1.

Introduction

Magnetic resonance imaging (MRI) dynamic contrast enhanced (DCE) myocardial perfusion data have been shown to have a high sensitivity and specificity for diagnosing myocardial ischemia.^1,2 DCE-MRI perfusion datasets can be analyzed to provide quantitative myocardial perfusion estimates, which have also been shown to perform well diagnostically.^3,4 Quantitation of myocardial perfusion requires regions of interest (ROIs) to be drawn over the myocardium and blood pool in every frame in the DCE-MRI dataset to obtain signal enhancement versus time curves. However, in the presence of myocardial displacement due to respiration, this task is prohibitively time consuming for clinical use. The main challenge of manual motion correction is the respiratory motion, causing the imaging plane to pass through an entirely different location (above or below the intended slice location), which breaks the underlying assumption of perfusion analysis. Motion correction methods attempt to remove the respiratory motion from the dataset so that ROIs are required on a single frame only. However, automated motion correction is challenging in DCE-MRI due to poor signal-to-noise ratio in the images, the temporally changing image contrast, and through-plane motion.

The work of McLeish et al.⁵ reports that the magnitude of the respiration-induced through-plane motion of the heart is largest in the cranio-caudal direction with smaller displacements in the left–right and anterior–posterior directions; the authors report respiration-induced through-plane translation of up to 23 mm combined with rotation and nonrigid deformation. In the work of Milles et al.,⁶ it is pointed out that through-plane motion violates the underlying principle of perfusion imaging, which relies on the idea of tracking the concentration of the contrast agent for the same location in the myocardium over time. In the literature on perfusion series registration, the respiration-induced motion is often mistaken for in-plane two-dimensional (2-D) motion because the shape of the myocardium does not vary significantly around the medial slice, which may create an impression of the respiration motion occurring only in 2-D without through-plane motion. In practice, small magnitudes of through-plane motion can be ignored, which cannot be said about severe cases of through-plane motion. The problem of through-plane motion cannot be solved perfectly with postacquisition methods only, and it has the potential of reducing the sensitivity of perfusion analysis. All postacquisition solutions for automated motion correction in perfusion series aim to offer a sensible compromise to achieve the best estimate for the perfusion-related parameters. Various registration methods based on free-form deformations and collectively known as nonrigid or deformable methods have been reported in the literature over the past years. However, keeping the problem of through-plane motion in mind, it can be concluded that deformable motion correction is unlikely to improve the diagnostic accuracy of perfusion analysis because it solves an incorrectly posed registration problem. For these reasons, pragmatic simplifications may produce more useful motion correction solutions than complex deformable approaches.

Typically, the accuracy of motion correction algorithms is assessed on the basis of geometric metrics such as the Dice similarity coefficient^7,8 and Hausdorff distance.⁹ The Hausdorff distance measures the distance between two subsets of a metric space; Hausdorff distance between two sets is small if every point of either set is close to some point of the other set. In the context of image analysis, the Hausdorff distance metric is used for determining the degree of similarity between two objects when they are superimposed on one another. These evaluation methods require ground-truth motion correction parameters obtained manually against which to compare the automated results. Inevitably, manual definition of ground-truth motion correction is subject to human operator error, and in some cases may be less accurate than automated motion correction. Although automated perfusion motion correction techniques offer tangible benefits, the effects of automated solutions on the clinical outcome measures are rarely assessed.

