Phase-Sensitive Inversion Recovery for Myocardial T1 Mapping with Motion Correction and Parametric Fitting

Abstract

The assessment of myocardial fibrosis and extra-cellular volume requires accurate estimation of myocardial T1s. While image acquisition using the Modified Look-Locker Inversion Recovery technique is clinically feasible for myocardial T1 mapping, respiratory motion can limit its applicability. Moreover, the conventional T1 fitting approach using the magnitude inversion recovery images can lead to less stable T1 estimates and increased computational cost. In this paper, we propose a novel T1 mapping scheme which is based on phase sensitive image reconstruction and the restoration of polarity of the MR signal after inversion. The motion correction is achieved by registering the reconstructed images after background phase removal. The restored signal polarity of the inversion recovery signal helps the T1 fitting resulting in an improved quality of the T1 map and reducing the computational cost. Quantitative validation on a data cohort of 45 patients proves the robustness of the proposed method against varying image contrast. Compared to the magnitude T1 fitting, the proposed phase sensitive method leads to less fluctuation in T1 estimates.

Introduction

Recent progress in MR cardiac imaging enables myocardial T1 mapping with multiple heart beats. The basic imaging sequences rely on inverting the magnetization and acquiring images along the longitudinal recovery curve. Examples include the modified Look-Locker inversion recovery (MOLLI) (1,2) and variations such as shortened-MOLLI (ShMOLLI) (3,4). Unlike T1 mapping in neuro or musculoskeletal imaging applications (5,6), the inversion recovery curves of the myocardium typically cannot be uniformly sampled with a fixed interval, because the native T1 value of myocardium is around 950ms at 1.5T which is on the order of typical cardiac cycle (7). In order to sample the inversion recovery curve and subsequently estimate T1 values with sufficient precision, as shown in Fig. 1, 5 to 11 images are typically acquired at different inversion times (TI), which are ECG triggered with imaging at a mid-diastolic phase. The maximal number of MOLLI samples is constrained by the breath-hold duration that is viable in a clinical workflow (1,4,8).

FIG 1.

A MOLLI sequence scheme showing two sets of Look-Locker experiments were performed with increasing inversion time (TI) within one breath-hold. A total of 8 images are acquired, as shown by the vertical bar. Images were acquired with the specific trigger delay (TD) selected for imaging at mid-diastole. Each R-R interval is measured and the actual values of inversion time (TI) are used for T1-mapping. In this scheme, 5 images are acquired during the first inversion recovery and 3 are acquired from the second inversion recovery.

Respiratory motion often occurs despite breath-holding due to either diaphragmatic drift or the patient’s inability or non-compliance to hold the breath. In a previous study (9) involving 50 consecutive patients that underwent MOLLI imaging, 230 MOLLI series were acquired for both pre- and post-contrast scenarios. Noticeable motion was found in 40% of all acquired datasets. This undesired respiratory motion can lead to errors in the pixel-wise estimation of T1 maps and motion correction is necessary to maximize the clinical robustness of myocardial T1-mapping.

The main challenge of robust myocardial motion correction using image registration in inversion recovery images is the dramatic variation in image contrast(9), because the MR signal of different tissue (e.g. blood, fat, myocardium, infarcted tissue) will be nulled at different inversion times due to different specific T1s. In particular, the contrast between different tissues can change or even invert with the TIs.

Previously published myocardial T1 mapping techniques utilize magnitude reconstructed images (1,4,9), which means the signal intensity used for inversion recovery fitting is the magnitude of complex signal and does not contain information on polarity of the magnetization. As shown in Fig. 2, given the magnitude detection of MOLLI images, for the pre-contrast cases, the signal of blood is higher than the myocardium shortly after inversion. At longer TIs, the contrast is inverted and the signal of myocardium is higher. In the post-contrast imaging, due to the injection of T1 shortening contrast agent, the blood signal can be lower than the myocardium for short TIs; for longer TIs, the blood become brighter. This contrast inversion causes a dramatic change in image appearance that appears to be the major challenge for registration algorithms; even state of the art registration approaches using information based metrics can result in suboptimal alignment (9). On the other hand, as illustrated in Fig. 2, if the real part of the phase sensitive reconstructed image (not its magnitude) is considered, the contrast inversion can be completely avoided. The image registration can be further compounded by partial volume cancellation at the boundaries between tissues of different T1s. Because of the number of tissue types in the FOV, it is not practical to find a set of inversion time that can avoid these problems.

FIG 2.

Pre- and post-contrast image series acquired using the MOLLI sequences. The magnitude images and corresponding phase sensitive images are plotted together with the inversion recovery signal curves for blood and myocardium. The magnitude images of pre-contrast series show that the blood is first brighter then darker than myocardium, while in the phase sensitive images, the blood is darker than myocardium. Thus, the phase sensitive detection eliminates the blood-myocardium contrast inversion. The similar phenomenon can be observed in post-contrast where the blood is brighter than myocardium due to the injection of contrast agent.

