The influence of inhomogeneous volume conductor models on the ECG and the MCG

The authors investigated the influence of human body inhomogeneities such as the lungs, blood masses and the skeletal muscle layer on the electrical body surface potential and the magnetic field. The surface potentials and magnetic fields are calculated using a boundary element method. As a rule the blood masses have a large influence on both potential and magnetic field amplitude as well as on the potential and magnetic field map orientation, but the influence on the topology of the map is less in the electric case than in the magnetic case. The single-dipole reconstruction was applied to estimate the error caused by neglecting inner inhomogeneities in source localization. The neglect of lungs and blood masses results in a localization error of less than 1 cm in the electric case but more than 1 cm for deep sources at the posterior side of the heart in the magnetic case. The authors tried to assess the influence of the skeletal muscle layer by both an analytical two-layered anisotropic half-space model and the torso extension method. The skeletal muscle layer causes a smoothing effect on the electrical surface potential and to a lesser extent on the magnetic field, leading to an overestimation of the actual source depth of about 1-2 cm. In principle this can be reduced by taking data from all over the thoracic surface. The authors designed experiments for simultaneous measurement of body surface potential and extracorporeal magnetic field from the same subject. The evaluation of data from two patients showing Wolff-Parkinson-White syndrome has shown that localization results from electric potential data and magnetocardiographic data are consistent.     

Influence of anisotropic compartments on magnetic field and electric potential distributions generated by artificial current dipoles inside a torso phantom

The purpose of this study is the analysis of the influence of anisotropic conductivity on magnetic fields and electric potentials by means of phantom measurements. An artificial rotating current dipole was placed in the middle of an anisotropic skein arrangement in a torso phantom filled with saline solution. The signal strength and the change of the shape of potential and field patterns due to anisotropic volume conduction were investigated. Different directions of the dipole were compared to corresponding orientations of measured fields and potentials (angle difference). For electric and magnetic data, the angle difference between observed signal orientations and true dipole orientations continuously increased with the angle between dipole and anisotropy (up to 80 degrees ) and then decreased back to zero at their orthogonal orientation. Both signal strengths decreased about 10% with an increasing angle between dipole and anisotropy. While the magnetic field showed a generally stronger shape change, the changed shape of the electric potential showed similarity to an extended source. Our phantom study demonstrated that anisotropic compartments influence directions, amplitudes and shapes of potentials and fields at different degrees. We concluded that anisotropic structures should be considered in volume conductor modelling, when source orientation, extension and strength are of interest.     

基于头部组织不同电导率特性的阻抗成像正问题仿真研究

目的 通过建立5层有限元真实头模型,研究了各层组织非均质和颅骨、脑白质各向异性电特性对电阻抗成像问题中电磁场分布的影响.方法 对头部各组织建立4种电导率分布模型:均质分布、非均质分布以及颅骨和脑白质各向异性电导率模型;通过正问题数值求解得到不同模型下的磁场分布和电场分布,并通过定量的统计分析研究非均质和各向异性电导率特...     

The potential induced in anisotropic tissue by the ultrasonically-induced Lorentz force

In the presence of a magnetic field, an ultrasonic wave propagating through tissue will induce Lorentz forces on the ions, resulting in an electrical current. If the electrical conductivity is anisotropic, this current is tilted toward the fiber direction, causing charge to accumulate between half-wavelengths: positive charge where the current vectors converge and negative where the current vectors diverge. This charge produces an electric field in the direction of propagation that is associated with an electrical potential, and this electric field causes an additional current that is also tilted by the anisotropy. The final result is the total current pointing perpendicular to the direction of propagation and a charging of the tissue every half wavelength. The potential has a greater magnitude than that obtained from colloidal suspensions or ionic solutions (ultrasonic vibration potentials) and may be used as the basis of a technique to image conductivity.     

MRI assessment of cartilage ultrastructure

In T2-weighted MRI images joint cartilage can appear laminated. The multilaminar appearance is visualized as zones of different intensity. This appearance is based on the dipolar interaction of water molecules within cartilage zones of different collageneous network structures. Therefore, the MR visualization of zones of anisotropic arrangement of the collagen fibers depends upon their orientation to the static magnetic field (magic-angle effect). The aim of this article is to demonstrate the potential of high-resolution MRI for characterizing cartilage network structuring and biomechanical properties. Information equivalent to that from polarization light microscopy can be derived noninvasively. Based on NMR microscopic (microMRI) data, potential new possibilities of MRI for quantitative assessment of collagen structuring and intracartilagenous load distribution are presented. These methods use MR intensity angle dependence and load influence on cartilage visualization. Alternatively to the determination of mechanical parameters from cartilage deformation, it is demonstrated that stress distribution and biomechanical properties can be derived in principle from the local intensity variation of anisotropic fiber orientation zones. The limitations with respect to a clinical application of the proposed methods are discussed.     

