Electric properties tomography: Biochemical, physical and technical background, evaluation and clinical applications

Developments in Electrical-Property Tomography Based on the Contrast-Source Inversion Method

The main objective of electrical-property tomography (EPT) is to retrieve dielectric tissue parameters from B ^ 1 + data as measured by a magnetic-resonance (MR) scanner. This is a so-called hybrid inverse problem in which data are defined inside the reconstruction domain of interest. In this paper, we discuss recent and new developments in EPT based on the contrast-source inversion (CSI) method. After a short review of the basics of this method, two- and three-dimensional implementations of CSI-EPT are presented along with a very efficient variant of 2D CSI-EPT called first-order induced current EPT (foIC-EPT). Practical implementation issues that arise when applying the method to measured data are addressed as well, and the limitations of a two-dimensional approach are extensively discussed. Tissue-parameter reconstructions of an anatomically correct male head model illustrate the performance of two- and three-dimensional CSI-EPT. We show that 2D implementation only produces reliable reconstructions under very special circumstances, while accurate reconstructions can be obtained with 3D CSI-EPT.

Mapping electrical properties heterogeneity of tumor using boundary informed electrical properties tomography (BIEPT) at 7T

PURPOSES

To develop and evaluate a boundary informed electrical properties tomography (BIEPT) technique for high-resolution imaging of tumor electrical properties (EPs) heterogeneity on a rodent tumor xenograft model.

METHODS

Tumor EP distributions were inferred from a reference area external to the tumor, as well as internal EP spatial variations derived from a plurality of relative transmit B1 measurements at 7T. Edge sparsity constraint was enforced to enhance numerical stability. Phantom experiments were performed to determine the imaging accuracy and sensitivity for structures of various EP values, as well as geometrical sizes down to 1.5 mm. Numerical simulation of a realistic rodent model was used to quantify the algorithm performance in the presence of noise. Eleven athymic rats with human breast cancer xenograft were imaged in vivo, and representative pathological samples were acquired for comparison.

RESULTS

Reconstructed EPs of the phantoms correspond well to the ground truth acquired from dielectric probe measurements, with the smallest structure reliably detectable being 3 mm. EPs heterogeneity inside a tumor is successfully retrieved in both simulated and experimental cases. In vivo tumor imaging results demonstrate similar local features and spatial patterns to anatomical MRI and pathological slides. The imaged conductivity of necrotic tissue is higher than that of viable tissues, which agrees with our expectation.

CONCLUSION

BIEPT enables robust detection of tumor EPs heterogeneity with high accuracy and sensitivity to small structures. The retrieved quantitative EPs reflect tumor pathological features (e.g., necrosis). These results provide strong rationale to further expand BIEPT studies toward pathological conditions where EPs may yield valuable, non-invasive biomarkers.

bSSFP phase correction and its use in magnetic resonance electrical properties tomography

PURPOSE

Balanced steady-state free precession (bSSFP) sequence is widely used because of its high SNR and high speed. However, bSSFP images suffer from "banding artifact" caused by B₀ inhomogeneity. In this article, we propose a method to remove this artifact in bSSFP phase images and investigate the usage of the corrected phase images in phase-based magnetic resonance electrical properties tomography (MREPT).

THEORY AND METHODS

Two bSSFP phase images, obtained with different excitation frequencies, are collaged to get rid of the regions containing banding artifacts. Phase of the collaged bSSFP image is the sum of the transceive phase of the RF system and an error term that depends on B₀ and T₂ . By using B₀ and T₂ maps, this error is eliminated from bSSFP phase images by using pixel-wise corrections. Conductivity maps are obtained from the uncorrected and the corrected phase images using the phase-based cr-MREPT method.

RESULTS

Phantom and human experiment results of the proposed method are illustrated for both phase images and conductivity maps. It is shown that uncorrected phase images yield unacceptable conductivity images. When only B₀ information is used for phase correction conductivity, reconstructions are substantially improved, and yet T₂ information is still needed to fully recover accurate and undistorted conductivity images.

CONCLUSIONS

With the proposed technique, B₀ sensitivity of the bSSFP phase images can be removed by using B₀ and T₂ maps. It is also shown that corrected bSSFP phase images are of sufficient quality to be used in conductivity imaging.

