was used to measure slice-to-slice displacement. After Z-dependent filtering to preserve true object shape, the displacements were used to correct slice position. The method was tested in a phantom moved slowly (0.16 – 0.63 mm/pass) under computer control and in vivo in 16 patients having prostate MRI.

Results

Over the motion range the correlation method had accuracy within 0.03 mm/pass and precision ±0.20 mm; i.e. sub-pixel. Corrected images visually resemble the true object. Over the patient studies the mean range of motion in the anterior/posterior direction was 1.63 mm. Motion-corrected axial images and the sagittal reformats were evaluated as significantly superior over those formed without motion correction.

Conclusion

The retrospective correlation-based motion correction method provides significant improvement in the slice-to-slice registration necessary for effective super resolution using overlapped slices.

INTRODUCTION

T2-weighted spin-echo (T2SE) imaging is one of the most commonly used pulse sequences in MRI, performed in close to 100% of all clinical exams. This is generally done with a two-dimensional (2D) multislice acquisition [1] with a fast-spin-echo readout [2]. Although the spatial resolution is variable depending on the anatomic region under study, the slice thickness, generally no smaller than 2 mm, is typically 3 – 6× coarser than the inplane resolution. Multiple approaches have been studied to obtain improved through-plane resolution such as use of smaller slice thicknesses, e.g. [3], or three-dimensional (3D) T2SE [4–9] or T2-prepared SSFP [10, 11] with centric encoding [12]. However, in general these have not replaced the 2D multislice T2SE technique, and consequently T2SE is often done in multiple orientations.

Another means for attempting to obtain improved through-plane resolution is the approach called “super resolution” (SR) [13]. In general, SR methods take multiple “low resolution” image sets and somehow combine them to obtain a “high resolution” set. This has been studied extensively using low resolution image sets acquired in two or more orientations [14–17]. However, more recently investigators have used 2D data sets from only one orientation to generate high through-plane resolution images along that orientation. Specifically, applications in 2D time-of-flight MR angiography [18] and T2SE prostate MRI [19] used overlapped slices as proposed years ago [20], and in brain diffusion-weighted imaging (DWI) used intra-slice Hadamard encoding [21].

2D multislice T2SE is often performed using multiple passes, where a pass is defined as the acquisition of some subset of the overall set of acquired slices. For example, for T2SE with abutting slices, to avoid slice-to-slice interference a common approach is to use one pass to acquire the odd-numbered slices and a second pass for the even-numbered slices. If slices are overlapped, such as for single-orientation SR, the number of passes must necessarily increase. Each pass is itself a T2SE multislice acquisition. A consequence of this is that the minute-long times over which the individual passes are acquired are distinct from each other, and thus even slight motion causes the mean object positions over the multiple passes to differ. The resultant inconsistency of position of the aggregate multi-slice data set can confound and cause artifact in subsequent SR processing. Thus, in Ref. [19] although the 1.0 mm thick SR axial images of the prostate were often sharper than conventional 3.0 mm thick axial images for equal inplane resolution, they were also more prone to signal dropout due to the above-described slice-to-slice positional inconsistency. Sensitivity to such inconsistency is particularly high in reformats which are orthogonal to the acquisition orientation, e.g. sagittal reformats for axial acquisition and manifest as signal oscillation or “scalloping.”

Variability in position of the prostate was studied in the 1990s in radiation therapy with respect to day-to-day positioning [22–24]. The principal dependence was found to be on rectal distension, with prostate displacement primarily anterior/posterior (A/P), the order of 1 cm. Dependence on bladder distension which primarily affects superior/inferior (S/I) prostate position, was negligible. Cine MRI methods showed similar, primarily A/P displacement with several-mm amplitude over a six-minute scan [25]. Based on this data this work focuses on displacement in the lateral, primarily A/P, direction; i.e. within the axial plane of section, as caused by rectal peristalsis. Administration of anti-spasmodic drugs such as glucagon can be used to reduce peristaltic motion for prostate MRI, but this requires extra patient preparation, and motion effects in T2SE are still reported in 23% of patients [26]. Anti-spasmodic drugs were not used in this work.

Recently investigators have explained how motion in multi-pass multislice acquisition can cause scalloping artifact in reformatted orientations, and further, by segmenting the acquisition it can largely be suppressed [27]. However, this extends the time over which data are acquired for any slice to essentially the entire scan time, increasing the potential for intra-slice motion artifact. The goal of this work is to devise a means for correction of scalloping while continuing to limit the acquisition time for any slice to a single pass.

