A Method for Electrical Property Tomography Based on a Three-Dimensional Integral Representation of the Electric Field

Eda, Naohiro; Fushimi, Motofumi; Hasegawa, Keisuke; Nara, Takaaki

doi:10.1109/tmi.2021.3139455

Cited by 5 publications

(6 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, in TP reconstructions, the measured temperature and the introduced heat flux respectively correspond to the magnetic and electric fields in MREPT. Based on this analogy, we extended our previously reported technique for MREPT (Eda et al 2021) in this study to TP reconstructions. However, there are two differences between TP and EP reconstructions.…”

Section: Resultsmentioning

confidence: 90%

“…In order to derive the integral representations of the relative heat flux δJ(r, t), we first decompose δJ(r, t) by Helmholtz decomposition (Kustepeli 2016, Freeden andGerhards 2019) in Ω given by δJ(r, t) = δJ sol (r, t) + δJ irr (r, t), where δJ sol and δJ irr are the solenoidal and irrotational components of δJ, respectively. It is shown in (Eda et al 2021) that δJ irr (r, t) can be expressed by the following two different integral representations:…”

Section: Reconstruction Of Blood Perfusion Rate Based On Helmholtz De...mentioning

confidence: 99%

“…In the socalled magnetic resonance electrical properties tomography (MREPT) (Katscher et al 2022), EPs such as electrical conductivity and permittivity are reconstructed from the magnetic field measured using MRI by solving Maxwell's equations. We have previously proposed a method (Eda et al 2021) for MREPT based on Helmholtz decomposition of the electric field without the Laplacian computation of the magnetic field or the need to assume EP distributions. We extend this method for EP reconstructions to TP reconstructions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Magnetic resonance imaging of blood perfusion rate based on Helmholtz decomposition of heat flux

Eda,

Nara

2024

Phys. Med. Biol.

Self Cite

View full text Add to dashboard Cite

Objective: Thermal property (TP) maps of human tissues are useful for tumor treatment and diagnosis. In particular, the blood perfusion rate is significantly different for tumors and healthy tissues. Noninvasive techniques that reconstruct TPs from the temperature measured via magnetic resonance imaging (MRI) by solving an inverse bioheat transfer problem have been developed. A few conventional methods can reconstruct spatially varying TP distributions, but they have several limitations. First, most methods require the numerical Laplacian computation of the temperature, and hence they are sensitive to noise. In addition, some methods require the division of a region of interest (ROI) into sub-regions with homogeneous TPs using prior anatomical information, and they assume an unmeasurable initial temperature distribution. We propose a novel robust reconstruction method without the division of an ROI or the assumption of an initial temperature distribution. Approach: The proposed method estimates blood perfusion rate maps from relative temperature changes. This method avoids the computation of the Laplacian by using integral representations of the Helmholtz decomposition of the heat flux. Main Result: We compare the reconstruction results of the conventional and proposed methods using numerical simulations. The results indicate the robustness of the proposed method. Significance: This study suggests the feasibility of thermal property mapping with MRI using the robust proposed method.

show abstract

Section: Resultsmentioning

confidence: 90%

Section: Reconstruction Of Blood Perfusion Rate Based On Helmholtz De...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Magnetic resonance imaging of blood perfusion rate based on Helmholtz decomposition of heat flux

Eda,

Nara

2024

Phys. Med. Biol.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Nevertheless, since

B_{z}

information is required to solve the full Helmholtz equation, it may still be difficult to apply the method in practice for phase‐based EPT reconstruction algorithms. Thus, for applications, it would be worthwhile to investigate the methods of composing the physics‐driven loss by (1) utilizing modified equations with their underlying assumptions (e.g., piece‐wise assumption or neglecting

B_{z}

component), (2) partially combining the network with the physics equation included in estimating

B_{z}

(Eda et al, 2022; Guo et al, 2017), or (3) applying iterative integral based EPs estimation methods (Balidemaj et al, 2015b; Giannakopoulos et al, 2021).…”