Electrical properties tomography: Available contrast and reconstruction capabilities

MR-based electrical properties tomography converts the MRI transmit/receive RF field measurements to tissue electrical property maps through dedicated reconstruction algorithms. Recent reports showed that despite limitations, electrical properties tomography holds promise for generating additional contrast for tumor detection and patient-specific modeling of tissue-RF field interactions. This review summarizes the available tissue electrical property contrasts and compares them with the capabilities of the most commonly used electrical properties tomography reconstruction method. Future directions and prospects of clinical translation are discussed.

On the accuracy and precision of PLANET for multiparametric MRI using phase-cycled bSSFP imaging

Purpose

In this work we demonstrate how sequence parameter settings influence the accuracy and precision in T₁, T₂, and off‐resonance maps obtained with the PLANET method for a single‐component signal model. In addition, the performance of the method for the particular case of a two‐component relaxation model for white matter tissue was assessed.

Methods

Numerical simulations were performed to investigate the influence of sequence parameter settings on the accuracy and precision in the estimated parameters for a single‐component model, as well as for a two‐component white matter model. Phantom and in vivo experiments were performed for validation. In addition, the effects of Gibbs ringing were investigated.

Results

By making a proper choice for sequence parameter settings, accurate and precise parameter estimation can be achieved for a single‐component signal model over a wide range of relaxation times at realistic SNR levels. Due to the presence of a second myelin‐related signal component in white matter, an underestimation of approximately 30% in T₁ and T₂ was observed, predicted by simulations and confirmed by measurements. Gibbs ringing artifacts correction improved the precision and accuracy of the parameter estimates.

Conclusion

For a single‐component signal model there is a broad “sweet spot” of sequence parameter combinations for which a high accuracy and precision in the parameter estimates is achieved over a wide range of relaxation times. For a multicomponent signal model, the single‐component PLANET reconstruction results in systematic errors in the parameter estimates as expected.

Redesign of the Laplacian kernel for improvements in conductivity imaging using MRI

PURPOSE

To develop an electrical property tomography reconstruction method that achieves improvements over standard method by redesigning the Laplacian kernel.

THEORY AND METHODS

A decomposition property of the governing PET equation shows the possibility of redesigning the Laplacian kernel for conductivity reconstruction. Hence, the discrete Laplacian operator used for electrical property tomography reconstruction is redesigned to have a Gaussian-like envelope, which enables manipulation of the spatial and spectral response. The characteristics of the proposed kernel are investigated through numerical simulations and in vivo brain experiments.

RESULTS

The proposed method reduces textured noise, which hampers observing features of the conductivity image. Furthermore, the proposed scheme can mitigate the propagation of local phase error such as flow-induced phase. By doing so, the proposed method can recover feature information in conductivity (or resistivity) images. Lastly, the proposed kernel can be extended to other electrical property tomography reconstructions, improving the quality of images.

CONCLUSION

An alternative design of the Laplacian kernel for conductivity imaging has been developed to mitigate the textured noise and the propagation of local phase artifact.

Dictionary-based electric properties tomography

PURPOSE

To develop and validate a new algorithm called "dictionary-based electric properties tomography" (dbEPT) for deriving tissue electric properties from measured B₁ maps.

METHODS

Inspired by Magnetic Resonance fingerprinting, dbEPT uses a dictionary of local patterns ("atoms") of B₁ maps and corresponding electric properties distributions, derived from electromagnetic field simulations. For reconstruction, a pattern from a measured B₁ map is compared with the B₁ atoms of the dictionary. The B₁ atom showing the best match with the measured B₁ pattern yields the optimum electric properties pattern that is chosen for reconstruction. Matching was performed through machine learning algorithms. Two dictionaries, using transmit and transceive phases, were evaluated. The spatial distribution of local matching distance between optimal atom and measured pattern yielded a reconstruction reliability map. The method was applied to reconstruct conductivity of 4 volunteers' brains. A conventional, Helmholtz-based Electric properties tomography (EPT) reconstruction was performed for reference. Noise performance was studied through phantom simulations.

RESULTS

Quantitative values of conductivity agree with literature values. Results of the 2 dictionaries exhibit only minor differences. Somewhat larger differences are visible between dbEPT and Helmholtz-based EPT. Quantified by the correlation between conductivity and anatomic images, dbEPT depicts brain details more clearly than Helmholtz-based EPT. Matching distance is minimal in homogeneous brain ventricles and increases with tissue heterogeneity. Central processing unit time was approximately 2 minutes per dictionary training and 3 minutes per brain conductivity reconstruction using standard hardware equipment.