The purpose of this work is to describe a means for retrospective correction of slice-to-slice displacements of the set of overlapped slices acquired for single-orientation SR T2SE imaging. In doing this we have identified and attempted to exploit two specific aspects of the SR acquisition. First, the overlap of consecutive slices in the aggregate set means that such slices are correlated, facilitating estimation of their relative displacement. Second, the multi-pass aspect of the acquisition causes slices within a pass to be correlated in their displacements. We incorporate these into our correction and study the hypothesis that the motion correction method provides improved image quality vs. no correction. In the following sections we describe means to measure inplane motion, describe the overall correction algorithm and its implementation, and then apply the method in phantoms and to 16 cases of T2SE multislice imaging of the prostate.

METHODS

Description of Data Acquisition

All human studies were performed under an IRB-approved protocol for which all participants provided written informed consent. The data acquisition for this work used the parameters for the super resolution T2SE prostate MRI study of Ref. [19], shown here in Table 1. The sequence parameters TR, TE, and inplane resolution were selected to approximately match the recommendations of Prostate Imaging-Reporting and Data Systems (PI-RADS) v2 [28] which have largely been maintained in v2.1 [29]. In this work the acquired slice thickness was 3 mm with a 1-mm slice-to-slice increment, or equivalently, a 2-mm overlap slice to slice. Acquisition was done using six passes of 13 slices each for a total of 78 slices in a typical scan time of 6:38. The nominal acquisition orientation was axial, but the slice select direction was adjusted on a patient-specific basis to be aligned with the interface between the posterior aspect of the prostate capsule and the anterior rectal wall, as determined from sagittal localizer images. This tended to keep the prostate within the central region of the axial slices. Although anti-spasmodic drugs were not used, all subjects were instructed to fast for three hours before the MRI exam and to empty the rectum and void immediately prior to the exam.

Table 1.

Acquisition parameters for axial T2-weighted spin-echo multislice of prostate with overlapped slices.

Parameter	Value
Phase × Frequency Directions	L/R × A/P
Field-of-View (L/R × A/P)	24×24 cm2
Inplane Sampling (Phase × Frequency)	320×320
Inplane Resolution (Phase × Frequency)	0.75×0.75 mm2
Slice Thickness	3 mm
No. of Slices	78
Slice-to-Slice Increment	1 mm (2 mm overlap)
S/I Field-of-View	7.8 cm
Repetition Time (TR)	2758 msec
Effective Echo Time (TE)	100 msec
Echo Train Length	21
Signal Bandwidth	64 kHz (±32 kHz)
Acceleration (ARC, along Phase)	1.5
No. of Averages	2
*No Phase Wrap (NPW)	Enabled
Receiver Coil	16 elements (8 anterior, 8 posterior)
No. of Passes	6
Scan Time per Pass	1:07
Scan Time	6:38

A/P: anterior/posterior; L/R: left/right; S/I: superior/inferior

^*Enabling of NPW doubles the phase FOV but halves the No. of Averages

Description of Motion Measurement

The basic idea of the algorithm is to first determine the lateral (anterior/posterior (A/P) and left/right (L/R)) offsets of each axial slice from a fiducial, superior-inferior (S/I)-oriented axis and then to correct each slice by the offset. Offsets were determined as follows.

When slices are acquired with overlap in the slice direction, such as for the SR acquisition, a correlation is expected between adjacent slices. With two images that are significantly correlated, a small translational shift occurring between the images can be determined via their two-dimensional cross correlation. If the set of acquired axial images is denoted {I_n(x,y)}, then the cross correlation R_MN(x,y) between images I_M(x,y) and I_N(x,y) can be efficiently calculated via 2D Fourier transformations [30]:

$$R_{MN}(x,y)=F^{-1}\{F\{I_M(x,y)\}•F\{I_N(-x,-y)\}\}$$ (1)

Where F and F⁻¹ are forward and inverse 2D Fourier transforms and “•” denotes point by point multiplication.

