Faster 3D saturation-recovery based myocardial T1 mapping using a reduced number of saturation points and denoising

Purpose To accelerate the acquisition of free-breathing 3D saturation-recovery-based (SASHA) myocardial T1 mapping by acquiring fewer saturation points in combination with a post-processing 3D denoising technique to maintain high accuracy and precision. Methods 3D SASHA T1 mapping acquires nine T1-weighted images along the saturation recovery curve, resulting in long acquisition times. In this work, we propose to accelerate conventional cardiac T1 mapping by reducing the number of saturation points. High T1 accuracy and low standard deviation (as a surrogate for precision) is maintained by applying a 3D denoising technique to the T1-weighted images prior to pixel-wise T1 fitting. The proposed approach was evaluated on a T1 phantom and 20 healthy subjects, by varying the number of T1-weighted images acquired between three and nine, both prospectively and retrospectively. Following the results from the healthy subjects, three patients with suspected cardiovascular disease were acquired using five T1-weighted images. T1 accuracy and precision was determined for all the acquisitions before and after denoising. Results In the T1 phantom, no statistical difference was found in terms of accuracy and precision for the different number of T1-weighted images before or after denoising (P = 0.99 and P = 0.99 for accuracy, P = 0.64 and P = 0.42 for precision, respectively). In vivo, both prospectively and retrospectively, the precision improved considerably with the number of T1-weighted images employed before denoising (P<0.05) but was independent on the number of T1-weighted images after denoising. Conclusion We demonstrate the feasibility of accelerating 3D SASHA T1 mapping by reducing the number of acquired T1-weighted images in combination with an efficient 3D denoising, without affecting accuracy and precision of T1 values.


Introduction
Late gadolinium enhancement (LGE) is the reference technique for the visualization of myocardial scar and focal fibrosis, however it cannot visualize diffuse fibrosis (1). In contrast, myocardial T1 mapping allows detection of both focal and diffuse fibrosis and has been extensively investigated as a potential diagnostic tool for the assessment of different cardiomyopathies, such as acute myocarditis, hypertrophic cardiomyopathy, amyloidosis, and dilated cardiomyopathy (2). Several myocardial T1 mapping techniques have been proposed and are based on the acquisition of multiple T1-weighted images along the recovery curve of the magnetization after an initial inversion recovery (3), saturation recovery (4) or a combination of both inversion and saturation recovery (5). The modified Lock-Locker inversion recovery (MOLLI) (3) technique is the most widely used T1 mapping approach, and involves acquiring a single 2D T1 map during a breath-hold (3) or multiple 2D slices during free-breathing (3).
MOLLI is highly reproducible and provides precise myocardial T1 maps, however it underestimates T1 due to the acquisition of multiple single-shot T1-weighted images (typically in mid-diastole) spaced over multiple heartbeats after a single inversion pulse (6,7). An alternative technique, the 2D saturation recovery single-shot (2D SASHA) technique, employs a saturation-recovery pulse followed by the acquisition of one T1-weighted image in the same heartbeat, which is then repeated with varying saturation delays (in the order of 9) to sample the entire saturation recovery curve and subsequently generate the myocardial T1 map (4). SASHA permits to obtain more accurate and heart-rate independent T1 maps than MOLLI but its precision is lower, due to the smaller dynamic range compared to inversion recovery based techniques (7,8). Recently, we demonstrated the feasibility of a free-breathing 3D SASHA (9) imaging technique, which allows to provide whole-heart coverage with higher signal-to-noise ratio (SNR) and image resolution than with conventional 2D approaches. The acquisition time of the 3D SASHA sequence is considerably longer than a breath-hold (in the order of 12 min), thus 1D diaphragmatic navigator gating (and tracking) was employed to enable 3D freebreathing T1 mapping (9).
2D and especially 3D T1 mapping techniques suffer from long acquisition times due to the need of acquiring several images along the inversion or saturation recovery curve. Different sampling schemes along the recovery curve have been proposed for 2D MOLLI in order to reduce the number of heartbeats and thus shorten the length of the breath-hold, reducing the total number of heartbeats per breath-hold from 17 to 9 (10). Simultaneous multi-slice imaging techniques have been also investigated, both in free-breathing and under breath-hold, in order to accelerate the acquisition and to increase volume coverage (11,12). However, this approach suffers from limited spatial resolution and does not provide whole-heart coverage. Undersampling reconstruction techniques have also been investigated to accelerate the acquisition and improve the image resolution of T1 maps (13)(14)(15).
In this study, we propose to accelerate the 3D SASHA acquisition by reducing the number of the T1weighted images acquired along the saturation recovery curve. To overcome the expected loss in accuracy and precision due to the reduced number of T1-weighted images acquired, we sought to use a 3D denoising technique based on Beltrami regularization applied directly to the T1-weighted images prior to T1 fitting, enabling accurate and precise 3D SASHA T1 mapping from fewer saturation points and thus shorter scan times. The proposed approach was tested on a standardized T1 phantom, 10 healthy subjects with retrospectively reduced number of T1-weighted images, 10 healthy subjects with prospectively varied number of T1-weighted images and three patients with suspected cardiovascular disease.