Image reconstruction of anisotropic conductivity tensor distribution in MREIT: computer simulation study

We describe a novel method of reconstructing images of an anisotropic conductivity tensor distribution inside an electrically conducting subject in magnetic resonance electrical impedance tomography (MREIT). MREIT is a recent medical imaging technique combining electrical impedance tomography (EIT) and magnetic resonance imaging (MRI) to produce conductivity images with improved spatial resolution and accuracy. In MREIT, we inject electrical current into the subject through surface electrodes and measure the z-component Bz of the induced magnetic flux density using an MRI scanner. Here, we assume that z is the direction of the main magnetic field of the MRI scanner. Considering the fact that most biological tissues are known to have anisotropic conductivity values, the primary goal of MREIT should be the imaging of an anisotropic conductivity tensor distribution. However, up to now, all MREIT techniques have assumed an isotropic conductivity distribution in the image reconstruction problem to simplify the underlying mathematical theory. In this paper, we firstly formulate a new image reconstruction method of an anisotropic conductivity tensor distribution. We use the relationship between multiple injection currents and the corresponding induced Bz data. Simulation results show that the algorithm can successfully reconstruct images of anisotropic conductivity tensor distributions. While the results show the feasibility of the method, they also suggest a more careful design of data collection methods and data processing techniques compared with isotropic conductivity imaging.     

Anisotropic conductivity imaging with MREIT using equipotential projection algorithm

Magnetic resonance electrical impedance tomography (MREIT) combines magnetic flux or current density measurements obtained by magnetic resonance imaging (MRI) and surface potential measurements to reconstruct images of true conductivity with high spatial resolution. Most of the biological tissues have anisotropic conductivity; therefore, anisotropy should be taken into account in conductivity image reconstruction. Almost all of the MREIT reconstruction algorithms proposed to date assume isotropic conductivity distribution. In this study, a novel MREIT image reconstruction algorithm is proposed to image anisotropic conductivity. Relative anisotropic conductivity values are reconstructed iteratively, using only current density measurements without any potential measurement. In order to obtain true conductivity values, only either one potential or conductivity measurement is sufficient to determine a scaling factor. The proposed technique is evaluated on simulated data for isotropic and anisotropic conductivity distributions, with and without measurement noise. Simulation results show that the images of both anisotropic and isotropic conductivity distributions can be reconstructed successfully.     

Magnetoacoustic tomography with magnetic induction (MAT-MI)

We report our theoretical and experimental investigations on a new imaging modality, magnetoacoustic tomography with magnetic induction (MAT-MI). In MAT-MI, the sample is located in a static magnetic field and a time-varying (micros) magnetic field. The time-varying magnetic field induces an eddy current in the sample. Consequently, the sample will emit ultrasonic waves by the Lorentz force. The ultrasonic signals are collected around the object to reconstruct images related to the electrical impedance distribution in the sample. MAT-MI combines the good contrast of electrical impedance tomography with the good spatial resolution of sonography. MAT-MI has two unique features due to the solenoid nature of the induced electrical field. Firstly, MAT-MI could provide an explicit or simple quantitative reconstruction algorithm for the electrical impedance distribution. Secondly, it promises to eliminate the shielding effects of other imaging modalities in which the current is applied directly with electrodes. In the theoretical part, we provide formulae for both the forward and inverse problems of MAT-MI and estimate the signal amplitude in biological tissues. In the experimental part, the experimental setup and methods are introduced and the signals and the image of a metal object by means of MAT-MI are presented. The promising pilot experimental results suggest the feasibility of the proposed MAT-MI approach.     

Volume conductor effects on the spatial resolution of magnetic fields and electric potentials from gastrointestinal electrical activity

An analysis of the relative capabilities of methods for magnetic and electric detection of gastrointestinal electrical activity is presented. The model employed is the first volume conductor model for magnetic fields from GEA to appear in the literature. A mathematical model is introduced for the electric potential and magnetic field from intestinal electrical activity in terms of the spatial filters that relate the bioelectric sources with the external magnetic fields and potentials. The forward spatial filters are low-pass functions of spatial frequency, so more superficial external fields and potentials contain less spatial information than fields and potentials near the source. Inverse spatial filters, which are reciprocals of the forward filters, are high-pass functions and must be regularised by windowing. Because of the conductivity discontinuities introduced by low-conductivity fat layers in the abdomen, the electric potentials recorded outside these layers required more regularisation than the magnetic fields, and thus, the spatial resolution of the magnetic fields from intestinal electrical activity is higher than the spatial resolution of the external potentials. In this study, two smooth muscle sources separated by 5 cm were adequately resolved magnetically, but not resolved electrically. Thus, sources are more accurately localized and imaged using magnetic measurements than using measurements of electric potential.     