Section: Discussionmentioning

confidence: 99%

Data‐driven electrical conductivity brain imaging using 3 T MRI

Jung

Mandija

Cui

et al. 2023

Human Brain Mapping

View full text Add to dashboard Cite

Magnetic resonance electrical properties tomography (MR‐EPT) is a non‐invasive measurement technique that derives the electrical properties (EPs, e.g., conductivity or permittivity) of tissues in the radiofrequency range (64 MHz for 1.5 T and 128 MHz for 3 T MR systems). Clinical studies have shown the potential of tissue conductivity as a biomarker. To date, model‐based conductivity reconstructions rely on numerical assumptions and approximations, leading to inaccuracies in the reconstructed maps. To address such limitations, we propose an artificial neural network (ANN)‐based non‐linear conductivity estimator trained on simulated data for conductivity brain imaging. Network training was performed on 201 synthesized T2‐weighted spin‐echo (SE) data obtained from the finite‐difference time‐domain (FDTD) electromagnetic (EM) simulation. The dataset was composed of an approximated T2‐w SE magnitude and transceive phase information. The proposed method was tested three in‐silico and in‐vivo on two volunteers and three patients' data. For comparison purposes, various conventional phase‐based EPT reconstruction methods were used that ignore magnitude information, such as Savitzky–Golay kernel combined with Gaussian filter (S‐G Kernel), phase‐based convection‐reaction EPT (cr‐EPT), magnitude‐weighted polynomial‐fitting phase‐based EPT (Poly‐Fit), and integral‐based phase‐based EPT (Integral‐based). From the in‐silico experiments, quantitative analysis showed that the proposed method provides more accurate and improved quality (e.g., high structural preservation) conductivity maps compared to conventional reconstruction methods. Representatively, in the healthy brain in‐silico phantom experiment, the proposed method yielded mean conductivity values of 1.97 ± 0.20 S/m for CSF, 0.33 ± 0.04 S/m for WM, and 0.52 ± 0.08 S/m for GM, which were closer to the ground‐truth conductivity (2.00, 0.30, 0.50 S/m) than the integral‐based method (2.56 ± 2.31, 0.39 ± 0.12, 0.68 ± 0.33 S/m). In‐vivo ANN‐based conductivity reconstructions were also of improved quality compared to conventional reconstructions and demonstrated network generalizability and robustness to in‐vivo data and pathologies. The reported in‐vivo brain conductivity values were in agreement with literatures. In addition, the proposed method was observed for various SNR levels (SNR levels = 10, 20, 40, and 58) and repeatability conditions (the eight acquisitions with the number of signal averages = 1). The preliminary investigations on brain tumor patient datasets suggest that the network trained on simulated dataset can generalize to unforeseen in‐vivo pathologies, thus demonstrating its potential for clinical applications.

show abstract

“…The use of EPT has been proposed to compute the electrical permittivity and conductivity based on the Helmholtz equation. The manipulation of the Helmholtz equation leads to a representation of the conductivity and permittivity in relation to the Laplacian of the magnetic field |B1| 11 , 12 . This method requires a condition in which the gradient of the sum of permittivity and conductivity is zero.…”

Section: Introductionmentioning

confidence: 99%

Correlation analysis between the complex electrical permittivity and relaxation time of tissue mimicking phantoms in 7 T MRI

Hernández

Kim

2022

Sci Rep

View full text Add to dashboard Cite

Dielectric relaxation theory describes the complex permittivity of a material in an alternating field; in particular, Debye theory relates the time it takes for an applied field to achieve the maximum polarization and the electrical properties of the material. Although, Debye’s equations were proposed for electrical polarization, in this study, we investigate the correlation between the magnetic longitudinal relaxation time T1 and the complex electrical permittivity of tissue-mimicking phantoms using a 7 T magnetic resonance scanner. We created phantoms that mimicked several human tissues with specific electrical properties. The electrical properties of the phantoms were measured using bench-test equipment. T1 values were acquired from phantoms using MRI. The measured values were fitted with functions based on dielectric estimations, using relaxation times of electrical polarization, and the mixture theory for dielectrics. The results show that, T1 and the real permittivity are correlated; therefore, the correlation can be approximated with a rational function in the case of water-based phantoms. The correlation between index loss and T1 was determined using a fitting function based on the Debye equation and mixture theory equation, in which the fraction of the materials was taken into account. This phantom study and analysis provide an insight into the application relaxation times used for estimating dielectric properties. Currently, the measurement of electrical properties based on dielectric relaxation theory is based on an antenna, sometimes invasive, that irradiates an electric field into a small sample; thus, it is not possible to create a map of electrical properties for a complex structure such as the human body. This study could be further used to compute the electrical properties maps of tissues by scanning images and measuring T1 maps.

show abstract

A Method for Electrical Property Tomography Based on a Three-Dimensional Integral Representation of the Electric Field

Cited by 5 publications

References 29 publications

Magnetic resonance imaging of blood perfusion rate based on Helmholtz decomposition of heat flux

Magnetic resonance imaging of blood perfusion rate based on Helmholtz decomposition of heat flux

Data‐driven electrical conductivity brain imaging using 3 T MRI

Correlation analysis between the complex electrical permittivity and relaxation time of tissue mimicking phantoms in 7 T MRI

Contact Info

Product

Resources

About