Observation of the correlation between Electrical Conductivity and Apparent Diffusion Coefficient values
Sung-Min Gho1, Jaewook Shin1, Min-Oh Kim1, Min Jung Kim2, Sooyeon Kim2, Jun-Hyeong Kim1, and Dong-Hyun Kim1

1School of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea, Republic of, 2Department of Radiology, Yonsei University College of Medicine, Seoul, Korea, Republic of

### Synopsis

Electric conductivity and apparent diffusion coefficient (ADC) give meaningful information to the clinicians and researchers, however, studies related to the relationship of these two phenomena were not substantially proceeded.

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

### Purpose

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 properties1,2. 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).

### Methods

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 = 120o, voxel size = 2 x 2 mm2, slice thickness = 4 mm) and single-shot EPI based DWI (TR = 3300 ms, TE = 90 ms, flip angle = 90o, 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 phase3,4. 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.

### Results

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 studies1,2.

### Discussion

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 studies1,2. 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 transfer9,10. 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.

### Acknowledgements

No acknowledgement found.

### References

1. Hancu I, Roberts JC, Bulumulla S, et al. On conductivity, permittivity, apparent diffusion coefficient, and their usefulness as cancer markers at MRI frequencies. Magn Reson Med. 2015;73:2025-2029.

2. Kim MJ, Kim SY, Kim DH, et al. Correlation between the electric conductivity measured by MREPT and apparent diffusion coefficient in invasive breast cancer. Proc Intl Soc Mag Reson Med. 2015. p.3307.

3. Katcher U, Voigt T, Findeklee C, et al. Determination of electrical conductivity and local SAR via B1 mapping. IEEE Trans Med Imaging. 2009;28:1365-1374.

4. Voigt T, Katcher U, Doessel O. Quantitative conductivity and permittivity imaging of the human brain using electric properties tomography. Magn Reson Med. 2011;66:456-466.

5. van Lier AL, Raaijmakers A, Voigt T, et al. Electrical properties tomography in the human brain at 1.5, 3, and 7T: a comparison study. Magn Reson Med. 2014;71:354-363.

6. Helenius J, Soinne L, Perkiö J, et al. Diffusion-weighted MR imaging in normal human brains in various age groups. AJNR Am J Neuroradiol. 2002;23(2):194-199.

7. Annet L, Duprez T, Grandin C, et al. Apparent diffusion coefficient measurements within intracranial epidermoid cysts in six patients. Neuroradiology. 2002;44(4):326-328.

8. McKnight AL, Kugel JL, Rossman PJ, et al. MR elastography of breast cancer: preliminary results. AJR Am J Roentgenol. 2002;178(6):1411-1417.

9. van Lier AL, de Bruin PW, Aussenhofer SA, et al. 23Na-MRI and EPT: Are sodium concentration and electrical conductivity at 298 MHz (7T) related? Proc Intl Soc Mag Reson Med. 2013. p.115.

10. Doneva M, Katscher U, Stehning C, et al. 3D fast spin echo acquisition for combined amide proton transfer and elecric properties tomography. Proc Intl Soc Mag Reson Med. 2013. p.4237.

11. Pethig R, Kell DB. The passive electrical properties of biological systems: their significance in physiology, biophysics and biotechnology. Phys Med Biol. 1987. 32(8):933-970.

### Figures

Figure 1. Phantom results. (a): phantom design, (b): magnitude image, (c): ADC map, (d): conductivity map, and (e): correlation between conductivity and ADC.

Figure 2. Brain results. (a): ADC map, (b): conductivity map, and (c): correlation between conductivity and ADC in GM and WM regions.

Figure 3. (a): T2-weighted FSE, (b): T1-weighted fat-suppressed contrast-enhanced image, (c): ADC map, (d) conductivity map, (e): correlation between conductivity and ADC.

Table 1. Literature conductivity values in brain regions.

Table 2. Literature ADC values in brain regions.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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