Local frequency shift (LFS) mapping techniques have shown potential for visualizing white matter microstructure (1). Extending these techniques to the heart may provide important information about the integrity and organization of myofibers. However, LFS values associated with myofibers (< 0.1 ppm) (2) are at least one-order of magnitude smaller than confounding variations in magnetic field homogeneity (ΔB0, ~ 1 ppm) and the chemical shift (CS) between fat and water (~ 3.5 ppm). Therefore joint estimation of myofiber LFS, ΔB0 and CS is challenging (3-4). We present a method to extract myocardial LFS maps by explicitly removing the ΔB0 and the CS-related components from multi-echo data (B0CS-LFS) and compare results with those from a previously described cardiac SWI method (5).

Data acquisition: Data were acquired at 1.5 T with a dark blood double inversion recovery gradient echo sequence (1 slice per breath-hold, repetition time 20 ms; 12 echo times, 2.4 – 15.5 ms (1.2 ms spacing); flip angle 20°; bandwidth 1860 Hz/pixel; in-plane resolution 2.3 ×1.7 mm², slice thickness 8 mm; flow compensation in read and slice directions). The bipolar multi-echo data were split into odd- and even-echo data sets; the first echo was excluded from the odd-echo group because of significant image corruption caused by eddy currents (6).

The B0CS-LFS approach comprises three steps. First, a field (Δf_b0) map and fat-fraction (FF) map are generated from the even- and odd-echo groups separately. For this purpose, we used the unwrapping-based B0 mapping technique B0-NICE (7), which also estimates a T2* map from all echoes. To mitigate issues related to the presence of local field information in the B0 map, we performed low-pass filtering of the B0 complex image, which is the Hermitian product between the sixth and the second echoes (even-echo) or the seventh and the third echoes (odd-echo). Both Hanning and moving-average filters were evaluated.

The second step is to remove the unwanted constant, B0, and CS phase components. To remove the constant phase term, the Hermitian products between echoes were calculated as follows:

$I_j,hp =I_j×I₂*, even, $ [1a]

$I_j,hp =I_j×I₃*, odd, $ [1b]

where I_j is the complex image at the jth echo and * denotes the complex conjugate. The LFS at each individual echo (f_j) were estimated by removing the B0- and CS-related phase terms:

$f_j =angle(I_j,hp×exp(-φ_b0,j)×exp(-φ_CS,j))/(2π×ΔTE_j) $ [2]

where φ_b0,j is equal to 2π×Δf_b0×ΔTE_j; φ_CS,j is calculated using the six-peak fat model and FF map determined from step 1; ΔTE_j is equal to (TE_j – TE₂) and (TE_j – TE₃) for the even and odd echoes, respectively.

The third step is to calculate the final LFS map, defined as the mean over all included echoes on a pixel-by-pixel basis.

While no reference standard exists for myocardial LFS mapping, we compared the B0CS-LFS results to a high-pass filtered approach (HPF-LFS) adapted from the cardiac SWI method described in (5), where filtered phase was scaled to frequency and averaged over the last nine echoes.

Successful Δf_b0 and FF maps were generated (Fig. 1), as demonstrated by the lack of fat-water swaps in the heart. More importantly, the circled region in the T2* map matches well with an infarct identified in a corresponding LGE image (not shown), while the field map in the region remains smooth. A decrease in LFS values (calculated using both HPF-LFS and B0CS-LFS approaches) is also observed in the infarct region (Fig. 2). Interestingly, spatial LFS gradients of approximately 4 Hz are observed across the myocardium in the vertical long axis (VLA) plane (Fig. 3), but are not observed in the short axis (SA) or horizontal long axis (HLA) planes (Fig. 4). Overall the HPF-LFS is smoother (less tissue textures) while the B0CS-LFS method increases visibility of edges, clearly separating tissue from blood pool and surrounding tissue.An acute hemorrhagic infarct-related LFS hypo-intensity was clearly seen in Fig. 2, as expected. The magnitude of the measured LFS gradient agrees with the ex vivo values (2). Variations of the fiber orientation with respect to B0 are likely responsible for the fact that the gradient is visualized in the VLA (Fig. 3) but not in the SA and HLA planes. Because the orientation-dependent LFS values are also very sensitive to the types of filters as well as the kernel-sizes used, caution should be exercised when using LFS for quantitative applications. Myocardial LFS mapping promises to be an effective and rapid tool for quantifying myofiber orientation, compared to alternative techniques, such as DTI. Myocardial LFS mapping can identify hemorrhagic infarct zones and has potential to depict myofiber orientation.