Local Maxwell Tomography

Local Maxwell Tomography

Maxwell’s equations dictate the relationship between the electrical conductivity and permittivity of a body and the curvature of electromagnetic fields applied to that body. Our Local Maxwell Tomography technique uses MR-based measurements of local field curvature to derive unknown electrical property distributions, effectively inverting Maxwell’s equations. This has been attempted in the past using surface-measurement-based approaches such as Electrical Impedance Tomography (EIT), but all such surface-based techniques are fundamentally ill-posed and none have proven to be practical for routine use. MR provides cross-sectional information about selected magnetic field distributions, and this has recently been leveraged in the low-frequency MREIT technique (which solves for conductivity based on the fields produced by applied currents) or the Larmor-frequency Electrical Properties Tomography (EPT) technique (which uses field curvature to estimate RF conductivity and permittivity). However, certain key information, such as the distribution of absolute RF phase and magnetization, is missing from MR-based measurements, forcing EPT to rely upon symmetry assumptions which break down at high frequency – precisely where accurate electrical property determination is most critical. LMT begins by dividing true RF magnetic fields into products of coil-dependent measurable quantities (such as B1(+) amplitude and relative phase) and coil-independent unknowns such as absolute reference phase and magnetization. Plugging these fields into suitable formulations of Maxwell’s equations (such as generalized Helmholtz equations) and inserting measured field-related quantities enables simultaneous solution for electrical permittivity and conductivity together with missing gradients of absolute RF phase and magnetization density. Use of complementary field/sensitivity information from a sufficient number of transmit and receive coil elements renders solution of the resulting local matrix equations unique. This approach eliminates symmetry assumptions associated with EPT, and enables electrical property mapping at arbitrary field strength for a wide range of coil configurations.

Principal Investigator: 
Daniel Sodickson

Sponsors

Latest Updates

06/23/2017 - 10:49
06/23/2017 - 10:42

Philanthropic Support

We gratefully acknowledge generous support for radiology research at NYU Langone Medical Center from:
 
• The Big George Foundation
• Raymond and Beverly Sackler
• Bernard and Irene Schwartz

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