Magn Reson Mater Phy DOI 10.1007/s10334-014-0440-9

RESEARCH ARTICLE

Motion correction of multi-contrast images applied to T1 and T2 quantification in cardiac MRI Anne Menini • Glenn S. Slavin • Jeffrey A. Stainsby Pauline Ferry • Jacques Felblinger • Freddy Odille

•

Received: 24 May 2013 / Revised: 26 February 2014 / Accepted: 27 February 2014 Ó ESMRMB 2014

Abstract Object The ability to manipulate image contrast and thus to obtain complementary information is one of the main advantages of MRI. Motion consistency within the whole data set is a key point in the context of multi contrast imaging. In cardiac and abdominal MRI, the acquisition strategy uses multiple breath-holds and often relies on acceleration methods that inherently suffer from a signalto-noise ratio loss. The aim of this work is to propose a free-breathing multi-contrast acquisition and reconstruction workflow to improve image quality and the subsequent data analysis. Materials and methods We extended a previously proposed motion-compensated image reconstruction method for multi-contrast imaging. Shared information throughout the imaging protocol is now exploited by the image reconstruction in the form of an additional constraint based on image gradient sparsity. This constraint helps to mini-

mize the amount of data needed for efficient non-rigid motion correction. T1 and T2 weighted images were reconstructed from free-breathing acquisitions in 4 healthy volunteers and in a phantom. The impact of multi-contrast motion correction was evaluated in a phantom in terms of precision and accuracy of T1 and T2 quantification. Results In the phantom, the proposed method achieved an accuracy of 97.5 % on the quantified parameters against 88.0 % before motion correction. In volunteers, motion inconsistency in T1 and T2 quantification were noticeably reduced within 5 min of free-breathing acquisition. Conclusion An efficient, free-breathing, multi-contrast imaging method has been demonstrated that does not require prior assumptions about contrast and that is applicable to a wide range of examinations. Keywords Motion correction  Quantitative MRI  Cardiac MRI  Image reconstruction Abbreviations BH FB GRICS

A. Menini  P. Ferry  J. Felblinger  F. Odille IADI, Universite´ de Lorraine, Nancy, France e-mail: [email protected] G. S. Slavin GE Healthcare, Bethesda, MD, USA J. A. Stainsby GE Healthcare, Toronto, ON, Canada J. Felblinger  F. Odille (&) U947, INSERM, Nancy, France e-mail: [email protected]

MC-GRICS FSE ME-FSE SMART1Map TEeff ESP ETL TI TD

Breath-hold Free-breathing Generalized reconstruction by inversion of a coupled system Multi-contrast GRICS Fast spin echo (pulse sequence) Multi-echo FSE (pulse sequence) Saturation method using adaptive recovery times for T1 mapping (pulse sequence) Effective echo time Echo spacing Echo train length Inversion time Trigger delay

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Introduction The ability to manipulate image contrast is one of the main advantages of MRI. It allows complementary information to be obtained for a better detection and a more precise diagnosis [1]. For example, in cardiac MRI, a lesion in the myocardium can be distinguished from healthy muscle using gadolinium enhancement contrast, but another contrast mechanism may be necessary to distinguish the lesion from the blood pool [2]. Moreover, lesion classification and patient follow-up benefit from further contrast manipulation to achieve quantitative parameter mapping such as T1 and T2 [3]. Multi-contrast images benefit from being analyzed as a whole, but data are likely to be corrupted by intra- and/or inter-acquisition inconsistencies. Inconsistencies related to patient motion are critical and can manifest in three different ways: (1) motion artifacts can arise within individual images; (2) misregistration of images with similar types of contrast (e.g., images with different echo times in a T2 mapping sequence) can result in a corrupted quantitative map; (3) misregistration of images with different types of contrast (e.g., from a T1 mapping and a T2 mapping sequence) can impair the combined analysis of the data. In cardiac MRI, although heart motion is effectively addressed with cardiac gating, respiratory motion remains more challenging. While breath-holding is the most common solution, in the context of multi-contrast cardiac MRI, this results in a significant number of breath-holds. (In our clinical center, a typical cardiac MR examination comprises more than 30 breath-holds.) Breath-holding has limitations beyond patient discomfort and capability. First, multiple breath-holds lead to intra- and inter-sequence misregistration. Second, image quality (SNR, resolution, etc.) has to be traded for acquisition time, although acceleration methods have been proposed to save acquisition time with a minimal loss of signal [4, 5]. More recent breakthroughs in compressed-sensing have been shown to improve this tradeoff between acceleration and signal loss [6–8]. Nevertheless, all of these methods require multiple breath-holds and do not guarantee inter-contrast consistency. In addition, for an acceleration factor R, there is still pffiffiffi an inherent SNR loss of at least R, compared to an ideal fully sampled acquisition. Free-breathing using respiratory gating is another option, but this significantly decreases acquisition efficiency. Motion correction methods suitable for freebreathing imaging (i.e., those that allow non-rigid deformations) have been suggested [9, 10] such as GRICS [11]. This joint reconstruction method solves for the artifact-free image and the motion model that occurs during the acquisition using all the data acquired, thus optimizing the

