Patent ID: 7603158

Claim:
A method of non-invasive imaging of electrical impedance of an object, comprising the steps of: a) making measurements of at least two nonparallel current density vector fields, {right arrow over (J)} 1 (x,y,z) and {right arrow over (J)} 2 (x,y,z), within a region of interest in the object by utilizing an apparatus for inducing current in the object and simultaneously using a magnetic resonance imaging (MRI) system to synchronously apply a magnetic resonance imaging sequence to the object and using image data detected by the MRI system to measure a magnetic field created by the current induced in the object, and using a computer device to calculate said at least two nonparallel current density vector fields, {right arrow over (J)} 1 (x,y,z) and {right arrow over (J)} 2 (x,y,z); b) utilizing a computer device to directly calculate, without iteration a logarithmic gradient of local conductivity,∇ ln σ(x, y, z), within the region of interest without requiring an electric potential value using a formula ∇ ln ⁢ ⁢ σ = ( ∇ × J 2 ) · ( J 1 × J 2 )  J 1 × J 2  2 ⁢ J 1 + ( ∇ × J 1 ) · ( J 2 × J 1 )  J 1 × J 2  2 ⁢ J 2 + ( ∇ × J 1 ) · J 2  J 1 × J 2  2 ⁢ J 1 × J 2 ( 1 ) where J 1 ={right arrow over (J)} 1 (x,y,z), J 2 ={right arrow over (J)} 2 =(x, y, z), and ∇ lnσ=∇ lnσ(x,y,z), and where J 1 and J 2 are a pair of measured nonparallel current densities at point (x,y,z) and ∇ denotes a gradient operator; and c) producing a conductivity image based on the calculated logarithmic gradient of local conductivity within the region of interest.