Multiple current dipole estimation in a realistic head model using R-MUSIC.

Neural activity in the human brain can be modeled as a volume conductor with current dipoles representing collections of neuronal sources. Determining the spatio-temporal characteristics of the sources from such models requires a solution to the inverse electrostatic problem. In this study, the Recursive MUSIC algorithm was used to invert combinations of synchronous and asynchronous dipolar sources in an anatomically realistic head model. The performance was analyzed at signal-to-noise ratios from 0 to 30 dB. Localization of independent sources was excellent, even at low signal-to-noise ratios, demonstrating the potential performance advantages of a spatio-temporal analysis over a purely spatial treatment. Localization for synchronous sources was substantially degraded at signal-to-noise ratios below 20 dB, demonstrating a need for improved methods to distinguish between asynchronous and synchronous sources.

Effect of model complexity on EEG source localizations.

How model complexity influences the EEG source localizations was studied with three different finite element models of the head, constructed from segmented MR images of an adult male subject. The complexity of the models varied from 9 to 11 tissue types. The lead fields due to dipolar sources in the motor cortex were computed for all three models. The inverse source localizations were performed with an exhaustive search pattern in the motor cortex area. A set of 100 trial inverse runs was made. It was found that the model with most complexity performed best in localizing the sources in the motor cortex area of the brain.

The influence of brain tissue anisotropy on human EEG and MEG.

The influence of gray and white matter tissue anisotropy on the human electroencephalogram (EEG) and magnetoencephalogram (MEG) was examined with a high resolution finite element model of the head of an adult male subject. The conductivity tensor data for gray and white matter were estimated from magnetic resonance diffusion tensor imaging. Simulations were carried out with single dipoles or small extended sources in the cortical gray matter. The inclusion of anisotropic volume conduction in the brain was found to have a minor influence on the topology of EEG and MEG (and hence source localization). We found a major influence on the amplitude of EEG and MEG (and hence source strength estimation) due to the change in conductivity and the inclusion of anisotropy. We expect that inclusion of tissue anisotropy information will improve source estimation procedures.

Analysis of defibrillation efficacy from myocardial voltage gradients with finite element modeling.

Increasing defibrillation efficacy by lowering the defibrillation threshold (DFT) is an important goal in positioning implantable cardioverter-defibrillator electrodes. Clinically, the DFT is difficult to estimate noninvasively. It has been suggested that the DFT relates to the myocardial voltage gradient distribution, but this relation has not been quantitatively demonstrated. We analyzed the relation between the experimentally measured DFT's and the simulated myocardial voltage gradients provided by finite element modeling. We performed a series of experiments in 11 pigs to measure the DFT's, and created and solved three-dimensional subject-specific finite element models to assess the correlation between the computed myocardial voltage gradient histograms and the DFT's. Our data show a statistically significant correlation between the DFT and the left ventricular voltage gradient distribution, with the septal region being more significant (correlation coefficient of 0.74) than other myocardial regions. The correlation between the DFT and the right ventricular and the atrial voltage gradient, on the other hand, is not significant.

Geometric effects on resistivity measurements with four-electrode probes in isotropic and anisotropic tissues.

We studied via computer simulation the effects of electrode diameter, electrode length, interelectrode spacing, and tissue size on the accuracy of measured tissue resistivities and anisotropy ratios obtained with the widely used four-electrode technique. Such measurements commonly assume an ideal situation in which the four electrodes are infinitesimally small and the tissue is semi-infinite. Our study shows that these geometric factors can significantly affect measured resistivities, particularly for anisotropic tissues. The measured anisotropy ratio is decreased by either 1) increasing the electrode diameter or length relative to the interelectrode spacing of the probe or 2) decreasing tissue size. We have provided an equation for estimating errors in the measured anisotropy ratio from the parameters of electrode and tissue geometries. The simulation findings are supported by our in vitro experimental results.