CONCLUSION

A new, dictionary-based approach for reconstructing electric properties is presented. Its conductivity reconstruction is able to overcome the EPT transceive-phase problem.

3-D Contrast Source Inversion-Electrical Properties Tomography

Contrast source inversion-electrical properties tomography (CSI-EPT) is an iterative reconstruction method to retrieve the electrical properties (EPs) of tissues from magnetic resonance data. The method is based on integral representations of the electromagnetic field and has been shown to allow EP reconstructions of small structures as well as tissue boundaries with compelling accuracy. However, to date, the CSI-EPT has been implemented for 2-D configurations only, which limits its applicability. In this paper, a full 3-D extension of the CSI-EPT method is presented, to enable CSI-EPT to be applied to realistic 3-D scenarios. Here, we demonstrate a proof-of-principle of 3-D CSI-EPT and present the reconstructions of a 3-D abdominal body section and a 3-D head model using different settings of the transmit coil. Numerical results show that the full 3-D approach yields accurate reconstructions of the EPs, even at tissue boundaries and is most accurate in regions where the absolute value of the electric field is highest.

MRI-based, wireless determination of the transfer function of a linear implant: Introduction of the transfer matrix

PURPOSE

We introduce the transfer matrix (TM) that makes MR-based wireless determination of transfer functions (TFs) possible. TFs are implant specific measures for RF-safety assessment of linear implants. The TF relates an incident tangential electric field on an implant to a scattered electric field at its tip that generally governs local heating. The TM extends this concept and relates an incident tangential electric field to a current distribution in the implant therewith characterizing the RF response along the entire implant. The TM is exploited to measure TFs with MRI without hardware alterations.

THEORY AND METHODS

A model of rightward and leftward propagating attenuated waves undergoing multiple reflections is used to derive an analytical expression for the TM. This allows parameterization of the TM of generic implants, e.g., (partially) insulated single wires, in a homogeneous medium in a few unknowns that simultaneously describe the TF. These unknowns can be determined with MRI making it possible to measure the TM and, therefore, also the TF.

RESULTS

The TM is able to predict an induced current due to an incident electric field and can be accurately parameterized with a limited number of unknowns. Using this description the TF is determined accurately (with a Pearson correlation coefficient R ≥ 0.9 between measurements and simulations) from MRI acquisitions.

CONCLUSION

The TM enables measuring of TFs with MRI of the tested generic implant models. The MR-based method does not need hardware alterations and is wireless hence making TF determination in more realistic scenarios conceivable.

Error analysis of helmholtz-based MR-electrical properties tomography

PURPOSE

MR electrical properties tomography (MR-EPT) aims to measure tissue electrical properties by computing spatial derivatives of measured B1+ data. This computation is very sensitive to spatial fluctuations caused, for example, by noise and Gibbs ringing. In this work, the error arising from the computation of spatial derivatives using finite difference kernels (FD error) has been investigated. In relation to this FD error, it has also been investigated whether mitigation strategies such as Gibbs ringing correction and Gaussian apodization can be beneficial for conductivity reconstructions.

METHODS

Conductivity reconstructions were performed on a phantom (by means of simulations and MR measurements at 3T) and on a human brain model. The accuracy was evaluated as a function of image resolution, FD kernel size, k-space windowing, and signal-to-noise ratio. The impact of mitigation strategies was also investigated.

RESULTS

The adopted small FD kernel is highly sensitive to spatial fluctuations, whereas the large FD kernel is more noise-robust. However, large FD kernels lead to extended numerical boundary error propagation, which severely hampers the MR-EPT reconstruction accuracy for highly spatially convoluted tissue structures such as the human brain. Mitigation strategies slightly improve the accuracy of conductivity reconstructions. For the adopted derivative kernels and the investigated scenario, MR-EPT conductivity reconstructions show low accuracy: less than 37% of the voxels have a relative error lower than 30%.

CONCLUSION

The numerical error introduced by the computation of spatial derivatives using FD kernels is one of the major causes of limited accuracy in Helmholtz-based MR-EPT reconstructions. Magn Reson Med 80:90-100, 2018. © 2017 International Society for Magnetic Resonance in Medicine.