The work presented here was a retrospective substudy using data from the CE-MARC trial.¹ The CE-MARC trial evaluated the performance of a multiparametric cardiac MR protocol for diagnosing significant coronary artery disease and compared this to single photon-computed emission computed tomography (SPECT) using the reference standard of invasive x-ray angiography. The dataset allowed an evaluation of quantitative MR perfusion estimates diagnostically. The CE-MARC trial¹ dataset provides an ideal opportunity to test motion correction for quantitative perfusion in terms of the diagnosis of myocardial ischemia, which is ultimately the purpose of motion correction in cardiac perfusion DCE-MRI. The aim of our study was to use the clinical gold standard, provided by CE-MARC, to evaluate diagnostically and compare the outcomes of four strategies for motion correction of varying complexity. The strategies included combinations of translation, rotation, and deformable registration approaches as described in the Sec. 2. Our hypotheses were first, that motion correction of the basal slice, with transform propagation to the other slices, provides results that are at least as good as independent motion corrections for each slice; and second, that image translation alone is sufficient to account for respiratory motion for the purposes of quantitative perfusion. We would like to point out that the comparison of registration strategies was made on the basis of their impact on the diagnostic accuracy. Evaluation in terms of diagnostic accuracy provides evidence based on which pragmatic decisions can be made about the necessary complexity and accuracy of motion correction for cardiac perfusion DCE-MRI datasets.

2.

Methods

Three short axis slices (basal, medial, and apical) were acquired during the first pass of the contrast agent through the myocardium. The correspondence of the cardiac phase within each spatial location was achieved through electrocardiogram (ECG) gating. Adenosine-induced stress imaging was performed 15 min before rest imaging. Myocardial perfusion MR imaging was performed using bolus intravenous injection of $0.05\mathrm{mmol}/\mathrm{kg}$ of body weight gadopentetate dimeglumine (Magnevist; Schering, West Sussex, England). Images were acquired using a T1-weighted saturation recovery turbo field-echo imaging sequence. A shared (nonslice-selective) saturation pulse was used, giving prepulse delay times of 126 ms, 272 ms, and 418 ms for the basal, middle, and apical slices, respectively. The pulse sequence parameters were as follows: repetition time/echo time, $2.7/1.0\mathrm{ms}$; flip angle, 15 deg; sensitivity encoding factor, 2; matrix, 144 3 144; field of view, 320 to 460 mm; slice thickness, 10 mm; and partial Fourier factor, 0.67.

The independent Clinical Trials Unit at the University of Leeds selected 50 patients as a subset of the CE-MARC trial population representative for risk factors and disease severity. All CE-MARC patients underwent x-ray angiography, SPECT, and a multiparametric MR examination. In order to have a consistent dataset, patients with any x-ray angiography defined stenosis severity between 50% and 70% or whose SPECT and x-ray angiography results were discordant were excluded from the study. Patients were recruited from Leeds Teaching Hospitals NHS Trust, Leeds, United Kingdom, and Pinderfields Hospital, Wakefield, United Kingdom. All SPECT and CMR scans were undertaken at Leeds General Infirmary. The study was performed in accordance with the Declaration of Helsinki (October 2000), with all patients providing informed written consent. The study protocol and other relevant documentation were approved by the Leeds (West) Research Ethics Committee.

2.1.

Registration Strategies Overview

The registration methods for motion correction in perfusion series compared here draw on the basic frame-by-frame registration approach reported by Li and Sun.¹⁰ In this approach, the motion correction process is started with the first two frames, labeled as fixed and moving images accordingly. For each consecutive registration step, the moving image from the previous step is resampled and treated as the new fixed image. The key novelty of the solution presented here is in the use of average frames as fixed images during registration to avoid the issue of the accumulated registration error, which is common for frame-by-frame registration methods. As noted earlier, with these methods, for each pair of adjacent images, the moving (corrected) image becomes the reference image for the next registration step. Under this scheme, individual registration errors in early frames tend to be exacerbated for the later frames in the series. Use of average images draws on the ideas of groupwise registration published by Cootes et al.¹¹ The rationale behind the use of average images is that they contain all features from the series, which makes them suitable to be used as the fixed images for the correction of slices from precontrast, right-ventricular contrast, left-ventricular contrast, and contrast wash-out phases of the series. Average images are used as the fixed images in the rigid and deformable versions of motion correction methods. An example of average images and their progressive refinement is given in Fig. 1.

Fig. 1

Examples of average images. Evolution of average images for a stress perfusion series; rows: apical, medial, and basal locations; columns: prior to correction, after translation, and after rigid correction; the improvement of the clarity of the cardiac features from noncorrected average images to translation-corrected images supports the general observation that the bulk of the motion is compensated by translation correction; the rigidly corrected average images also usually show improvement in clarity that may vary from patient to patient.