The use of magnitude reconstructed images for T1 fitting poses additional challenges. In order to fit an inversion recovery signal model (e.g. the three-parameter model (10)) to the signal curve, it is necessary to identify the data points that shall be inverted to recovery signal polarity. As proposed in (11), the signal polarity can be estimated by the multi-fitting inversion recovery method (MF-MAGIR). This approach performs an initial fit assuming that all data points are positive; a subsequent fit inverts the first data point, the third fit inverts the first two points, and so on. Finally, the fit with the lowest residual error is selected. Although this strategy is more robust than a direct fit to the magnitude without polarity recovery, the need for multiple trials leads to linearly increasing computational costs. If the pixel-wise T1 map is estimated, the multi-fitting needs to be performed for every pixel in the FOV and significant computational time will be spent to perform trial fits. Second, the signal-noise-ratio (SNR) of inversion recovery images near the signal null is low and therefore the signal can be biased by the noise magnitude, which can lead to errors in T1s. Furthermore, data points around signal nulling may lead to ambiguity in polarity recovery, thus increases the variance of the estimated T1. Finally, the selection of TI times can influence the signal recovery curve. For pixels with extreme T1s, the magnetization may not even across zero for the specific inversion times. This can cause the failure of multi-fitting approach.

Recently, a synthetic image estimation based motion correction (SynMOCO) approach was proposed to effectively register individual MOLLI images (9). This method addresses the problem of large variation of image contrast by estimating motion-free synthetic images by solving an energy minimization problem. These synthetic images present similar contrast to the acquired MOLLI images at every TI. The myocardial motion is finally corrected by registering every MOLLI image to its corresponding synthetic image. This method still utilizes the time-consuming MF-MAGIR method to estimate T1s and its complexity is further increased by the synthetic image estimation step.

To address the challenges caused by the magnitude detection, in this study we propose a novel motion correction and T1 mapping scheme using phase sensitive inversion recovery (PSIR) reconstruction. The proposed approach produces inversion recovery signal with known polarity to remove the background phase while preserving the polarity of inversion recovery magnetization. Because of the background phases are often contaminated by noises and field inhomogeneity, the real part of reconstructed complex images may not reflect the correct magnitude and polarity of inversion magnetization. Similar to the well established phase sensitive delayed enhancement imaging (12), PSIR reconstruction is needed to preserve the polarity of magnetization by removing contaminating background phase errors. Because the PSIR reconstructed images do not exhibit the contrast inversion appearing in magnitude images, the need for multiple fitting is eliminated and the possible confusion of whether to invert data points near signal nulling is avoided. This can lead to an improved T1 map with less fitting errors. The effectiveness of the proposed technique was verified in vivo on a large cohort of patient datasets. We will show that the PSIR motion correction (PSIR-MOCO) is capable of correcting MOLLI images with different motion patterns and contrast concentrations. While the SynMOCO method achieves similar motion correction accuracy, the PSIR-MOCO is conceptually simpler and computationally faster. With the correction of myocardial motion and restoration of signal polarity, the PSIR fitting improves the quality of T1 map.

Materials and Methods

We propose to perform myocardial T1 mapping by exploiting the phase sensitive image reconstruction. This approach exploits the fact that the MOLLI image with long TI has well recovered magnetization; therefore, the phase of this image can be used to restore the signal polarity for the entire MOLLI series. In this way, the varying image contrast during the MOLLI series can be removed, and registering MOLLI frames becomes robust. Moreover, the fitting on MOLLI signals with restored polarity is more efficient and leads to better T1 maps with less erroneous fluctuation. Fig. 3 illustrates the entire process, including phase sensitive reconstruction, motion correction and inversion recovery fitting.

FIG 3.

Flow chart of phase sensitive inversion recovery MOLLI mapping with motion correction and non-linear parametric fitting.

Phase sensitive image reconstruction

The benefits of phase-sensitive reconstruction for cardiac imaging have been well accepted for the delayed enhancement imaging of infarction (12). In PSIR delayed enhancement imaging (12), an extra proton density (PD) image is acquired besides the IR image. This PD image is used as the source for background phase estimation. In the proposed PSIR MOLLI reconstruction, the phase reference image is selected as the image with the longest TI which has sufficiently recovered magnetization.

