Benjamin C Tendler^{1}, Sean Foxley^{2}, Moises Hernandez-Fernandez^{3}, Michiel Cottaar^{1}, Olaf Ansorge^{4}, Saad Jbabdi^{1}, and Karla Miller^{1}

^{1}Wellcome Centre for Integrative Neuroimaging, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, United Kingdom, ^{2}Department of Radiology, University of Chicago, Chicago, IL, United States, ^{3}Centre for Biomedical Image Computing and Analytics, University of Pennsylvania, Philadelphia, PA, United States, ^{4}Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, United Kingdom

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.

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 dependent

Recently, we have proposed a theoretical framework

The work presented here builds on previous work

The DW-SSFP datasets were fitted with a diffusion tensor model incorporating the full Buxton signal model

Figure 5 displays the L

By incorporating a noise-floor correction, we improve the diffusivity estimates by reducing the bias in some regions of tissue

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Figure 1: (a) DW-SSFP consists of a single RF pulse and
diffusion gradient per TR. Transverse magnetisation is not spoiled at the end
of each TR. A short TR leads to magnetization that persists and evolves over
multiple TRs, generating a signal which is very sensitive to flip angle (b –
left). At low flip angles (b – middle), $$$B_1^+$$$-inhomogeneity leads to high
signal at the brain centre, low signal near the edge. High flip angle datasets
(b – right) have the opposite distribution. We can utilize these two datasets
to obtain high signal across the whole brain. (b) shows signal change
(CNR).

Figure 2: DW-SSFP diffusion attenuation is dependent on the
flip angle (a). In non-Gaussian systems, this will give rise to flip angle
dependent ADC estimates (b). From experimental DW-SSFP data acquired at
multiple flip angles in a post-mortem brain (c), we observe an increased ADC with
flip angle over the corpus callosum (d – blue crosses). By fitting a model of
non-Gaussian diffusion which is able to explain this variation in ADC (d –
orange line), we can simulate the ADC at any flip angle. Alternatively, using our framework^{9}, ADCs can be defined in terms
of an effective b-value.

Figure 3: PDD estimates for a single post-mortem brain with
(top) and without (bottom) signal-weighting and a noise-floor correction. Here, three different axial slices (a,b and
c) are shown (denoted in the coronal slice on the left). We observe that
by incorporating signal weighting and a noise-floor correction, we generate
improved coherence estimates, particularly within superior (a) and inferior (c)
regions of the brain (white arrows). These areas are associated with very low $$$B_{1}^{+}$$$ and low signal in the 24^{o} dataset.

Figure 4: Angular uncertainty estimates of the PDD over
white matter as a function of $$$B_{1}^{+}$$$. By incorporating signal weighting and a noise-floor correction (orange lines),
we observe a reduction in the angular uncertainty, most notable in areas of low/high
$$$B_{1}^{+}$$$, associated with low signal in the 24^{o}/94^{o}
datasets. Error bars denote the standard error in the PDD angular uncertainty,
but are generally too small to be easily visible.

Figure 5: L_{1} maps in a single brain with/without noise-floor
correction. ADC estimates are generally higher at 94^{o} vs 24^{o},
consistent with Fig. 2b. By adding in a noise-floor correction, we reduce the
bias on ADC estimates in some areas (visible in the difference maps). This is
most notable in deep grey matter (green arrows), where ADC estimates are more
consistent with the surrounding tissue. However, in areas of very low signal,
the noise-floor correction generates spuriously high ADC estimates (pink
arrows), leading to artefacts which propagate into $$$b_{eff}=7600s/mm^2$$$.