Purpose: To develop a fast, practically applicable, and boundary artifact free electrical conductivity imaging method that does not use transceive phase assumption, and that is more robust against the noise. Theory: Starting from the Maxwell's equations, a new electrical conductivity imaging method that is based solely on the MR transceive phase has been proposed. Different from the previous phase based electrical properties tomography (EPT) method, a new formulation was derived by including the gradients of the conductivity into the equations. Methods: The governing partial differential equation, which is in the form of a convection-reaction-diffusion equation, was solved using a three-dimensional finite-difference scheme. To evaluate the performance of the proposed method numerical simulations, phantom and in vivo human experiments have been conducted at 3T. Results: Simulation and experimental results of the proposed method and the conventional phase-based EPT method were illustrated to show the superiority of the proposed method over the conventional method, especially in the transition regions and under noisy data. Conclusion: With the contributions of the proposed method to the phase-based EPT approach, a fast and reliable electrical conductivity imaging appears to be feasible, which is promising for clinical diagnoses and local SAR estimation.
INTRODUCTIONImaging electrical properties (EPs, conductivity ðsÞ and permittivity ðeÞ) of tissues can potentially be useful in several applications. For example, conductivity is a key parameter in the calculation of the specific absorption rate (SAR) map of a patient, which is a crucial issue at high field MRI. Additionally, EPs can be used for diagnostic purposes. In in vivo studies, especially in oncology, it has been shown that the conductivity of a tumor region increases (1-3). Furthermore, EPs may also be used in therapy monitoring (or planning) such as transcranial magnetic stimulation (TMS) (4), hyperthermia treatment (5), and radiofrequency (RF) ablation (6).Over the years, many methods have been proposed to image EPs at various frequencies. For low-frequency applications (1 kHz to 1 MHz), electrical impedance tomography (EIT) and magnetic induction tomography (MIT) have been developed to calculate EPs (7-12). In these methods, sinusoidal currents are either injected into tissue through surface electrodes (EIT) or induced in the tissue using external coils (MIT), and induced voltages are measured between surface electrodes. The current-voltage data sets are used to calculate impedance maps, but the resulting images lack spatial resolution because of the insensitivities of the surface measurements to inner regions. To improve the spatial resolution, magnetic resonance electrical impedance tomography (MREIT) has been proposed (13)(14)(15)(16)(17)(18)(19)(20). In MREIT, additional magnetic field is generated by injecting currents into the tissue through surface electrodes, and this additional magnetic field is then measured using an MRI scanner to reconstruct ...