As the first step, complex images are reconstructed using parallel imaging with GRAPPA acceleration factor 2 and individual coil images are adaptively combined to produce a single complex image for each inversion time. The MOLLI image with the longest TI is used to remove the background phase of all MOLLI images on a pixel-by-pixel basis. The real part of resulting image has the correct polarity of IR signal. Although the phase is spatially smooth in general, the initial misalignment between MOLLI images may still lower the accuracy of background phase removal. To alleviate its influence on registration, an initial motion correction is applied between the last images of every IR experiments. In the current protocol with 2 inversions, the last image of the first IR is co-registered to the last image of the second IR. These two images have similar contrast because of sufficiently long TIs, but can have noticeable mis-alignment as they are acquired six heartbeats apart. The deformation fields are applied to all other images of the first IR, leading to a reduction in phase error (Fig. 4).

FIG 4.

Initial registration leads to reduced errors in the phase sensitive images. (a) A MOLLI phase sensitive frame without the initial registration. (b) The same frame after applying the deformation fields of initial registration. The abrupt intensity changes in the phase sensitive images are reduced.

Motion correction of MOLLI series

Given the MOLLI images with signal polarity restored, robust motion correction can be achieved by registering the MOLLI images in a frame-by-frame manner, since the contrast inversion is removed. Because of the non-rigid nature of cardiac deformation, a fast variational non-rigid image registration framework (13,14) is applied. In this framework, a dense deformation field is estimated as the solution to a calculus of variation problem. It is solved by performing compositional update steps for a partial differential transport equation. The regularization is added by low-pass filtering the gradient images of the cost function. The outcomes are used as velocity field to drive the transport equation. To speed up the convergence and avoid local minima, a multi-scale image pyramid is created. The local cross correlation is used as the image similarity measure, as its explicit derivative can be more efficiently calculated than mutual information and still be general enough to cope with noise and intensity difference between PSIR MOLLI images.

Phase sensitive inversion recovery T1 fitting

After motion correction, the deformation field is used to warp the original complex MOLLI images and the phase of IR image with the longest TI is removed from all images. The motion corrected complex inversion-recovery signal is first phase corrected and the real-part of the resulting complex signal is extracted for T1 fitting. The T1 map is generated via the pixel-wise curve fitting using the three parameter signal model (10):

$$\begin{array}{c}\hfill S(x,y,t_n)=A(x,y)-B(x,y)\times \exp (-t_n∕\mathrm{T}{1}^{\ast }(x,y\left)\right)\hfill \\ \hfill \mathrm{T}1(x,y)=\mathrm{T}{1}^{\ast }(x,y)\times \left(B\right(x,y)∕A(x,y)-1)\hfill \end{array}$$ (1)

where A, B, and T1* are estimated by a 3 parameter nonlinear fit to the measured data with restored polarity. Here t is the accumulative time from the inversion pulse. T1* is the apparent, modified T1 in an IR experiment. Fig. 5 demonstrates the advantages of PSIR T1 fitting for both pre- and post-contrast cases. For the pre-contrast case of this example (Fig. 5(a)), the MF-MAGIR fitting needs 4 trials to find the best inversion time for pre-contrast, while the phase sensitive reconstruction already provides this information. Also, the confusion of whether to invert the points near the signal nulling leads to errors in MF-MAGIR fitting. For this post-contrast case (Fig. 5(b)), the T1 is so short in the blood pool that the MF-MAGIR fitting is confused by whether to invert the first sample, while the PSIR fitting ensures the correct polarity of the first data point (in this example, assigning all data points as “positive” leads to lower fitting residual (155.0), while inverting the first data point gives higher residual (176.7); thus the MF-MAGIR fitting which always favor the minimal residual cannot make the correct polarity assignment and gives underestimated T1). As a result, the increased ambiguity in MF-MAGIR fitting leads to a noisy T1 map, especially for post-contrast cases where the magnetization generally crosses zero earlier due to shortened T1s.

FIG 5.

MOLLI inversion recovery signal curves with MF-MAGIR and PSIR fitting. The phase sensitive fitting does not require the multiple trials to find the polarity for every data point. For data samples near the signal nulling, the incorrect determination of signal polarity can lead to reduced accuracy in T1 estimation. (a) T1 map of a pre-contrast MOLLI dataset. For the pixel marked by the white cross, estimated signal curves are plotted for MF-MAGIR and PSIR fitting. Note the phase sensitive fitting resolves the signal polarity for the third and fourth data points. (b) T1 map of a post-contrast MOLLI dataset with shortened T1s. For the marked pixel, the MF-MAGIR fitting did not find a zero-crossing and incorrectly gave ‘positive’ signs to all data points, including the first one (Note in this example, giving all data points “positive sign” leads to a lower residual of 155.0,while inverting the first data point has a higher residual of 176.7). This gives the fitting results shown by the solid line. With the PSIR fitting, the sign of first data point is correctly assigned as ‘negative’. This leads to the fitting curve shown by the dash line. The T1 maps show the PSIR fitting is correct and leads to improved estimates. In this case, the MF-MAGIR fitting does give a reasonable recovery curve; however, the resulting T1 value is inaccurate due to the mis-assigned signal polarity for the first data point.