This approach was applied to the set of axial images acquired according to Table 1. Assume that the slices are numbered from 1 to N with Slice 1 most inferiorly located. Define ΔX(n) and ΔY(n) as the correlation-determined shifts along X (assumed to be A/P) and Y (L/R), respectively, of Slice n from Slice n-1. To focus the region of correlation on the prostate, an ROI comprising the central 20% of the each axial image (here a 4.8 × 4.8 cm² patch, or 64 × 64 pixels) formed the input for each cross correlation. Complex images of consecutive slices were processed according to Eq. 1 and the point of maximum value of the resulting R_MN was identified. All points whose values were within 90% of this maximum were then selected, and the center of mass (COM) of these was calculated and recorded as the shift providing the highest correlation. Use of 1× (none), 2×, and 4× interpolation by zero padding in k-space [31] was studied during this process in assessing accuracy and precision. The overall lateral A/P and L/R offsets of Slice k were then determined by integrating ΔX(n) and ΔY(n) for all n ≤ k.

Description of Motion Correction Algorithm

The purpose of the correction algorithm is to account for the measured lateral offsets (A/P and L/R) of each axial slice from the fiducial, S/I-oriented axis. The corrected image set is then input to the super resolution reconstruction. Directly applying the inverses of the detected shifts would have the potentially undesirable effect of trying to straighten out anatomic features of the body in the through-plane direction. For example, consider the multislice acquisition of a cylinder whose central axis is nominally aligned with but tilted relative to the slice direction. Each slice would have a detected shift which upon correction would undesirably straighten or “detrend” the true tilt, misrepresenting ground truth. An additional factor, one that can be used advantageously, is knowledge of the specific multi-pass acquisition. In the acquisition of Table 1, 13 slices were acquired in each of six passes. Because they are acquired within the same time and subject to the same motion, slices within a specific pass tend to have correlated offsets.

Both of the above phenomena, potential undesirable straightening of truly tilted objects and correlation of slices acquired within the same pass, can be analyzed by considering the Fourier transform along the slice select direction of the shift functions ΔX(n) and ΔY(n). The sampling of 78 slices, 13 slices over each of six passes, causes signal power in the detected shift spectrum at frequency 13/78 and its harmonics, and correction at these frequencies should be preserved. Conversely, signal power at or near zero spatial frequency corresponds to gradual shifting of the object across the entire S/I FOV, corresponding to true anatomical placement, and thus should not be corrected.

The above was accounted for by defining a filter along k_Z which consists of Gaussian functions of unit amplitude and adjustable width centered at the k_C frequencies of desired correction (here at ±13, ±26, ±39 cycles per 78 slices). Each Gaussian was parameterized:

$$\text{G}(\text{k})=e^{-{\left[(k-k_c)\frac{A}{10}\right]}^2}$$ (2)

with k the index on spatial frequency (k = −39 to +38) and A a tuning parameter. For each k the maximum of the multiple Gaussians was used as the filter value. For inappropriately small A the resultant wide Gaussians give non-zero response at zero frequency, causing artifactual misalignment of the object as described above. For inappropriately large A the narrow Gaussians in effect cause identical correction for all slices within each pass, suppressing slice-specific correction. Values of A in the range of 1.0 to 10.0 were studied using the Dice coefficient [32, 33] to evaluate the match of motion-free and motion-corrected images.

Implementation

Processing was performed on the acquired axial images using complex values to preserve the Gaussian nature of the noise. The filtered A/P and L/R shifts were used to correct via phase ramps in k-space the axial images in the direction opposite the detected shift. The corrected images were then input to the SR reconstruction of Ref. [19], yielding nominal 1-mm thick axial images. Reformats were made in sagittal orientation, typically 3 mm thick. Magnitude axial and sagittal images were presented for display. A flow diagram of the algorithm is shown in Supporting Information Figure S1.

Phantom Studies

Imaging of a phantom was performed to test the algorithm. To mimic the size of the prostate, a lime was used, suspended in a one-gallon plastic tub, with the lime’s central axis tilted approximately 20 degrees from the up-down direction within the tub. The tub was filled with bovine gelatin which was allowed to harden. To simulate the level of motion observed in prostate MRI, a computer-controlled motion assembly was used. The tub phantom was placed on a platform within the scanner bore, and the platform was then moved along the direction through the bore using a computer-controlled stepper motor attached to a threaded rod assembly, calibrated so that 1000 steps/revolution provides 1.95 mm linear motion. Image acquisition was done using the sequence of Table 1 in an orientation axial to the tub and lime, coronal in standard scanner coordinates, while the phantom was stationary as well as with continuous speeds providing 0.65, 0.49, 0.33, and 0.16 mm displacement per pass. This provides motion purely along one inplane direction. To provide motion along both inplane directions, acquisition was also done with an approximate 30 degree rotation of the acquisition plane about the slice select direction.

