Joonsung Lee

Error Analysis of Nonconstant Admittivity for MR-Based Electric Property Imaging

Magnetic resonance electrical property tomography (MREPT) is a new imaging modality to visualize a distribution of admittivity γ = σ+iωε inside the human body where σ and ε denote electrical conductivity and permittivity, respectively. Using B1 maps acquired by an magnetic resonance imaging scanner, it produces cross-sectional images of σ and ε at the Larmor frequency. Since current MREPT methods rely on an assumption of a locally homogeneous admittivity, there occurs a reconstruction error where this assumption fails. Rigorously analyzing the reconstruction error in MREPT, we showed that the error is fundamental and may cause technical difficulties in interpreting MREPT images of a general inhomogeneous object. We performed numerical simulations and phantom experiments to quantitatively support the error analysis. We compared the MREPT image reconstruction problem with that of magnetic resonance electrical impedance tomography (MREIT) to highlight distinct features of both methods to probe the same object in terms of its high- and low-frequency conductivity distributions, respectively. MREPT images showed large errors along boundaries where admittivity values changed whereas MREIT images showed no such boundary effects. Noting that MREIT makes use of the term neglected in MREPT, a novel MREPT admittivity image reconstruction method is proposed to deal with the boundary effects, which requires further investigation on the complex directional derivative in the real Euclidian space \BBR3.

Initial study on in vivo conductivity mapping of breast cancer using MRI

To develop and apply a method to measure in vivo electrical conductivity values using magnetic resonance imaging (MRI) in subjects with breast cancer.

Electrical tissue property imaging using MRI at dc and Larmor frequency

Cross-sectional imaging of conductivity and permittivity distributions inside thehumanbodyhasbeenactivelyinvestigatedinimpedanceimagingareassuch as electrical impedance tomography (EIT) and magnetic induction tomography (MIT). Since the conductivity and permittivity values exhibit frequencydependent changes, it is worthwhile to perform spectroscopic imaging from almost dc to hundreds of MHz. To probe the human body, we may inject current using surface electrodes or induce current using external coils. In EIT and MIT, measured data are only available on the boundary or exterior of the body unless we invasively place sensors inside the body. Their image reconstruction problems are nonlinear and ill-posed to result in images with a relatively low spatial resolution. Noting that an MRI scanner can noninvasively measure magnetic fields inside the human body, electrical tissue property imaging methods using MRI have lately been proposed. Magnetic resonance EIT (MREIT) performs conductivity imaging at dc or below 1 kHz by externallyinjectingcurrentintothehumanbodyandmeasuringinducedinternal magneticfluxdensitydatausinganMRIscanner.Magneticresonanceelectrical property tomography (MREPT) produces both conductivity and permittivity images at the Larmor frequency of an MRI scanner based on B1-mapping techniques. Since internal data are only available in MREIT and MREPT, we may formulate well-posed inverse problems for image reconstructions. To develop related imaging techniques, we should clearly understand the basic principles of MREIT and MREPT, which are based on coupled physics of bioelectromagnetism and MRI as well as associated mathematical methods. In this paper, we describe the physical principles of MREIT and MREPT in a unified way and associate measurable quantities with the conductivity and permittivity. Clarifying the key relations among them, we examine existing image reconstruction algorithms to reveal their capabilities and limitations. We discuss technical issues in MREIT and MREPT and suggest future research

MR-Based Conductivity Imaging Using Multiple Receiver Coils

To propose a signal combination method for MR‐based tissue conductivity mapping using a standard clinical scanner with multiple receiver coils.

Metabolite-selective hyperpolarized 13C imaging using extended chemical shift displacement at 9.4 T

PURPOSE To develop a technique for frequency-selective hyperpolarized (13)C metabolic imaging in ultra-high field strength which exploits the broad spatial chemical shift displacement in providing spectral and spatial selectivity. METHODS The spatial chemical shift displacement caused by the slice-selection gradient was utilized in acquiring metabolite-selective images. Interleaved images of different metabolites were acquired by reversing the polarity of the slice-selection gradient at every repetition time, while using a low-bandwidth radio-frequency excitation pulse to alternatingly shift the displaced excitation bands outside the imaging subject. Demonstration of this technique is presented using (1)H phantom and in vivo mouse renal hyperpolarized (13)C imaging experiments with conventional chemical shift imaging and fast low-angle shot sequences. RESULTS From phantom and in vivo mouse studies, the spectral selectivity of the proposed method is readily demonstrated using results of chemical shift spectroscopic imaging, which displayed clearly delineated images of different metabolites. Imaging results using the proposed method without spectral encoding also showed effective separation while also providing high spatial resolution. CONCLUSION This method provides a way to acquire spectrally selective hyperpolarized (13)C metabolic images in a simple implementation, and with potential ability to support combination with more elaborate readout methods for faster imaging.

