Pedro Ferreira^{1}, Sonia Nielles-Vallespin^{2}, Ranil de Silva^{1}, Andrew Scott^{1}, Daniel Ennis^{3}, Daniel Auger^{4}, Jonathan Suever^{5}, Xiaodong Zhong^{6}, Bruce Spottiswoode^{7}, Dudley Pennell^{1}, Andrew Arai^{2}, and David Firmin^{1}

Myocytes have a laminar organization, where sheets of myocytes interleave with collagen-lined shear layers. Cardiac diffusion tensor imaging is capable of probing sheet dynamics with secondary diffusion directions, although questions remain about cardiac strain being a possible confounder. Here we study the validity of strain-correcting cardiac diffusion tensor data by directly comparing in vivo DTI data without and with strain correction, to ex vivo DTI data of the same porcine hearts arrested in a diastolic or systolic conformation. Results show that the current strain correction model exaggerates the contribution of microscopic strain to diffusion resulting in an over-correction.

Myocytes
have a laminar organization, where sheets of myocytes are separated by collagen-lined
shear layers. The rotation of these myolaminae, also named sheetlets, plays a
major role in explaining wall thickening during cardiac contraction^{1}.
Cardiac diffusion tensor imaging (cDTI) with a STEAM sequence is capable of
probing sheetlet orientation with the secondary eigenvector of diffusion^{2},
although questions remain about the possible confounding effects of tissue
strain throughout the cardiac cycle^{3 4}.

Recent
work has shown that strain correction greatly affects the secondary diffusion
eigenvector, but no validation of the correction was possible^{5}. Herein,
we evaluate the validity of strain-correcting cDTI data by directly comparing
in vivo cDTI data without and with
strain correction, to ex vivo cDTI data
of the same porcine hearts arrested in a diastolic or systolic conformation.
The ex vivo hearts provide cDTI data
free of any possible cardiac tissue strain during diffusion encoding.

All
imaging was performed at 3T (MAGNETOM
Skyra, Siemens, Germany) using investigational prototype sequences. 11
pigs were successfully scanned with a multi-slice spiral cine DENSE sequence
with displacement encoded in 3D^{6} (2.5x2.5x8 mm^{3}), and
with a STEAM-EPI DTI sequence (6 directions, b=500smm^{-2}, diffusion
weighting time 1 cardiac cycle, 2x2x8 mm^{3}) during diastasis, at end systole,
and at the strain sweet-spots (see figure 1A for definition) in a
mid-ventricular slice. The same cDTI sequence was repeated after the hearts
were excised with a diastolic (KCl) arrest induced in n=6 swine and systolic-like
(BaCl_{2}) arrest in n=5 swine.

The multi-slice DENSE data was used to calculate the two sweet-spot times of the cardiac cycle where strain effects are minimized (figure 1A), and to strain correct the in vivo cDTI data acquired at end systole and during diastasis on a pixelwise basis (figure 1B). The orientation of the primary (E1A or helix-angle, HA) and secondary (E2A) eigenvectors was compared in diastole (without/with strain correction), in systole (without/with strain correction), at both strain sweet-spots, and in the strain-free ex vivo data arrested in either systole or diastole.

1 – LeGrice, I. J., Takayama, Y., and Covell, J. W. Transverse shear along myocardial cleavage planes provides a mechanism for normal systolic wall thickening. Circ Res (1995): 182-93.

2 - Kung, G. L., Nguyen, T. C., Itoh, A., et al. The presence of two local myocardial sheet populations confirmed by diffusion tensor MRI and histological validation. J Magn Reson Imaging (2011): 1080-91.

3 - Reese, Wedeen, and Weisskoff Measuring Diffusion in the Presence of Material Strain. J Magn Reson B (1996): 253-8.

4 - Axel, L., Wedeen, V. J., and Ennis, D. B. Probing dynamic myocardial microstructure with cardiac magnetic resonance diffusion tensor imaging. J Cardiovasc Magn Reson (2014): 89.

5 - Stoeck, C. T., Kalinowska, A., von Deuster, C., et al. Dual-phase cardiac diffusion tensor imaging with strain correction. PLoS One (2014): e107159.

6 - Zhong, X., Spottiswoode, B. S., Meyer, C. H., et al. Imaging three-dimensional myocardial mechanics using navigator-gated volumetric spiral cine DENSE MRI. Magn Reson Med (2010): 1089-97.

Figure 1 - A: diagram showing how the sweet-spot times are calculated. Strain effects are minimized at
these times. B: flowchart showing how the strain correction is applied to the diffusion tensors. D_{obs} is the
diffusion tensor without strain correction; U(t) is the stretch tensor throughout an entire cardiac cycle Δ;
D is the diffusion tensor with strain correction. This equation needs to be solved for D in order to obtain
diffusion data that is strain corrected.

Figure 2 - Radial (Err), circumferential (Ecc), and longitudinal (Ell) strain curves. The thin lines represent
the subjects’ mean strain curves, and the thick lines represent the intersubject mean strain curve.

Figure 3 - HA and E2A normalized histograms of all myocardial voxels at diastole (without/with strain
correction), systole (without/with strain correction), the two sweet-spots, and for the explanted hearts
arrested in a diastolic/systolic like state. The histograms show the inter-subject median and interquartile
range.

Figure 4 – Table showing the root mean square deviation for histogram bins. The values are color-coded
according to the colorbar on the right.

Figure 5 - Median absolute E2A values. The in vivo values show the mobility of E2A from a diastolic to a
systolic phase without/with strain-correction and at the two time points closest to the sweet-spot times.
The respective color-coded ex vivo hearts are also shown for either a diastolic or systolic arrest.