Other means to avoid multiple trial fitting could include directly performing the fitting on the magnitude of inversion recovery signal ∣ A(x, y)– B(x, y)× exp(–t_n/T1*(x, y))∣ without trying to detect the polarity. This strategy is hereby named as MAGIR fitting to be differentiated from the multi-fit magnitude (MF-MAGIR) method. The major drawback of this strategy is that for the post-contrast imaging with shortened T1 values, there may be insufficient number of data samples before the signal nulling. This often leads to the failed fitting (Fig. 6c-d). Because the T1 shortening is compounded by the dose of injected contrast, heart rate, blood flow and other physiological and physical parameters, it is difficult to optimize the protocol to completely avoid this phenomenon. In our experiments, the MAGIR fitting frequently failed for post-contrast cases and gave inferior results on pre-contrast cases.

FIG 6.

MOLLI inversion recovery signal curves with MAGIR and PSIR fitting. Both strategies do not require the multiple trials to find the polarity for every data point. However, for post-contrast imaging with largely shortened T1 values, there may not be sufficient number of data points sampled before the inversion, which frequently leads to the failure of MAGIR fitting. For the pre-contrast cases, this strategy often leads to inferior mapping quality. (a) T1 map of a pre-contrast MOLLI dataset using PSIR fitting. (b) T1 map estimated using the absolute magnitude fitting for the same dataset, showing overestimation of T1s. (c-d) T1 map of a post-contrast MOLLI dataset using the PSIR and MAGIR fitting. The latter shows incorrect estimation of T1. For the marked pixel, the estimated signal intensity curves are plotted with the sampled intensities for the pre- (e) and post-contrast (f) cases. Especially in (f), the MAGIR fitting fails because only two data points are sampled before the nulling points, while the phase sensitive fitting with the known signal polarity is much more robust against T1 shortening.

Fig. 7 illustrates the benefits of motion correction and PSIR fitting. In this pre-contrast case, the motion correction is able to improve the boundary sharpness of the T1 map. Compared to the MF-MAGIR fitting, the PSIR fitting further improves the homogeneity of T1 estimation. The plots of fitting residuals (Fig.7d-f) show the reduced least square error after motion correction and the PSIR fitting, which corresponds to the improved T1 estimation shown in the map (Fig. 7c).

FIG 7.

T1 maps and fitting residual errors of a pre-contrast dataset. (a,d) T1 map and fitting residuals without motion correction. (b,e) T1 map and residuals with SynMOCO and MF-MAGIR fitting. (c,f) T1 map and residuals with PSIR MOCO and fitting. The residual plots are windowed at the identical level. Both SynMOCO and PSIR-MOCO have improved the boundary sharpness of T1 map and reduced the residual along the septum wall. The PSIR fitting further reduce the residuals and leads to better T1 homogeneity, compared to MF-MAGIR fitting.

The downhill simplex minimization algorithm proposed by Nelder and Mead (so-called Nelder–Mead method (15)) is applied in all experiments and gives similar outputs as the Levenberg-Marquardt minimization (16), while the Nelder–Mead method is more efficient since only function evaluations are required. The maximal intensity was used to initialize A, approximating the fully recovered magnetization. B was initialized as A minus the minimal intensity, approximating the magnetization at t_n = 0 . T1* was initialized as the linearly interpolated zero-crossing time estimated from the polarity corrected signal intensity curve.

Imaging experiments

Imaging experiments were performed on 1.5T clinical MRI systems (MAGNETOM Espree and MAGNETOM Avanto, Siemens AG Healthcare Sector, Erlangen, Germany) equipped with 32 receiver channels. All subjects were scanned at the National Heart, Lung and Blood Institute, Bethesda, Maryland, USA. This study was approved by the local Institutional Review Board, and written informed consent was given by all participants.

A total of 45 patients (23 men, 22 women; mean age 47.1±15.9 years) were imaged both before and after contrast injection. Typical sequence parameters are as following: inversion recovery prepared MOLLI with balanced SSFP readout, TR=2.4/TE=1.05ms, acquired matrix 192×126, reconstructed matrix size 192×144, flip angle 35°, in-plane spatial resolution 1.9×2.1mm², rectangular FOV 360×270mm², slice thickness 6mm, bandwidth 1000 Hz/pixel. 8 images were acquired with 11 heart beats using 2 inversions. All acquisitions were ECG-gated and breath-held.

For every patient, the MOLLI imaging was performed for at least 2 slices (mid-ventricular short axis and four chamber long axis views) for both pre- and post-contrast. The post-contrast acquisition was performed at approximated 15-20 minutes following the intravenous injection of Gd-DTPA at 0.15 mmol/kg dose. The entire data cohort consists of 180 MOLLI series (90/90 pre/post-contrast, 95/85 short/long axis).

