Systems and methods 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:

apply, via one or more coils, an ultra-short echo time (TE) pulse sequence in a Magnetic Resonance Imaging (MRI) system;

acquire, via one or more receivers, a complex B 1 + B 1 − quantity from an object following the application of the ultra-short TE pulse sequence, where B 1 + is a complex value of a transmit radio-frequency (RF) magnetic field and B 1 − is a complex value of a receive RF magnetic field;

estimate one or more electrical properties including a permittivity and conductivity of the object using the complex values of the transceive field B 1 + B 1 − ; and

reconstruct an image of the permittivity and conductivity of the object using the estimated one or more electrical properties, wherein the image is reconstructed using a single MRI acquisition.

2. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to estimate the one or more electrical properties using the following:

For permittivity

ɛ

r

≈

-

1

μɛ

0

⁢

ω

2

⁢

Re

⁡

(

∇

2

⁢

B

1

+

⁢

B

1

-

B

1

+

⁢

B

1

-

)

For conductivity

σ

≈

-

1

μω

⁢

Im

⁡

(

∇

2

⁢

B

1

+

⁢

B

1

-

B

1

+

⁢

B

1

-

)

where k 2 is a complex wave vector, Re is the real component of the complex B 1 + B 1 − quantity, Im is the imaginary component of the complex B 1 + B 1 − quantity, B 1 + is the complex amplitude of the transmit RF magnetic field at a given three dimensional location and B 1 − is the complex amplitude of the receive RF magnetic field.

3. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to produce the ultra-short TE pulse sequence as the rotating ultra-fast imaging sequence (RUFIS).

4. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to use as the ultra-short TE pulse sequence a pulse sequence having an echo time below 1 millisecond, non-selective excitations of about 12 microseconds and incremental gradient updates.

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

6. The non-transitory computer readable storage medium of claim 1 , wherein the instructions command the processor to calculate a √{square root over (B 1 + B 1 − )} complex quantity to estimate the one or more electrical properties of the object.

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

applying, with one or more coils, an ultra-short echo time (TE) pulse sequence in a Magnetic Resonance Imaging (MRI) system;

acquiring, with one or more receivers, a complex B 1 + B 1 − quantity from an object following the application of the ultra-short TE pulse sequence, where B 1 + is a complex amplitude of a transmit radio-frequency (RF) magnetic field and B 1 − is a complex amplitude of a receive RF magnetic field;

estimating, with a processor, one or more electrical properties including a permittivity and conductivity of the object using the complex amplitudes of the transmit RF magnetic field and the receive RF magnetic field;

reconstructing an image of the permittivity and conductivity of the object using the estimated one or more electrical properties; and

determining a tissue abnormality using the image of the permittivity and conductivity reconstructed using the one or more estimated electrical properties.

8. The method of claim 7 , wherein the one or more electrical properties are estimated using the following:

For permittivity

ɛ

r

≈

-

1

μɛ

0

⁢

ω

2

⁢

Re

⁡

(

∇

2

⁢

B

1

+

⁢

B

1

-

B

1

+

⁢

B

1

-

)

For conductivity

σ

≈

-

1

μω

⁢

Im

⁡

(

∇

2

⁢

B

1

+

⁢

B

1

-

B

1

+

⁢

B

1

-

)

Where k 2 is a complex wave vector, Re is the real component of the complex B 1 + B 1 − quantity, Im is the imaginary component of the complex B 1 + B 1 − quantity, B 1 + is the complex amplitude of the transmit RF magnetic field at a given three dimensional location and B 1 − is the complex amplitude of the receive RF magnetic field.

9. The method of claim 7 , further comprising using as the ultra-short TE pulse sequence a rotating ultra-fast imaging sequence (RUFIS).

10. The method of claim 7 , further comprising using as the ultra-short TE pulse sequence a pulse sequence having an echo time of below 1 millisecond, non-selective excitations of about 12 microseconds and incremental gradient updates.

11. The method of claim 7 , further comprising calculating a √{square root over (B 1 + B 1 − )} complex quantity to estimate the one or more electrical properties of the object.

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

an imaging portion comprising one or more coils, one or more transmitters, and one or more receivers, the imaging portion configured to generate an MRI transmit B 1 + radio-frequency (RF) magnetic field using the one or more transmitters by applying an ultra-short echo time (TE) pulse sequence to the one or more coils, and acquire receive magnetic resonance (MR) B 1 − RF data from an object using the one or more receivers, where B 1 + is a complex amplitude of the transmit RF magnetic field and B 1 − is a complex amplitude of the receive RF magnetic field; and

a processing portion having an electrical properties estimation module configured to estimate electrical properties including a permittivity and conductivity of the object by acquiring a complex B 1 + B 1 − quantity resulting from the ultra-short TE pulse sequence and to reconstruct an image of the permittivity and conductivity of the object using the estimated permittivity and conductivity, wherein the image is reconstructed using a single MRI acquisition.

13. The MRI system of claim 12 , wherein the electrical properties estimation module is further configured to estimate the one or more electrical properties using the following:

For permittivity

ɛ

r

≈

-

1

μɛ

0

⁢

ω

2

⁢

Re

⁡

(

∇

2

⁢

B

1

+

⁢

B

1

-

B

1

+

⁢

B

1

-

)

For conductivity

σ

≈

-

1

μω

⁢

Im

⁡

(

∇

2

⁢

B

1

+

⁢

B

1

-

B

1

+

⁢

B

1

-

)

Where k 2 is a complex wave vector, Re is the real component of the complex B 1 + B 1 − quantity, Im is the imaginary component of the complex B 1 + B 1 − quantity, B 1 + is the complex amplitude of the transmit RF magnetic field at a given three dimensional location and B 1 − is the complex amplitude of the receive RF magnetic field.

14. The MRI system of claim 12 , wherein the electrical properties estimation module is further configured to use as the ultra-short TE pulse sequence a rotating ultra-fast imaging sequence (RUFIS).

15. The MRI system of claim 12 , wherein the electrical properties estimation module is further configured to use as the ultra-short TE pulse sequence a pulse sequence having an echo time of less than 1 millisecond, non-selective excitations of about 12 microseconds and incremental gradient updates.

16. The MRI system of claim 12 , wherein the imaging portion is configured to generate an MRI transmit B 1 + radio-frequency (RF) magnetic field using one or more transmitters by applying a single pulse sequence.

17. The MRI system of claim 12 , wherein the imaging portion is configured to generate an MRI transmit B 1 + radio-frequency (RF) magnetic field using a plurality of transmitters in a parallel transmit operation.

18. The MRI system of claim 12 , wherein the imaging portion is configured to generate an MRI transmit B 1 + radio-frequency (RF) magnetic field using one or more transmitters by applying a single pulse sequence for permittivity or conductivity reconstruction, wherein the single pulse sequence is gradient echo.