To validate the use of water content maps and a priori information to estimate the electrical conductivity and permittivity of brain tissue.

Based on Maxwell's mixture theory we introduced the water content assisted Electrical Properties Tomography (wEPT) method to estimate electrical properties (EPs) maps of brain tissue from water content maps using modeling equations derived from literature data.¹ This study is a continuation to our previous work. We evaluate the capabilities of wEPT by imaging the EPs of a phantom where all its physical parameters are measured and compared with the outcomes of wEPT. The influence of nonuniform flip angle excitations into wEPT is also examined.

Models: Following mixture theory, a correlation between water content and tissue electrical properties has been found.^2,3 To confirm those findings by MRI, we developed a phantom having similar parameters to human brain tissue. A strong electrolyte was created by dissolving NaCl (12.8g/L), KCl (0.224g/L), CaCl (0.294g/L), and MgCl (0.264g/L) in distilled water, which has similar ion concentrations as artificial CSF solutions.^4,5 Whey protein was dissolved in the electrolyte solution (mimicking cells) to prepare 8 different mixtures having 100%, 98%, 90%, 84%, 75%, 70%, 65% and 60% of electrolyte. The EPs of each mixture was measured at 128 MHz (25°C) using a dielectric assessment kit (DAK-SPEAG,Switzerland). The water content of each solution was measured by weight difference (5g) after dehydration at 70°C. A cylindrical phantom was filled with the protein mixtures and measure its T₁ map by multi-point inversion recovery.⁶ The whole measured parameters are summarized in Table 1. From these parameters, we performed a least square fitting procedure to model the electrical conductivity (σ) and relative permittivity (ε_r) in terms of water content (W), obtaining $$\sigma=-7.52W^2+17.1W-7.2 [1]$$ and $$\epsilon_r=-201.9W^2+415.5W-134.4 [2]$$, respectively. Similarly, measured W and T₁ values were related by a fitting function combined with an analytical image ratio, I_r, formed by dividing two spin echo (SE) images, to model W in terms of I_r by $$W=1.74exp^{-1.89I_r} [3]$$, just as described to derive the models for brain tissues.¹

Influence of B₁ Inhomogeneities: The main error contributor in wEPT may be originated by erroneous W measurements. In estimating W by I_r, inhomogeneous 90° excitations can be a concern. By dividing two SE images having the same parameters but one with short TR (TR_s) and the other with long TR (TR_l), the signal intensity of I_r is $$I_r(T_1,θ)=κ(\frac{1-exp^{-TR_s/T_1}}{1-cosθcos(2θ)exp^{-TR_s/T_1}})/(\frac{1-exp^{-TR_l/T_1}}{1-cosθcos(2θ)exp^{-TR_l/T_1}}) [4]$$, where κ is a constant given by the sequence parameters and the signal gain compensations of a particular MRI scanner. The flip angle of RF excitation is represented by θ while the refocusing pulse is considered 2θ. Figure 1 shows the variation of I_r as a function of T₁ and flip angle.

Experiments: We acquired two spin echo images of the phantom at 3T (FOV=220mm, THK=5mm, matrix size=128×128, TE=13ms, FA=90°) with TR_s=0.7s and TR_l=3s to reconstruct its EPs maps. Same scanning parameters were used to acquire brain I_r images of a volunteer and σ and ε_r images were reconstructed following the model equations for human brain wEPT.¹ B₁ map of the brain was also obtained by double angle method to obtain θ.⁶ The W and EPs maps reconstructed by the measured I_r images were compared with the maps reconstructed by the I_r images after B₁-compensation as described in Fig. 1.

Figure 2 shows the resultant wEPT models of the electrolyte-protein phantom together with the reconstructed W and EPs maps. The wEPT-estimated mean values at each phantom compartment are also shown in Table 1. A decent prediction was obtained by wEPT when compared with the bench measurements for all the mixtures. Figure 3 shows the resultant wEPT maps of the volunteer together with its percentage difference images before and after B₁-compensation. The average percentage difference for W-map was 2.6% while for the σ-map was 8.5% and 4.9% for the ε_r-map.

The developed phantom successfully follows the principles of mixture theory. The dielectric parameters of the mixtures decrease as the water content decreases. The modeling equations of this relationship well predicted the measured values. The error contribution due to B₁ inhomogeneities in the brain does not represent a big concern at 3T since the flip angle variations are not substantial.⁷ However, B₁ information should be considered for more accurate EPs estimations especially at peripheral regions. The findings of this study suggest that wEPT maps could represent a good predictor of tissue EPs, encouraging for further clinical studies aiming to find extra contrast information to support clinical diagnosis.