TY - JOUR
T1 - Noninvasive Estimation of Electrical Properties from Magnetic Resonance Measurements via Global Maxwell Tomography and Match Regularization
AU - Serrallés, Jose E.C.
AU - Giannakopoulos, Ilias I.
AU - Zhang, Bei
AU - Ianniello, Carlotta
AU - Cloos, Martijn A.
AU - Polimeridis, Athanasios G.
AU - White, Jacob K.
AU - Sodickson, Daniel K.
AU - Daniel, Luca
AU - Lattanzi, Riccardo
N1 - Publisher Copyright:
© 1964-2012 IEEE.
PY - 2020/1
Y1 - 2020/1
N2 - Objective: In this paper, we introduce global Maxwell tomography (GMT), a novel volumetric technique that estimates electric conductivity and permittivity by solving an inverse scattering problem based on magnetic resonance measurements. Methods: GMT relies on a fast volume integral equation solver, MARIE, for the forward path, and a novel regularization method, match regularization, designed specifically for electrical property estimation from noisy measurements. We performed simulations with three different tissue-mimicking numerical phantoms of different complexity, using synthetic transmit sensitivity maps with realistic noise levels as the measurements. We performed an experiment at 7 T using an eight-channel coil and a uniform phantom. Results: We showed that GMT could estimate relative permittivity and conductivity from noisy magnetic resonance measurements with an average error as low as 0.3% and 0.2%, respectively, over the entire volume of the numerical phantom. Voxel resolution did not affect GMT performance and is currently limited only by the memory of the graphics processing unit. In the experiment, GMT could estimate electrical properties within 5% of the values measured with a dielectric probe. Conclusion: This work demonstrated the feasibility of GMT with match regularization, suggesting that it could be effective for accurate in vivo electrical property estimation. GMT does not rely on any symmetry assumption for the electromagnetic field, and can be generalized to estimate also the spin magnetization, at the expense of increased computational complexity. Significance: GMT could provide insight into the distribution of electromagnetic fields inside the body, which represents one of the key ongoing challenges for various diagnostic and therapeutic applications.
AB - Objective: In this paper, we introduce global Maxwell tomography (GMT), a novel volumetric technique that estimates electric conductivity and permittivity by solving an inverse scattering problem based on magnetic resonance measurements. Methods: GMT relies on a fast volume integral equation solver, MARIE, for the forward path, and a novel regularization method, match regularization, designed specifically for electrical property estimation from noisy measurements. We performed simulations with three different tissue-mimicking numerical phantoms of different complexity, using synthetic transmit sensitivity maps with realistic noise levels as the measurements. We performed an experiment at 7 T using an eight-channel coil and a uniform phantom. Results: We showed that GMT could estimate relative permittivity and conductivity from noisy magnetic resonance measurements with an average error as low as 0.3% and 0.2%, respectively, over the entire volume of the numerical phantom. Voxel resolution did not affect GMT performance and is currently limited only by the memory of the graphics processing unit. In the experiment, GMT could estimate electrical properties within 5% of the values measured with a dielectric probe. Conclusion: This work demonstrated the feasibility of GMT with match regularization, suggesting that it could be effective for accurate in vivo electrical property estimation. GMT does not rely on any symmetry assumption for the electromagnetic field, and can be generalized to estimate also the spin magnetization, at the expense of increased computational complexity. Significance: GMT could provide insight into the distribution of electromagnetic fields inside the body, which represents one of the key ongoing challenges for various diagnostic and therapeutic applications.
KW - Electrical properties mapping
KW - global Maxwell tomography
KW - inverse scattering
KW - match regularization
UR - http://www.scopus.com/inward/record.url?scp=85077174792&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85077174792&partnerID=8YFLogxK
U2 - 10.1109/TBME.2019.2907442
DO - 10.1109/TBME.2019.2907442
M3 - Article
C2 - 30908189
AN - SCOPUS:85077174792
SN - 0018-9294
VL - 67
SP - 3
EP - 15
JO - IEEE Transactions on Biomedical Engineering
JF - IEEE Transactions on Biomedical Engineering
IS - 1
M1 - 8673893
ER -