Evaluation

MRI-based measurements of slice-to-slice displacement in the phantom studies were compared with known shifts programmed into the motion assembly as calibrated outside the scanner bore with a micrometer with accuracy 0.01 mm. Evaluation of the correction was done by comparing images acquired with motion and reconstructed with and without motion correction to analogous images acquired with no motion and also done by use of difference images and mean square error (MSE).

In Vivo Studies

The motion correction algorithm was evaluated using images acquired from 16 human subjects consecutively recruited, all subjects in whom prostate cancer was suspected and prostate MRI was clinically indicated. SR axial images and sagittal reformats were generated with and without motion correction as described for the phantom studies.

Evaluation of the images from the human subjects was performed by a radiologist with over 10 years of experience in prostate MRI. Images were reviewed on a work station (Advantage Windows, GE Healthcare, Waukesha WI) allowing standard functions (selection of slices, window/level, zooming, image compare). For each subject both the SR axial images and sagittal images reformatted from them with and without motion correction were evaluated with all identifying annotation (motion corrected or not) removed. For the axial images the series of corrected and non-corrected images were presented side by side with random (L vs. R) positioning. The radiologist was asked to compare the two series using multiple criteria using a five-point scale (−2: L considerably better than R; −1: L better than R; 0: L and R equivalent; +1: R better than L; +2: R considerably better than L). The evaluation criteria were sharpness of: (i) prostate capsule, (ii) peripheral zone (PZ) vs. transition zone (TZ) differentiation, (iii) seminal vesicles, and structures in the (iv) PZ or (v) TZ if present. Criterion (vi) was prominence of any artifact such as blurring. One week after the side-by-side comparison the two series were also evaluated individually for Overall Diagnostic Quality using a four-point scale (1: Non-Diagnostic; 2: Marginal; 3: Good; 4: Excellent). This was done in two sessions of 16 axial series each, one series for each subject, with a one-week memory extinction period between sessions.

Approximately one week after the axial evaluation the series of motion-corrected and non-motion-corrected sagittal images were also evaluated side-by-side as described for the axial images. The evaluation criteria were sharpness of: (i) prostate capsule, (ii) seminal vesicles, (iii) bladder base contour, (iv) rectal wall contour, and (v) membranous urethra. Criterion (vi) was PZ vs. TZ differentiation. Criterion (vii) was level of artifact, typically scalloping. After an additional one-week memory extinction period the two sagittal series were also evaluated individually for Overall Diagnostic Quality in the same manner and using the same four-point scale as for the axial series.

Results of the evaluations were tested for significance using the Wilcoxon signed-rank test with p<0.05 taken as significant.

RESULTS

Figure 1 shows images from the phantom study illustrating performance of the correction. Figures 1A-C are super resolution (SR) 1-mm thick axial images through the lime acquired with no motion (A), and with continuous 0.49 mm/pass S/I motion without (B) and with (C) motion correction. In (B) and in all other figures the presence of a cyan arrow indicates that motion was present in the indicated direction during data collection for that image. The yellow box in (B) shows the 4.8 × 4.8 cm² ROI used to determine cross correlation, fixed in position for all axial images. (B) has motion artifact, for example displacement artifact at the high contrast edge of the rind (thick orange arrows) and blurring at the 3 o’clock and 8 o’clock partitions (thin orange arrows). These are eliminated in (C), the motion-corrected result, which closely resembles (A). Figures 1D-I are sagittal reformats through the lime. (D) was made from SR axial images with no motion. (E-H) were all acquired with 0.49 mm/pass in the direction shown. (E) shows the sagittal reformat of acquired images without SR reconstruction; the pass-to-pass displacements are manifest as sawteeth (arrows) with a clear six-line period. (F) shows the sagittal reformat of the SR-reconstructed axial slices without motion correction. The SR reconstruction maintains the six-line period but alters the sawtooth pattern into the prominent scalloping artifact (arrows). (G) shows the sagittal reformat of SR axial images with slice-to-slice displacement correction but without the anti-detrending filter. Although the scalloping artifact is removed, the image is badly distorted vs. (D). Finally, (H) shows the sagittal reformat of the SR axial images with full motion correction, showing a high resemblance to (D) as desired. (I) is a sagittal reformat from SR axial images acquired during continuous motion of 0.16 mm/pass, or 0.80 mm total, comparable to the 0.75 mm inplane resolution, without motion correction. The scalloping artifact is visible (arrows). (J) was formed from the same data set as (I) but using motion correction, again showing a high resemblance with (D). Difference images are presented in Supporting Information Figure S2.

