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.     

Accuracy of single-dipole inverse solution when localising ventricular pre-excitation sites: simulation study

Different factors are investigated that may affect the accuracy of an inverse solution that uses a single-dipole equivalent generator, in a standardised inhomogeneous torso model, when localising the pre-excitation sites. An anatomical model of the human ventricular myocardium is used to simulate body surface potential maps (BSPMs) and magnetic field maps (MFMs) for 35 pre-excitation sites positioned on the epicardial surface along the atrioventricular ring. The sites of pre-excitation activity are estimated by the single-dipole method, and the measure for the accuracy of the localisation is the localisation error, defined as the distance between the location of the best-fitting single dipole and the acutal site of pre-excitation in the ventricular model. The findings indicate that, when the electrical properties of the volume conductor and lead positions are precisely known and the ‘measurement’ noise is added to the simulated BSPMs and MFMs, the single-dipole method optimally localises the pre-excitation activity 20 ms after the onset of pre-excitation, with 0.71±0.28 cm and 0.65±0.30 cm using BSPMs and MFMs, respectively. When the standard torso model is used to localise the sites of onset of the pre-excitation sequence initiated in four individualised torso models, the maximum errors are as high as 2.6–3.0 cm (even though the average error, for both the BSPM and MFM localisations, remains within the 1.0–1.5 cm range). In spite of these shortcomings, it is thought that single-dipole localisations can be useful for non-invasive pre-interventional planning.     

Comparison between electrocardiographic and magnetocardiographic inverse solutions using the boundary element method

The accuracy of imaging cardiac sources using electrocardiographic and magnetocardiographic signals is influenced by thoracic inhomogeneities, e.g. the lungs and cardiac blood masses. The effects is investigated of such inhomogeneities on the body-surface potential maps (BSPM) and magnetic-field maps (MFM) inverse solutions for a single moving dipole as the source model and a realistic torso model as the volume conductor, by employing a node-based boundary element method. Using the same number and placement of the body-surface potential and magnetic field leads, a comparison is obtained of the numerical accuracy of body-surface potential and magnetic field leads. The results show that, with no noise added, the body-surface potential solution is less sensitive to the exclusion of the inhomogeneities than the magnetic field solution. The influence of noise on the BSPM and MFM localization is comparable for x (left-right) and y (foot-head) oriented dipoles, and the BSPM localisation is more accurate than the MFM localisation for z (anterior-posterior) oriented dipoles.     

The use of the singular value decomposition in electrocardiography

In the paper it is shown that singular value decomposition (s.v.d.) is an excellent tool for studying the limit properties of a feasible solution for the inverse problem in electrocardiography. When s.v.d. is applied to the transfer matrix, relating equivalent heart sources to the skin potentials, it provides a measure of the observability. In an example presented, a series of orthonormal potential patterns on a pericardial surface are found in an order of decreasing observability. When s.v.d. is applied to a data matrix, consisting of skin potentials as a function of time and position, one finds the normalised principal components both in time and space. An appropriate use of the singular values leads to a noise filtering algorithm, which at the same time results in useful data reduction. Comparison of spatial potential patterns derived from both the transfer matrix and the data matrix may, finally, be used to evaluate the assumptions on the transfer.     

Accuracy of Quadratic Versus Linear Interpolation in Noninvasive Electrocardiographic Imaging (ECGI)

Electrocardiographic Imaging (ECGI) is a cardiac functional imaging modality, noninvasively reconstructing epicardial potentials, electrograms and isochrones (activation maps) from multi-channel body surface potential recordings. The procedure involves solving Laplace’s equation in the source-free volume conductor between torso and epicardial surfaces, using Boundary Element Method (BEM). Previously, linear interpolation (LI) on three-noded triangular surface elements was used in the BEM formulation. Here, we use quadratic interpolation (QI) for potentials over six-noded linear triangles. The performance of LI and QI in ECGI is evaluated through direct comparison with measured data from an isolated canine heart suspended in a human-torso-shaped electrolyte tank. QI enhances the accuracy and resolution of ECGI reconstructions for two different inverse methods, Tikhonov regularization and Generalized Minimal Residual (GMRes) method, with the QI-GMRes combination providing the highest accuracy and resolution. QI reduces the average relative error (RE) between reconstructed and measured epicardial potentials by 25%. It preserves the amplitude (average RE reduced by 48%) and morphology of electrograms better (average correlation coefficient for QI ∼ 0.97, LI ∼ 0.92). We also applied QI to ECGI reconstructions in human subjects during cardiac pacing, where QI locates ventricular pacing sites with higher accuracy (≤ 10 mm) than LI (≤ 18 mm).     

Noninvasive Localization of Electromagnetic Epileptic Activity. II. Demonstration of Sublobar Accuracy in Patients with Simultaneous Surface and Depth Recordings

Seven patients with complex partial epileptic seizures undergoing invasive video/EEG-monitoring were investigated with a combination of 10 subdural strip electrode contacts (subtemporal + lateral temporal), and 22 extracranial recording sites. In each patient spikes with different intracranial distributions were identified, and for those with similar distributions the extracranial activity was averaged. A new inverse solution method called EPIFOCUS (Grave et al. 2001, this issue) was used to reconstruct the sources of both single and averaged spikes in a standard 3D-MRI, and a statistical analysis was performed in order to demonstrate location differences between spikes with different intracranial distributions. The results revealed significantly more anterior and ventral source locations for subtemporal compared to lateral temporal spikes. Within the subtemporal group, medial spikes had more mesial and dorsal locations compared to lateral ones. In the lateral temporal group, more anterior and ventral locations were obtained for anterior compared to posterior spikes. The results demonstrate the applicability of EPIFOCUS in the localization of sources in the temporal lobe with sublobar accuracy. This possibility may become important in the future, for instance in identifying cases where amygdalo-hippocampectomy or other limited temporal lobe resections may replace the standard en bloc resections.     