Imaging sequence
The 2D SASHA T1 mapping sequence involves acquiring eleven T1-weighted images at different saturation points (4). The original 3D SASHA T1 mapping sequence previously proposed in (9) acquires and fits nine T1-weighted images along the T1 recovery curve. In this study, the number of images acquired along the saturation recovery curve with the 3D SASHA sequence was varied between three and nine in order to investigate the effect of this parameter on the accuracy and precision of the T1 maps. Fig 1 shows the distribution of three and five time points along the T1 recovery curve used in this study. An image without any saturation preparation was acquired at the beginning of the scan, which corresponds to a measurement of the fully recovered magnetization (last point on the graphs).
The saturation time points were then acquired with equal distribution between the minimum and the maximum saturation time (54 ms and 740 ms, respectively, for a heart rate of 60 bpm), following the original implementation of the 2D SASHA (4) imaging sequence.

3D Denoising
A reduced number of T1-weighted images is expected to decrease the precision of the corresponding T1 maps, which could result in noisy T1 maps. In order to achieve high precision in spite of the reduced number of saturation recovery time points, we propose to apply a novel 3D Beltrami denoising technique to the T1-weighted images prior to the T1 fitting. The Beltrami framework for image denoising and enhancement was introduced for 2D natural images by Sochen, Kimmel and Malladi (16), proposed for 2D myocardial T1 mapping denoising by Bustin et al (16), and have been recently extended to 3D T1 mapping denoising (17). The Beltrami regularization allows to preserve the edges, while reducing the noise of the images without introducing staircasing artefacts (18) .
In this work, the 3D Beltrami denoising framework is applied to 3D T1 mapping with reduced number of time points, by exploiting the redundant information in both the 3D spatial and T1 recovery dimensions, to accelerate the acquisition.
The 3D Beltrami regularization can be expressed as following: is the set of 3D denoised T1-weighted images for contrast , are the corresponding 3D T1-weighted images before denoising, is the regularization parameter that controls the trade off between the fidelity to the original acquired data and the Beltrami regularization term, is the Beltrami constant that allows selection of any arbitrary interpolation between quadratic or total variation gradient penalties and is the 3D weighted-gradient transformation applied to being the smoothing parameter. ℎ The optimization problem described above was solved using a primal-dual hybrid gradient algorithm (19,20). For all experiments the regularization parameter was set to 0.25, while the smoothing parameter was set to 5. These parameters were empirically optimized on several dataset (not reported ℎ here) to provide the best image quality in terms of SNR and image sharpness. A weight of 1.0 was employed for the Beltrami constant as indicated in (21).

Imaging
The proposed approach was evaluated in a standardized phantom, 20 healthy subjects and three patients with suspected cardiovascular disease. All imaging studies were performed on a 1.5T MR scanner (Ingenia, Philips, Best, The Netherlands). The study was performed in accordance with the Declaration of Helsinki (2000). All subjects recruited to this study provided written informed consent with study approval from the Institutional Review Board (1/11/12).