Motion correction was performed on the 50 rest and 50 stress perfusion datasets in accordance with four registration strategies. These strategies vary among themselves in the following aspects:

• 1. Complexity of the geometric transform: translation-based, rigid, and deformable transforms were used in the experiments. It is common in image registration practice to start motion correction with the simplest possible transform to compensate for gross displacement: translation transform. If further correction is required to account for the rotational motion component, the output of the translation correction method is used to initialize the rigid (combination of translational and rotational displacements) correction method. Similarly, the deformable motion correction method needs to be initialized with gross motion correction obtained either with translation or rigid transform. Complex registration solutions in practice form registration pipelines, where motion correction results for distinct stages of the pipeline are used to initialize subsequent motion correction stages. Depending on the nature of the experiments, the results from distinct stages of motion correction can be treated as independent results for distinct types of registration strategies: translation, rigid, and deformable. This was the case with the experiments described here.

• 2. Choice between the two options of dealing with motion in different slices: one option involves independent motion correction in all slices, basal, medial, and apical, while the other option involves motion correction in the basal slice with transform propagation to the medial and apical slices. It is hypothesized here that it is sufficient to correct the motion only for the basal slice in the whole series, and propagate the transforms to the medial and apical slices. This hypothesis is based on the following observations:

  • a. Basal slices contain the greatest information density, while the clarity and scale of image features usually progressively decrease from basal to apical slices with the decreasing size of the ROIs. Transform optimization based on any given image similarity metric provides better results for larger objects even with significant initial displacements because the image similarity metric produces stronger gradients for larger features. Thus it is likely that motion correction of basal slices will provide the most accurate results.

  • b. The perfusion imaging protocol ensures that all three slices in each dynamic frame, basal, medial, and apical, are acquired within 150 ms of each other in the same cardiac cycle. Since respiratory motion is relatively slow, the difference of respiratory motion for the three slices in each frame can be considered negligible. The contractile myocardial motion is much faster than respiratory motion, but with ECG gating functioning correctly, the phase remains consistent for all slices for a given location. This ensures the consistency of spatial position and shape of myocardium with the given location. Thus, transform parameters for all three slices are expected to be similar even in the presence of respiratory motion.

The hypothesis about basal-only slice correction can be applied to translation and rigid motion correction methods; the deformable correction naturally has to involve the optimization of distinct transforms, one for each of the apical, medial, and basal slices within each dynamic frame.

2.2.

Common Registration Components

Apart from transform type, its initialization, and parameter propagation, the rest of the registration components were identical for all compared registration methods. Motion correction was achieved through two-level multiresolution registration (half resolution for the first level and full resolution for the second) with a basic gradient-descent optimizer.¹² Nonlinear intensity variations during contrast uptake captured in perfusion series and the intensity values averaged across the whole series call for the use of the mutual information (MI) image similarity metric; Mattes’ implementation of the MI image similarity metric¹³ was used in all compared registration strategies. Manually defined ROIs were used during registration to exclude irrelevant anatomical features in the images. The ROIs were defined in the key frame of each perfusion series. The key frame is identified visually by the maximal contrast agent concentration in the left ventricle (LV), where image contrast between the blood pool, myocardium, and surrounding structure are optimal. Rectangular ROIs were drawn around the heart, including both LV and right ventricle (RV; as shown in Fig. 2), because the features of the RV are important for recovering the rotational motion. All instances of registration described here were carried out with elliptical masks fitted inside the ROIs. Following are descriptions of the registration strategies used in this research.

Fig. 2

Examples of manually defined ROIs. An illustration of ROIs in stress perfusion series; the ROIs were defined in a way that aimed to exclude irrelevant features, such as liver and lung tissue, which may move independently of the myocardium; the fixed image masks for registration were obtained from ellipses fitted inside the ROIs; the ROIs and masks were intended to exclude the features irrelevant (or possibly detrimental) to registration.

2.2.1.

