On the contribution of volume currents to the total magnetic field resulting from the heart excitation process: a simulation study

The magnetocardiogram

The magnetic field produced by the heart's electrical activity is called the magnetocardiogram (MCG). The first 20 years of MCG research established most of the concepts, instrumentation, and computational algorithms in the field. Additional insights into fundamental mechanisms of biomagnetism were gained by studying isolated hearts or even isolated pieces of cardiac tissue. Much effort has gone into calculating the MCG using computer models, including solving the inverse problem of deducing the bioelectric sources from biomagnetic measurements. Recently, most magnetocardiographic research has focused on clinical applications, driven in part by new technologies to measure weak biomagnetic fields.

Examining the Impact of Prior Models in Transmural Electrophysiological Imaging: A Hierarchical Multiple-Model Bayesian Approach

Noninvasive cardiac electrophysiological (EP) imaging aims to mathematically reconstruct the spatiotemporal dynamics of cardiac sources from body-surface electrocardiographic (ECG) data. This ill-posed problem is often regularized by a fixed constraining model. However, a fixed-model approach enforces the source distribution to follow a pre-assumed structure that does not always match the varying spatiotemporal distribution of actual sources. To understand the model-data relation and examine the impact of prior models, we present a multiple-model approach for volumetric cardiac EP imaging where multiple prior models are included and automatically picked by the available ECG data. Multiple models are incorporated as an Lp-norm prior for sources, where p is an unknown hyperparameter with a prior uniform distribution. To examine how different combinations of models may be favored by different measurement data, the posterior distribution of cardiac sources and hyperparameter p is calculated using a Markov Chain Monte Carlo (MCMC) technique. The importance of multiple-model prior was assessed in two sets of synthetic and real-data experiments, compared to fixed-model priors (using Laplace and Gaussian priors). The results showed that the posterior combination of models (the posterior distribution of p) as determined by the ECG data differed substantially when reconstructing sources with different sizes and structures. While the use of fixed models is best suited in situations where the prior assumption fits the actual source structures, the use of an automatically adaptive set of models may have the ability to better address model-data mismatch and to provide consistent performance in reconstructing sources with different properties.

Finite element modelling and simulations in cardiovascular mechanics and cardiology: A bibliography 1993–2004

The paper gives a bibliographical review of the finite element modelling and simulations in cardiovascular mechanics and cardiology from the theoretical as well as practical points of views. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1993 and 2004. At the end of this paper, more than 890 references are given dealing with subjects as: Cardiovascular soft tissue modelling; material properties; mechanisms of cardiovascular components; blood flow; artificial components; cardiac diseases examination; surgery; and other topics.

Facilitating arrhythmia simulation: the method of quantitative cellular automata modeling and parallel running

Background

Many arrhythmias are triggered by abnormal electrical activity at the ionic channel and cell level, and then evolve spatio-temporally within the heart. To understand arrhythmias better and to diagnose them more precisely by their ECG waveforms, a whole-heart model is required to explore the association between the massively parallel activities at the channel/cell level and the integrative electrophysiological phenomena at organ level.

Methods

We have developed a method to build large-scale electrophysiological models by using extended cellular automata, and to run such models on a cluster of shared memory machines. We describe here the method, including the extension of a language-based cellular automaton to implement quantitative computing, the building of a whole-heart model with Visible Human Project data, the parallelization of the model on a cluster of shared memory computers with OpenMP and MPI hybrid programming, and a simulation algorithm that links cellular activity with the ECG.

Results

We demonstrate that electrical activities at channel, cell, and organ levels can be traced and captured conveniently in our extended cellular automaton system. Examples of some ECG waveforms simulated with a 2-D slice are given to support the ECG simulation algorithm. A performance evaluation of the 3-D model on a four-node cluster is also given.

