Conductivity and Permittivity Image Reconstruction at the Larmor Frequency Using MRI

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This paper presents a new method of providing both conductivity ($\sigma$) and permittivity ($\epsilon$) images at the MR Larmor frequency in magnetic resonance electrical property tomography (MREPT), a relatively new MR-based electrical tissue property imaging modality. In MREPT, the RF coil of the MR scanner is used to feed a sinusoidal current at the Larmor frequency, $\omega/2\pi$ (approximately 128 MHz for a 3 Tesla MRI machine), to an imaging object within the MR scanner. Inside the object, this injection current induces a time-harmonic magnetic field, $\mathbf{H}=(H_x,H_y,H_z)$, that is influenced by the body's admittivity distribution, $\gamma=\sigma+i\omega\epsilon$, via Maxwell's equations. Currently, the positive rotating field, $H^+=(H_x+iH_y)/2$, is the only measurable quantity which can be obtained from $B_1$ mapping techniques. The inverse problem of MREPT is to reconstruct $\gamma$ from the $H^+$ data. Existing MREPT reconstruction methods use the local homogeneity assumption ($\nabla\gamm...