Strategy 1: Translation correction for all slices

Pairwise registration of individual basal slices to the maximal contrast basal slice with translation transform was followed by the same procedure for the medial and apical slices and the corresponding medial and apical maximal contrast slices. Pairwise registration starts with the slices adjacent to the maximal contrast frame and continues toward the start and end of the time series as shown in Fig. 3. For each pairwise registration, the initialization of the transform was achieved in the following manner: for the slices on either side of the maximum contrast slice $k$ (positions $k-1$ and $k+1$, respectively), the transform was initialized to identity. As the positions of the registered slices, $k-n$ and $k+n$ (where $n$ is the distance between the given slice and the maximal contrast frame) shift from the maximal contrast slice toward the start and end of the series, respectively, the transforms are initialized with the parameters which were obtained from the previously registered slices.

Fig. 3

Perfusion series registration. Perfusion motion correction for basal slice: in the translation correction step, the slices are registered to the basal slice from the key frame; after translation correction, average image is computed and preregistered rigidly to the key frame; during the rigid correction step, the average is used as the fixed image.

2.2.2.

Strategy 2: Translation correction for basal slice with transform propagation

Pairwise registration of individual basal slices to the maximal contrast basal slice with translation transform was followed by the application of the recovered transform for a given basal slice to the lower slices in the corresponding dynamic frames. Transform initialization followed the same pattern as in strategy 1.

2.2.3.

Strategy 3: Rigid correction for basal slice with transform propagation

The average image from all basal slices was computed after the application of transforms obtained with strategy 2. Pairwise registration of individual basal slices to the average image of the basal slice with a rigid transform (as shown in Fig. 3) was followed by the application of recovered transforms for a given basal slice to the lower slices in the corresponding dynamic frames. Transform initialization followed the same pattern as in the earlier strategies. The center of rotation was initialized to the center of the LV ROI. The registration algorithm for rigid transformation optimizes the center of rotation parameters along with the translation parameters. Thus the potentially suboptimal initial center of rotation parameters were adjusted by the transform optimizer to obtain optimal center of rotation position.

2.2.4.

Strategy 4: Deformable correction for all slices

The average image from all basal slices was computed after the application of transforms obtained with strategy 3. It is a common requirement for successful registration to supply best-guess initial parameters for any type of registration. As described by Ng and Ibáñez,¹⁴ the cascaded transform initialization in a registration pipeline was used in this study for initializing rigid and deformable transforms. Pairwise registration of individual basal slices to the average image of the basal slice with a B-spline transform¹⁵ was carried out in a manner identical to previously listed strategies. Next, deformable correction was independently carried out for medial and apical slices. Transform initialization followed the same pattern as in the earlier strategies.

2.3.

Protocol for Manual Contouring of Perfusion Images

Manually defined contours were used as the reference standard in all perfusion motion correction evaluation experiments. The contours were defined in the dedicated cardiac image analysis software QMass 7.0 by Medis Medical Imaging Systems, Leiden, The Netherlands. For all 50 datasets, LV endocardial, epicardial, and blood pool contours were defined for all frames and slices in rest and stress series. For each perfusion series, a key frame was chosen as the frame exhibiting the maximum contrast between the ventricular blood pool and the surrounding myocardium. First, all three types of contours were defined in the key frame as shown in Fig. 4 (top row); next, the contours from the key frame were copied to the rest of the series; finally, the contours were manually translated within each slice to compensate for respiratory motion. In many images, the observed negligible magnitude of motion did not warrant contour adjustment; in most series, this was the case for the frames acquired during breath-hold. Breath-holding in the CE-MARC study perfusion series was timed to coincide with the first pass of the contrast agent through the myocardium.

Fig. 4

Examples of manually defined contours. An example of manually defined LV endocardial, epicardial, and blood pool contours in the key frame for basal, medial, and apical slices (top row); a typical example of precontrast slices (from the same dataset as above), which are unsuitable for accurate manual contouring (bottom row).