Conclusions

Quantitative multicellular modeling with extended cellular automata is a highly efficient and widely applicable method to weave experimental data at different levels into computational models. This process can be used to investigate complex and collective biological activities that can be described neither by their governing differentiation equations nor by discrete parallel computation. Transparent cluster computing is a convenient and effective method to make time-consuming simulation feasible. Arrhythmias, as a typical case, can be effectively simulated with the methods described.

The effect of volume currents due to myocardial anisotropy on body surface potentials

Changes in anterior and posterior body surface potential maps (BSPMs) due to myocardial anisotropy were examined using a highly heterogeneous finite element model of an adult male subject constructed from segmented magnetic resonance images. A total of 23 different tissue types were identified in the whole torso. The myocardial fibre orientations in the human heart wall were mapped from the fibre orientations of a canine heart which are available in the literature using deformable mapping techniques. The current and potential distributions in the whole torso were computed using dipolar sources in the septum, apical area, left ventricular wall or right ventricular wall. For each dipole x, y, z orientations were studied. An adaptive finite element solver was used to compute currents and potential distributions in the whole torso with an element size of 0.78 x 0.78 x 3 mm in the myocardium and larger elements in other parts of the torso. For each dipole position two cases were studied. In one case the myocardium was isotropic and in the other it was anisotropic. It was found that BSPMs showed a very notable difference between the isotropic and the anisotropic myocardium for all dipole positions with the largest difference for the apical dipoles. The correlation coefficients for the BSPMs between the isotropic and anisotropic cases ranged from 0.83 for an apical dipole to 0.99 for an RV wall dipole. These results suggest that myocardial fibre anisotropy plays an important role in determining the body surface potentials.

The effect of geometric and topologic differences in boundary element models on magnetocardiographic localization accuracy

This study was performed to evaluate the changes in magnetocardiographic (MCG) source localization results when the geometry and the topology of the volume conductor model were altered. Boundary element volume conductor models of three patients were first constructed. These so-called reference torso models were then manipulated to mimic various sources of error in the measurement and analysis procedures. Next, equivalent current dipole localizations were calculated from simulated and measured multichannel MCG data. The localizations obtained with the reference models were regarded as the "gold standard." The effect of each modification was investigated by calculating three-dimensional distances from the gold standard localizations to the locations obtained with the modified model. The results show that the effect of the lungs and the intra-ventricular blood masses is significant for deep source locations and, therefore, the torso model should preferably contain internal inhomogeneities. However, superficial sources could be localized within a few millimeters even with nonindividual, so called standard torso models. In addition, the torso model should extend long enough in the pelvic region, and the positions of the lungs and the ventricles inside the model should be known in order to obtain accurate localizations.

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.

Cardiac biomagnetic source estimation with a heart-torso model and a trained neural network

The intensity of the cardiac sources for normal adult subjects was estimated from given magnetic field profiles with a trained neural network based on the relationship of the electrical activity of the heart to the cardiac magnetic fields. The input for training the neural network consisted of the magnetic field profiles above the torso during the heartbeat. The outputs were the dipole intensities which produced those magnetic field profiles. A back propagating algorithm with bias and momentum was utilized for training. The measured and simulated torso magnetic field profiles and magnetocardiograms were used for training the neural network. Estimation of the dipole intensities was performed for unknown magnetic field profiles with the trained neural network. The estimated cardiac dipole intensities were reasonably close to the true dipole intensities. These results show the feasibility of the estimation of cardiac dipole intensities with a trained neural network under a very restricted forward model of the cardiac magnetic fields. Generalization of the results to cover a large population base could be difficult because the activation isochrones are different from subject to subject.

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.

