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The impact of head orientation with respect to B0: An unexplored source of variance in diffusion MRI1CUBRIC, Cardiff University, Cardiff, United Kingdom, 2Inselspital, Bern University, Bern, Switzerland, 3Australian Catholic University, Melbourne, Australia, 4UMC Utrecht, Utrecht University, Utrecht, Netherlands
Synopsis
Recently observed anisotropy of compartmental white matter T2-values as a function of tissue orientation w.r.t. B0 in combination with echo-time-dependence of diffusion MRI signals suggest that similar tissue-orientational effects could be expected in standard diffusion tensor measures. In this work we show the change of up to 20-30% in diffusion tensor measures as a function of fibre orientation w.r.t. B0 from in vivo experiments and support these observations by simplified two-compartment white matter signal simulations.
Introduction
Several MRI contrasts have shown a dependence on tissue orientation in the MRI scanner w.r.t. $$$\vec{B}_0$$$, including $$$T_2^{(*)}$$$, $$$T_1$$$, magnetisation transfer.1-19 This also implies a dependence on head orientation in measures derived from diffusion MRI (dMRI), where typically only the orientation-dependence w.r.t. the gradient direction is considered. While providing additional information on tissue microstructure, MRI-contrast dependence on head-orientation w.r.t. $$$\vec{B}_0$$$ can also introduce potential variability in the results and as such decrease the statistical power in dMRI studies. In this work, we aim to simulate how diffusion tensor (DT) measures can be affected based on previously reported head-orientation dependence of compartmental $$$T_2$$$20,21, and characterise this dependence in in vivo human brain data at 3T.Theory
Consider a simplified two-compartment model of the diffusion weighted signal in white matter (WM) (no fibre dispersion, long-time limit) as a function of the echo time TE and $$$b$$$-value:$$S(b,\mathbf{g},t)\sim~f\cdot e^{-R_{2,\text{i}}\text{TE}}\cdot~e^{-b\mathbf{g}^T\mathbf{D}_\text{i}\mathbf{g}}+(1-f)\cdot~e^{-R_{2,\text{e}}\text{TE}}\cdot~e^{-b\mathbf{g}^T\mathbf{D}_\text{e}\mathbf{g}}~,\qquad\qquad\qquad(1)$$ where subscripts i/e denote intra-/extra-axonal compartments, respectively, $$$R_2$$$ are the relaxation rates, $$$\mathbf{D}$$$ are diffusion tensors, and $$$f$$$ is intra-axonal signal fraction. Suppose $$$\mathbf{D}_\text{i}$$$ and $$$\mathbf{D}_\text{e}$$$ have equal first eigenvectors (denoted by $$$\mathbf{n}$$$) and parallel&perpendicular eigenvalues $$$D_{\text{i},\parallel}\&D_{\text{i},\bot}=0$$$ and $$$D_{\text{e},\parallel}\&D_{\text{e},\bot}$$$ respectively, the signal can be simplified as
$$S(b,\mathbf{g},t)\sim~f\cdot e^{-R_{2,\text{i}}t}\cdot e^{-b{D}_\text{i}}+(1-f)\cdot~e^{-R_{2,\text{e}}t} \cdot~e^{-b{D}_\text{e}}~,\qquad\qquad\qquad\qquad\qquad(2)$$ where $$$D=D_\bot+(\mathbf{g}\cdot\mathbf{n})(D_\parallel-D_\bot)$$$.
The apparent diffusion coefficient (ADC) is the first order term of the Maclaurin series expansion of $$$\ln(S)$$$ in $$$b$$$:
$$\text{ADC}(\text{TE})=\frac{f\cdot~D_\text{i}\cdot~e^{-R_{2,\text{i}}\text{TE}}+(1-f)\cdot~D_\text{e}\cdot~e^{-R_{2,\text{e}}\text{TE}}}{f\cdot~e^{-R_{2,\text{i}}\text{TE}}+(1-f)\cdot~e^{-R_{2,\text{e}}\text{TE}}}~.\qquad\qquad\qquad\qquad\qquad(3)$$
Recent work suggests that the extra-axonal relaxation rate depends on WM fibre orientation $$$\theta$$$ to the magnetic field and could be described as $$$R_{2,\text{e}}(\theta)=A+B\sin^{4}\theta$$$.20 This orientational dependence of $$$R_{2,\text{e}}(\theta)$$$ will result in orientational dependence of the ADC.
Methods
Data acquisition. Multi-dimensional diffusion-$$$R_2$$$ data were acquired from 5 healthy participants (3 female, 25-31y.o.) on a 3T MRI scanner equipped with a 300mT/m gradient system and a 20ch head/neck receive coil, tiltable about the LR-axis. The acquisition was repeated in default (0°) and tilted (18°) coil-orientations. Acquisition parameters are summarised in Fig.1.Data processing. The data were checked for slice-wise outliers22 and signal drift, corrected for Gibbs ringing23, subject motion, geometrical distortions24-26 and Rician noise bias27-30. DTs were estimated for each $$$\text{TE}$$$ on the $$$b=[0,~750,~1500]\,\text{s}/\text{mm}^2$$$ data (Fig.2), using MRtrix3. Fibre orientation distribution functions (fODF)31,32 were estimated at $$$\text{TE}=54\,\text{ms}$$$ using multi-shell multi-tissue constrained spherical deconvolution33. From the fODFs single-fibre population (SFP) voxels34 with low dispersion (as quantified by $$$p_2$$$35) were identified, and fibre orientations $$$\theta$$$ w.r.t. $$$\vec{B}_0$$$ computed.