The proposed workflow was implemented using C++. All computation was performed on a 64bit Window 7 workstation containing two quad-core Intel Xeon E5620 2.4GHz processers and 24GB RAM. Typical processing time of PSIR-MOCO and fitting was less than 5 seconds per slice, including initial motion correction, background phase removal, MOLLI image registration and pixel-wise PSIR T1 fitting. The computational time is measured by recording the processing time per MOLLI series and computing the mean and standard deviation for all series.

Quantification of motion correction

All MOLLI series were first converted to animated movie files and viewed by an experienced reader who classified all datasets into two categories according to the presence of myocardial motion. As a result, motion was found in 87 series (48.3%). If the myocardium was found by visual inspection to move between any two frames, this series was classified as ‘with motion’. Only when the myocardium was still across all images, this series was classified as ‘no motion’.

To quantify the performance of motion correction, two frames with good contrast between blood and myocardium were selected for every “with motion” series (87 series in total). For series where the myocardium was stationary, 25 series were first randomly selected and two frames were picked per stationary series.

For all selected frames, the myocardium was manually delineated by the reader and the segmentation was propagated to the motion corrected images using the deformation fields. Because the motion correction should improve the overlap of myocardium between those two selected frames, the Dice similarity coefficient (DSC) (17) was computed before and after motion correction . For two segmented regions A and B, the DSC is defined as:

$$\mathit{DSC}=\frac{2\times \mathit{area}(\mathbf{A}\cap \mathbf{B})}{\mathit{area}\left(\mathbf{A}\right)+\mathit{area}\left(\mathbf{B}\right)}$$

The maximal possible Dice coefficient is 1, indicating a perfect overlap. The false positive (FP) and false negative (FN) errors were also computed. FP is defined as the area ratio of region A that is not overlapped by region B ( FP = area(A / B)/area(A)) and FN is defined as the area ratio of region B that is not overlapped by region A ( FN = area(B / A)/area(B)).

To quantify the local non-rigid misalignment, a myocardium boundary error (MBE) was computed for all series. This measure is defined as the mean distance between endo- and epi-myocardial contours of two selected frames.

Previous studies (9) showed that for the anatomy with simple geometry such as myocardium, the inter-rater variability is not severe and reasonable inter-rater reproducibility can be achieved. The reported DSC for inter-rater variability test for myocardium segmentation is 0.853±0.050 (computed on manual myocardial segmentation from two independent human raters) and the MBE is less than one pixel. Because a DSC measure above 0.7 indicates good agreement between two independent segmentations (18), in this study we did not further validate the inter-rater variability of myocardial segmentation.

Homogeneity of T1 estimation

With the hypothesis that PSIR fitting can lead to improved homogeneity of T1 estimation, the homogeneity of T1 maps was quantified by selecting a region-or-interest (ROI) within the blood pool for all 180 series and computing the standard deviation (STD) of T1s. First, the blood has rather stable T1 values. Second, with the injection of contrast, the T1 of blood is uniformly shortened, which may not be true for other tissues. Third, compared to the myocardium, it is more robust to select an ROI within the blood pool to avoid the disturbance of motion. Finally, the T1 homogeneity of the myocardium can be altered by potential pathologies, such as acute or chronic infarction or edema, while the blood T1 is not. Thus, the fluctuation of T1 estimation can be more precisely quantified within the blood pool. The homogeneity was measured for T1 maps computed using PSIR fitting and MF-MAGIR fitting after the PSIR MOCO; thus, the influences of cardiac motion can be ignored and the effects of phase sensitive fitting can be highlighted.

Results

The necessity of motion correction for MOLLI T1 mapping was confirmed by visual reading, as discernible motion was found in almost half of the entire data cohort. Examples of MOLLI motion correction are shown in Fig. 8, indicating the improved alignment of the myocardium.

FIG 8.

Example of motion correction. (a-c) A MOLLI series where myocardium shows noticeable motion. (d-f) Results by directly applying the non-rigid registration shows the failure of registration. (g-i) Results after SynMOCO. (j-l) Results after PSIR-MOCO. Both SynMOCO and PSIR-MOCO is capable of correcting the heart motion. 3 out of 8 images are shown here.

Directly aligning MOLLI magnitude images without handling the largely varying image contrast can lead to frequent failures in image registration. To demonstrate this phenomenon, the middle frame of every series was picked as the reference to which all other frames were registered. Visual reading confirmed that unrealistic deformation or failed registration was found in 124 cases among the whole cohort (68.9%). This failure rate is too high to accept direct registration as a solution for MOLLI motion correction. A more robust motion correction is thus needed.

