Synopsis

MR-Electrical Properties Tomography (MR-EPT) can provide accurate mean conductivity values in large homogeneous tissues such as the white matter, provided sufficient erosion to avoid boundary regions. Water-content-EPT (wEPT) has been recently proposed to reconstruct EPs on a voxel-to-voxel basis. However, wEPT uses an empirical model calibrated with literature EPs values, assumed correct, obtained from ex-vivo probe measurements. In this work, the validity of the model employed in wEPT is verified for white matter conductivity reconstructions by using in the wEPT model calibration the mean white matter conductivity value obtained from in-vivo MR-EPT reconstructions as an independent modality.

Introduction

MR-Electrical Properties Tomography (MR-EPT) aims to reconstruct tissue Electrical Properties (EPs: conductivity σ, permittivity ε_r) from complex $$$B_1^+$$$ field maps. However, MR-EPT reconstructions can only be used to compute mean EPs values in large volumetric areas¹, since they suffer from noise amplification and errors at tissue boundaries.

In parallel, water-content-EPT (wEPT) has been recently proposed to reconstruct EPs on a voxel-to-voxel basis from water-content maps. However, wEPT uses an empirical model² calibrated with literature EPs values, assumed correct, obtained from ex-vivo probe measurements. Here, the validity of wEPT is verified for white matter conductivity reconstructions (σ_WM) using in the wEPT model calibration the mean σ_WM value obtained from in-vivo MR-EPT reconstructions as an independent modality.

Methods

MR-measurements (3T, Achieva, Philips, NL) were performed on eight healthy volunteers using an 8-channel transmit/receive head coil (Fig.1: sequence parameters and equations).

MR-EPT reconstructions³ were performed according to eqs.[1-2]. The $$$B_1^+$$$ magnitude was measured with the AFI sequence⁴. For the $$$B_1^+$$$ phase, the transceive phase assumption⁵ was adopted (eq.[3]). RF phase maps were obtained by combining two phase maps acquired using two Spin-Echo sequences with opposite readout gradient polarities (eq.[4]). Gibbs ringing correction and k-space Gaussian apodization were also performed⁶.

wEPT reconstructions were performed as in ref.(2). Eq.[5] was used to compute water-content maps (W) from image-ratio maps (I_r: division of two T₁-weighted Spin-Echo maps with different TRs). Then, EPs maps were derived from water-content maps according to eqs.[6-7]. The parameters c_1/2/3/p_1/2/3 were calibrated using literature EPs values (first analysis), or the mean σ_WM value among subjects obtained from independent MR-EPT reconstructions (second analysis).

First analysis: the accuracy (eqs.[8-9]) of MR-EPT and wEPT reconstructions was assessed for WM, GM, and CSF (Fig.2) with respect to literature values. For MR-EPT reconstructions, a 2D-derivative kernel (K₇: 7×7 voxels) was used⁶. wEPT reconstructions were performed according to eqs.[6-7], whose parameters were calibrated using literature EPs values².

Second analysis: we verified eq.[6] of wEPT for the WM using independent MR-EPT reconstructions. First, MR-EPT reconstructions were performed using both K₇ and a smaller kernel (K₃, del2 Matlab function). Then, WM erosion of 2 voxels was performed to avoid regions affected by boundary errors (Fig.2). The mean MR-EPT-σ_WM value was therefore computed among the subjects ($$$σ_{WM-Eroded}^{MREPT}$$$). Finally, this $$$σ_{WM-Eroded}^{MREPT}$$$ value (average among subjects) was used to recalibrate the wEPT model parameters c_1/2/3. Mean wEPT-σ_WM values were recomputed for all subjects and compared with the values previously obtained from the wEPT model calibrated with the literature-σ_WM value.

Results and Discussion

First analysis: Fig.3 shows MR-EPT and wEPT reconstructions. Tab.1 reports mean EPs and standard deviations values for the GM, WM, and CSF tissue. MR-EPT conductivity reconstructions are not accurate on a voxel-to-voxel basis, as shown in ref.(6). The mean MR-EPT-σ_WM value among subjects is 0.4 S/m (~20% overestimation compared to the literature value). MR-EPT-σ_GM and MR-EPT-σ_CSF values are underestimated due to severe boundary errors. MR-EPT permittivity reconstructions are not feasible.

wEPT allows more spatial details than MR-EPT in less scan time, and the reconstructed EPs values agree with literature values (∆σ_%,∆ε_%<5%).

Second analysis: after WM erosion, $$$σ_{WM-Eroded}^{MREPT}$$$ values are: 0.31±0.23 and 0.31±1.00 S/m for K₇ and K₃, respectively (Tab.2). K₃ reconstructions are less noise-robust than K₇ reconstructions, but allow less boundary error extension. The good agreement between K₇ and K₃ reconstructions indicates that the performed erosion was sufficient to avoid boundary errors. Still, the reconstructed $$$σ_{WM-Eroded}^{MREPT}$$$ values show ~10% underestimation compared to the literature-σ_WM value. This can be attributed to the use of 2D derivative kernels. Additionally, the observed high standard deviations indicate low precision. Thus, the observed variability in mean MR-EPT-σ_WM values can not be linked to inter-subject variations.

Mean wEPT-σ_WM values reconstructed using $$$σ_{WM-Eroded}^{MREPT}$$$ in the calibration of eq.[6] show an underestimation of ~10% with respect to the mean wEPT-σ_WM values reconstructed in the first analysis (wEPT model calibrated with literature EPs values). The ~10% underestimation in the mean wEPT-σ_WM values is, however, just a consequence of the bias introduced by the use of 2D kernels in the $$$σ_{WM-Eroded}^{MREPT}$$$ reconstructions. This verifies the validity of the wEPT model calibrated using literature EPs values for the WM region. Unfortunately, since this erosion can not be applied for the GM and CSF due to their limited spatial extension, this verification can not be performed in these regions.

Conclusions

Acknowledgements

References

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