Conductivity and Permittivity Image Reconstruction at the Larmor Frequency Using MRI

MREPT: An overview •Magnetic Resonance Electrical Property Tomography (MREPT) aims to visualize both conductivity σ and permittivity ǫ distributions at the Larmor frequency (≈ 128 MHz for a 3 T MRI). • In MREPT, we feed an ac current at the Larmor frequency through a coil located outside of the imaging object Ω. In Ω, the injected current will induce a magnetic field H = (Hx Hy Hz). For r = (x, y, z) ∈ Ω, H is governed by −∇H(r) = ∇ ln γ(r)× (∇×H(r))− iωμ0γ(r)H(r). (♠) Here, μ0 = 4π × 10 H/m is the magnetic permeability in the free space, γ = σ + iωǫ is the admittivity distribution, where ω is the angular frequency. •Using the B1 mapping method, we can measure the positive rotating magnetic field H = 12(Hx + iHy). •The inverse problem in MREPT is to reconstruct the unknown admittivity distribution γ = σ + iωǫ from the given H data.