Noninvasive determination of electrical properties of tissues and materials using magnetic resonance measurements
A plurality of stimulations is transmitted to tissue or other material using one or more transmitters. The plurality of signals associated with the excited tissue and the transmitted stimulations are measured. The measured signals are processed to generate field-related quantities, such as B1+ and/or MR signal maps. Field-related quantities are generated also from simulation, by calculating the one or more incident fields from a simulator model of the one or more transmitters and assuming a given distribution of electrical properties in the tissue or other material. Field-related quantities generated from simulation and experimental procedures are compared to each other. The assumed electrical properties distribution is updated and the procedure is repeated iteratively until the difference between simulated and experimental field-related quantities is smaller than a threshold.
1. A method for determining at least one electrical property of at least one target, comprising:
transmitting, to the at least one target, a plurality of stimulations via one or more transmitters,
measuring signals associated with the stimulated target,
processing the measured signals to obtain electromagnetic field-related quantities,
generating a numerical model of incident electromagnetic fields of the one or more transmitters,
using the numerical model to calculate a first simulated electromagnetic field distribution in the at least one target based on initially estimated or otherwise assigned values of electrical properties of the at least one target,
generating simulated electromagnetic field-related quantities from the first simulated electromagnetic field distribution,
evaluating whether a difference between the electromagnetic field-related quantities obtained from processing of the measured signals and the simulated electromagnetic field-related quantities generated from the first simulated electromagnetic field distribution exceeds a threshold, and
when the difference exceeds the threshold:
using the numerical model to calculate a second simulated electromagnetic field distribution after adjusting one or more estimated values of electrical properties of the at least one target,
generating simulated electromagnetic field-related quantities from the second simulated electromagnetic field distribution, and
evaluating whether a difference between the electromagnetic field-related quantities obtained from processing of the measured signals and the simulated electromagnetic field-related quantities generated from the second simulated electromagnetic field distribution exceeds the threshold,
iteratively performing one or more of the above steps until the difference is less than or equal to the threshold.
2. The method of claim 1 , further comprising:
upon determining that the electromagnetic field-related quantities obtained from processing the measured signals are equivalent to the simulated electromagnetic field-related quantities, generating at least one map or image of the at least one electrical property of the at least one target.
3. The method of claim 1 , wherein the simulated electromagnetic field-related quantities are generated by defining basis functions to model incident electromagnetic fields of the one or more transmitters, and calculating an electromagnetic field distribution in the at least one target from the incident electromagnetic fields and estimated values of electrical properties of the at least one target.
4. The method of claim 1 , wherein the at least one target is a human tissue or non-tissue material.
5. The method of claim 1 , wherein the plurality of stimulations are RF excitations.
6. The method of claim 1 , wherein the electromagnetic field-related quantities include at least one of B1+ or an MR signal map.
7. The method of claim 1 , wherein using the numerical model comprises using the numerical model together with global Maxwell's equations.
8. A non-transitory computer readable medium including instructions thereon that are accessible by a processing arrangement, wherein, when the processing arrangement executes the instructions, the processing arrangement is configured to:
cause one or more transmitters to transmit, to at least one target, a plurality of stimulations,
measure signals associated with the stimulated target,
process the measured signals to obtain electromagnetic field-related quantities,
generate a numerical model of incident electromagnetic fields of the one or more transmitters,
use the numerical model to calculate a first simulated electromagnetic field distribution in the at least one target based on initially estimated or otherwise assigned values of electrical properties of the at least one target,
generate simulated electromagnetic field-related quantities from the first simulated electromagnetic field distribution,
evaluate whether a difference between the electromagnetic field-related quantities obtained from processing of the measured signals and the simulated electromagnetic field-related quantities generated from the first simulated electromagnetic field distribution exceeds a threshold, and
when the difference exceeds the threshold:
use the numerical model to calculate a second simulated electromagnetic field distribution after adjusting one or more estimated values of electrical properties of the at least one target,
generate simulated electromagnetic field-related quantities from the second simulated electromagnetic field distribution, and
evaluate whether a difference between the electromagnetic field-related quantities obtained from processing of the measured signals and the simulated electromagnetic field-related quantities generated from the second simulated electromagnetic field distribution exceeds the threshold,
iteratively perform one or more of the above steps until the difference is less than or equal to the threshold.
9. The computer readable medium of claim 8 , wherein the processing arrangement is further configured to:
upon determining that the electromagnetic field-related quantities obtained from processing the measured signals are equivalent to the simulated electromagnetic field-related quantities, generate at least one map or image of the at least one electrical property of the at least one target.
10. The computer readable medium of claim 8 , wherein the simulated electromagnetic field-related quantities are generated by defining basis functions to model incident electromagnetic fields of one or more transmitters, and using the model to calculate an electromagnetic field distribution in the at least one target from the incident electromagnetic fields.
11. The computer readable medium of claim 8 , wherein the signals are detected in at least one radiofrequency receiver coil.
12. The computer readable medium of claim 8 , wherein the at least one target is a human tissue or non-tissue material.
13. The computer readable medium of claim 8 , wherein the numerical model is used together with global Maxwell's equations.
14. A system for determining at least one electrical property of at least one target, comprising:
one or more transmitters configured to transmit a plurality of stimulations to the at least one target,
a signal detector configured to measure signals associated with the stimulated target,
a computing device configured to:
process the measured signals to obtain electromagnetic field-related quantities, and
generate a numerical model of incident electromagnetic fields of the one or more transmitters,
use the numerical model to calculate a first simulated electromagnetic field distribution in the at least one target based on initially estimated or otherwise assigned values of electrical properties of the at least one target,
generate simulated electromagnetic field-related quantities from the first simulated electromagnetic field distribution,
evaluate whether a difference between the electromagnetic field-related quantities obtained from processing of the measured signals and the simulated electromagnetic field-related quantities generated from the first simulated electromagnetic field distribution exceeds a threshold, and
when the difference exceeds the threshold:
use the numerical model to calculate a second simulated electromagnetic field distribution after adjusting one or more estimated values of electrical properties of the at least one target,
generate simulated electromagnetic field-related quantities from the second simulated electromagnetic field distribution, and
evaluate whether a difference between the electromagnetic field-related quantities obtained from processing of the measured signals and the simulated electromagnetic field-related quantities generated from the second simulated electromagnetic field distribution exceeds the threshold,
iteratively perform one or more of the above steps until the difference is less than or equal to the threshold.
15. The system of claim 14 , wherein the computing device is configured to:
upon determining that the electromagnetic field-related quantities obtained from processing the measured signals are equivalent to the simulated electromagnetic field-related quantities, generating at least one map or image of the at least one electrical property of the at least one target.
16. The system of claim 14 , wherein the computing device is configured to use the numerical model together with global Maxwell's equations.