A modified multi-echo AFI for simultaneous B1+ magnitude and phase mapping

To simultaneously acquire the B1(+) magnitude and B1(+) phase, a modified multi-echo actual flip-angle imaging (AFI) sequence is proposed. A multi-echo gradient echo sequence was integrated into every even TR of AFI to measure both magnitude and phase of B1(+). In addition, to increase the signal-to-noise ratio of the B1(+) phase, a double-angle multi-echo AFI sequence, in which the flip-angle of the RF pulses is α at the odd TR and 2α at the even TR is proposed. Images were simulated to evaluate the performance of this method under various imaging and physical parameters. The performance was compared to the spin echo based B1(+) mapping method in phantom and in vivo studies. In the simulation, the estimation error decreased as TR1/T1 decreased and TR2/TR1 increased. For double-angle AFI, flip-angle ranges that could estimate B1(+) magnitude and phase better than the original AFI were identified. Using the proposed method, B1(+) phase estimation was similar to spin echo phase. In the phantom study, correlation coefficient between the estimated B1(+) phases using the spin echo and the proposed method was 0.9998. The results show that the B1(+) magnitude and B1(+) phase can be simultaneously acquired and accurately estimated using the proposed double-angle AFI method.

Noninvasive measurement of conductivity anisotropy at larmor frequency using MRI.

Anisotropic electrical properties can be found in biological tissues such as muscles and nerves. Conductivity tensor is a simplified model to express the effective electrical anisotropic information and depends on the imaging resolution. The determination of the conductivity tensor should be based on Ohms law. In other words, the measurement of partial information of current density and the electric fields should be made. Since the direct measurements of the electric field and the current density are difficult, we use MRI to measure their partial information such as B1 map; it measures circulating current density and circulating electric field. In this work, the ratio of the two circulating fields, termed circulating admittivity, is proposed as measures of the conductivity anisotropy at Larmor frequency. Given eigenvectors of the conductivity tensor, quantitative measurement of the eigenvalues can be achieved from circulating admittivity for special tissue models. Without eigenvectors, qualitative information of anisotropy still can be acquired from circulating admittivity. The limitation of the circulating admittivity is that at least two components of the magnetic fields should be measured to capture anisotropic information.

An indirect method for in vivo T2 mapping of [1‐13C] pyruvate using hyperpolarized 13C CSI

An indirect method for in vivo T2 mapping of 13C–labeled metabolites using T2 and T2* information of water protons obtained a priori is proposed. The T2 values of 13C metabolites are inferred using the relationship to T2′ of coexisting 1H and the T2* of 13C metabolites, which is measured using routine hyperpolarized 13C CSI data. The concept is verified with phantom studies. Simulations were performed to evaluate the extent of T2 estimation accuracy due to errors in the other measurements. Also, bias in the 13C T2* estimation from the 13C CSI data was studied. In vivo experiments were performed from the brains of normal rats and a rat with C6 glioma. Simulation results indicate that the proposed method provides accurate and unbiased 13C T2 values within typical experimental settings. The in vivo studies found that the estimated T2 of [1‐13C] pyruvate using the indirect method was longer in tumor than in normal tissues and gave values similar to previous reports. This method can estimate localized T2 relaxation times from multiple voxels using conventional hyperpolarized 13C CSI and can potentially be used with time resolved fast CSI.

Magnetic resonance electrical properties tomography for small anomalies using boundary conditions: A simulation study

Purpose Magnetic resonance electrical property tomography (MREPT) is an emerging imaging modality using measured B1 maps from magnetic resonance imaging (MRI) to measure a distribution of electric conductivity and permittivity of the subject at the Larmor frequency. Conventional MREPT approaches at single transmit channel system using the Helmholtz equation rely on an assumption that conductivity and permittivity of the subject are locally homogeneous. For small tissue structures and tissue boundaries, in which the assumption of locally homogeneous conductivity and permittivity does not hold, the reconstructed conductivity values deviated from the actual values, so called “Boundary Artifacts.” The aim of this study is to propose new reconstruction processes based on time‐harmonic Maxwells equations to reconstruct conductivity for small tissue structures and tissue boundaries. Methods Instead of removing the electric fields from the equations as done in the Helmholtz equation, three key identities of circularly polarized and longitudinal components of electric fields, circularly polarized component of magnetic fields, and electric properties from time‐harmonic Maxwells equations are derived. Based on the three key identities, the proposed reconstruction methods determine conductivity, permittivity, and circularly polarized component and longitudinal component of electric fields using the measured H1+. In each iterative step, estimated conductivity, permittivity, electric fields, and artifact‐free mask region, Ω where the contribution of the boundary artifacts is small, were updated. Using the estimated values in the artifact‐free mask region as boundary conditions, the estimates beyond the mask region were updated. EM simulations were performed on three types of numerical phantoms with very small regions of homogeneous conductivity and permittivity. The performance of the proposed methods was evaluated using the simulated electric and magnetic fields. Results For the numerical simulation model, the proposed methods significantly reduced the boundary artifacts compared to conventional methods using Helmholtz equations. In addition, previous methods using the Helmholtz equation could measure conductivity of only large anomalies, but the proposed method can measure the conductivity of the small compartments whose size is 2–3 voxels. The proposed approaches are compatible with spatial filtering which can be used to reduce noise. If a good image segmentation is available as a prior information, better initial boundary conditions can be estimated, and thus the proposed approach can be more accurate for small tissue structures. Conclusions The proposed reconstruction method not only determines electrical properties, but also circularly polarized component and longitudinal component of electric fields using an iterative process. The proposed method can quantitatively detect the conductivity of the small anomalies better than conventional methods.

Flow‐suppressed hyperpolarized 13C chemical shift imaging using velocity‐optimized bipolar gradient in mouse liver tumors at 9.4 T

To optimize and investigate the influence of bipolar gradients for flow suppression in metabolic quantification of hyperpolarized 13C chemical shift imaging (CSI) of mouse liver at 9.4 T.