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acquisition efficiency. Although this motion correction method can be improved using sparsity constraints [12], such an approach relies on the repetitive acquisition of the same image, or the same type of contrast using prior knowledge [13–15], and thus does not take advantage of the information shared through the whole examination. In addition, methods have been proposed for reconstructing under sampled multi-contrast images using sparsity constraints on the image gradients [16–18] or using a Bayesian compressed sensing framework [19]. These frameworks can exploit information redundancy efficiently, but they rely on the assumption that images are perfectly static. In this work we propose a new method that can deal with both motion and contrast. The proposed method is based on the GRICS technique [11] and can handle multi-contrast imaging (MC-GRICS). The main objective is to exploit shared information between contrasts to counterbalance the lack of repetitions of the same contrast that are usually required. No prior assumption is made about the type of contrast, so the method can be applied to a wide range of free-breathing acquisitions. The method is validated using a multi-contrast imaging protocol that includes T1 and T2 quantitative mapping in a phantom and volunteers. The efficacy of the method is assessed quantitatively in a phantom in terms of precision and accuracy of T1 and T2 parameter estimation. Theory The aim of the method presented here is to obtain a motion compensated reconstruction of multi-contrast images acquired during free-breathing. This new method is a generalization of the previously proposed GRICS technique [11]. A brief description of the GRICS algorithm is presented, followed by the description of the two modifications necessary to handle multi-contrast imaging: (1) the optimization of a single motion model common to all images (those images having different contrasts) and (2) the joint reconstruction of all images under a gradient sparsity constraint. Review of GRICS GRICS is an algorithm that jointly reconstructs an image free of motion artifacts and the motion that occurs during the acquisition. A warping operator W(u), described by a time-varying motion field u, is integrated into the MR signal equation: s ¼ Eq ¼ nFrWðuÞq

ð1Þ

where s is the acquired k-space data, E is the encoding operator, q is the artifact-free image, n is the sampling

Magn Reson Mater Phy

operator in k-space, F is the Fourier transform, and r is the coil sensitivity weighting operator. If an estimate of the motion field u is available, then the image q can be approximated by solving the inverse problem defined in Eq. 1. Conversely, if the image is known, the motion field u can be optimized to best fit the signal equation. The optical flow equation gives the linear relation between the error du in the motion field and the error e between the acquired data and the simulated data (using the known image q and the current estimate of motion u): e ¼ s  Eq  ¼ nFrWðuÞðq  qÞ ¼ nFrWðuÞðrqÞdu ¼ Rðq; uÞdu

Thus, the first adaptation of the GRICS algorithm consists of pooling together the motion model optimization of the N different contrasts: 8 2 3 2 3 q1 s1 > > < 8c ¼ 1    N; s ¼ E q 6 7 6 c c c .. 7 .. 7 7 ; P¼6 with S ¼ 6 . . 5; 4 5 4 > e ¼ S  EP ¼ Rda > : sN qN 2 3 2 3 E1    0 R1    0 6 . . 7 6 . . 7 6 . . ... 7 . . ... 7 E¼6 4 .. 5 and R ¼ 4 .. 5 0    EN 0    RN ð4Þ

ð2Þ

The solution (q, u) can be iteratively obtained with the alternating optimization between the two inverse problems forming the following coupled system:  s ¼ EðuÞq ð3Þ e ¼ Rðq; uÞdu Note that a first estimate of the motion can easily be found by initializing the coupled system at a lower resolution: a null displacement is a good initialization in that case. Then the alternating optimization can be applied in a multi-resolution scheme. Note that the motion optimization problem can be simplified by restricting the search to a subspace of all possible motion fields. For example, a convenient assumption is that the amplitude of the displacement in a given voxel is linearly related to the signals Si coming from external devices such as a respiratory belt. Under this hypothesis, the temporal component of motion is given by the physiological signals; only the spatial components ai of motion need to be solved. Note that this motion model ai is the same for the whole examination if no bulk motion appears. X uðx; y; tÞ ¼ ai ðx; yÞSi ðtÞ i

This optimization can be further improved by solving for those parameters only in certain key points that form an adaptive mesh [20]. Shared optimization of the motion model With the previous framework, only one image can be obtained, i.e., only one contrast. Therefore, this method needs to be adapted for multi-contrast data. A naive solution would consist in running an independent GRICS reconstruction for each contrast of the set. Beyond the computational inefficiency, this solution would lack motion consistency from one contrast to another.

