Modified Look-Locker Inversion Recovery (MOLLI) $$$T_1$$$ Mapping with High Precision Composite Inversion Group (IG) Fitting

Marshall Stephen Sussman^{1,2} and Bernd Juergen Wintersperger^{1,2}

In conventional MOLLI, $$$T1_1$$$ maps are generated from a 3-parameter fit (2). In IG-MOLLI, a fitting function that is piecewise continuous over the *n* inversion groups is employed: $$S_i(A,B_1,...,B_n,T_1^*;TI)=A-B\cdot\exp^{-\frac{TI}{T_1^*}};\enspace i=1,..,n \qquad [1]$$

The true $$$T_1$$$ value may be derived as: $$T_1^i=T_1^*\cdot(\frac{B_i}{A}-1)/{\delta_i};\enspace i=1,..,n \qquad [2]$$

where $$$\delta_i$$$ is the inversion factor ($$$\equiv |M_z/M_0|$$$)
following the $$$i^{th}$$$ inversion pulse (3). In the original IG method, Eq. 2 was applied to the first inversion group only, as this was the only one where
$$$\delta_i$$$ is known *a priori *($$$\equiv$$$1). We hypothesize that improved precision could be achieved if all data were utilized.

To make use of all available data, we first determine $$$\delta_i$$$ for all *n* inversion groups: $$\delta_i=\frac{\Sigma_{j\space\epsilon\space Neighbourhood \space Pixels}\space (B_i/A-1)}{\Sigma_{j\space\epsilon\space Neighbourhood \space
Pixels}\space (B_1/A-1)};\enspace i=1,..,n \qquad [3]$$ where the sums are taken over a small neighbourhood surrounding each pixel. We next calculate $$$T_1^i$$$ for each inversion group via Eq. 2. Finally, all data is averaged together into a composite $$$T_1$$$: $$T_1^{composite}=average([T_1^1,...,T_1^n]);\qquad [4]$$

Five cardiac patients were scanned (1.5T) with three MOLLI acquisition schemes: 5(3)3, 5(0)3, and 5(0)3(0)3; where non-bracketed and bracketed numbers indicate inversion groups and rest periods respectively. 5(3)3 is a common scheme used in pre-contrast imaging (4). It is considered the reference standard due to its long rest period. 5(0)3 acquires the same number of TI's, but in three less heartbeats than 5(3)3. 5(0)3(0)3 acquires three more TI's in the same number of heartbeats.

$$$T_1$$$ maps were generated with original- and composite-IG fitting. Additionally, 3-parameter fits were applied to the 5(3)3 data to generate reference $$$T_1$$$ maps. The accuracy of IG fitting was determined by evaluating the discrepancy with the reference. Precision was defined as the standard deviation over a myocardial
ROI. Differences in precision relative to the reference were assessed with a *t*-test.

Figures 1 and 2 plot the quantitative results for all patients. The mean discrepancy relative to the reference scan is small -- ~1-2%. In terms of precision, all original IG MOLLI data are significantly worse than the reference -- as expected. For the composite IG technique,the 5(3)3 and 5(0)3 $$$T_1$$$ maps have the same precision. Due to the additional TI's, the 5(0)3(0)3 data has significantly better precision than the reference.

Figure 3 illustrates an example of a 5(0)3 acquisition, which acquired the same amount of data in three less heartbeats than the 5(3)3 reference. To appreciate the accuracy of IG fitting, note the conistency of $$$T_1$$$ maps relative to the reference. As expected (1), the precision of the original IG $$$T_1$$$ maps are significantly noisier than the reference. However, the composite IG $$$T_1$$$ maps have a similar precision to the reference.

Figure 4 shows an example of a 5(0)3(0)3 acquisition. As before, the original IG $$$T_1$$$ map has poorer precision than the reference. However, in this case, due to the larger number of TI's acquired, the composite IG $$$T_1$$$ map has *better* precision than the reference.

The composite IG $$$T_1$$$ mapping technique combines high precision with complete flexibility of inversion group and rest period selection. This study demonstrated two ways in which these features could be exploited: First, rest periods were eliminated to shorten scan time, whilst maintaining precision. Second, rest periods were replaced with additional data acquisition to achieve better precision in equivalent scan time. Further improvements may be possible with an appropriate optimization of inversion groups and rest periods.

With the improvements demonstrated in this study, we anticipate that composite IG $$$T_1$$$ mapping technique will better discriminate true pathology from artifacts and/or noise than current methods.

1. Yang IY, et al.,* ISMRM* 2015; 1677

2. Messroghli DR, et al., *MRM* 2004; 52(1):141-146

3. Kellman P, et al., *MRM* 2014; 71(4):1428-1434

4. Kellman P, et al., *JCMR* 2013; 15

Accuracy results for patient data
plotting fractional discrepancy with the reference 3-parameter 5(3)3 *T*_{1} maps. Data represents the mean +/- std. dev.
over all patients

Precision results for patient data.
Data is plotted as ratio of precision in *T*_{1} relative the reference 3-parameter 5(3)3 data. A
lower ratio means better precision. The "*" symbol indicates
statistically significant difference from unity at the 95% confidence level.
Data represents the mean +/- std. dev. over all patients.

Comparison of 5(0)3 original-, and
composite-IG *T*_{1} maps to the 3-parameter 5(3)3 reference.
The listed precision is calculated as the standard deviation over a
myocardial ROI. Note that a narrow colormap window is used to highlight
the myocardium.

Comparison of 5(0)3(0)3 original-, and
composite-IG *T*_{1} maps to 3-parameter 5(3)3 reference.
The listed precision is calculated as the standard deviation over a
myocardial ROI. A narrow colormap window is used to highlight the
myocardium.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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