Data analysis. Orientational anisotropy was analysed for MD, AD, RD and FA at each echo time by representing the values from SFP voxel by a function of $$$\theta$$$:
$$F(\theta)=A+B\cdot\sin^{2n}\theta,\quad~n=[0,1,2]~,\qquad\qquad\qquad(4)$$
$n=0$ is equivalent to the isotropic case ($$$F(\theta)=A$$$). The rescaled Akaike’s Information Criterion (AIC)36,37, ΔAICrepresentation=AICrepresentation-AICmin, estimated the relative performance of the representations.
Results
Simulations. Fig.3AB shows examples of MD, AD, RD, and FA as a function of fibre orientation $$$\theta$$$ to $$$\vec{B}_0$$$. For the parameter settings investigated, AD and FA increase with $$$\theta$$$ ($$$\hat{B}>0$$$), while RD decreases ($$$\hat{B}<0$$$). The magnitude of the orientational anisotropy, $$$|\hat{B}|$$$, increases with $$$\text{TE}$$$ for all measures (Fig.3C).The resulting behaviour of MD is non-trivial, with possible sign flips of $$$\hat{B}$$$ for increasing $$$\text{TE}$$$.In vivo data. Fig.4 shows DT measures as a function of $$$\theta$$$ ($$$x$$$-axis) and $$$\text{TE}$$$ (columns), where each scatterpoint represents an SFP voxel. The barplots in Fig.5 show isotropic ($$$\hat{A}$$$, first column) or anisotropic ($$$\hat{B}$$$, second column) components for a given measure (rows) for all three representations (Eq.4). Larger $$$\Delta\text{AIC}$$$ values (third column) for the isotropic representation indicate that all measures are better described by anisotropic representations. The anisotropic component $$$B$$$ decreases with increasing $$$\text{TE}$$$ for all DT measures. Its sign is negative for RD and changes from positive to negative for MD and AD, between TE=100ms and TE=150ms. The fibre-orientation-independent component $$$A$$$ (first column, Fig.5) evolves non-linearly as a function of TE for all representation (Eq.4), this effect appeared less pronounced when MD and AD were represented as a function of $$$\theta$$$. Last column in Fig.5 puts the relative anisotropy (B/A,$$$~$$$%) into statistical context, by comparing it to the relative standard deviation of DT measure (std/mean,$$$~$$$%, horizontal bars). The anisotropic effects reached up to 20-30% for some TEs/measures, but were outweighed by noise and anatomical WM variability across the brain at long TEs.
Discussion
We observed a dependence of estimated DT measures on fibre orientation w.r.t. B0. Already in simplified WM simulations, non-trivial orientational effects could be observed (e.g. sign flips in $$$\hat{B}$$$ as a function of TE for MD). The in vivo RD and MD estimates as a function of θ followed trends also seen in simulations, but $$$\hat{B}$$$-components of AD and FA decreased as a function of TE in vivo in contrast to the increase in the toy-example. This could be attributed to the tissue complexity (e.g. dispersion; distribution of diffusivity-T2-values within and across voxels) and noise, amongst others.A tiltable receive coil was used to increase the range of achievable tissue orientations w.r.t. B0. Future work will investigate whether DT measures are significantly altered in the tilted vs non-tilted orientation.
Conclsion
DT measures varied up to B/A=20-30% as a function of WM fibre orientation w.r.t. B0 and are comparable to the corresponding std/mean of MD and AD at lower TEs. Ignoring these effects could lead to misinterpretations in clinical studies.Acknowledgements
CMWT was supported by a Sir Henry Wellcome Fellowship (215944/Z/19/Z) and a Veni grant (17331) from the Dutch Research Council (NWO). DKJ, CMWT, and EK were all supported by a Wellcome Trust Investigator Award (096646/Z/11/Z) and DKJ and EK were supported by a Wellcome Strategic Award (104943/Z/14/Z).
The data were acquired at the UK National Facility for In Vivo MR Imaging of Human Tissue Microstructure funded by the EPSRC (grant EP/M029778/1), and The Wolfson Foundation.
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Figures
DT measures were simulated as a function of orientation θ w.r.t. B0 using Eq.3. The examples in A&B used following parameter settings: A. [Di,$$$\parallel$$$, De,$$$\parallel$$$, De,$$$\bot$$$, f]=[3,2.5,0.8,0.5]; B. [Di,$$$\parallel$$$, De,$$$\parallel$$$, De,$$$\bot$$$, f]=[3,2.5,0.2,0.4].
C. Estimated A and B (Eq.4, n=2) as a function of TE, for a range of scenarios Di,$$$\parallel$$$=3, De,$$$\parallel$$$=[2,2.2,2.4,2.6], De,$$$\bot$$$=[0.2,0.4,0.6,0.8,1], f=[0.1,0.3,0.5,0.7,0.9].
D is in μm2/ms. The settings for R2,i/e(θ) are shown in the plot.