By solving the coupled system in Eq. 4, all the reconstructed images should be co-registered. In addition, the second part of the problem (i.e., the inverse problem that solves for the motion) is much better conditioned. Consider N contrasts. With the conventional GRICS method, there are N ill-conditioned problems. Each of them, based on one known k-space, solves for one unknown image and one unknown motion model. With MC-GRICS, there are only N unknown images and one motion model to be optimized from N known k-spaces. Joint reconstruction of multi-contrast images under a gradient sparsity constraint Solving Eq. 1 when u is a non-rigid motion field leads to an ill-conditioned linear system. As discussed in [21], a practical implementation shows that a small number of scan repetitions (Nrep = 2 or more with repetitions in different motion states) brings sufficient over-determination to account for irregular k-space sampling effects and motion estimation errors. However, the problem may become unstable when no overdetermination is available (Nrep = 1). On one hand, this requirement for a higher Nrep improves motion correction and increases SNR in the final images, but on the other hand it decreases the scanning efficiency. As written in Eq. 4, this point remains valid for each independent equation of the first part of the coupled system. Unfortunately, in the multi-contrast context, the number of different acquisitions is already necessarily large to obtain all the complementary contrasts. Thus, it would be preferable to avoid any acquisition repetition. The aim is to take advantage of the redundancy of information within multi-contrast data sets in order to overcome the difficulties of non-rigid motion correction with insufficient over-determination (including when Nrep = 1). Even if there exists no direct transformation from one contrast to another (i.e., the different contrasts bring complementary information), redundant information does exist since images share common anatomical information. This translates into the spatial location

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of image gradients, which should be mostly preserved from one image to the other when motion is accounted for. This provides the motivation here to pool all images together and reconstruct them jointly under a constraint enforcing that all images share as much gradient information as possible. A similar idea has been proposed by Haldar et al. [16] in another context without motion correction. In the following, the construction and application of this regularization is presented. Considering an iterative reconstruction process as described above, it is assumed that a rough estimate of the multi-contrast images is available. From these, pseudo-probability maps (GX, GY) associated with the local occurrence of directional gradients can be defined: 8 > if DX;Y : i;j if DX;Y i;j [ e e 8 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 ð5Þ > PN > 2 c c  > b q  q  < DXi;j ¼ i;j  c¼1 c iþ1;j with rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 > PN > 2 c Y > c  : Di;j ¼ b q  q  i;j  c¼1 c i;jþ1 where e is a threshold parameter, and bc is the inverse of the average magnitude of image qc. In order to constrain the reconstructed images to share the same anatomy (i.e., to minimize differences from the common gradients), Tikhonov regularization [22] was used. This can be seen as a spatially varying smoothness constraint, and the regularization can be written as: (  2 ) rP 2  P ¼ min kS  EPk þk ð6Þ G P Note that this regularization requires fine-tuning of the parameters k and e. k is a usual regularization parameter that gives the relative weight of the constraint in the inverse problem. The second parameter e also needs to be carefully chosen. If it is too high, the spatial variation of the constraint is lost, and it becomes equivalent to a classic smoothness constraint (i.e., there is no contribution from one contrast to another). Multi-contrast GRICS MC-GRICS combines GRICS with the shared motion model optimization and the gradient-sparsity-constrained image reconstruction. The coupled system in Eq. 7 is iteratively solved with a fixed-point multi-resolution scheme described in Fig. 1. 8   rP < P ¼ min  s:t: S ¼ EðuÞP ð7Þ P G : e ¼ RðP; aÞda

