Benjamin C Tendler1, Sean Foxley2, Moises Hernandez-Fernandez3, Michiel Cottaar1, Olaf Ansorge4, Saad Jbabdi1, and Karla Miller1
1Wellcome Centre for Integrative Neuroimaging, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, United Kingdom, 2Department of Radiology, University of Chicago, Chicago, IL, United States, 3Centre for Biomedical Image Computing and Analytics, University of Pennsylvania, Philadelphia, PA, United States, 4Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, United Kingdom
Synopsis
Diffusion-weighted steady-state free precession (DW-SSFP)
generates high SNR diffusivity estimates in whole, post-mortem human brains.
Improved estimates at 7T has motivated its use at ultra-high field. However,
the DW-SSFP signal has a strong dependence on flip angle. This translates into
both variable signal amplitude and diffusion contrast. At 7T, transmit-($$$B_{1}^{+}$$$) inhomogeneity
leads to $$$B_{1}^{+}$$$-dependent SNR and ADC
estimates. Previous work corrected for $$$B_{1}^{+}$$$-inhomogeneity by
acquiring DW-SSFP datasets at two flip angles. Here, this approach is extended,
utilising the full Buxton model of DW-SSFP to model non-Gaussian diffusion. A
noise-floor correction and signal weighting are also incorporated to improve
diffusivity estimates.
Introduction
Post-mortem diffusion imaging of whole human brains allows validation
of the origins of diffusion contrast through comparisons with microscopy. However,
death and fixation leads to tissue samples characterised by a short T2
and low diffusivity1,2, resulting in low SNR when
using conventional diffusion imaging sequences.
Diffusion-weighted steady-state
free precession (DW-SSFP) (Fig. 1a) is a fast, highly SNR-efficient diffusion
imaging method that achieves strong diffusion weighting in clinical scanners with
limited gradient strengths3. Previous work4,5 has demonstrated the
potential of DW-SSFP to obtain high-SNR diffusivity estimates in whole human brains.
Further SNR gains have been reported at 7T compared to 3T6.
However, in order to fully take
advantage of the improved SNR and resolution at 7T, we need to overcome the
challenge of transmit-($$$B_{1}^{+}$$$) inhomogeneity.
This becomes particularly problematic in DW-SSFP, as both the signal (Fig. 1b) and
diffusion attenuation (Fig. 2a) are flip angle dependent7. One approach that has been
proposed to address $$$B_{1}^{+}$$$-inhomogeneity is to acquire
DW-SSFP datasets at two flip angles8, with the goal of combining
these two datasets to remove the spatially varying contrast.
Recently, we have proposed a
theoretical framework9 to model non-Gaussian
diffusion from DW-SSFP data acquired at two or more flip angles (Fig. 2). In
non-Gaussian diffusion regimes, the ADC is strongly dependent on flip angle (Fig
2c and 2d). Interestingly, this framework also provides a principled way to
combine measurements at multiple flip angles, by synthesising an ADC
corresponding to a chosen b-value. This approach simultaneously addresses $$$B_{1}^{+}$$$-inhomogeneity and the lack
of a well-defined b-value in DW-SSFP.
The work presented here builds on
previous work8,10,11 in several distinct ways.
Firstly, we incorporate the full Buxton model7 of DW-SSFP, where previous
work used the two-transverse period approximation11. Secondly, we have included a
noise-floor correction to reduce the bias on diffusivity estimates in conditions
of low signal12. Finally, the fitting cost
function is weighted by the DW-SSFP signal amplitude to improve the robustness
of the parameter fits.Methods
Whole, fixed post-mortem brains were scanned in a whole-body
7T system (Siemens, Nova-Medical 1TX/32RX coil). For each brain, DW-SSFP data
(q=300cm-1, TE=21ms, TR=28ms, 120 directions,
resolution=0.85x0.85x0.85mm3) were acquired at two flip angles (24o
and 94o). T1, T2 and B1 maps (dependencies
of the DW-SSFP signal model7) were also acquired. For more
information of the full acquisition and pre-processing, see10,13.
The DW-SSFP
datasets were fitted with a diffusion tensor model incorporating the full
Buxton signal model7 in cuDIMOT14. The model was designed to
fit to the DW-SSFP data acquired at both flip angles simultaneously to obtain a
shared set of eigenvectors and flip-angle-dependent eigenvalues. This fitting
was weighted by the signal amplitude to account for the available SNR at each
flip angle. A noise-floor term was incorporated into the fit to reduce bias in
low signal regions12,15, fitting to: $$S=(S_{SSFP}^{2}+S_{nf}^{2})^{\frac{1}{2}},\tag{1}$$ where $$$S_{SSFP}$$$ is the DW-SSFP signal from the full Buxton
model and $$$S_{nf}$$$ is the noise-floor (estimated from the
background signal). The unique
set of eigenvalues obtained at each flip angle were subsequently extrapolated
to a single SNR-optimal effective b-value, determined as $$$b_{eff}=7600s/mm^2$$$ from simulation. This extrapolation is based
on a gamma distribution of diffusivities16 embedded in the full
Buxton model of DW-SSFP, evaluated via numerical integration9.
Results and Discussion
Figure 3 displays the principal-diffusion-direction (PDD)
eigenvector estimates obtained from our dual-flip angle approach. By
incorporating signal weighting and a noise-floor correction, we observe clear improvements
in coherence in the PDD estimates in the superior and inferior regions of the
brain, areas associated with very low $$$B_{1}^{+}$$$. Reductions in angular
uncertainty (Fig. 4) are most apparent in areas of low/high $$$B_{1}^{+}$$$, associated with low SNR in
the 24o/94o datasets respectively. Reduced angular
uncertainty is generally predictive of improved tractography.
Figure 5
displays the L1 maps for a single brain. The ADC estimates at 94o
are generally higher than at 24o, consistent with a model of
non-Gaussianity (Fig. 2). At $$$b_{eff}=7600s/mm^2$$$, our maps display more
homogeneous contrast across the brain, with similar contrast to the 24o
dataset (from simulation, $$$b_{eff}=7600s/mm^2$$$ corresponds to a flip angle of 20o-24o).
By incorporating a noise-floor
correction, we improve the diffusivity estimates by reducing the bias in some
regions of tissue12 (visible in the difference maps). This is most notable at 24o
in the deep grey matter (green arrows). However, in areas of
very low signal, our noise floor correction is unable to rectify the ADC
estimates, leading to spuriously high values (pink arrows). Prior to noise
floor correction, these regions are characterised by very low ADCs. Though these
diffusivity estimates are biased before (low ADC) and after (high ADC) correction,
the high ADC values in our noise-floor corrected data are fundamentally incompatible
with our framework9 (Figure 2), leading to
artefacts which propagate into the final $$$b_{eff}=7600s/mm^2$$$ maps.Conclusion
By acquiring DW-SSFP data at two flip angles, we
simultaneously account for variable SNR and ADC estimates induced by transmit-inhomogeneity.
Signal weighting provides improved coherence and a reduced angular uncertainty
in eigenvalue estimates. ADC estimates derived at a single SNR optimal
effective b-value display more homogeneous contrast. Future work will
investigate approaches to reduce the bias in ADC estimates in regions of very
low signal.Acknowledgements
This
study was funded by a Wellcome Trust Senior Research Fellowship (202788/Z/16/Z)
and Medical Research Council grant MR/K02213X/1 and MR/L009013/1. Brain samples
was provided by the Oxford Brain Bank (BBN004.29852). The Wellcome Centre for Integrative
Neuroimaging is supported by
core funding from the Wellcome Trust (203139/Z/16/Z).References
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