The approach to manual motion correction described above possesses an inherent limitation because it is based on the assumption that observed motion in perfusion series includes only translation motion, while in practice, through-plane motion and nonrigid motion can be detected in most perfusion datasets. Theoretically, an alternative contouring approach could involve manual contour delineation in each slice and frame. In addition to the significant increase in time and effort this approach would entail, this would not guarantee more accurate contours for the precontrast stages of perfusion series, where low image contrast renders the boundary between myocardium and ventricular blood pool imperceptible, as shown in Fig. 4 (bottom row).

3.

Results

A visual example of perfusion motion correction is shown in Fig. 5; the images were obtained by extracting reformatted profiles along the $XZ$ image dimension from the 2-D slices for a given spatial location stacked into pseudo-three-dimensional (3-D) images (2-D + time). The extracted profiles were defined to pass through the center of manually defined ROIs shown in Fig. 5 to include the relevant cardiac features and contrast uptake events. The example shows the reformatted profiles for the series before motion correction, after translation correction, and after rigid correction. The main indicator of motion is the interventricular septum. In addition, the images clearly show magnitude of motion with respect to the precontrast, right-ventricular contrast, left-ventricular contrast, and wash-out phases of the series. In the images prior to correction, the magnitude of respiratory motion can be observed from the changing position of the interventricular septum and ventricles, while the series after the first correction stage show that the bulk of motion has been recovered with translation transform. The series after the rigid correction stage in this example are very similar to the images after translation correction. This observation is consistent with the examples of average images and their refinement observed after each correction stage is given in Fig. 1, where it is demonstrated how the clarity of the cardiac features in the ROI increases starting from the average images prior to correction, after translation and rigid correction steps. The average images after deformable registration do not show significant improvement in image clarity. The images of the series after deformable correction are not included in this example because visually, they appear identical to the images after rigid correction.

Fig. 5

Visual comparison of perfusion correction stages. Stacked reformatted images for stress perfusion series; rows: apical, medial, and basal locations; columns: before correction, after translation, and after rigid correction; the ROIs are shown with yellow boxes; within each ROI, the RV appears on the left, interventricular septum in the center, and the LV on the right; the last two columns indicate that the bulk of respiratory motion was recovered during translation correction; the interventricular septum is the most obvious feature that can be used for visual validation of motion correction.

3.2.

Diagnostic Evaluation

The ROC curves in Fig. 6 compare the four variants of perfusion motion correction versus manual perfusion correction in terms of the ability to diagnose myocardial ischemia. The AUC values with the associated confidence intervals are shown in Table 2. These values suggest that the results for all four variants of perfusion motion correction are equivalent to manual correction. The cut-off values that achieved the highest sensitivity and specificity for the diagnostic test were as follows: $\text{manual correction}=1.34$, translation for all $\text{slices correction}=1.31$, translation for basal slice with transform $\text{propagation correction}=1.37$, $\text{rigid correction}=1.20$, and $\text{deformable correction}=1.41$.

Fig. 6

MPR ROC curves. ROC curves for MPR scores generated for the four variants of perfusion motion correction: translation correction for all slices, translation correction for basal slices, rigid correction for all slices, and deformable correction for all slices; the four variants are compared to the ROC curve generated for the manual motion correction.

Table 2

ROC curve statistics.

Manual	Strategy 1 (translation, all slices)	Strategy 2 (translation, basal slice)	Strategy 3 (rigid, basal slice)	Strategy 4 (deformable, all slices)
AUC 0.93	AUC 0.89	AUC 0.92	AUC 0.93	AUC 0.92
	$p=0.41$	$p=0.88$	$p=1.00$	$p=0.92$
	(0.81, 0.98)	(0.84, 1.00)	(0.84, 1.00)	(0.83, 1.00)

AUC values and the corresponding confidence intervals for the four perfusion motion correction variants compared to manual motion correction; the AUC values indicate that all four perfusion correction variants are at least as good as manual motion correction. The confidence interval values given in parentheses are the lower and upper 95% confidence interval limits on the AUC values.

4.