For series with motion, the proposed method successfully corrects the myocardial movement (Fig. 8). The quantitative measures are reported in Table 1a. The paired t-test was used to quantify the statistical significance. With the PSIR-MOCO, the DSC is increased significantly (0.870±0.056, P<1e-5), compared to 0.812±0.108 measured on the original MOLLI images. Consistently, both FP and FN are significantly decreased (P<1e-5 for both). The MBE is 1.476±0.872mm for original MOLLI and reduced to 0.981±0.487mm after PSIR motion correction.

Table 1.

Quantitative measures of phase sensitive motion correction for MOLLI series with and without motion.

(a) With motion
	Dice			FP
	ORI	PS	SYN	ORI	PS	SYN
Mean	0.812	0.870	0.864	0.197	0.143	0.149
STD	0.108	0.056	0.061	0.118	0.071	0.078
P-value	ORI vs. PS : <1e-5			ORI vs. PS : <1e-5
	ORI vs. SYN : <1e-5			ORI vs. SYN : <1e-5
	PS vs. SYN : 0.214			PS vs. SYN : 0.247
	FN			MBE (mm)
	ORI	PS	SYN	ORI	PS	SYN
Mean	0.178	0.116	0.122	1.476	0.981	0.995
STD	0.110	0.061	0.065	0.872	0.487	0.446
P-value	ORI vs. PS : <1e-5			ORI vs. PS : <1e-5
	ORI vs. SYN : <1e-5			ORI vs. SYN : <1e-5
	PS vs. SYN : 0.235			PS vs. SYN : 0.648
(b) Without motion
	Dice			FP
	ORI	PS	SYN	ORI	PS	SYN
Mean	0.887	0.885	0.882	0.103	0.108	0.109
STD	0.026	0.027	0.029	0.045	0.049	0.049
P-value	ORI vs. PS : 0.408			ORI vs. PS : 0.118
	ORI vs. SYN : 0.116			ORI vs. SYN : 0.050
	PS vs. SYN : 0.248			PS vs. SYN : 0.700
	FN			MBE (mm)
	ORI	PS	SYN	ORI	PS	SYN
Mean	0.123	0.123	0.127	0.935	0.920	0.948
STD	0.047	0.045	0.050	0.411	0.405	0.525
P-value	ORI vs. PS : 0.962			ORI vs. PS : 0.465
	ORI vs. SYN : 0.340			ORI vs. SYN : 0.677
	PS vs. SYN : 0.218			PS vs. SYN : 0.357

ORI, original images; PS, phase sensitive motion correction; SYN, synthetic image estimation based motion correction.

For cases where the myocardium remains stationary, the PSIR-MOCO does not introduce unrealistic deformation and shows good robustness against the varying image contrast (Fig. 9). Table 1b summarizes the corresponding measures. The Dice coefficient which is originally 0.887±0.026 remains stable after PSIR-MOCO (0.885±0.027, P=0.408). The false positive and false negative errors are almost unchanged. The original MBE is 0.935±0.411 mm and after PSIR-MOCO, this measure is 0.920±0.405mm (P=0.465). These measures support the observation that unwanted deformation is not introduced by the PSIR-MOCO, indicating a reasonable degree of robustness.

FIG 9.

Example of MOLLI motion correction. (a-c) Original MOLLI images in studies for which the myocardium is “stationary”. (d-f) Results by directly applying the non-rigid registration. The unrealistic deformations caused by failed registration can be observed around the septum (arrow) in (d). (g-i) Results after SynMOCO. (j-l) Results after PSIR-MOCO.

The performance of PSIR-MOCO was compared to the synthetic image estimation based motion correction. Both methods were reasonably robust against rapid contrast changes and the overall performance was similar, as listed in Table 1. The PSIR-MOCO is more efficient because synthetic images are not needed anymore. The SynMOCO utilizes the MF-MAGIR fitting for the estimation of synthetic images. Because a T1 signal curve has to be estimated for each pixel in the synthetic image, the multiple fits required in the MF-MAGIR fitting actually consumed most computational time in the SynMOCO. On the contrary, the proposed scheme only needs one T1 fitting after the motion correction. The PSIR-MOCO decouples the motion correction and parametric fitting because of its ability to recover the signal polarity. The computational time of PSIR T1 fitting was found to be 4.4±0.3s per MOLLI series without the multi-threading. For the MF-MAGIR fitting, the time cost was 13.6±1.3s per MOLLI series. With the use of multi-threading (measurements were performed with 16 threads on 8 cores with hyper-threading enabled), ~2x speedup was still achieved (0.93±0.09s per MOLLI series for PSIR fitting and 1.90±0.19s per MOLLI series for MF-MAGIR fitting). The entire processing of PSIR-MOCO and SynMOCO with multi-threading took 6.43±0.83s and 11.8±1.2s per MOLLI series, including motion correction and T1 fitting. The time cost for GRAPPA reconstruction was excluded because this step is required in both cases when parallel imaging is used. All MOLLI series includes 8 inversion recovery images with the reconstructed image size 192×144.

