Introduction

Gliomas are known to show higher electrical conductivity values than the normal brain parenchyma¹. Recently, phase-only Helmholtz-Electrical Property Tomography (PO-HEPT) was employed to distinguish high grade from lower-grade gliomas with high efficiency². However, the validity of the assumptions of PO-HEPT has only been tested on highly symmetrical and homogeneous phantoms. This study aimed to assess whether the PO-HEPT reconstruction had enough sensitivity to accurately report conductivity values in a brain phantom designed to mimic the human brain anatomy, within an off-centre ROI where the transceive phase approximation (TPA) is less accurate, and using a clinically relevant sequence taking less than 3 mins of scan time.

Methods

A brain phantom was designed by segmenting the MRI image of a patient with a glioma. The tissue boundaries were 3D printed with polypropylene, and the CSF, white matter (WM) and grey matter (GM) compartments were filled with a mixture of 2% agarose, demi-water and NaCl to reach the conductivity of the specific tissue type at 128 MHz: 2.1 S/m (CSF), 0.34 S/m (WM) and 0.6 S/m (GM)³. The conductivity of the glioma-compartment was varied from 0.6 S/m to 2 S/m, in steps of 0.2 S/m and consisted of a water-NaCl solution to allow in-situ replacement in the glioma-compartment.

MRI data were acquired on a 3T clinical scanner (Ingenia, Philips, Best, The Netherlands) with a 3D-bSSFP sequence. The scan parameters were: FOV (mm)=240x240x37.5; acquired voxel size (mm)=2x2x1.5; reconstructed voxel size (mm)=1.25x1.25x1.5; flip angle 10 degrees; 16 signal averages; TR/TE=3/1.5 ms; Dummy pulses were included before each acquisition to minimize transient magnetization effects⁴; total scan duration was 2:23 mins. The signal was received with a 32-channel array head coil, while a body coil was used for transmission and phase referencing. The phantom was placed at the centre of the array. The electrical conductivity maps were reconstructed from the phase data and from the homogeneous Helmholtz equation⁵:
$$\sigma = -\frac{1}{\mu_0 \omega} \left(\frac{\nabla^2e^{i\phi+}}{e^{i\phi+}}\right) $$

where ω is the Larmor frequency, μ₀ the magnetic vacuum permeability and φ+ the transmit phase, which was assumed to be φ+= φ±/2 (TPA), where φ± is the transceive phase. The Laplacian was implemented by convolving the phase-data with a 7x3x3 kernel, for in-plane derivatives, and a 5x3x3 kernel for out-of-plane derivatives⁶. Conductivity maps were subsequently convolved with a 2D median filter to mitigate noise-related reconstruction artefacts, and subsequently three ROIs were drawn in the glioma compartment. Finally an additional ROI was placed in the ventricles, and this was used as a control. An ANOVA test with Bonferroni post-hoc correction for multiple comparisons was performed on the eight different glioma-conductivity values, for each different post-processing choice. The same statistical test was used to judge the stability of the method across different acquisitions in the ventricles' ROI.

Results

A picture of the phantom and the acquired magnitude and phase data are shown in Fig.1. Raw and filtered conductivity maps are shown in Fig.2. The accuracy and sensitivity of the method were tested against different choices of ROI and with different median filter sizes. As a “control” to validate the stability of the algorithms for a constant conductivity, the reconstructed conductivity values in the ventricles' ROI was quantified and it showed no significant changes in mean conductivity across different acquisitions, for all sample pairs except for one (Fig. 3). The best results in terms of sensitivity were obtained with ROI1 and a median filter of 4x4 pixels and show that, despite the rather large standard deviation (∼0.2 S/m), the differences in glioma-conductivities were statistically significant also between the two samples which differed only by ∼ 0.1 S/m. The best results in terms of accuracy were obtained with ROI2. However, these results are much less precise (larger standard deviation), due to the leakage of the boundary effects in the ROI. Finally, ROI3, although being far from the boundaries by several pixels (i.e. >> kernel size), was statistically the same as the other two ROI choices.

Discussion

In all ROI analyses, the conductivity was consistently underestimated and the error increased with the nominal conductivity (Fig.4), which is in line with literature⁶. One explanation could be that the TPA deteriorates at the periphery of the FOV, as previously reported^7,8. In one study⁷, when using PO-HEPT, σ underestimated independent conductivity-measurements by approximately 40% in peripheral regions, in agreement with our findings. Additionally, 3D-printed boundaries may have a detrimental effect on the spatial homogeneity of B₀ and B₁, therefore introducing further phase errors. Regardless of the above limitations, PO-HEPT was able to detect statistically significant changes in conductivity across different glioma-samples, thus showing promise of the approach of using3D bSSFP and PO- HEPT for clinical glioma applications¹. We anticipate that the accuracy of the method will improve in an in-vivo experiment, where hard boundaries with abrupt permittivity and magnetic susceptibility changes are absent⁸.

Conclusions

In this study we assessed the sensitivity of phase-only EPT in a realistic brain phantom with a glioma compartment. Despite the rather large σ errors, which we speculated to originate from the partial violation of the TPA phase and phase-only approximations, the method was able to measure significant differences across samples, therefore validating its potential use in the clinic.

Acknowledgements

This work was supported by the Netherlands Organization for Scientific Research (NWO) through a VENI fellowship to L. B (016.Veni.188.040) and to W. B (016.Veni.188.040 and TTW.16820). H. van de Stadt and J. Verhart are acknowledged for assistance in the phantom preparation. J. Bresser provided help in the design of the brain phantom. R. Leijsen is thanked for useful discussions. E. Ercan, T. Ruytenberg and J. Vonk-van Oosten helped with the data acquisition.