Discussion

The study described in this article compares a number of automated perfusion motion correction strategies of various levels of complexity. The proposed solution relies on the use of average images as the fixed images during registration. In the method presented in this article, the average images undergo refinement during the translation-based, rigid, and deformable stages of motion compensation. The MI image similarity metric allows the modeling of complex mappings between pixel intensities, where the actual form of dependency between the intensities in the registered images does not need to be specified. The use of the MI image similarity metric allows the average images to be used as fixed images during correction of perfusion slices from precontrast, RV contrast, LV contrast, and wash-out parts of the perfusion series. The evaluation results prove the validity of the correction approach with translation for basal slices with subsequent transform propagation to medial and apical slices. The Dice metric values for LV endocardial overlap and the ROC curves for MPR scores both confirm the initial hypothesis that the recovery of translation motion in the basal slice is at least as good if not better than translation correction for all slices. The motion correction provides more reliable results with basal images due to the larger scale of the ventricles and other image features, and the transforms from the basal slice can be applied to the medial and apical slices because of the negligible magnitude of respiratory motion observed between the acquisitions of basal, apical, and medial slices within one cardiac cycle.

In most cases, the motion correction based on the rigid 2-D transform provided reliable results. However, during the initial stages of prototyping and exploration, it was observed that the rate of failures was significantly reduced when the translation parameters in the rigid transform were fixed. Most importantly, this study confirms that rigid and deformable correction strategies do not enhance diagnostic accuracy. In practice, the rigid and deformable automated motion correction methods in perfusion analysis are often used incorrectly as a means to deal with myocardium shape variation induced by through-plane motion. Through-plane motion compensation violates the underlying principle of perfusion imaging, which relies on the idea of tracking the concentration of the contrast agent for the same location in the myocardium over time. In such cases, the automated motion compensation methods force the images to show two different slices through the myocardium to be registered to each other. The main message of this study is that the type of automated motion correction does not affect the diagnostic accuracy. In addition, it must be noted that postacquisition image processing methods such as image registration are not suitable for solving the problem of through-plane motion, which breaks the underlying assumptions of quantitative perfusion analysis. Instead, this problem is more suitable for being tackled with methods applicable during image acquisition, such as prospective tissue tracking. It is yet to be explored how motion correction methods can be adapted to emerging 3-D myocardial perfusion techniques such as reported in the work of Jogiya et al.²¹ and Manka et al.²²

The difficulty in evaluating motion correction in DCE-MRI was a key motivation for using clinical diagnosis as a reference standard. Although we are evaluating at the contouring stage and the final diagnosis stage, we are not evaluating at the time versus signal intensity curve stage. If there were a single time point registration error causing “spikes” in these curves, or systematic translational shifts that incorporated blood pool voxels in the myocardial curve, then these could cause errors in MBF. However, it is not clear how a summary signal intensity value could detect these changes. Average values over time would be insensitive to localized changes and would also require normalization for signal gain. Thus, a summary measure would be needed to look at systematic differences in curves between registration methods.

The limitations of this study involved the comparison against translation-only manual motion compensation. However, the ROC curves for MPR scores provide strong evidence of the overall soundness of the study described here. X-ray angiography is limited as a reference standard for myocardial ischemia because the degree of stenosis is not always linked to a reduction in coronary, or ultimately MBF. This study used a consensus diagnosis between SPECT and x-ray angiography to obtain the best reference standard available with the CE-MARC dataset; however, measurements could have been improved if fractional flow reserve pressure wire measurement had been used.

It is important to note that the diagnostic accuracies achieved in this study are not clinically representative. Ambiguous cases, where x-ray and SPECT measurements did not agree, were removed. This created a reliable reference standard for our comparison study, but our results cannot be considered representative of clinical diagnostic performance.

5.

Conclusions

This study has shown that automated motion correction does not significantly change the diagnostic accuracy of quantitative myocardial perfusion imaging for diagnosing myocardial ischemia. This provides important evidence in support of the use of such methods in practice. Furthermore, this study has shown that the apparently more sophisticated method of deformable registration does not improve diagnostic accuracy above that of simple rigid registration.