Figure 1.

Image results using lime phantom. Absence or presence of motion is indicated in cyan, and if present the direction is shown by arrow and extent by number (in mm/pass, where each pass is 1:07). (A-C) Super resolution (SR) 1-mm thick axial images through the lime acquired with no motion (A), and 0.49 mm/pass motion without (B) and with (C) motion correction. Artifacts (orange arrows, B) are largely eliminated in (C). (D-J) Sagittal reformats from axial images acquired with no motion (D) and with motion of 0.49 mm/pass (E-H) and 0.16 mm/pass (I, J). Corrected results (H, J), visually resemble the no motion case (D) as desired, and are largely devoid of the scalloping artifacts (orange arrows in E, F, I). (G) was formed using motion correction but with anti-detrending disabled, causing distortion. Additional description is in the text. Directions in scanner coordinates are shown in gray boxes in (A) and (D). S: superior; I: inferior; L: left; R: right; A: anterior; P: posterior.

Figure 2 illustrates detection of displacement by cross correlation. Figures 2A-C show contour plots of the cross correlation between Slices 41 and 42 of the phantom, a level similar to that in Figures 1A-C, when moved at 0.49 mm/pass at an oblique angle of 30 degrees with respect to the X (L/R) and Y (S/I) axes. Figures 2A-C correspond to 1× (none), 2×, and 4× interpolation in X-Y space as performed by zero padding in k-space. The square colored pixel size in (A) corresponds to the acquired 0.75 × 0.75 mm² resolution. The dashed boxes in (A-C) outline those pixels whose values are within 90% of the maximum. Note the improved match of the detected shift to the expected, lab-measured result with increased interpolation. (D-F) show how the accuracy is close to the expected 0.424 and 0.245 mm/pass while the standard deviation (std) improves with interpolation. Each point in each plot corresponds to an individual slice of the acquisition containing the lime. Figures 2G-J show sagittal reformats of SR axial images of the same slice made with no correction (G) and with correction using 1× (H), 2× (I), and 4× (J) interpolation in the motion detection step.

Figure 2.

Demonstration of cross correlation. (A-C) show contour plots of the cross correlation for 1× (none), 2× and 4× interpolation using k-space zero padding. The square, colored pixel size in (A) corresponds to the acquired 0.75 × 0.75 mm² resolution. (D-F) Plots of detected position of the phantom using 1×, 2×, and 4× interpolation. Sagittal reformats from motion-corrupted data without correction (G) and correction using 1× (H), 2× (I), and 4× (J) interpolation in motion detection. Cyan arrows and dots indicate in-plane and through-plane motion, respectively, and numerical values indicate extent (in mm/pass). Note the subtle residual oscillation artifact (H, arrows) is eliminated with increased interpolation in (I-J). Additional description is in the text.

Figure 3 shows tuning of the filter to preserve object shape. (A-E) show representations of a sagittal reformat of the lime as a function of parameter A which controls the width of the Gaussians (Eq. 2). The data are from phantom motion of 0.49 mm/pass. To highlight object shape, only the outer rind and internal inter-partition membranes of the lime were used to create the images shown. Pixels for which the true object shape and motion-corrected shape match are shown in blue. Pixels of the true object shape not matched by motion correction are in cyan, and those in the motion-corrected object not matching the true object in magenta. For A=0 the distorted, magenta shape was formed from Figure 1G. As A increases note how the blue shape converges to the true underlying cyan shape (formed from Figure 1D), and magenta pixels disappear. Figure 3F is a plot of the Dice coefficient, peaking at a value of about 0.94 for A=2. The coefficient for the non-motion data set with and without correction has a value of 0.98 (<1.00) while that between non-motion and motion without correction has a value of 0.81. Similar results were obtained for other levels of motion. A=2 was used for all studies.

Figure 3.

Demonstration of tuning of anti-detrending filter. (A-E) show images of motion-free (cyan), distorted (magenta), and common (blue) pixels as a function of filter parameter A. For (A-E) the cyan arrow indicates direction and value indicates the extent (mm/pass) of motion. (F) Dice coefficient vs. A. Additional description is in the text.