To verify the performance on pre- and post-contrast cases, quantitative measures were computed separately for 37 pre- and 47 post-contrast series with motion. The DSC after PSIR-MOCO is 0.856±0.072 for pre-contrast and 0.882±0.035 for post-contrast (P>0.05). The decreases of MBE errors after PSIR-MOCO were 0.648±0.734mm for pre-contrast and 0.375±0.521mm for post-contrast (P>0.05). Significant deviation on motion correction performance was not found between pre- or post-contrast imaging.

With effective motion correction, T1 maps show reduced motion artifacts and improved boundary sharpness, as illustrated in Fig. 10. To demonstrate the insufficient robustness of MAGIR fitting (fitting using absolute magnitude signal), this strategy is applied to all images after the PSIR-MOCO and T1 maps are computed and reviewed visually. Clearly failed fitting within myocardium, similar to the one shown in Fig. 6d, were found in 81 series (45.0%), including 7 pre-contrast and 74 post-contrast series. This high rate of failure indicates the insufficient performance of MAGIR fitting strategy, especially for post-contrast scenario. For the pre-contrast cases, the map quality is often degraded due to local minima which trap the non-linear optimization (e.g. Fig. 6b). Better approaches to achieve stable T1 estimation such as MF-MAGIR or PSIR fitting are necessary.

FIG 10.

T1 maps of pre- (a-h) and post-contrast (i-t) MOLLI series. The first column (a,e,i,m,q) shows the T1 maps without motion correction. The second column (b,f,j,n,r) is with SynMOCO. The third (c,g,k,o,s) and fourth column (d,h,l,p,t) is generated after PSIR-MOCO. The first, second and third columns are produced with MF-MAGIR fitting and the last column is with PSIR fitting. With motion correction (more prominent for the first and third rows), the motion blurring is reduced and myocardial boundary sharpness is improved. For cases where there is very little cardiac motion, e.g. the second and fifth rows, the motion correction does not introduce unwanted deformation or lead to degraded mapping quality. Comparing the fitting method (columns 3 and 4) for a given motion correction scheme (PSIR MOCO), the PSIR T1 fitting (the last column) improves the T1 estimation (e.g. the second, fourth and fifth rows) as compared to the MF-MAGIR fitting (the third column).

Compared to the MF-MAGIR, the PSIR fitting is not only considerable faster, but leads to less fluctuation of T1 estimates. The MF-MAGIR fitting leads to a standard deviation of 60.594±23.784ms for pre-contrast and 17.876±7.371ms for post-contrast series. With the PSIR fitting, statistically significant changes were found for both pre- and post-contrast T1s (Pre-contrast, 57.804±21.872ms, paired t-test, P<1e-4; Post-contrast, 15.519±6.224ms, P<1e-5). The measured standard deviations were shown in Fig. 11. The mean T1 values estimated with both fitting approaches remain statistically unchanged (pre-contrast: 1520.175±152.642ms for MF-MAGIR and 1517.459±150.903ms for PSIR; Post-contrast: 319.007±70.061 for MF-MAGIR and 318.272±69.835ms for PSIR, P>0.1 for all cases). Additionally, a human rater reviewed the T1 maps generated with both methods for all 180 series. Compared to the MF-MAGIR fitting, the PSIR fitting leads to visible improvements in 83 series (46.1%), including 34 pre-contrast and 49 post-contrast series. This observation is consistent with the quantitative results that favor the improved fitting with PSIR.

FIG 11.

Measured standard deviation of T1 values (ms) for a region in the blood pool comparing MF-MAGIR and PSIR fitting for (a) pre-contrast and (b) post-contrast MOLLI series. The phase sensitive fitting leads to more uniform T1 estimation in the blood pool ROI. (c) The plot of the difference between standard deviation (STD) of T1 obtained with MF-MAGIR minus the STD for PSIR fitting shows that the MF-MAGIR tends to have greater variation for both pre- and post-contrast cases.

Discussion

While the feasibility of myocardial T1 mapping using MOLLI imaging sequences and related variations has been proven by previous studies, the undesired patient movement or imperfect breath-holding often impair the mapping quality. Severe heart motion can lead to significant bias in the estimated T1s. To correct the myocardium motion and improve the quality of T1 mapping, a novel motion correction and T1 estimation scheme is proposed. The specialty of this method lies on utilizing the phase sensitive reconstruction. In this way, the polarity of inversion recovery magnetization is restored and the contrast inversion among MOLLI images is avoided. Robust motion correction can thus be achieved. Moreover, the known signal polarity eliminates the need for time-consuming multi-trial fitting. The performance of proposed technique was evaluated in vivo on a cohort of 45 patients. We have shown that this scheme leads to very robust motion correction and does not introduce unrealistic deformation.

