Darryl McClymont1, Irvin Teh1, Hannah Whittington1, Vicente Grau2, and Jurgen Schneider1
1Division of Cardiovascular Medicine, University of Oxford, Oxford, United Kingdom, 2Department of Engineering Science, University of Oxford, Oxford, United Kingdom
Synopsis
Non-Gaussian diffusion MRI allows the quantification of diffusion
signals that deviate from mono-exponential decay. In cardiac MRI, very little
has been reported on non-Gaussian models. In this work, the diffusion tensor,
stretched exponential, bi-exponential, and diffusion kurtosis models were fit
to data from fixed rat hearts. Performance was measured using the Akaike
Information Criterion (AIC). All models demonstrated the presence of
non-Gaussian diffusion, particularly in the right ventricle. The bi-exponential
model fit the data best and had the lowest AIC. Non-Gaussian diffusion was greater
perpendicular, rather than parallel, to cardiac fibers, corresponding to greater
restrictions to diffusion.Introduction
Diffusion MRI may be used to non-invasively
provide information about tissue microstructure. The diffusion tensor model is
commonly fit to data, representing the diffusivity in each voxel as an
ellipsoid. However, complex tissue rarely exhibits mono-exponential diffusion$$$^1$$$. To address this, several models have been proposed to capture
the non-Gaussian nature of diffusion. In this work, we compare the performance
of the diffusion tensor to non-Gaussian diffusion models in ex-vivo cardiac
tissue.
Methods
Five hearts were excised from female Sprague-Dawley rats.
These were fixed, doped with 2mM Gd and embedded in 1% agarose gel.
Non-selective 3-D fast spin echo diffusion spectrum imaging (DSI) data were
acquired on a 9.4 T preclinical MRI scanner (Agilent, CA, USA) with a shielded
gradient system (max gradient strength = 1 T/m, rise time = 130 μs), and
transmit/receive birdcage coil (inner diameter = 20 mm; Rapid Biomedical,
Rimpar, Germany). TR / TE1 = 250 / 15.3 ms, echo spacing = 3.9 ms, echo train
length = 8, FOV = 20 x 16 x 16 mm,
resolution = 200 μm isotropic, number of
non-DW images = 4, number of DW directions = 257, bmax = 10 000 s/mm2.
Data were sampled in q-space in a Cartesian grid over a half-sphere.
Each of the four models in Table 1 was fit to
the five datasets using non-linear least squares regression. The performance
was measured in a voxel-wise manner using the corrected Akaike Information
Criterion (AICc)$$$^2$$$. In the case of the diffusion kurtosis model, a maximum
b-value of 5 000 s/mm2 was imposed. All models were fit in Matlab
R2013A (Mathworks, Natick, USA) using a trust-region-reflexive algorithm.
Results
As shown in Fig. 1a, the stretched exponential model
parameter $$$\alpha$$$ was 0.8 – 0.9 in the LV and approximately 0.7
in the RV, indicating the presence of non-Gaussian diffusion in both
ventricles, but to a greater extent in the RV.
Parameter maps derived from the bi-exponential model are
shown in Fig. 1b-f. The eigenvalues (primary, secondary, tertiary) of the fast
component were $$$(1.4\pm0.05, 0.95\pm0.05, 0.81\pm0.14)*10^{-3}mm^2/s$$$,
and the eigenvalues of the slow component were approximately $$$(0.45\pm0.08, 0.17\pm0.02, 0.10\pm0.01)*10^{-3}mm^2/s$$$.
As a result, the fractional anisotropy of the slow component was higher than
the fast component. The volume fraction of the fast component, $$$S_{0,f}/{S_{0,f}+S_{0,s}}$$$,
was generally higher in the LV than in the RV. All three eigenvectors were well
aligned between the fast and slow components (normalised dot product > 0.98).
Fig. 1g-i displays the (excess) kurtosis in the direction of
the 1st, 2nd and 3rd eigenvectors. The
kurtosis values in the direction of the 2nd and 3rd
eigenvectors are considerably larger than that of the 1st
eigenvector. We also note that the kurtosis of the all eigenvectors is larger
in the RV than in the LV.
Figure 2 presents a histogram of the AICc values
for each of the four models over all cardiac tissue. In general, the diffusion
tensor and stretched exponential models were not able to accurately model the
data at high b-values, and yielded higher AICc values. Both the
bi-exponential model and the diffusion kurtosis model produced mean square
errors that approached the noise floor. Consequently, the bi-exponential model yielded
the lowest AICc in the majority of voxels, due to it having a
smaller number of parameters than the DKI model.
Discussion
In this work, we have investigated the non-Gaussian behaviour
in ex-vivo rat hearts. All models show evidence of increased non-Gaussian
diffusion in the right ventricle compared to the left. The higher kurtosis
values in the direction of the secondary and tertiary eigenvectors are likely
to arise from restrictions perpendicular to cardiac fibers.
The bi-exponential model yielded a lower AICc
than the diffusion tensor, stretched exponential, and diffusion kurtosis models.
The parameters derived from this model are consistent with describing the
tissue as containing two distinct components with fast and slow diffusivities. However,
this interpretation must be treated with caution, as it is well established that
diffusion within a single compartment can give rise to bi-exponential decay as
a result of barrier effects$$$^3$$$.
Acknowledgements
This work is supported by the British Heart Foundation (PG/13/33/30210,
RG/13/8/30266, and FS/11/50/29038), the Engineering and Physical Sciences
Research Council (EP/J013250/1) and the Biotechnology and Biological Sciences
Research Council (BB/1012117/1). The authors acknowledge a Wellcome
Trust Core Award (090532/Z/09/Z).References
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K et al. Model Selection and Multimodel Inference: A Practical
Information-Theoretic Approach (2nd ed.). Springer-Verlag. 2002
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