Figure 4 illustrates the correction process for the phantom. (A) shows the S/I offsets unfiltered and shifts and offsets filtered vs. the slice number along Z. This is for motion of 0.49 mm/pass at a 30 degree angle to the X-Y acquisition axes. (B) shows the power spectrum of the S/I shifts before and after filtering as well as the anti-detrending filter as a function of k_Z. Estimated S/I and L/R offsets for all slices containing the lime are shown pre- (C) and post- (D) filtering. Points are grouped by color according to what pass each slice was acquired in. (E) is similar to (D) for the smallest motion studied, 0.16 mm/pass. In (D) and (E) consistent spacing between clusters is an indicator of accuracy, and the spread of each cluster is a measure of precision. For both (D) and (E) the latter is seen to be well within ±0.2 mm. Accuracy is demonstrated (F) by comparing displacement measurements made by the MRI-based motion detection and correction process vs. the reference, micrometer-based laboratory measurements. For the smallest motion, 0.16 mm/pass, the MRI measurement was within 17% of the reference; for all others it was within 7%.

Figure 4.

Data results from imaging of lime phantom. (A) Plot of filtered slice-to-slice shifts and unfiltered and filtered offsets in the S/I direction vs. slice number for 0.49 mm/pass motion at angle oblique to X-Y axes. (B) Plot of the measured power spectrum vs. k_Z of the S/I shifts before (green) and after (orange) application of the anti-trending filter (red), shown for A=2. (C-D) Plots of unfiltered and filtered offsets in the S/I and L/R directions for all slices containing the lime colored by pass for motion of (A-B). (E) Plot of post-filtering offsets for 0.16 mm/pass solely in the S/I direction. (F) Plot of motion detected by MRI correlation-filtering technique in phantom vs. calibration from laboratory bench tests.

Figure 5 shows results from an in vivo study (Study #13). Although not as extensive as for the phantom, note in (F) some separation of the offsets according to the pass of the acquisition. Plots of A/P and L/R offsets after filtering for all 16 subjects are presented in Supporting Information Figure S3. The mean displacement range for A/P motion was 1.63 mm and for L/R motion it was 0.50 mm.

Figure 5.

Data results from in vivo (Study #13). (A) Axial section and the ROI used for cross correlation. (B) Sample cross correlation contour plot analogous to those in Figure 2. (C) Shifts and unfiltered and filtered offsets plotted vs. slice number. (D) Plot of the measured power spectrum vs. k_Z of the S/I shifts before (green) and after (orange) application of the anti-detrending filter (red), shown for A=2. (E) Unfiltered and (F) filtered offsets plotted vs. the A/P and L/R directions for the central 66 slices, with the slices in each pass noted in the same color.

Figure 6 shows results of the radiological evaluation of sagittal reformats from the 16 prostate MRI studies. For the side-by-side comparisons presented (A-E), the motion correction provided statistically significant improvement over no correction (original). Here μ is the mean value. The other two evaluation criteria, not presented in the figure for brevity, were sharpness of the seminal vesicles and sharpness of the membranous urethra and had results (μ = +0.690, p<0.005) and (μ = +0.062, not significant), respectively. Figure 6F compares scores of overall diagnostic quality and shows a significant improvement with motion correction.

Figure 6.

Results of radiological evaluation of sagittal reformats made from super resolution axial images without (original) and with motion correction (MC). Results from blinded side-by-side comparisons are shown for sharpness of (A) prostate capsule, (B) bladder base contour, (C) rectal wall contour, (D) peripheral zone (PZ) vs. transition zone (TZ) differentiation, and for (E) level of artifact. For these criteria MC is significantly superior to original. (F) Overall diagnostic quality of each sagittal series as evaluated individually. Colored lines connect the two scores for a given exam. Mean values (μ) of each are noted in red. For all cases MC was equivalent or superior to the original.

Figure 7 shows results of the radiological evaluation of the SR axial series without and with motion correction. For the side-by-side comparisons of prostate capsule (A) and artifact (B) the improvement with motion correction was significant. For the other criteria (TZ-PZ differentiation, sharpness of seminal vesicles), the mean values were positive (+0.12, +0.19, respectively), but the difference was not statistically significant. For blinded evaluation of the individual axial series (C) the motion correction provided a significant improvement.

Figure 7.

Results of radiological evaluation of super resolution axial images reconstructed without (original) and with motion correction (MC) for (A) sharpness of prostate capsule and (B) level of artifact. In both cases the preference for MC is statistically significant. (C) Overall diagnostic quality of each axial series as evaluated individually. Colored lines connect the two scores for a given exam. Mean values (μ) of each are noted in red. For all cases MC was equivalent or superior to the original.