Phantom study
A standardized T1 phantom with nine agar/NiCl2 vials was used for imaging, with T1 values in the range of 250 to 1500 ms (22). The phantom was imaged using the original 3D SASHA sequence, with nine images acquired at different saturation points (54-650 ms). The nominal scan time for the 3D SASHA sequence was of 4:14 minutes:seconds. The number of T1-weighted images for the T1 fitting was reduced retrospectively from three to nine (step size of one). For each case, T1 maps were obtained using a three parameter-fitting model before and after 3D denoising. An inversion recovery spin-echo

Healthy subject study
The effect of reducing the number of T1-weighted images acquired along the recovery curve was studied in healthy subjects retrospectively and prospectively. For the retrospective study, data was collected in 10 healthy subjects using the original 3D SASHA sequence with nine images acquired at different saturation points. The number of T1-weighted images for the T1 fitting was modified retrospectively from three to nine (step size of one) and mapping was performed before and after denoising. For the prospective study, data was acquired in 10 additional healthy subjects using the 3D SASHA sequence with three, five and nine T1-weighted images along the recovery curve. The acquisition parameters used for the 3D SASHA sequence (both retrospective and prospective studies) were: FOV = 300 x 300 mm 2 , image resolution = 1.4 x 1.4 mm 2 , slice thickness = 8 mm, flip angle = 35˚, TR/TE = 3.3/1.6 ms, subject specific mid-diastolic trigger delay and saturation times, short-axis orientation, and 32-channel coil. 1D diaphragmatic navigator gating and tracking was used for respiratory motion compensation with a 5mm end-expiratory gating window. For both prospective and retrospective studies, the 3D SASHA T1 map with nine images along the recovery curve was considered as the reference standard. 3D SASHA with nine images along the recovery curve has been previously compared against 2D MOLLI showing excellent agreement in terms of accuracy (17).

Patient study
The feasibility of using a reduced number of T1-weighted images was investigated in patients using five saturation points along the recovery curve. The number of saturation points for the prospective patient scan was set conservatively based on the results obtained in healthy subjects. 3D SASHA was acquired before contrast injection in three patients with suspected cardiovascular disease with the same parameters used in the healthy subject study but with a lower in plane resolution of 1.6 x 1.6 mm 2 to further reduce scan time. Late gadolinium enhancement images were acquired 10-20 minutes after injection of 0.1-0.2 mmol/kg of Gadovist and used as ground truth to determine if fibrosis was present.

Image analysis
3D denoising and three-parameter fitting were performed offline using MATLAB (MathWorks, Natick, MA). A myocardial T1 map was obtained for each acquisition, using different number of T1-weighted images, both before and after applying the 3D denoising method.

Phantom study
There was good agreement in terms of accuracy between the original 3D SASHA imaging sequence with nine T1-weighted images and the gold standard IRSE sequence, both before and after denoising, as shown in the Bland Altman plot in Fig S1. Accuracy and precision measured in three phantom vials are shown in Fig 2, with T1 values similar to healthy native myocardium (vial #2), post-contrast myocardium (vial #4) and native blood (vial #6), and for different numbers of T1-weighted images in comparison to the gold standard spin echo values, indicated for each vial in Fig 2. For all the vials, there was no significant difference in terms of accuracy for the different number of T1-weighted images before or after denoising (respectively P = 099 and P = 0.99), as well as in terms of precision before or after denoising (respectively P = 0.64 and P = 0.42).
The nominal scan time for the 3D SASHA sequence with three images acquired along the recovery curve was 1min 25s.

