Methods and systems for generating a conductivity map of an in vivo tissue

1. A non-invasive method of generating a conductivity map of an in vivo tissue, the method comprising:

a) measuring a concentration of a carrier ion in the tissue using magnetic resonance imaging (MRI);

b) measuring a water proton diffusivity (D) in the tissue using diffusion tensor MRI (DT-MRI); and

c) generating a conductivity map of the tissue, using the formula:

σ=( D n q 2 )/ kT

wherein σ is conductivity, D is the water proton diffusivity, n is the concentration of the carrier ion, q is a charge of the carrier ion, k is Boltzmann constant, and T is temperature in degrees Kelvin.

2. The method of claim 1 , wherein the tissue is brain tissue.

3. The method of claim 1 , wherein the tissue is heart tissue.

4. The method of claim 1 , wherein the concentration of the carrier ion and the water proton diffusivity are measured using a single coil.

5. The method of claim 1 , wherein the carrier ion is selected from a sodium ion, a chloride ion, a potassium ion, and a calcium ion.

6. The method of claim 1 , wherein the DT-MRI is performed at 0.3 T.

7. The method of claim 1 , wherein the DT-MRI is performed at 1.5 T.

8. The method of claim 1 , wherein the DT-MRI is performed at 3 T.

9. The method of claim 1 , wherein the DT-MRI is performed at 7 T.

10. The method of claim 1 , wherein the DT-MRI is performed at 9 T.

11. The method of claim 1 , wherein the DT-MRI is performed at 12 T.

12. A system for generating a conductivity map of an in vivo tissue, the system comprising:

a) a magnetic resonance imaging (MRI) device configured to measure a concentration of a carrier ion in the tissue and a water proton diffusivity (D) in the tissue;

b) a processor; and

c) a non-transient memory comprising instructions that, when executed by the processor, cause the processor to generate a conductivity map of the tissue based on measurements from the MRI device, wherein the instructions comprise the formula:

σ=( D n q 2 )/ kT

wherein σ is conductivity, D is the water proton diffusivity, n is the concentration of the carrier ion, q is the charge of the carrier ion, k is Boltzmann constant, and T is temperature in degrees Kelvin.

13. The system of claim 12 , further comprising a data storage that is configured to store conductivity map data.

14. The system of claim 12 , further comprising a user interface and a data connector that transmits data between the processor and the user interface.

15. The system of claim 12 , wherein the MRI device comprises a coil for measuring the concentration of the carrier ion in the tissue.

16. The system of claim 12 , wherein the MRI device comprises electronic devices configured to generate frequencies, gradients and pulses for measuring the concentration of the carrier ion in the tissue.

17. The system of claim 12 , wherein the MRI device comprises a coil for measuring the water proton diffusivity (D) in the tissue.

18. The system of claim 12 , wherein the MRI device comprises a single coil for measuring the concentration of the carrier ion in the tissue and the water proton diffusivity (D) in the tissue.