Figure 8 illustrates how the motion correction can provide an improvement in the axial SR images and the sagittal reformats in the same subject. Figure 9 illustrates results in sagittal reformats in three additional subjects. Supporting Information Video S1 compares multiple reformatted sagittal slices in the same subject. Supporting Information Figure S4 illustrates use of inappropriately large A in the filter.

Figure 8.

Example from Study #2 of improvement of image quality in both axial and sagittal images by use of motion correction (MC). (A) SR axial image formed with no motion correction prior to super resolution (SR) reconstruction. (B) Axial image of same section as (A) with motion correction applied to the same acquired data prior to SR reconstruction. Note improved sharpness of nodules in transition zone (yellow arrows, B). (C) Conventional 3-mm thick axial T2SE image for comparison. (D) Sagittal reformat made from SR axial images without motion correction. (E) Sagittal reformat made from SR axial images with motion correction. Note reduced level of scalloping in anterior prostate contour as well as interface between peripheral zone and transition zone with MC (E) vs. without MC (D) (yellow arrows). (F) 3-mm thick image best-matched to (D) and (E) taken from a directly acquired sagittal T2SE series for reference. For the axial image series the overall diagnostic quality score improved from +2 to +4 with MC; for the sagittal images it improved from +2 to +3. Axial image in (C) was acquired using technique of Table 1 except abutting 3 mm thick slices, 4 averages, scan time 4:14. Sagittal conventional T2SE image in (F) was acquired using TR 5400 TE 108, 3 mm thick, 1.0 mm gap, scan time 3:21.

Figure 9.

Results from three patient studies comparing sagittal reformats of SR axial images without (A, D, G) vs. with (B, E, H) motion correction (MC). Also shown are images of the same nominal section from directly acquired sagittal T2SE series (C, G, I). Principal anatomic landmarks are identified in (B): P: prostate; R: rectum; B: bladder; PS: pubic symphysis. Study #12: note in (B) vs. (A) reduction of artifact of prostate capsule both anteriorly (white arrows, A) and posteriorly (yellow arrows, A). Study #13: note in particular improvement of interface between transition zone and peripheral zone in (E) vs. (D) (arrows, D). Study #11: (G) was rated non-diagnostic, but motion correction allows visualization of nodule encapsulation (arrow, H). Overall image quality scores without / with motion correction were +2 / +4 (Study #12), +2 / +2 (Study #13), and +1 / +2 (Study #11). Sagittal images (C, F, I) were acquired using same technique as described in Figure 8.

DISCUSSION

We have presented a motion correction algorithm which can be used to align a set of slices having slice-to-slice overlap as used for super resolution (SR) in the slice direction. The method is based on two specific characteristics of the acquisition. First, because consecutive slices are overlapped, they are correlated, and cross correlation can be used as an estimate of relative misalignment. Second, because slices within an individual pass are all acquired within the same time, their relative motion and alignment are also known to be correlated. This is exploited in the filtering of measured offsets along the slice select direction. The algorithm solely uses post processing methods and requires no additional measurements such as navigator echoes.

The algorithm attempts to account for the slice-to-slice misregistration that may occur due to consecutive slices being acquired over different times. Such registration is important prior to performing any subsequent processing to provide super resolution along the slice direction. Uncorrected misregistration as small as 0.16 mm/pass was seen to cause noticeable artifact (Figure 1I). The algorithm does not account for motion occurring during an individual pass. Such motion can cause intra-slice artifact. Although retrospective methods have been developed to correct for this [34–36], these are not designed for and do not account for the slice-to-slice misregistration targeted here.

The motion detection and correction algorithm were evaluated in experimental phantom studies. The detection was seen to estimate known slice-to-slice displacement with accuracy of 17% error at 0.16 mm/pass to less than 7% at the higher speeds (Figure 4E). The precision at all speeds was in the range of 0.20 mm or less, seen from the spread of points in Figure 4C-D. This sensitivity and precision are finer than the 0.75 mm inplane resolution of the acquisition. When applied to motion-corrupted data in phantoms, the correction provided images which essentially match the non-motion-corrupted images in both the native and reformatted planes.

The algorithm was applied to prostate T2SE. From previous studies involuntary prostate motion such as due to rectal peristalsis is known to occur primarily within the axial plane of section, approximately orthogonal to the rectum, and we focused the correction technique on this assumption. Evaluation of the correction algorithm in 16 consecutive clinical prostate MRI studies showed consistent and statistically significant improvement in both the SR axial images and in the sagittal reformats.