MCG simulations of myocardial infarctions with a realistic heart-torso model

Data from simulations of the anterior myocardial infarction (AMI) and inferior myocardial infarction (IMI) are presented. One infarct located in the anterior section of the left ventricle and a second one in the inferior wall of the left ventricle were modeled. A high-resolution finite element model of a heart and torso was used in this study. Differences in the normal and infarcted fields were computed. Our data suggest that the infarcted region contribution to the total magnetic field can be accounted for by an equivalent current dipole. It might also be possible to detect an infarct from these difference fields constructed for different cases of myocardial infarction. More simulations are needed to determine the relations between infarct sizes and locations and magnetic fields. These relations might then be used to detect various cases of myocardial infarction.

MCG simulations with a realistic heart-torso model

Magnetocardiograms (MCG's) simulated with a high-resolution heart-torso model of an adult subject were compared with measured MCG's acquired from the same individual. An exact match of the measured and simulated MCG's was not found due to the uncertainties in tissue conductivities and cardiac source positions. However, general features of the measured MCG's were reasonably represented by the simulated data for most, but not all of the channels. This suggests that the model accounts for the most important mechanisms underlying the genesis of MCG's and may be useful for cardiac magnetic field modeling under normal and diseased states. MCG's were simulated with a realistic finite-element heart-torso model constructed from segmented magnetic resonance images with 19 different tissue types identified. A finite-element model was developed from the segmented images. The model consists of 2.51 million brick-shaped elements and 2.58 million nodes, and has a voxel resolution of 1.56 x 1.56 x 3 mm. Current distributions inside the torso and the magnetic fields and MCG's at the gradiometer coil locations were computed. MCG's were measured with a Philips twin Dewar first-order gradiometer SQUID-system consisting of 31 channels in one tank and 19 channels in the other.

Comparison of cardiac-induced endogenous fields and power frequency induced exogenous fields in an anatomical model of the human body

Time-domain potentials measured at 64 points on the surface of a large canine heart, considered comparable with those of a human heart, were used to calculate the electric fields and current densities within various organs of the human body. A heterogeneous volume conductor model of an adult male with a resolution of approximately 6 mm3 and 30 segmented tissue types was used along with the admittance method and successive over-relaxation to calculate the voltage distribution throughout the torso and head as a function of time. From this time-domain voltage description, values of [E(t)] and [J(t)] were obtained, allowing for maximum values to be found within the given tissues of interest. Frequency analysis was then used to solve for [E(f)] and [J(f)] in the various organs, so that average, minimum and maximum values within specific bandwidths (0-40, 40-70 and 70-100 Hz) could be analysed. A comparison was made between the computed results and measured data from both EKG waveforms and isopotential surface maps for validation, with good agreement in both amplitude and shape between the computed and measured results. These computed endogenous fields were then compared with exogenous fields induced in the body from a 60 Hz high-voltage power line and a 60 Hz uniform magnetic field of 1 mT directed from the front to the back of the body. The high-voltage power line EMFs and 1 mT magnetic field were used as 'bench' marks for comparison with several safety guidelines for power frequency (50/60 Hz) EMF exposures. The endogenous electric fields and current densities in most of the tissues (except for organs in close proximity to the heart, for example lungs, liver, etc) in the frequency band 40-70 Hz were found to be considerably smaller, between 5% and 10%, than those induced in the human body by the electric and magnetic fields generated by the 60 Hz sources described above.

Effects of tissue conductivity variations on the cardiac magnetic fields simulated with a realistic heart-torso model

Cardiac magnetic fields with varying tissue conductivities are simulated. A high-resolution finite-element torso model composed of 19 tissue types and with a voxel resolution of 1.5 mm x 1.5 mm x 3 mm is used. It has a detailed description of tissue geometries and therefore is well suited for analysing the effects of tissue conductivities on the cardiac magnetic fields. The computed results show the greatest sensitivity of the magnetic fields to the changes in the conductivity of blood and myocardium, and less significant sensitivity to the conductivity of the lungs, muscle, fat and other tissues. These results are relevant to future modelling of magnetocardiograms and solving the inverse problem. They also emphasize the importance of careful modelling of the blood and heart regions, and suggest that less attention needs to be directed to bone or fat tissue.