Scientists, clinicians, and researchers interested in electrical conductivity imaging of tissues using only MR phase, and the conductivity distribution in neurovascular diseases.One of the ultimate goals of electrical conductivity ($$$\sigma$$$) imaging is to use the conductivity maps of tissues for clinical diagnosis. There has been several case studies that have shown promising results for the conductivity maps of ischemic stroke¹, brain tumors², pelvic tumors³, and breast cancer⁴. Recently proposed generalized phase based electrical conductivity imaging method⁵ (generalized phase based EPT) brings us one step further to the ultimate goal, and paves the way for fast and reliable electrical conductivity reconstruction compared to the conventional phase based EPT method^6-8. This is because the method eliminates the boundary artifact issue in the conventional method, and also is more robust against noise. To explore the clinical applicability of this method, this study investigates the electrical conductivity reconstructions made by the proposed method for two patients with neurovascular diseases in the subacute phase, i.e. hemorrhagic and ischemic stroke.

The governing equation of the generalized phased based EPT is given as

$$$-c\nabla^2\rho+(\nabla\phi^{tr}\cdot\nabla\rho)+\nabla^{2}\phi^{tr}\rho-2\omega\mu_0=0$$$

where $$$\rho=\frac{1}{\sigma}$$$ (resistivity), c is the constant diffusion coefficient, $$$\phi^{tr}$$$ is the measured MR transceive phase, $$$\omega$$$ is the Larmor frequency, and $$$\mu_0$$$ is the free space permeability. This equation is in the form of convection-reaction-diffusion equation, and is solved for $$$\rho$$$ using finite difference scheme, i.e. partial derivatives are represented with central finite difference formulations. Final matrix equation constructed for the region of interest (ROI) is solved using Dirichlet boundary condition. Detailed theoretical explanation of this method can be found in (5). This study was approved by our Institutional Review Board, and informed consent were filled by the patients. In the first case, a 52-year-old woman with hemorrhage in the right hemisphere, near the lateral ventricle, was scanned seven days after hemorrhage. In the second case, a 50-year-old man with ischemia in the right cerebellum and the right posterior cerebral artery territory was scanned seven days after the infarction. Examinations for the conductivity measurement were performed on 3T Siemens Tim Trio MR scanner (Erlangen, Germany) using a quadrature body coil and 12-channel receive only phased array head coil. The transceive phase was acquired using 3D balanced SSFP sequence (with the parameters of FA=40 deg, TE/TR=2.32/4.64ms, FOV=200x200x187.2 mm (1.56x1.56x1.56 mm), NEX=5, total scan time~6min) for both cases. Along with these scans, we had also cranial CT, T2-weighted FLAIR images for the first case, and DWI/ADC images for the second case, which had been gathered for the clinical diagnosis in the first day of strokes in Ankara Ataturk Training and Research Hospital Emergency Department.

In the first case, a hyperdense region at the high frontal level in the right hemisphere appears in CT image (Fig. 1a). This lesion is consistent with acute phase intra-parenchymal hematoma with penumbral edema. The same lesion also appears in the T2/FLAIR image (Fig. 1b) with more heterogonous interior. Fig. 1d shows the reconstructed conductivity distribution of the corresponding slice. Although the conductivity of the surrounding edema region is found to be increased, the hematoma region itself depicts conductivity values similar to that of brain tissue. In the second case, on the other hand, the patient has two separate infarcts, one in the left cerebellum and the other in the occipital lobe. Fig. 2b and c show a constrained diffusion region in the DWI and ADC images acquired during acute phase, respectively. This indicates acute infarction. Fig 2e shows the reconstructed conductivity map of the corresponding slice. Conductivity value increases consistent with the lesion both in location and heterogeneity. Similar findings are also observed in Fig. 3 which is given for the occipital lesion.In this study, generalized phase based EPT method was applied to two different cases of neurovascular disease. In the case of subacute ischemic stroke, conductivity was found to be increased in the lesion area. In the case of subacute hematoma, on the other hand, conductivity distribution of the hematoma itself is found to be not significantly different from the brain tissue. Although in acute phase, hemorrhage may cause increased conductivity, in subacute phase this may not be so due to clot formation. These results indicate promising potential for clinical use of the generalized phase based EPT method, provided acute phase strokes are studied as future work.