MagnetoHemoDynamics in the aorta and electrocardiograms

This paper addresses a complex multi-physical phenomenon involving cardiac electrophysiology and hemodynamics. The purpose is to model and simulate a phenomenon that has been observed in magnetic resonance imaging machines: in the presence of a strong magnetic field, the T-wave of the electrocardiogram (ECG) gets bigger, which may perturb ECG-gated imaging. This is due to a magnetohydrodynamic (MHD) effect occurring in the aorta. We reproduce this experimental observation through computer simulations on a realistic anatomy, and with a three-compartment model: inductionless MHD equations in the aorta, bi-domain equations in the heart and electrical diffusion in the rest of the body. These compartments are strongly coupled and solved using finite elements. Several benchmark tests are proposed to assess the numerical solutions and the validity of some modeling assumptions. Then, ECGs are simulated for a wide range of magnetic field intensities (from 0 to 20 T).     

Transmembrane potential generated by a magnetically induced transverse electric field in a cylindrical axonal model

During the electrical stimulation of a uniform, long, and straight nerve axon, the electric field oriented parallel to the axon has been widely accepted as the major field component that activates the axon. Recent experimental evidence has shown that the electric field oriented transverse to the axon is also sufficient to activate the axon, by inducing a transmembrane potential within the axon. The transverse field can be generated by a time-varying magnetic field via electromagnetic induction. The aim of this study was to investigate the factors that influence the transmembrane potential induced by a transverse field during magnetic stimulation. Using an unmyelinated axon model, we have provided an analytic expression for the transmembrane potential under spatially uniform, time-varying magnetic stimulation. Polarization of the axon was dependent on the properties of the magnetic field (i.e., orientation to the axon, magnitude, and frequency). Polarization of the axon was also dependent on its own geometrical (i.e., radius of the axon and thickness of the membrane) and electrical properties (i.e., conductivities and dielectric permittivities). Therefore, this article provides evidence that aside from optimal coil design, tissue properties may also play an important role in determining the efficacy of axonal activation under magnetic stimulation. The mathematical basis of this conclusion was discussed. The analytic solution can potentially be used to modify the activation function in current cable equations describing magnetic stimulation.     

Source localization in an inhomogeneous physical thorax phantom.

The influence of lung inhomogeneities on focal source localizations in electrocardiography (ECG) and magnetocardiography (MCG) is investigated. A realistically shaped physical thorax phantom with cylindrical lung inhomogeneities is used for electric and magnetic measurements. The lungs are modelled with a special ionic exchange membrane which allows different conductivity compartments without influencing the free ionic current flow. The dipolar current sources are composed of platinum wire and located at different depths and directions between the lung inhomogeneities. We localized the current dipoles with different boundary element method (BEM) models, based on electrical data and simultaneous electrical and magnetic data. Our results indicate the possibility of superadditive information gain by combining electrical and magnetic data for source reconstructions. We found a significant influence of the inhomogeneities on both the calculated source location and the calculated source strength. Mislocalizations of up to 16 mm and wrong dipole strengths of up to 52% were obtained when the lung inhomogeneities were not taken into account for source localization. Dipoles parallel to the lungs showed a larger localization error in depth than dipoles perpendicular to the lungs. We conclude that the incorporation of lung inhomogeneities will improve source localization accuracy in ECG and MCG.     

An Experimental Study on the Effect of the Anisotropic Regions in a Realistically Shaped Torso Phantom

Determination of electrically active regions in the human body by observing generated bioelectric and/or biomagnetic signals is known as source reconstruction. In the reconstruction process, it is assumed that the volume conductor consists of isotropic compartments and homogeneous tissue bioelectric parameters but this assumption introduces errors when the tissue of interest is anisotropic. The aim of this study was to investigate changes in the measured signal strengths and the estimated positions and orientations of current dipoles in a realistically shaped torso phantom having a heart region built from single guar gum skeins. Electric data were recorded with 60 electrodes on the front of the chest and 195 sensors measured the magnetic field 2 cm above the chest. The artificial rotating dipoles were located underneath the anisotropic skeins distant from the sensors. It was found that the signal strengths and estimated dipole orientations were influenced by the anisotropy while the estimated dipole positions were not significantly influenced. The signal strength was reduced between 17% and 43% for the different dipole positions when comparing the parallel alignment of dipole orientation and anisotropy direction with the orthogonal alignment. The largest error in the estimation of dipole orientation was 42 degrees. The observed changes in the magnetic fields and electric potentials can be explained by the fact that the anisotropic skeins force the current along its direction. We conclude that taking into account anisotropic structures in the volume conductor might improve signal analysis as well as source strength and orientation estimations for bioelectric and biomagnetic investigations.     

