Introduction

Electrical tissue conductivity has the potential to become a quantitative diagnostic parameter, particularly for the characterization of brain^1,2 and breast tumors^3,4. These studies typically show an increase of tissue conductivity with tumor malignancy. However, a high conductivity per se is no indication for abnormal tissue, i.e., many tissue types are highly conductive without being abnormal. An empirical rule correlates tissue conductivity with tissue water content W^5,6. One possibility to analyze abnormality of tissue is thus to compare tissue conductivity as measured (σ_meas) with tissue conductivity as expected from tissue water content (σ_exp). The obtained difference yielding a “normalized” conductivity σ_norm = σ_meas - σ_exp might serve as a more direct measure of tissue abnormality. In this study, the concept of normalized conductivity is presented and illustrated by in vivo cases.

Theory and Methods

Electrical tissue conductivity σ_meas can be estimated from the transceive phase φ of a SSFP image via σ_meas(φ) = Δφ / (2μ₀ω) with Δ the Laplacian operator, μ₀ the magnetic vacuum permeability, and ω the Larmor frequency (“Electrical Properties Tomography”, EPT)⁷. The tissue water content W can be estimated from the magnitude M of a SSFP image due its joined dependence on T₁⁸. Combining these two features results in a relation σ_exp(M). A typical example σ_exp(M) for a healthy brain region is shown in Fig. 1, revealing

σ_exp(M)=a/(1+b/(M-c)) (1)

in line with the previously reported relation M(W)^5,6. Once σ_exp(M) is fitted, the normalized conductivity is calculated voxel-by-voxel via σ_norm = σ_meas - σ_exp as mentioned above. The three constants in Eq. (1) (a adjusting global scaling, b adjusting curvature, c adjusting shift in M direction) depend on acquisition parameters and have to be fitted for each measurement individually. Ideally, this fit is performed on the healthy part of the brain only. In practice, however, it is sufficient to perform the fit on the whole brain including both, abnormal and healthy tissue, since much less voxels with abnormal than healthy tissue are typically found, which are thus not able to alter the fit significantly.
To validate the approach, four subjects of a study published earlier were revisited¹, where SSFP measurements (TR/TE = 3.5 ms/1.7 ms, α = 25°, acquired voxel size = 1.3 × 1.2 × 1 mm³, acquisition time = 3:40 min) were performed on a commercial 3T MR system (Achieva TX, Philips Medical Systems, Best, the Netherlands) with a standard 32-channel RF head coil. For subject 1 and subject 2, the approach of normalized conductivity was applied to normal-appearing brain tissue. For subject 3, the approach was applied to cystic metastasis, and for subject 4, the approach was applied to radiation necrosis and edema.

Results

Figure 2 compares σ_meas , σ_exp , and σ_norm for the two examples of normal-appearing brain regions, showing σ_norm close to zero throughout the FOV. Figure 3 compares σ_meas , σ_exp , and σ_norm for the two pathologic examples, showing a pronounced increase of σ_norm within the pathologic areas, while the contrast of the remaining brain structure is almost gone.

Discussion

The relationship between tissue conductivity / SSFP signal on one hand and tissue water content on the other hand opens up the possibility to normalize measured conductivity by the conductivity expected empirically due to tissue water content. The resulting normalized conductivity might be able to depict pathologic tissue areas more clearly, and thus could be helpful to identify such areas.
More dedicated sequences for tissue water content determination are available⁵, but would require additional scan time for the additional, dedicated sequence, and also bearing the risk of registration issues between the separate scans of determining conductivity and water content. In this study, SSFP has been used to estimate water content, which might be less accurate than using a dedicated sequence. However, it has the invaluable advantage that both, water content and conductivity, can be derived from the same image. Thus, the described normalization can be performed voxel-by-voxel in a straight-forward manner, and comes without additional scan time.

Conclusion

Normalizing measured tissue conductivity by the conductivity expected empirically from tissue water content has the potential to yield a new quantitative tissue parameter. Its diagnostic usefulness to support identification of pathologic areas shall be subject to future, systematic studies, also investigating the physiologic and biochemical background of the approach in more detail.

Acknowledgements

The authors thank Christian Stehning for fruitful discussions.