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Materials and methods The free-breathing acquisition workflow for multi-contrast imaging was validated in two steps. First, the ability of MC-GRICS to recover high quality images from motioncorrupted data was evaluated. Then, the quality of MCGRICS images was compared to that from a standard breath-held acquisition. Multi-contrast imaging protocol To evaluate the ability of the reconstruction method to compensate for motion in multi-contrast images, a reference acquisition was necessary. Because this acquisition had to be free of motion or acceleration artifacts, a phantom was use for this purpose. The phantom was composed of 12 dissolution tubes designed to have a wide range of T1 and T2 values thus enabling different contrasts. Breathing motion was simulated using the rocking feature of the MR table (motion along the longitudinal axis of the bore); ECG simulation was also used. MR experiments were performed using a 3T GE Signa HDxt MR system (General Electric, Milwaukee, WI). 2D images were acquired in a phantom and in four healthy volunteers. For each examination, two data sets were acquired: 1 in free-breathing (FB) and one in breath-hold (BH). In the volunteers, a respiratory belt was used to record the breathing signal required by the GRICS reconstruction. For each data set, five T1-weighted images were acquired using the SMART1Map sequence [23] and eight T2-weighted images using black-blood multi-echo fast spin echo (ME-FSE). So in total, two different types of contrast and 13 different contrasts were used. A mid-ventricular short-axis slice was imaged in diastole using a finger clip sensor and an 8-channel cardiac array coil. Acquisition parameters are listed in Table 1. Saturation Method using Adaptive Recovery Times for cardiac T1 Mapping (SMART1Map) is a single-point, saturation-recovery myocardial T1 mapping sequence. Compared to common methods such as MOLLI [24], SMART1Map measures true T1 instead of the apparent T1, and can sample the entire magnetization recovery curve for optimal accuracy and precision. As a reference, theoretical TIs for a nominal heart rate of 60 bpm and TD = 600 ms would be TI = [100; 350; 600; 1,600; 3,600 ms]. A view per segment of 28 was chosen for the free-breathing acquisitions against 38 for the breath held acquisitions. For ME-FSE, eight images were acquired. For freebreathing acquisitions, an echo train length ETL = 8 and an echo spacing ESP = 10 ms were used, resulting in a true TE for each of the eight images: TE = [10, 20, 30, 40, 50, 60, 70, 80 ms]. For breath-hold acquisitions, a parallel

Magn Reson Mater Phy Fig. 1 Alternating optimization of images and shared motion in MC-GRICS

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Magn Reson Mater Phy Table 1 Acquisition parameters SMART1Map

ME-FSE

FB

BH

FB

BH

Resolution in the frequency direction

224

Resolution in the phase direction

224

160

224

160

Field of view reduction in the phase direction (%)

100

75

100

75

Partial Fourier in phase direction (%)

100

63

100

63

ASSET factor (parallel imaging acceleration factor)

1

1

2

1

4.2

Final acceleration factor

1

Acquired data ratio (FB vs. BH)

3.0

2.1

Acquisition time

18 s

1 min07 s

18 s

Trigger windows (ms) Bandwidth (kHz)

100 250

150

80 125

RR interval

n/a

Slice thickness (mm)

8

5.9 3 min 45 s

1

imaging (ASSET) factor of 2 was used with ETL = 16 and ESP = 5 ms, resulting in effective TEeff = [5, 15, 25, 35, 45, 55, 65, 75 ms]. The TIs used for SMART1Map and the TEs used for FSE were chosen to target the T1 and T2 values of native myocardium (1,200 ms for T1 at 3T [25] and 55 ms for T2 [2]). Tubes with T1 or T2 values substantially different from these nominal values were not considered for analysis. In the phantom, four additional data sets were acquired. One acquisition was performed with the same parameters as in free-breathing experiments (i.e., fully-sampled) but without motion in order to independently analyze the impact of the acceleration. The acquisition with motion was repeated three other times in order to analyze the impact of the number of repetitions in the reconstructed images. Image reconstruction For each examination, the 13 images of the 13 different contrasts were reconstructed with the MC-GRICS algorithm from the free-breathing data. In the phantom, additional reconstructions were processed. In order to compare the MC-GRICS method with the standard GRICS method, different reconstruction methods were applied: (a) 13 independent standard GRICS reconstructions (one for each contrast), (b) one MC-GRICS reconstruction without the sparsity constraint of the

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gradient in the image reconstruction step (i.e., an intermediate method equivalent to standard GRICS reconstructions with a common optimization of the motion), and c) one complete MC-GRICS. In order to assess the impact of the number of repetitions Nrep of each contrast (i.e., to analyze the conditioning of the inverse problem posed by these different methods) reconstructions were also computed with Nrep = [1–4] in the phantom. Volunteer images were reconstructed only using Nrep = 1 with the standard GRICS and MC-GRICS algorithms. Note that the encoding operator E used in the reconstruction algorithm requires the calibration of the sensitivity maps r. Auto-calibration was performed exclusively using the SMART1Map data. Using ME-FSE for autocalibration would lead to corrupted values in the ventricular cavity due to the lack of signal with this back-blood sequence, which could impair the reconstruction of the SMART1Map images. Regularization parameters were tuned empirically, and the following values were used: (k, e) = (10-2, 10-3) for the phantom study and (k, e) = (10-1, 10-4) for the in vivo study. A mixed Matlab/C?? parallelized implementation of the algorithm was used on an 8-processor workstation. Data analysis The reconstructed images from the phantom acquisition were analyzed both qualitatively (SNR, motion artifact occurrence, misregistration) and quantitatively (T1 and T2 measurements). T1 and T2 were fitted with the non-linear Levenberg– Marquardt fitting routine of Matlab using the following models:  TI   i qTi 1 ¼ qT0 1 1  e T1 ; i ¼ 1    5 ð8Þ TE  i qTi 2 ¼ qT0 2 e T2 ; i ¼ 1    8 T1 and T2 maps were computed using a pixel-wise fitting. In the phantom, ROI-wise analyses of the quantitative parameters were also computed. In this case, the signals from all of the pixels in the ROI were used as input data for the fitting (without prior averaging). The accuracy of T1 and T2 measurements as well as the 95 % CI (precision) returned by the fitting was analyzed against the number of repetition and the image type: without motion (reference), with motion, with motion correction (with the three different methods). In the volunteers, the accelerated breath-held images cannot be considered the gold standard because: (1) the breath-hold may not be perfect; (2) the accelerated images