经颅磁刺激的时域有限元电磁场研究

研究了空心圆柱线圈激励下三层同心导电球模型的瞬态电磁场边值问题,通过时域有限元方程的求解获得头内矢量磁位,进而模拟了磁通密度、感应电场的分布及时域变化特性,为进一步探索脉冲电磁场对人脑的最佳刺激方式和新型磁刺激仪器的研制提供理论基础.     

Application of the boundary element method to the solution of anisotropic electromagnetic problems

The paper discusses the application of the boundary element method to the computation of the electric potential and magnetic field generated by bioelectric sources in an anisotropic inhomogeneous volume conductor, using a proper coordinate transformation. It is shown that the co-ordinate transformation generally not only affects the conductivity and geometry of the volume conductor under consideration, but also the current source term and the continuity relation on the interfaces bounding regions of different conductivity. To illustrate these results, the electric potentials in an anisotropic finite length cylinder and in an anisotropic volume conductor of irregular (torso) shape, computed by the boundary element method, are compared with the results obtained by the analytical solution and the finite element method, respectively.     

Effect of myocardial anisotropy on the torso current flow patterns, potentials and magnetic fields

The effects of myocardial anisotropy on the torso current flow patterns, voltage and the magnetic field were examined using an anatomically realistic torso model of an adult male subject. A finite element model of the torso was built with 19 major tissue types identified. The myocardial fibre orientation in the heart wall was included with a voxel resolution of 0.078 x 0.078 x 0.3 cm. The fibre orientations from the canine heart which are available in the literature were mapped to our adult male subject's human heart using deformable mapping techniques. The current and potential distribution in the whole torso were computed using an idealized dipolar source of +/-1.0 V in the middle of the septum of the heart wall as a boundary condition. An adaptive finite element solver was used. Two cases were studied. In one case the myocardium was isotropic and in the other it was anisotropic. It was found that the current density distribution shows a very noticeable difference between the isotropic and anisotropic myocardium. The resultant magnetic field in front of the torso was computed using the Biot-Savart law. It was found that the magnetic field profile was slightly affected by the myocardial anisotropy. The potential on the torso surface also shows noticeable changes due to the myocardial anisotropy.     

A Controllably Anisotropic Conductivity or Diffusion Phantom Constructed from Isotropic Layers

Phantoms with controllable and well-defined anisotropy are needed to test methods for imaging electrical anisotropy. We developed and tested a phantom that had properties similar to a homogeneous anisotropic conductive medium. The phantom was constructed with alternate slices of isotropic gel having different conductivities. The degree of anisotropy in the phantom could be varied easily by changing the relative conductivity of the two gels. We tested the stability of several phantoms and found their properties were maintained for approximately 8 h following construction. The phantom has application to electrical impedance tomography, magnetic resonance electrical impedance tomography, EEG and ECG source imaging and diffusion tensor imaging.     

人体组织电特性磁共振断层成像（MR EPT）技术进展

科学研究早已证实,人体组织的电特性参数（包括电导率和电容率）在正常组织与肿瘤组织之间差异较大,因此测量人体活体组织的电特性参数变化有可能成为肿瘤早期诊断的有效手段。磁共振成像（MRI）本质上是非电离电磁场,即强的静磁场、梯度磁场和射频电磁场与人体组织的相互作用,因此MRI影像信息中必然包含人体组织的电特性信息。MRI领域近年来新兴的研究热点之一人体组织电特性磁共振断层成像（MR EPT）技术,其就是研究如何从MRI影像信息中有效提取人体组织电特性信息。本文概述MR EPT技术的产生背景,从反映电磁场基本运动规律的麦克斯韦方程组出发,解析给出MR射频场与人体组织电特性参数之间的量化关系,深入剖析了3 T和7 T不同场强下MR EPT成像方法的国际研究进展以及潜在的技术突破口。同时,还介绍目前运用MR EPT技术开展的动物实验和前期临床人体测试等情况,展示这一新兴技术的诱人前景。     

Magnetic fields of the human brain accompanying voluntary movement: Bereitschaftsmagnetfeld

Summary A slow magnetic field shift has been detected in the human brain occurring in the foreperiod of a voluntary finger movement. This magnetic field accompanies a slow negative electrical cerebral potential which occurs in the same foreperiod, the Bereitschaftspotential (BP) of Kornhuber and Deecke. The present report is the first of a magnetic field associated with the BP, and has been named the Bereitschaftsmagnetfeld (BM) or readiness magnetic field. The BM is oriented with the field lines directed out of the head in the pre-rolandic region and with the field lines directed into the head in post-rolandic areas, suggesting a source in the sensorimotor area for the contralateral hand. Distribution of the magnetic fields has so far not revealed a source in the fronto-central midline where the BP is recorded maximally. The time course and morphology of the BP and BM are similar, but they have different topography over the skull.Supported by grants from the Secretariat on Science Research and Development and the Programmes of Distinction of British Columbia, Canada