Healthy subjects study
Retrospective study: The accuracy and precision averaged over all ten healthy subjects for the retrospective study (three to nine images considered for mapping) both before and after denoising is shown in Fig 3. There was no statistical significant difference between the accuracy measured on the T1 maps reconstructed with three compared to nine T1-weighted images, both before and after denoising (respectively P = 0.48 and P = 0.14). There was a statistical difference (P < 0.05) between the precision measured on the T1 maps reconstructed with three and nine T1-weighted images before denoising, while there was no statistical difference after denoising (P = 0.99). There was no statistical difference between the precision measured on the T1 maps reconstructed with four to nine T1-weighted images, both before and after denoising (P = 0.99). Prospective study: The accuracy and precision averaged over all ten healthy subjects for the prospective study (three, five and nine T1-weighted images) both before and after denoising is shown in Fig 6a. There was no statistical difference between the accuracy measured on the T1 maps reconstructed using different number of T1-weighted images, both before (P = 0.73) and after (P = 0.64) denoising.
However, a statistical difference (P < 0.05) was found between the precision measured on the T1 map acquired with three and nine T1-weighted images before denoising. After applying the 3D denoising technique, the precision was recovered with no statistical difference (P = 0.27) when three or nine images where used for T1 mapping. However, if five images were acquired instead of three, the precision improved by about 12%. The average scan time for the original 3D SASHA sequence (nine images along the recovery curve) was 12 ± 1.9 minutes. Scan time was reduced to 7.55 ± 0.7 and 5.6 ± 1.2 minutes when acquiring 5 and 3 images respectively. Fig 6b shows the Bland-Altman plots of the accuracy and precision of the 3D SASHA non-denoised vs. denoised for the three different acquisitions using three, five and nine T1-weighted images. The difference in terms of accuracy between nondenoised and denoised 3D SASHA is smaller when five and nine images are used. In terms of precision, the 3D denoising method has a major impact on the T1 maps acquired with three and five images, with a bias equal to 15.5 compared to 9.6 with nine images.
The 3D denoising technique permitted to preserve image quality of the 3D SASHA T1 maps when five T1-weighted images were acquired, as shown in Fig 7 in two representative healthy subjects for the prospective acquisition. However, if only three T1-weighted images were acquired, the delineation of the myocardial borders and the papillary muscles was slightly degraded, as indicated by the white arrows. As the acquisition becomes longer with a higher number of saturation time points, it is also more prone to motion artefacts, as indicated by the blue arrows in the T1 maps for subject 1. values for scar tissue (24). The third patient, who did not show any cardiac disease, has T1 values in agreement with reference values for native pre-contrast healthy myocardial T1 (25). There was no statistical difference regarding the accuracy and precision measured on non-denoised or denoised 3D SASHA T1 maps (respectively P = 0.91 and P = 0.19). The average scan time for the 3D SASHA sequence with five images along the recovery curve was about 8 minutes.