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Fig. 2 T1 (top) and T2 (bottom) maps obtained (from left to right) without motion correction, with motion correction using the standard GRICS method, MC-GRICS without the sparsity constraint, the

complete MC-GRICS, and without motion (reference). Only one repetition of each contrast was used here

Fig. 3 T1 (top) and T2 (bottom) measurements from the moving phantom. Measurements are compared before motioncorrection, after motion correction with standard GRICS, MC-GRICS without sparsity constraint, and complete MC-GRICS, and without motion. Error bars represent 95 % CI

may be corrupted by residual aliasing artifacts, and (3) the accelerated images have lower and non-uniform SNR which impacts the statistical analysis.

Results Phantom experiments T1 and T2 maps are shown in Fig. 2. In the uncorrected motion-corrupted maps (first column), T1 (resp. T2) values

are affected by surrounding T1 (resp. T2) due to motion artifacts. With Nrep = 1, no improvement is observed with the standard GRICS method. When the motion optimization is shared between contrasts, the motion artifacts are effectively minimized, but the maps remain noisy. With the complete MC-GRICS method, motion artifacts are removed and image quality is recovered. Quantification of the T1 and T2 parameters in the phantom are shown in Fig. 3. Without motion correction, T1 and T2 quantification is corrupted by motion artifacts. Accuracy and precision are

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Magn Reson Mater Phy Table 2 Impact of the motion correction on accuracy and precision of the quantification in the phantom

Error (%) Confidence interval (%)

Motion-corrupted

Standard GRICS

MC-GRICS without sparsity constraint

MC-GRICS

No Motion

12.0

12.3

5.3

2.5

–

9.7

9.6

6.2

3.4

3.23

Accuracy is given in terms of relative error, and precision in terms of relative confidence interval, relative to the nominal T1 and T2 measured without motion

In vivo experiments

Fig. 4 T1 quantification versus data redundancy (Nrep) for the different methods: without motion correction, with standard GRICS, with MC-GRICS, without motion on tube#2

improved when motion optimization is shared between contrasts (standard GRICS vs MC-GRICS without sparsity constraint, p = 0.046). Further improvement is seen when the sparsity constraint is used (MC-GRICS without sparsity constraint vs. MC-GRICS, p = 0.02). Table 2 summarizes the average normalized accuracy and precision obtained with the different methods: We also evaluated the impact of the acceleration method in the phantom without motion. The confidence interval of T1 quantification was 2.5 % with the fully sampled acquisition and 3.9 % with the accelerated acquisition. The confidence interval of T2 quantification was 4.4 % with the fully sampled acquisition and 5.6 % with the accelerated acquisition. The impact of the amount of data redundancy was evaluated by analyzing the T1 quantification versus Nrep on a representative tube (#2). The results are shown in the Fig. 4. As Nrep increases, the accuracy of T1 mapping increases due to averaging out of the motion artifacts. As expected, the standard GRICS method requires at least two repetitions to be able to correct motion artifacts, and accuracy and precision increase with the data redundancy. Quantification obtained with MC-GRICS also benefits from increasing Nrep, but accuracy and precision are already very close to the reference for Nrep = 1.

