Systems and methods for spatial gradient-based electrical property properties tomography using magnetic resonance imaging
Systems and methods for producing an image of the electrical properties of an object using magnetic resonance imaging (“MRI”) are provided. The electrical properties are determined based on estimated gradient values of the electrical properties of the object. For instance, electrical property maps are reconstructed using a spatial integration on gradient values that are estimated from the magnitude and relative phase values derived from measurements of multiple transmit and receive B 1 fields. Specific absorption rate (“SAR”) maps can also be produced based on the estimated electrical properties.
1. A method for measuring electrical properties of a tissue using a magnetic resonance imaging (MRI) system, the steps of the method comprising:
a) directing the MRI system to acquire B 1 + map data for each channel in a multichannel transmitter while a subject is present in the MRI system;
b) directing the MRI system to acquire a B 1 − map data for each channel in a multichannel receiver while the subject is present in the MRI system;
c) generating from the acquired B 1 + map data, B 1 + field magnitude map and a B 1 + relative phase map for each channel in the multichannel transmitter;
d) generating from the acquired B 1 − map data, a B 1 − field magnitude map and a B 1 − relative phase map for each channel in the multichannel receiver;
e) estimating a spatial gradient value that is based on a spatial gradient of electrical properties of the tissue, the spatial gradient value being estimated from the derived B 1 + field magnitude maps, B 1 + relative phase maps, B 1 − field magnitude maps, and B 1 − relative phase maps;
f) estimating electrical property values in the subject by spatially integrating the estimated spatial gradient values; and
g) generating a report comprising an image that depicts a spatial distribution of the computed electrical property values in the subject.
2. The method as recited in claim 1 , wherein the multichannel transmitter and the multichannel receiver comprise a multichannel transceiver.
3. The method as recited in claim 1 , wherein step f) includes spatially integrating the estimated gradient values to calculate logarithm values of complex permittivity values in the subject, and computing the electrical property values includes calculating the complex permittivity values from the logarithm values.
4. The method as recited in claim 3 , wherein step f) includes determining at least one of conductivity values and permittivity values in the subject based on the calculated complex permittivity values.
5. The method as recited in claim 1 , wherein the estimated gradient values are spatially integrated in step f) using at least one of a finite difference method, a finite element method, and a layer potential method.
6. The method as recited in claim 5 , wherein step f) includes assigning known electrical property values to at least one seed point before spatially integrating the estimated gradient values.
7. The method as recited in claim 1 , wherein step f) includes estimating the electrical property values for at least one seed point before spatially integrating the estimated spatial gradient values.
8. The method as recited in claim 1 , wherein step e) includes solving a set of equations that relates the derived B 1 + field magnitude maps, B 1 + relative phase maps, B 1 − field magnitude maps, and B 1 − relative phase maps to the gradient value that is based on a complex permittivity, which is an unknown in the set of equations.
9. The method as recited in claim 1 , wherein the B 1 + map data acquired for a given channel in the multichannel transmitter in step a) includes a series of images acquired while transmitting only on the given channel in the multichannel transmitter and receiving on all channels in the multichannel receiver.
10. The method as recited in claim 9 , wherein the series of images is acquired using a nominal flip angle of around ten degrees.
11. The method as recited in claim 1 , wherein the B 1 − map data acquired for a given channel in the multichannel receiver in step b) includes a series of images acquired while transmitting on all channels in the multichannel transmitter and receiving only on the given channel in the multichannel receiver.
12. The method as recited in claim 11 , wherein the series of images is using a nominal flip angle of around ninety degrees.
13. The method as recited in claim 1 , wherein the B 1 − field magnitude maps generated in step d) are proton density-weighted B 1 − field magnitude maps, and step d) includes removing the proton density weighting based on estimated proton density values in the subject.
14. The method as recited in claim 1 , further comprising providing a flip angle map, and wherein step c) includes using the provided flip angle map to generated the B 1 + field magnitude map from the acquired B 1 + map data, and step d) includes using the provided flip angle map to generated the B 1 − field magnitude map from the acquired B 1 − map data.
15. The method as recited in claim 1 , further comprising calculating a local specific absorption rate (SAR) distribution in the subject based on the electrical property values computed in step f).
16. The method as recited in claim 15 , further comprising estimating a temperature distribution in the subject due to the local SAR distribution, and using at least one of the calculated local SAR distribution and the estimated temperature distribution to guide an optimization of an MRI pulse sequence design.
17. The method as recited in claim 1 , wherein the report generated in step g) also provides information associating the estimated electrical properties with a pathological state of tissues in the subject.
18. The method as recited in claim 1 , wherein the report generated in step g) also provides an indication of whether tissues in the subject are cancerous based on the estimated electrical properties.
19. The method as recited in claim 1 , further comprising estimating at least one of:
a B 1 + absolute phase distribution from the generated B 1 + magnitude maps and B 1 + relative phase maps; and
a B 1 − absolute phase distribution from the generated B 1 − magnitude maps and B 1 − relative phase maps.
20. The method as recited in claim 1 , further comprising producing a radio frequency (RF) hyperthermia treatment plan based on the report generated in step g).
21. The method as recited in claim 1 , further comprising generating a report that indicates a pathological state of a tissue or anatomical structure; wherein the report is generated based on the estimated spatial gradient values.