Discussion
In this study, we proposed to accelerate the 3D SASHA myocardial T1 mapping technique by reducing the number of saturation time point images acquired along the recovery curve. Our retrospective experiments in a standardized phantom and healthy subjects demonstrate that reducing the number of T1-weighted images used for the T1 fitting has little impact on the accuracy of the T1 maps. However, reducing the number of images has a direct impact on image quality and precision of the T1 maps. To recover the loss in precision and image quality of the myocardial T1 maps when a reduced number of T1-weighted images is acquired, we propose to employ a recently introduced 3D denoising technique based on the Beltrami regularization. The proposed approach was validated prospectively in healthy subjects and feasibility was shown in 3 patients with suspected cardiovascular disease.
The phantom and healthy subjects' retrospective experiments demonstrated that the accuracy of 3D SASHA T1-mapping was not affected if the number of T1-weighted images considered for T1 mapping was reduced to three images. Moreover, the accuracy was not affected by the application of the 3D denoising technique. Conversely, the precision was reduced when a smaller number of T1-weighted images was employed, with a statistical difference between using three and nine images. No statistical difference was observed in precision after denoising when the number of T1-weighted images was reduced from nine to three. Image quality was affected by the number of time point images used for mapping, which was improved after applying the proposed 3D denoising technique.
For the prospective experiments in healthy subjects, the 3D SASHA was acquired using three, five and nine T1-weighted images along the recovery curve. These experiments confirmed the results obtained in the initial retrospective study: the accuracy of the T1 maps was not affected by the different number of T1-weighted images acquired nor with the application of the 3D denoising technique. There was a statistical difference in precision between the T1 maps acquired with three and nine images before denoising, however no statistical difference was observed after denoising. The AHA segmentation provided a 3D visualization of the accuracy and precision across the whole left ventricle, both before and after 3D denoising. The AHA segmentation confirmed that the accuracy is maintained despite the smaller number of T1-weighted images acquired when combined with the 3D denoising technique. The T1 variability was comparable to 2D MOLLI data previously published in the literature (10) when the 3D SASHA data was acquired with three and five T1-weighted images. The denoised 3D SASHA data acquired with nine T1-weighted images showed higher T1 variability within the left ventricle, probably due to residual respiratory motion. In contrast the precision decreased when a reduced number of acquired T1-weighted images was used for T1 mapping. However, precision improved considerably after denoising. Although not statistically significant, the precision of the T1 map obtained from five T1-weighted images before denoising was about 12% higher than that of the T1 map obtained from three images. In terms of image quality, the delineation of the myocardial borders was in general worst in the T1 maps reconstructed from three images in comparison to the corresponding T1 maps reconstructed from five images (Fig 7). Some respiratory motion related artefacts were observed in the acquisitions with five and nine images consistent with the longer required scan times. In general, a better compromise between image quality and motion related artefacts is observed when the T1 map is reconstructed using five images.
Results from the patient study showed that the proposed accelerated 3D SASHA T1 mapping technique achieves good image quality and provides quantitative values consistent with the complementary LGE images and corresponding diagnosis. The proposed approach enabled a reduction in scan time of about 33% from 12 minutes for the original 3D SASHA technique to approximately ~8 minutes for the proposed accelerated approach with five T1-weighted images along the recovery curve.
The scan time was considerably reduced with the proposed approach by acquiring a smaller number of T1-weighted images. Nevertheless, it was still dependent on the efficiency of the diaphragmatic navigator and its unpredictable scan time, which can severely drop in patients with irregular breathing patterns. Alternative motion compensation techniques, such as image-based navigation and selfnavigation (26)(27)(28), will be investigated in future studies to achieve 100% respiratory scan efficiency and consequently to further accelerate the scan, which can provide more comfort to the patient and reduce the risk of introducing additional bulk motion artifacts associated with long scans.
The saturation time points were selected along the T1 recovery curve in order to provide an equal distribution between the shortest and the longest saturation time, following the original implementation of the 2D SASHA (4) imaging sequence. Further investigation is warranted to understand the effect of a different selection of the sampling points in terms of accuracy and precision of the T1 map (29).
The 3D Beltrami denoising technique employed in this study permits to considerably improve image quality and the precision of the 3D SASHA T1 maps, independently of the number of T1-weighted images acquired (ranging from nine to three). The denoising is a post-processing step and is applied to the T1-weighted images. Future studies will investigate the integration of the denoising technique as regularization directly in the reconstruction process to further accelerate the scan.
Due to time constraints, only native 3D SASHA T1-mapping was performed in this study. Further studies will investigate the acquisition of accelerated native and post-contrast 3D SASHA myocardial T1 maps in patients with cardiovascular disease to enable the measurement of extracellular volume fraction, which has been demonstrated to be useful to detect diffuse myocardial fibrosis (30). Larger clinical studies are now warranted to validate the clinical value of the proposed imaging technique.

Conclusions
In conclusion, we have demonstrated the feasibility of accelerating free-breathing 3D SASHA T1 mapping by acquiring fewer (three to five) saturation time point images along the recovery curve. This was achieved by using a 3D denoising method to maintain the high precision of the T1 maps and ensure adequate image quality. The proposed technique permits to acquire a whole-heart high-resolution T1 map in approximately 7 minutes, achieving both high accuracy and precision.  T1 phantom (native myocardium, post-contrast myocardium, native blood), measured before and after 3D denoising. The number of T1-weighted images used to generate the T1 maps was modified retrospectively from three to nine (step size of one), indicated by the different colors. Accuracy and precision averaged between the ten healthy subjects for the retrospective study (3 to 9 images considered for T1 mapping). A ROI was manually drawn in the septum of the myocardium in the mid slice of the 3D SASHA T1 maps before (non-denoised) and after (denoised) denoising. Statistical significance difference is indicated by * (p value < 0.045).    and nine T1-weighted images along the saturation recovery curve. The accuracy and precision measured in the myocardial septum are indicated for each T1 map. T1 maps were reconstructed before and after 3D denoising. There was an improvement in the image quality in terms of myocardial and papillary muscles delineation after 3D denoising (white arrows). Motion artefact (blue arrows) can be observed when more images are acquired due to the longer scan time. maps from the ten healthy subjects of the prospective study. The T1 maps were acquired using three, five and nine T1-weighted images and they were obtained both before and after denoising.