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The acquisition time for SMART1Map averaged 18 s for breath-holds and 1min07 s in free-breathing, while for MEFSE it averaged 18 s for breath-holds and 3min45 s in freebreathing (the acquisition time depends on the cardiac frequency). Thus, the total acquisition time including the efficient acquisition periods and the potential preparation periods required for breath-holds was around 1 min for the breath-hold data set and below 5 min in free-breathing. Note that the ratio of acquired data in FB (fully sampled) versus BH (accelerated) was around three (resp. 6) for the T1(resp. T2)-weighted images. The reconstruction time was approximately 4 min. Representative T1- and T2-weighted images obtained from volunteer #4 are shown in Fig. 5. The comparison of images before and after motion correction with only one repetition shows that no clear improvement is obtained with the standard GRICS reconstruction. However, MCGRICS does reduce motion artifacts compared to uncorrected images, increases the sharpness on the myocardium and increases SNR. With full sampling of k-space now achievable, MC-GRICS image quality is also improved compared to breath-hold in the T2-weighted images. T1weighted images showed higher SNR with MC-GRICS than breath-held images but residual artifacts can be seen. In return, the acquisition has to be extended proportionally to the acceleration factor reduction. Breath-held images show speckle artifacts and T2-weighted images show SENSE reconstruction artifacts. Even with successful breath-holds, slight diaphragmatic drift was observed between the first and the last SMART1Map images. In the ME-FSE images, a slight drift of the heart phase can be observed between the first and the last TE. Finally, banding artifacts were noted in all T1-weighted images. The previous observations on image quality are also reflected in the T1 and T2 maps. Figure 6 shows the maps obtained in volunteer #1. The T1 values obtained in freebreathing are significantly different from those obtained after motion correction with MC-GRICS or in breathhold. In breath-hold, the SENSE reconstruction artifacts and the slight misregistration between weighted images result in locally corrupted maps. In addition, a gradient of T1 and T2 values within the myocardium can be observed in all maps.

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Fig. 5 T1- (top) and T2-weighted images (bottom) obtained in volunteer #4 in free-breathing, with standard GRICS and MC-GRICS motion correction, and in breath-hold. Only one repetition of each contrast was used

Fig. 6 T1 (top) and T2 (bottom) quantification maps obtained in volunteer #1 in free-breathing, with standard GRICS, with MCGRICS motion correction, and in breath-hold. Only one repetition of

each contrast was used. Pseudo proton density obtained in the T2 quantification was used to mask both T2 and T1 maps, thus reducing the confusion between blood pool and myocardium in the latest map

Since no gold standard is available in vivo, it is difficult to assess the impact of the motion correction on the quantification. Nevertheless, maps obtained with MCGRICS present better sharpness and local homogeneity compared to the other maps.

Discussion In the phantom, the proposed motion correction method has been shown to efficiently recover T1 and T2 parameters from motion-corrupted measurements. In volunteers, the

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method can be considered to improve quantification methodology compared to both uncorrected free-breathing and breath-hold acquisitions. Thus it appears feasible to correct intra and inter-acquisition motion in a multi-contrast data set for the purpose of improving T1 and T2 quantification. In addition, the proposed method does not required additional acquisition. It allows the acquisition of the full k-spaces for a better SNR. In return, the acquisition time has to be extended proportionally to the acceleration factor reduction. Finally, it can be achieved within 5 min of acquisition and 4 min of reconstruction. The standard GRICS method was unable to correct motion in this multi-contrast context with only one repetition per contrast. The two features we added to build the new MC-GRICS method both participate in the improvement of the results obtained. They improve the conditioning of the problem by taking advantage of the common information shared between the different contrasts, specifically motion and image gradient distribution. Thus, the number of repetitions required for MC-GRICS is lower than for the standard GRICS (Nrep = 1 instead of 2 or 3). Quantification methodology This study was limited to the evaluation of the impact of motion consistency in the T1 and T2 quantification process. This only impacts the statistical analysis of the data independently of the particular MRI hardware and sequence used for measuring T1 and T2. Problems related to T1 and T2 quantification methodology, such as B1 inhomogeneities or pseudo weighting, are out the scope of this paper and do not change our conclusions. This would be a concern for absolute T1 and T2 quantification though. Here both interand intra-examination variability in T1 and T2 were observed. The T1 variations and the large differences between values in the septum and lateral wall may be explained by B1? inhomogeneity. A variation between prescribed B1? and actual B1? can lead to an incomplete saturation pulse with a flip angle a \ 90°. Thus, the real signal equation h TI i  i should be: qi ¼ q0 1  ð1  cos aÞe T1 . This signal equation explains the gradient of signal observed in the raw images. If the signal is fitted with a signal equation where a = 90° instead of the real a (for instance a = 70°), it results in a corrupted value of T1, where the error depends on the ratio aprescribed/areal and on the sampling times of the recovery curve. This phenomenon is independent from motion correction and is thus considered out of the scope of this study. Nevertheless, methods have been proposed to overcome this limitation [26, 27]. T2 variations were observed and can be explained by the use of 1RR gated acquisitions. Because the magnetization

