Synopsis

Keywords: Gray Matter, Relaxometry

Non-exponential transverse relaxation in the brain’s basal ganglia has been investigated in theoretical studies but little evidence from in-vivo MRI data exists in support of this behaviour. Here, we provide experimental observation of non-exponential transverse relaxation in-vivo MRI data in the basal ganglia at 3T. The strongest deviations from exponential behaviour take place in the iron-rich pallidum and substantia nigra. Our results suggest that water diffusion through the inhomogeneous magnetic field induced by paramagnetic iron deposits may be at the source of non-exponential transverse relaxation in the basal ganglia.

Introduction

Theoretical studies of the effect of magnetic material within brain tissue (e.g. iron-loaded cells) anticipate a transition from a Gaussian transverse relaxation at short echo times to an exponential decay at long echo times^1–5. However, little experimental evidence exists in support of non-exponential transverse relaxation in in-vivo data of the basal ganglia, and the exponential decay rate R₂* remains the primary measure to monitor microscopic brain changes in these iron-rich structures^6,7.
Two mechanisms exist that describe the biophysics of non-exponential relaxation in iron-rich grey matter. In the static dephasing regime (SDR), water diffusion is negligible and transverse relaxation is driven by the volume of dephased spins around the magnetic perturbers, which increases with the echo time^1,2. In the diffusion narrowing regime (DNR), transverse relaxation is driven by water diffusion between magnetic perturbers^2–5. The relative contribution of these two regimes to transverse relaxation was examined in an ex-vivo study of the substantia nigra⁶.
Here, we provide experimental evidence of non-exponential MRI transverse relaxation in basal ganglia data acquired in-vivo at 3T. We provide estimates of the Gaussian and exponential decay rates at short and long echo times and investigate which of the SDR or DNR may be the cause of this behaviour.

Theory

The signal decay can be expressed using the following Padé approximation of the crossover from Gaussian to exponential transverse relaxation:
$$S=exp\left [-\frac{<\Omega^{2}>{T_{E}}^{2}}{2\left (1+\frac{<\Omega^{2}>}{2R_{2}^{*}}T_{E} \right )} \right ] \ \ \ \ \ \ \ \ [1]$$
where $$$<\Omega^{2}>$$$ is the mean square frequency deviation due to the field inhomogeneities induced by the magnetic material and $$$T_{E}$$$ is the echo time of the MRI data. $$$S \sim e^{-\frac{1}{2}<\Omega^{2}>T_{E}^{2}}$$$ at short echo times ($$$T_{E}<<\frac{2R_{2}^{*}}{<\Omega^{2}>}$$$) and $$$S \sim e^{-R_{2}^{*}T_{E}} $$$ at long echo times ($$$T_{E}>>\frac{2R_{2}^{*}}{<\Omega^{2}>}$$$) .

Within the basal ganglia, the magnetic material is assumed to consist of randomly distributed iron-rich spherical cells that occupy a fraction $$$\zeta$$$ of the voxel volume and have a characteristic frequency deviation $$$\delta\omega$$$. The following equations link the MRI signal and the properties of the magnetic material: $$$<\Omega^{2}>=0.8\zeta\delta\omega^{2}$$$; $$$R_{2}^{*}=A\zeta\delta\omega$$$ in the SDR ¹ and $$$R_{2}^{*}=B\zeta\delta\omega^{2}\tau$$$ in the DNR, where $$$\tau=\frac{R^{2}}{6D}$$$ is the time scale for water molecules to diffuse away from magnetic perturbers, $$$D$$$ is the water diffusion coefficient^3–5. For spherical perturbers $$$A=1.209$$$ and $$$B=1.920$$$^1,3–5. The dimensionless parameter $$$\alpha=\sqrt{<\Omega^{2}>}\tau$$$ represents the dephasing due to the field inhomogeneities during $$$\tau$$$. $$$\alpha<<1$$$ ensures the validity of the DNR regime².

Methods

The study was approved by the local ethics committee. 3D FLASH data was collected on 5 human subjects (2 females, mean 33 y.o.) with a 3T Prisma Siemens MRI scanner. 16 gradient-echo images were acquired with a bipolar readout ( $$$T_{E}$$$=1.25 to 19.25 ms, 1.2 ms spacing). Image resolution was 1.2mm isotropic. To minimize the spurious effect of cardiac pulsation, data acquisition was suspended during the systole of the cardiac cycle⁸.
The data was fitted with Eq. [1] to obtain estimates of $$$<\Omega^{2}>$$$ and $$$R_{2}^{*}$$$. From the values of $$$R_{2}^{*}$$$ and the expression of the decay rate in the SDR, we computed estimates of bulk magnetic susceptibility $$$\zeta\Delta \chi =\zeta\delta\omega*\frac{3}{\gamma B_{0}}$$$. From the values of $$$<\Omega^{2}>$$$ and $$$R_{2}^{*}$$$, we estimated $$$\delta\omega$$$ and $$$\zeta$$$ in the SDR and $$$\zeta\delta\omega^{2}$$$ and $$$\tau$$$ in the DNR. From the values of $$$<\Omega^{2}>$$$ and $$$\tau$$$, we estimated the parameter $$$\alpha$$$ in the DNR.

Results

The log-signal decays in the basal ganglia (Fig. 1) show a transition between a quadratic dependence at short times and a linear dependence at long times, characteristic of the effect of paramagnetic inclusions². The $$$R_{2}^{*}$$$ and $$$<\Omega^{2}>$$$ are highest in the iron-rich substantia nigra and pallidum (Fig. 2 and Table 1). The estimates of $$$\zeta\Delta \chi $$$, shown in Fig. 3 for the pallidum, are in good agreement with the literature (e.g. 0.13 ppm⁹).
Separate estimation of $$$\delta\omega$$$ and $$$\zeta$$$ under the assumption of the SDR leads to an overestimation of $$$\zeta$$$ (~0.05) compared to literature values⁹ (Fig. 4a). Under the assumption of the DNR (Fig. 4b), the value of the parameter $$$\tau$$$ is ~1 ms and the value of $$$\alpha$$$ (Fig. 4b ~0.1-0.2) is consistent with the assumptions of the DNR ($$$\alpha << 1$$$).

Discussion

In the basal ganglia, transverse relaxation shows a transition between Gaussian and exponential behaviours consistent with the effects of the paramagnetic iron deposits present within the tissue. The strongest deviations from exponential behaviour take place in the iron-rich substantia nigra and pallidum regions. To investigate the microscopic mechanisms at the source of this behaviour, the parametric fitting estimates of the signal decay were linked to the properties of iron deposits under the assumption of the SDR and DNR. Our results suggest that water diffusion through the inhomogeneous magnetic field induced by paramagnetic iron deposits may be the mechanism underlying our findings, in-line with recent literature⁹. However, the transition times between the Gaussian and exponential behaviours lie near the shortest echo times of our data, which may prevent the accurate characterization of the Gaussian curvature with the parametric fitting approach used here⁹. Alternative fitting procedures should therefore be considered.

Conclusions

We provide experimental evidence of non-exponential decay in in-vivo gradient-echo MRI data of the basal ganglia at 3T. This behaviour may result from the presence of iron deposits distributed within the tissue.

Acknowledgements

No acknowledgement found.

References

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