To efficiently utilize the phase sensitive reconstruction, we make the assumption that the background phase can be readily estimated from the MOLLI images with the longest TI even at the high heart rates with the longest T1’s (i.e., pre-contrast administration). Given the current imaging protocol, the magnetization will be well recovered after five heart-beats for the post-contrast scenario. For the pre-contrast imaging cases, if the heart rate is within the common range (e.g. <100) which holds true for most subjects, our experiments show the background phase can be well estimated. If the heart rate is further increased, it will quickly become impractical to perform MOLLI imaging since the single shot images do not have sufficient temporal resolution and image quality will be degraded by motion blurring. To conduct MOLLI imaging for very high heart rate, the imaging matrix size has to be reduced and more heart rates beats shall be allowed for good recovery of magnetization.

The imaging protocols used in this study requires one breath-hold lasting 11 heart beats. While this is achievable in clinical setting, our experiments show that more than 60% of the acquired series present discernible motion. This observation highlights the necessity for either shortening the imaging protocol or even conducting free-breathing acquisition. The recently published shortened-MOLLI protocol (ShMOLLI (4)) proposes to acquire a shorter MOLLI series for T1 mapping (9 heartbeats). This strategy can slightly reduce the sensitivity to breathing motion at the cost of decreased SNR because less data points are used for curve fitting. More evaluation is needed to further optimize the MOLLI imaging protocol and pursue better tradeoff between total acquisition time, SNR of T1 map and sensitivity to patient motion.

The proposed method has some potential to correct in-plane motion of myocardium in a free-breathing acquisition; but it may not be capable of correcting large through-plane motion as current image registration is performed on 2D frames. Its applicability on datasets with large R-R interval variations, such as arrhythmias, may be limited. One possible extension to make the proposed method handle free-breathing MOLLI could be detecting and excluding frames with strong through-plane motion from fitting and registration. The cost here may include an increased number of acquired heart beats and IR images.

Compared to MAGIR fitting, the PSIR fitting is similarly efficient, but much more robust against the data sampling pattern along the IR curve because the signal polarity can be determined before the non-linear optimization. As illustrated in Fig. 6, the fitting on absolute magnitude signals leads to error-prone estimation of T1 values. The accuracy of MAGIR fitting might be improved with better initialization; however, the T1s within the FOV experience significant variations for different tissue types and contrast concentration. The inversion times of MOLLI acquisition depend on the heart rate as well. As a result, there is no clear solution to constraint the data sampling along the inversion recovery curve to favor the magnitude fitting. One possible way might be to apply a brute-force search among possible combinations of A, B and T1^* to find a better starting point; but it will prolong the parametric estimation.

The proposed PSIR fitting is much faster than the MF-MAGIR fitting. Depending on the T1 of a pixel and the inversion times, the PSIR fitting can reduce ambiguity for whether to invert signal points near the zero-crossing of magnetization. The multiple trial strategy may not always assign the correct polarity for these points, while the phase sensitive reconstruction readily provides this information. Furthermore, the influences of MOLLI signal points on the final T1 estimate depend on the derivative magnitude of the inversion recovery curve at the corresponding inversion times. For example, the magnitude of IR recovery derivative is larger for smaller TI and quickly decreases for longer TI (the derivative of IR recovery is $2e^{\frac{\mathit{TI}}{T_1}}/T_1$). Thus, the signal points sampled at the beginning period of IR recovery can have more influences on the final T1 estimate. This may indicate that the improvement of PSIR fitting on the T1 mapping is more prominent for post-contrast cases than for pre-contrast, as the former has significantly shortened T1 values.

For the experiments conducted in this paper, the T1 value is computed as T1^*(x, y)× (B(x, y)/ A(x, y)−1), following the suggestion of the original MOLLI sequence paper (1). Given the balanced SSFP readout in current MOLLI experiments, this formula can lead to underestimation of real T1s, as reported in (1). More precise formula specifically considering SSFP readout scheme could further improve the T1 estimate. On the other hand, the potential benefits of PSIR T1 mapping, including more accurate signal polarity determination and robust motion correction, are independent of the correction of apparent T1*. With the known signal polarity, the ambiguity of whether to invert signal points around magnetization nulling is removed.

Conclusions

We have presented a new scheme to perform the motion correction and parametric fitting for myocardial T1 mapping. The key idea is to restore the signal polarity of inversion recovery magnetization using phase sensitive reconstruction. This method is fully automated and does not require any preprocessing. The in vivo validation on a data cohort of 45 patients illustrates the robustness of the proposed method. The phase sensitive inversion recovery fitting with the restored signal polarity can further improve the mapping process with decreased computational cost and improved T1 estimation.