As part of developing the algorithm we measured the degree of motion in a typical prostate MRI exam. In this work the subject preparation comprised fasting for three hours before the exam and voiding and emptying the rectum immediately prior to the exam. Glucagon, enema, and laxatives were not used, but in our experience these are not 100% effective in elimination of rectal peristalsis and add time and complexity to the MRI exam. Over the 16 subjects the ranges of A/P and L/R motion were 1.63 mm and 0.50 on average, respectively. Due to the high sensitivity of sagittal reformats from axial images to A/P motion, motion of this magnitude if uncorrected can lead to objectionable artifact.

This work was motivated by the goal to make the image set from the axial orientation more self-consistent in image-to-image registration prior to SR reconstruction. This is similar conceptually to making image sets from multiple orientations spatially consistent in fetal MRI prior to forming an SR 3D image [37–39]. The ultimate goal in the present work is to generate SR axial images with adequate quality in the reformats to allow elimination of one or both of the direct sagittal and coronal T2SE acquisitions which are currently included in the typical prostate MRI exam, each of which requires ≈3 minutes of scan time in addition to the 4-minute scan time for 3 mm thick axial slices. Although not yet demonstrated rigorously, the SR approach offers the potential of providing images in three orientations and 1 mm vs. 3 mm thick axial sections from a single scan of 6 min vs. three scans totaling 10 min.

Although developed for prostate T2SE, the method is in principle applicable to other studies of the pelvis subject to similar motion such as the staging of anorectal cancer, gynecological cancer, and perianal fistula.

As seen from the in vivo examples, although the correction consistently provided improved results it was not perfect, and the method has limitations. First, we did not consider any motion of the prostate in the S/I direction. However, based on previous studies [22–24] this is much less prominent than that due to subtle distensions in the A/P direction due to rectal peristalsis. Second, we only considered rigid translation of each slice based on the motion measurement. Modulating (reducing) the degree of correction as one moves anteriorly from the anterior rectal wall may be more accurate. Third, multiple aspects of the algorithm can likely be improved, such as selection of the ROI for cross correlation. As seen in Figure 5A this did not always encompass the full prostate. Fourth, the correction can artifactually induce motion effects in structures known or expected to be stationary, such as the pubic symphysis. Fifth, as stated above this method does not correct motion that might occur within the ≈1 min acquisition time of a single slice. We hypothesize that results are currently limited by the second and fifth factors of the above.

In summary we have developed a means for retrospective measurement and correction of subtle (±1 mm) inplane motion of 2D multislice axial T2SE images acquired with overlapped slices, and we have demonstrated significantly improved quality in the resultant super resolution axial images and in sagittal reformats in prostate MRI. The method exploits known characteristics of the acquisition.

Supplementary Material

Supp video

Supporting Information Video S1 Side-by-side comparison of series of sagittal reformats from Study #1 through the prostate without (left) and with (right) motion correction. Images are abutting slices, each 3 mm thick. Overall Image Quality scores without and with motion correction were +2 and +3.

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Supporting Information Figure S1 Flow diagram of motion correction algorithm and its placement within the super resolution acquisition and reconstruction process

Supporting Information Figure S2 Difference images without (A-C) and with (D-F) motion correction. In all cases the reference image was a sagittal reformat of SR axial images of the stationary phantom formed without motion correction. Yellow text indicates MSE relative to (A). (A) and (D) were formed using a repeat scan of the stationary phantom and compared with the reference. (D) indicates MSE increase due solely to the motion correction algorithm. (B) and (E) were formed from data acquired with motion of 0.49 mm/pass as for Figs. 1E-H. (C) and (F) were from data acquired at 0.16 mm/pass, corresponding to Figs. 1I-J.

Supporting Information Figure S3 Summary for the 16 subjects of A/P and L/R motion offsets after filtering. Units are in mm.

Supporting Information Figure S4 Illustration of effect of overemphasis of harmonics. Data are from Study #11. (A) Reference T2SE image acquired directly in sagittal orientation. (B) Sagittal image reformatted from axial T2SE data set and super resolution without motion correction. (C) Sagittal image reformatted from axial data set, motion correction with filter parameter A=2, and super resolution. Note reduced scalloping vs. (B) as desired. (D) Sagittal image reformatted using same input data set as (B) and (C) but with filter parameter A=20, causing orange Gaussians in Fig. 5D to become very narrow about the 13, 26, and 39 cycle harmonics with negligible response elsewhere. The effect causes all slices within a pass to have the same correction. Scalloping (D, yellow arrows) is more prominent than in (C).