Evaluation of sLORETA in the Presence of Noise and Multiple Sources

The standardized Low Resolution Brain Electromagnetic Tomography method (sLORETA) can be used to compute statistical maps from EEG and MEG data that indicate the locations of the underlying source processes with low error. These maps are derived by performing a location-wise inverse weighting of the results of a Minimum Norm Least Squares (MNLS) analysis with their estimated variances. In this contribution, we evaluate the performance of the method under the presence of noise and with multiple, simultaneously active sources. It is shown that the sLORETA method localizes well, as compared to other linear approaches such as MNLS and LORETA. However, simultaneously active sources can only be separated if their fields are distinct enough and of similar strength. In the context of a strong or superficial source, weak or deep sources remain invisible, and nearby sources of similar orientation tend not to be separated but interpreted as one source located roughly in between.     

Minimum-norm estimation in a boundary-element torso model

The paper deals with the bioelectric and biomagnetic inverse problems. The authors present a method to estimate primary-current distributions in a homogeneous, realistically shaped boundary-element torso model. The reconstruction surface is triangulated to keep the procedure computationally feasible. The minimum-norm estimate is computed on the basis of separate electric and magnetic signals, as well as from combined data. The method can be used both for heart and brain studies. Simulation results for current-dipole sources in a homogeneous realistic torso are discussed.     

Two Dimensional Inverse Imaging (2DII) of Current Sources in Magnetoencephalography

A new magnetoencephalographic (MEG) technique for imaging the cortical distribution of neuronal activity is described. An iterative algorithm is employed, which successively alters an initial estimate of cortical source structure until it corresponds to the measured magnetic field data. In this new technique, the continuum of electrical activity across the cortical surface is modeled as a dense grid of thousands of single equivalent current dipoles. MEG imaging of both compact and extended sources is facilitated by a wavelet-like transformation of the source space into a sequence of successively smaller composite source structures. Two of these composite source structures are combined during each iterative step to generate an improved estimate of the cortical source structure. Thus, inversion of the complete gain matrix corresponding to thousands of cortical sources is not performed. The technique requires only moderate PC based resources even for very large source grids. In contrast to minimum norm MEG imaging methods, this new algorithm is insensitive to random noise in the data. If available, prior knowledge of source structure from other imaging techniques, such as PET, MRI and fMRI, is easily incorporated as additional constraints on the source structure solution. Source images solutions corresponding to simulated data are presented. In addition, the technique is applied to source imaging of real MEG data incorporating cortical structure from volumetric MRI data. These results demonstrate the capability of our new technique for imaging combinations of compact and extended source structures.     

Comparison of multipole and mean value methods to quantify dust in human lungs: Simulating the magnetopneumography procedure

Magnetopneumography (MPG) can quantify the retention of magnetisable particles in the lung acquired, for instance, in welding work. MPG is non-invasive and is used in occupational health, industrial hygiene and lung physiology. Following a brief magnetisation, the remanent magnetic field is mapped with magnetometers outside the thorax. There is no unique analytical inverse solution to this class of magnetostatic problem, and various inverse methods have been proposed. In the present study, the influence of variations in size and shape of the lungs and chest, magnetic measurement noise, positional noise and spatial dust distribution are investigated in five inverse methods. The mean value of the field map, calibrated against a lung phantom, is the commonly used method. Lung and chest size influence the mean value method solutions strongly. Correction for chest size reduces these errors, but bias errors and sensitivity to the deposition pattern remains a problem. A multipolar expansion, including dipolar, quadrupolar and octopolar moments, yields best results overall, provided the signal-to-noise ratio is sufficient. This inverse solution is unbiased, requires no calibration with phantom lung models and serves to minimise errors due to inter-individual differences in anatomy and to inhomogeneous retention of inhaled dust.     

Prevalence of Atrial Fibrillation and Relation to Echocardiographic Parameters in a Healthy Asymptomatic Rural Korean Population

Atrial fibrillation (AF) is the most common arrhythmia worldwide and a potent independent risk factor for stroke. This study aimed to determine the prevalence of AF in a population-based sample of adults in a rural region of Korea. Between January 2005 and December 2009, 4,067 individuals (60.2 ± 11.2 yr old, M: F = 1,582:2,485) over 21 who were residents of the county of Yangpyeong, Korea, participated in the study. AF was assessed on a resting 12-lead electrocardiogram (ECG) in 4,053 of the participants. Blood tests and transthoracic echocardiography (TTE) were also performed to investigate the relationship between left ventricular mass and AF in the study group. Fifty-four cases (32 men) were diagnosed as AF among the 4,053 subjects. The crude prevalence of AF was 1.3%. It was highest (2.3%) among sixty- and seventy- year olds, and higher in men than women in all age groups over 50. The prevalence in men was 2.0%, and in women 0.9%. In univariate analysis, age, male gender, body mass index, total serum cholesterol, alanine transaminase, serum creatinine, adiponectin level, and ischemic heart disease were associated with AF. Among the TTE parameters, systolic and diastolic left ventricular systolic internal dimension (LVID), and LV ejection fraction were associated with AF. In this relatively healthy population in a rural area of Korea, the prevalence of AF is 1.3%, and increases with age. Of the TTE parameters, systolic and diastolic LVID and left atrial diameter are related to prevalence of AF.

Graphical Abstract

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