Sensitivity of transvenous defibrillation models to adaptive mesh density and resolution: the potential for interactive solution times.

The voltage gradients induced in ventricular myocardium by an electric shock have been shown to correlate to the probability of the shock producing a successful defibrillation. Finite element modeling is one method for computing these voltage gradients, although the meshing of complex biomedical domains is difficult on a patient-specific basis. We recently described an adaptive algorithm that automates the generation of finite element meshes for complex 3-D domains from bitmapped images. This article examines the sensitivity of the computed distribution of ventricular voltage gradients to the resolution of the images and to the adapted density of the mesh. The results allow us to establish an adaptation stopping criterion and a minimum input image resolution for modeling transvenous defibrillation. The sensitivity to adapted mesh density was analyzed by comparing voltage gradient histograms from successively finer meshes to histograms from a uniform mesh at the maximum possible density. Comparisons were made using the Kolmogorov-Smirnov test with the number of samples required to detect a 5% difference in the histograms at the 0.05 significance level. Adaptation to a global current density error estimate of 5% or less was required in order to achieve acceptance of the null hypothesis that the distributions were the same in all cases. Defibrillation efficacy, however, is predicted from the voltage gradient in the first quartile, and the results suggest that this region of the cumulative histogram converges faster during mesh adaptation than the histogram as a whole. We also compared histograms from models generated from successively finer input images. The histogram of each model was compared with the histogram obtained from the finest possible resolution. In all cases, the null hypothesis of no difference was accepted at resolutions of 2.3 x 2.3 x 3.0 mm. The average time required to build and adapt models to a 5% accuracy at the first quartile at this resolution was 1.8 min. on a common workstation. We believe that this demonstrates a potential for the eventual synthesis of finite element computations into interactive electrode placement tools on a subject-specific basis.

Object-free adaptive meshing in highly heterogeneous 3-D domains.

Traditional approaches to the generation of finite element meshes are well suited for modeling the homogeneous or mildly heterogeneous domains presented by man-made objects, but are difficult to apply to the complex 3-D domains encountered in some biomedical applications. In this paper, we describe an adaptive algorithm that automates the modeling of these domains. The method differs from traditional approaches in that no explicit description is required of the boundaries between objects with dissimilar material properties. The algorithm uses images of the tissue class to build irregular meshes, and continuity is enforced by constraining the solution at irregular nodes. Local estimates of the error in the flux solution are used to refine the mesh. For an analytic problem with a rapid change along a spherical boundary, the adaptive method converges to a 1% voltage error using 25% of the degrees of freedom required by a uniform refinement, and to a 5% voltage gradient error using 11% of the degrees of freedom. For a defibrillation model in a pig thorax, the voltage gradient solution in the ventricles of the heart converges to within 5% of a uniform mesh solution using less than 8% of the memory and processing resources required by a uniform mesh, which has been the only practical alternative for subject-specific modeling.

Predicting cardiothoracic voltages during high energy shocks: methodology and comparison of experimental to finite element model data.

Finite element modeling has been used as a method to investigate the voltage distribution within the thorax during high energy shocks. However, there have been few quantitative methods developed to assess how well the calculations derived from the models correspond to measured voltages. In this paper, we present a methodology for recording thoracic voltages and the results of comparisons of these voltages to those predicted by finite element models. We constructed detailed 3-D subject-specific thorax models of six pigs based on their individual CT images. The models were correlated with the results of experiments conducted on the animals to measure the voltage distribution in the thorax at 52 locations during synchronized high energy shocks. One transthoracic and two transvenous electrode configurations were used in the study. The measured voltage values were compared to the model predictions resulting in a correlation coefficient of 0.927 +/- 0.036 (average +/- standard deviation) and a relative rms error of 22.13 +/- 5.99%. The model predictions of voltage gradient within the myocardium were also examined revealing differences in the percent of the myocardium above a threshold value for various electrode configurations and variability between individual animals. This variability reinforces the potential benefit of patient-specific modeling.