Electrical conductivity is a measure of material's ability to conduct an electric current. The dielectric conductivity can be measured by induced current in response to an applied electric field which is related to the quantity of ions and ion mobility inside the tissues. Diffusion, on the other hand, is based upon the random Brownian motion of water molecules within a voxel of tissue which is also related to the water mobility. Several studies suggest that there are correlations between these two properties^1,2. However, the relationship between these two properties which is largely based on different mechanisms is not clear.

In this abstract, we observe and investigate the correlation between conductivity and ADC under various situations (i.e. phantom, in vivo healthy brain, and breast tumor).

1) Data acquisition

Figure 1a shows the phantom design. The phantom was composed of various NaCl and agar concentration (i.e. NaCl: 0.5%, 1 %, and 1.5%, Agar: 0.5%, 1.5%, and 3%). The phantom and in vivo brain data from healthy volunteers were collected using 3T Siemens Tim Trio MRI scanner. A 2D SE (TR = 1000 ms, TE = 12 ms, flip angle = 120^o, voxel size = 2 x 2 mm², slice thickness = 4 mm) and single-shot EPI based DWI (TR = 3300 ms, TE = 90 ms, flip angle = 90^o, b-value = 0, 800 s/mm², voxel size = 2 x 2 mm², slice thickness = 4 mm, GRAPPA reduction factor = 2) were applied. Breast MRI examinations were performed on a 3T system (MR750, GE Healthcare, Waukesha, WI, USA) with an 8-channel breast receiver coil. T2-weighted fast SE (FSE) axial images (TR = 9100 ms, TE = 100 ms, flip angle = 110°, field of view = 320 mm, matrix size = 416 x 256 pixels, slice thickness = 3 mm) were used and 53 invasive breast cancers larger than 1 cm on T2-weighted FSE were evaluated (we acquired additional patient data compare to the previous study²).

2) Data processing

For conductivity mapping, we employed phase-based electric properties tomography using the SE phase^3,4. A 2D weighted polynomial fitting technique was applied to calculate the second order spatial derivative of phase.

ADC values were calculated by the equation $$$ADC = ln[S2/S1]/(b2-b1)$$$, where S1 is the signal intensity obtained at b = 0 s/mm² and S2 is the signal intensity obtained at b = 800 s/mm². After image reconstruction, we estimate the correlation between conductivity and ADC at each voxel.

Figure 1 represents the phantom results. As the NaCl concentration increases, the estimated conductivity values increases. As the agar concentration increases, ADC values decreases. In this phantom study, the conductivity values depend only on the NaCl concentration and the ADC rely on the agar concentration. Therefore, there seems to be no specific correlation between the conductivity and ADC values in this phantom result.

Figure 2 shows the reconstructed images of the in vivo brain. The estimated conductivity and ADC values represent the positive correlation and this result is similar to the literature values (Table 1 and 2)^4-7.

The representative reconstructed breast tumor images are shown in Figure 3. Negative correlation between the conductivity and ADC is shown, which is consistent with the findings of previous studies^1,2.

A positive correlation between conductivity and ADC can be observed in brain for normal appearing gray (GM) and white matter (WM) while a negative correlation in tumor regions were seen for breast tumors similar to previous studies^1,2. However, a simple phantom experiment can be devised which showed no specific correlation.

Since dense cellular tissues or cellular swelling exhibit lower diffusion coefficients, the high agar concentration in phantom and WM regions which are composed of myelin structures in the brain have decreased the ADC values. Similarly, increased stiffness in breast tumor could have decreased the ADC as well⁸.

Estimated conductivity values are influenced by various components such as proteins and amide proton transfer^9,10. However, tissue boundaries or structures are not influenced in the MR frequency range⁹. Furthermore, conductivity increase in tumors might be from the difference of the water content and sodium concentration including reduced membrane potential¹¹.

Our results show that the correlation between the conductivity and ADC does not simply defined. Additional theoretical and experimental studies will be required for understanding the in-depth mechanism. In practice, these two parameters can provide additional information in characterizing structural changes, disease state, etc.