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has not fully recovered between excitations, the images obtained with ME-FSE were not purely T2-weighted and included sone contribution fron T1. Since data consistency was ensured within the whole examination, T2 images could be corrected using knowledge of T1. Also note that 2RR acquisitions could have been used since the acquisition duration is not limited to a breath-hold any more. Assumptions in MC-GRICS The proposed method relies on several assumptions. As with conventional GRICS [21], a first assumption is that there is a linear relationship between the displacement amplitude and the signal coming from an external sensor. A potential concern is whether this relationship holds during the longer period of time necessary to acquire the full multi-contrast data set. In this regard, the pneumatic respiratory sensor belt used in this study may not be optimal as it may be subject to drifting over time. The use of MR navigators might overcome this limitation. For similar reasons, MC-GRICS would not recover motionconsistent images in case of large non-physiological or voluntary movements of the patient during the protocol. The second important assumption involves the gradient sparsity hypothesis. In the data set used for the validation of the method, two different types of contrasts were used, each type being composed of at least five different contrasts. This means that the gradients were effectively sparse. Alternative constraints might be investigated for multi-contrast imaging, other than those based on gradient sparsity, as proposed by Bilgic et al. [19]. One possible limitation of the gradient sparsity constraint is that residual artifacts in the images can also take the form of image gradients. Therefore, the method would benefit from being used with a randomized sampling of k-space. This would minimize the occurrence of gradients at similar locations in the images and would make sure no residual artifact can be propagated from one image to another. Similarly, non-Cartesian sampling may also perform better. Data inconsistencies As discussed previously, the proposed method improves transversal analysis of the data while reducing inconsistencies usually encountered in multi-contrast exams. Not all of these inconsistencies were corrected since not all limitations of conventional GRICS are addressed in this work. In terms of motion inconsistencies, large throughplane motion should still be avoided in 2D acquisitions by keeping the slice thickness sufficiently large. Nevertheless, the reconstruction could be handled on 3D acquisitions [20] to address this problem.

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In terms of contrast inconsistencies, only contrast changes from one image to another are handled by the proposed framework. Contrast inconsistencies within k-space data from a given image should also be avoided, such as those introduced by RR variability.

4.

5.

Regularization tuning The Theory section highlighted the need for tuning two regularization parameters. The first one controls the relative weight of the constraint. This Tikhonov regularization is well known from the literature and automatic optimization methods have been proposed [28]. The second parameter is equivalent to the thresholds found in sparsity techniques: it forces the small gradients bellow this value to disappear. For this second parameter, like for most of the regularization methods, the optimization process can be tedious. For this study, these parameters were determined empirically.

6. 7.

8.

9.

10.

11.

Conclusion 12.

To our knowledge, the proposed MC-GRICS method is the first that can correct intra- and inter-acquisition motion in multi-contrast imaging. An acquisition and reconstruction workflow adapted to T1 and T2 quantification was demonstrated. This method could be used to reconstruct other types of contrasts such as perfusion, late gadolinium enhancement, diffusion, or phase contrast because no prior assumption about the contrast was made. Nevertheless, the workflow proposed here is general and could easily be adapted and tuned to target specific examinations. Only the multi-contrast regularization constraint might have to be adapted.

13.

14.

15.

16. Acknowledgments The authors would like to thank Marine Beaumont for her helpful discussions about T1 mapping and Jonathan Sperl for his comments on sparse constraint for multi-contrast imaging. The Lorraine region and the European Regional Development Fund are acknowledged for co-funding the system.

17. 18.

References 1. Cai JM, Hatsukami TS, Ferguson MS, Small R, Polissar NL, Yuan C (2002) Classification of human carotid atherosclerotic lesions with in vivo multicontrast magnetic resonance imaging. Circulation 106:1368–1373 2. Kellman P, Chung YC, Simonetti OP, McVeigh ER, Arai AE (2005) Multicontrast delayed enhancement provides improved contrast between myocardial infarction and blood pool. Magn Reson Med 22(5):605–613 3. Marie PY, Angioı¨ M, Carteaux JP, Escanye JM, Mattei S, Tzvetanov K, Claudon O, Hassan N, Danchin N, Karcher G, Bertrand A, Walker PM, Villemot JP (2001) Detection and prediction of

19.

20.

21.

