System and method for determining electrical properties using magnetic resonance imaging

1. A non-transitory computer readable storage medium for estimating electrical properties of an object using a processor, the non-transitory computer readable storage medium including instructions to command the processor to:

determine a magnitude of a Magnetic Resonance Imaging (MRI) B 1 + field applied to an object;

determine a phase of the MRI B 1 + field applied to the object;

combine the determined magnitude and phase to determine a complex B 1 + field estimate;

estimate one or more electrical properties of the object using the complex B 1 + field estimate by directly solving at least one discrete difference equation, wherein a spatial variation of the complex B 1 + field is defined with respect to the one or more electrical properties; and

display an image of the one or more electrical properties of the object.

2. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to reconstruct the image of the electrical properties of the object.

3. The non-transitory computer readable medium of claim 1 , wherein the one or more electrical properties comprise a conductivity or a permittivity of a tissue or a sample.

4. The non-transitory computer readable medium of claim 1 , wherein the difference equation is a discrete Laplacian equation and the instructions command the processor to estimate a Laplacian using the discrete Laplacian equation.

5. The non-transitory computer readable medium of claim 4 , wherein the instructions command the processor to estimate the Laplacian using a curve fitting.

6. The non-transitory computer readable medium of claim 4 , wherein the instructions command the processor to estimate the Laplacian using a multi-dimensional fitting.

7. The non-transitory computer readable storage medium of claim 4 , wherein the instructions command the processor to calculate the discrete Laplacian equation on a plurality of scales.

8. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to perform B 1 + mapping using a Bloch-Siegert shift to determine the magnitude of the MRI B 1 + field.

9. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to remove a system introduced linear phase shift when determining the phase of the MRI B 1 + field.

10. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to divide a central axial plane image into a plurality of segments and use average pixel values to replace all pixel values within at least one of the plurality of segments.

11. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to estimate heating effects due to radio frequency from the MRI B 1 + field using the one or more estimated electrical properties.

12. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to determine a tissue abnormality using the one or more estimated electrical properties.

13. The non-transitory computer readable storage medium of claim 1 , wherein the MRI B 1 + field comprises a transmit field with B 1 + data.

14. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to determine the magnitude and phase, combine the determined magnitude and phase, and estimate one or more electrical properties using B 1 − data.

15. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to determine the complex B 1 + field estimate using B 1 + maps from (i) at least one of a single transmitter or a single receiver of an MRI system applying the MRI B 1 + field, (ii) a plurality of transmitters or receivers of the MRI system or (iii) a combination of (i) and (ii).

16. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to directly solve the at least one discrete difference equation without the use of receiver sensitivity information.

17. A method for non-invasively imaging tissue properties, the method comprising:

generating Magnetic Resonance Imaging (MRI) B 1 + maps to determine a magnitude of an MRI B 1 + field applied to a subject using a plurality of Bloch-Siegert phase shift images;

generating MRI phase maps to determine a phase estimate of the MRI B 1 + field applied to the subject using real and imaginary images of the subject;

combining the determined magnitude and phase to determine a complex B 1 + field estimate;

estimating one or more tissue properties of the subject using the complex B 1 + field estimate and a discrete set of Laplacian equations, wherein a spatial variation of the complex B 1 + field is defined with respect to the one or more tissue properties; and

displaying an image of the one or more tissue properties of the subject.

18. The method of claim 17 , further comprising acquiring spin echo images to generate the MRI phase maps.

19. The method of claim 18 , further comprising removing a system introduced phase shift to determine a subject induced phase variation in the spin echo images.

20. The method of claim 17 , wherein estimating one or more tissue properties of the subject further comprises calculating a Laplacian on a plurality of scales using the discrete set of Laplacian equations.

21. The method of claim 17 , wherein estimating one or more tissue properties further comprises calculating at least one of a permittivity or a conductivity of tissue of the subject.

22. The method of claim 17 , wherein the one or more tissue properties comprise electrical properties and further comprising reconstructing the electrical properties by calculating an average value of the electrical properties in each of a plurality of segments of a region of interest of the subject and using an average value to replace all of the values for pixels within each segment.

23. The method of claim 17 , wherein estimating the one or more tissue properties of the subject estimates the discrete set of Laplacian equations without the use of receiver sensitivity information.

24. A Magnetic Resonance Imaging (MRI) system comprising:

an imaging portion configured to generate an MRI B 1 + field using one or more transmitters and acquire magnetic resonance (MR) B 1 + data from an object using one or more receivers;

a processing portion having an electrical properties estimation module configured to estimate electrical properties of the object by determining a magnitude of the MRI B 1 + field applied to the object, determining a phase of the MRI B 1 + field applied to the object, combining the determined magnitude and phase to determine a complex B 1 + field estimate and estimating one or more electrical properties of the object using the complex B 1 + field estimate by directly solving at least one discrete difference equation, wherein a spatial variation of the complex B 1 + field is defined with respect to the one or more electrical properties; and

a display device configured to display an image of the electrical properties of the object.

25. The MRI system of claim 24 , wherein the processing portion is further configured to use transmit field B 1 + data of the MRI B 1 field to estimate the one or more electrical properties.

26. The MRI system of claim 24 , wherein the processing portion is further configured to use receive field B 1 − data to estimate the one or more electrical properties.

27. The MRI system of claim 24 , wherein the processing portion is further configured to perform B 1 + mapping using a Bloch-Siegert shift to determine the magnitude of the MRI B 1 + field.

28. The MRI system of claim 24 , wherein the processing portion is further configured to determine the complex B 1 + field estimate using B 1 + maps from (i) at least one of a single transmitter of the one or more transmitters or a single receiver of the one or more receivers, (ii) a plurality of the one or more transmitters or receivers or (iii) a combination of (i) and (ii).

29. The MRI system of claim 24 , wherein the processing portion is configured to directly solve the at least one discrete difference equation without the use of receiver sensitivity information.