22.

acute heart transplant rejection with the myocardial T2 determination provided by a black-blood magnetic resonance imaging sequence. J Am Coll Cardiol 37(3):825–831 Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P (1999) SENSE: sensitivity encoding for fast MRI. Magn Reson Med 42:952–962 Lai P, Fung MM, Vasanawala SS, Brau AC (2012) Single breathhold three-dimensional cardiac cine MRI with whole ventricular coverage and retrospective cardiac gating using kat ARC. J Cardiovasc Magn Reson 14(1):69 Lustig M, Donoho DL, Santos JM, Pauly JM (2008) Compressed sensing MRI. IEEE Trans Med Imag 25(2):72–82 Doneva M, Bo¨rnert P, Eggers H, Stehning C, Se´ne´gas J, Mertins A (2010) Compressed sensing reconstruction for magnetic resonance parameter mapping. Magn Reson Med 64:1114–1120 Wu B, Millane RP, Watts R, Bones PJ (2011) Prior estimatebased compressed sensing in parallel MRI. Magn Reson Med 65:83–95 Batchelor PG, Atkinson D, Irarrazaval P, Hill DLG, Hajnal J, Larkman D (2005) Matrix description of general motion correction applied to multishot images. Magn Reson Med 54(5):1273–1280 Kellman P, Viallon M, Chefd’hotel C, Stemmer A, Croisille P (2009) Improved image reconstruction incorporating non-rigid motion correction for cardiac MRI using BLADE acquisition. J Card Magn Reson 11:227 Odille F, Vuissoz PA, Marie PY, Felblinger J (2008) Generalized reconstruction by inversion of coupled systems (GRICS) applied to free-breathing MRI. Magn Reson Med 60(1):146–157 Usman M, Atkinson D, Odille F, Kolbitsch C, Vaillant G, Schaeffter T, Batchelor PG, Prieto C (2013) Motion corrected compressed sensing for free-breathing dynamic cardiac MRI. Magn Reson Med 70(2):504–516 Lohezic M, Menini A, Escanye´ JM, Marie PY, Marie PY, Mandry D, Vuissoz PA, Felblinger J (2011) Free-breathing myocardial T2 measurements at 1.5 T. J Card Magn Reson 13(1):11 Filipovic M, Vuissoz P, Codreanu A, Claudon M, Felblinger J (2011) Motion compensated generalized reconstruction for freebreathing dynamic contrast-enhanced MRI. Magn Reson Med 65(3):812–822 Menini A, Clique H, Beaumont M, Felblinger J, Odille F (2012) Motion Correction for 3D T1 Mapping using GRICS: Phantom Validation. In: Proceedings of the 20th scientific meeting, International Society for Magnetic Resonance in Medicine, Melbourne, p 2391 Haldar JP, Wedeen VJ, Nezamzadeh M, Dai G, Weiner MW, Schuff N, Liang ZP (2012) Improved diffusion imaging through SNR-enhancing joint reconstruction. Magn Reson Med 69(1):277–289 Junzhou H, Chen C, Leon A (2012) Fast Multi-contrast MRI Reconstruction. MICCAI 7510:281–288 Ma D, Gulani V, Seiberlich N, Liu K, Sunshine JL, Duerk JL, Griswold MA (2013) Magnetic resonance fingerprinting. Nature 495(7440):187–192 Bilgic B, Goyal VK, Adalsteinsson E (2011) Multi-contrast reconstruction with Bayesian compressed sensing. Magn Reson Med 66:1601–1615 Menini A, Vuissoz PA, Felblinger J, Odille F (2012) Joint reconstruction of image and motion in MRI: implicit regularization using an adaptive 3D mesh. MICCAI 7510:264–271 Odille F, Cıˆndea N, Mandry D, Pasquier C, Vuissoz PA, Felblinger J (2008) Generalized MRI reconstruction including elastic physiological motion and coil sensitivity encoding. Magn Reson Med 9:1401–1411 Engl HW, Kunisch K, Neubauer A (1989) Convergence rates for Tikhonov regularisation of nonlinear ill-posed problems. Inverse Probl 5:523

123

Magn Reson Mater Phy 23. Slavin GS, Stainsby JA (2013) True T1 Mapping with SMART1Map (saturation method using adaptive recovery times for cardiac T1 mapping): a comparison with MOLLI. J Card Magn Reson 15(1):3 24. Messroghli DR, Radjenovic A, Kozerke S, Higgins DM, Sivananthan MU, Ridgway JP (2004) Modified look-locker inversion recovery (MOLLI) for high-resolution T1 mapping of the heart. Magn Reson Med 52(1):141–146 25. Stainsby JA, Slavin GS (2013) Myocardial T1 mapping using SMART1Map: initial in vivo experience. J Card Magn Reson 15(1):13

123

26. Sacolick LI, Sun L, Vogel MW, Dixon WT, Hancu I (2011) Fast radiofrequency flip angle calibration by Bloch-Siegert shift. Magn Reson Med 66(5):1333–1338 27. Nehrke K, Bo¨rnert P (2012) DREAM—a novel approach for robust, ultrafast, multislice B1 mapping. Magn Reson Med 68(5):1517–1526 28. Ying L, Liu B, Steckner MC, Wu G, Wu M, Li SJ (2008) A statistical approach to SENSE regularization with arbitrary k-space trajectories. Magn Reson Med 60(2):414–421