Yoshiwo Okamoto

Electric Dipole Tracing in the Brain by Means of the Boundary Element Method and Its Accuracy

A method of localizing an electrical dipole in the brain from the scalp potential distribution has been developed with the aid of the boundary element method, in which a real geometry of the head is exactly taken into account and homogeneous electrical conductivity is assumed. Accuracy of the method was evaluated through animal experiments with a cat in which a current dipole was artificially generated in the brain. Deviation of the estimated dipole location from the true one was not random, but rather systematic (probably due to in-homogeneous conductivity distribution). It is numerically found that cavities in the skull disturb the inverse solution especially when the dipole is oriented toward the cavities. In vivo tests of the method were also done for primary somatosensory evoked potentials as a response to median nerve stimulation of a cat and myoclonic EEG. Although the homogeneous approximation was made, it does not change the significance of the results obtained by the present method.

Location of electric current sources in the human brain estimated by the dipole tracing method of the scalp-skull-brain (SSB) head model

Using a realistic, 3-shell head model including the scalp (S), skull (S) and brain (B) with conductivity ratios of 1:1/80:1, respectively, the electrical activity in the human brain recorded by conventional electroencephalography was approximated by 1 or 2 equivalent current dipoles. The dipole locations and vector moments were estimated by minimizing the squared difference between the potentials actually recorded from the scalp and those theoretically calculated from the equivalent dipoles. The validity of this dipole tracing method (the DT of the SSB head model) was tested in patients with focal epileptic seizures undergoing presurgical evaluation with intracranial subdural strip electrodes. Weak currents were passed through 1 or 2 pairs of subdural electrodes to create artificial dipoles. The dipole estimations correctly distinguished between single and double generator sources, but there were certain dislocations of the calculated dipoles. The average error of dislocation was found to be 8.5 mm for the 1-dipole model. That for the 2-dipole model was 6 mm for one of the components and 18 mm for the other. It was concluded that the DT method of the SSB head model can be a valuable clinical tool in 3-dimensional localization of focal epileptic discharges in the human brain.

Three-Dimensional Simulation of the Ventricular Depolarization and Repolarization Processes and Body Surface Potentials: Nornal Heart and Bundle Branch Block

A three-dimensional computer model has been constructed to simulate the ventricular depolarization and repolarization processes in a human heart. The electrocardiogram (ECG), the vectorcardiogram(VCG), and the body surface potential map (BSPM) during the QRS-T period are obtained automatically under certain heart conditions such as bundle branch block and myocardial infarctions. The ventricles, together with bundle branches and the Purkinje fibers, are composed of approximately 50 000 cell units which are arranged in a cubic close-packed structure. A different action potential waveform was assigned to each unit. The heart model is mounted in a homogeneous human torso model. Electric dipoles, which are proportional to the spatial gradient of the action potential, are generated in all the cell units. These dipoles give rise to a potential distribution on the torso surface, which is calculated by means of the boundary element method. The resulting ECGs, VCGs, and BSPMs are within the expected range of clinical observations.

Limitation of the Inverse Problem in Body Surface Potential Mapping

The inverse problem in electrocardiography is ill-conditioned, and small noise included in the measured potentials causes large errors in the solution. Since the inverse problem is mostly described as a linear problem, the entire problem has often been treated in terms of a transfer matrix. The degree of linear independence among the vectors in the transfer matrix, which is directly related to the stability of the solution, is well represented by the singular values of the transfer matrix. By means of the singular value decomposition of the transfer matrix, the stability of solution to the inverse problem has been discussed when the potential data contain noise or the transfer matrix includes some error. We have derived expressions of maximum possible error magnification and a root-mean-square error magnification and, in terms of these parameters, found that only 4 equivalent cardiac dipoles or only 15 independent epicardial potentials can be estimated from body surface potentials when they are measured with an accuracy as high as 99 percent.

Conductivity ratios of the scalp-skull-brain head model in estimating equivalent dipole sources in human brain

The dipole tracing (DT) method estimates the position and vector dipole moment of an equivalent current dipole by minimizing the mean squared error of the dipole potentials at the surface electrode positions. In the scalp-skull-brain/DT (SSB/DT) method, which we have developed, the head model consists of three compartments of uniform conductors corresponding to the scalp, skull and brain. The accuracy of the calculations are mainly dependent on the ratios of the conductivities of the three compartments. The best result was obtained with the conductivity ratios of 1:1/80:1 for the scalp, skull and brain compartments, respectively.

Comparison of source localization of interictal epileptic spike potentials in patients estimated by the dipole tracing method with the focus directly recorded by the depth electrodes

The purpose of the study was to investigate the accuracy of location of equivalent current dipoles estimated by the dipole tracing method (DT) utilizing a realistic 3-shell (scalp-skull-brain) head model (SSB-DT). Three patients with intractable complex partial seizures, diagnosed as having typical temporal seizures were investigated. We recorded the interictal spike potentials with surface electrodes (International 10/20 system) and with intracerebral depth electrodes simultaneously. We compared the location of dipoles of the spikes estimated by the SSB-DT with the focus of the spikes determined by the recording from the depth electrodes. We found that the location of the dipoles estimated by SSB-DT corresponded to the location of the depth electrodes, which could record the epileptic spikes. This finding proved that SSB-DT is reliable and valid for estimating neural activity in deep locations such as the limbic system.

Use of the ventricular propagated excitation model in the magnetocardiographic inverse problem for reconstruction of electrophysiological properties

A novel magnetocardiographic inverse method for reconstructing the action potential amplitude (APA) and the activation time (AT) on the ventricular myocardium is proposed. This method is based on the propagated excitation model, in which the excitation is propagated through the ventricle with nonuniform height of action potential. Assumption of stepwise waveform on the transmembrane potential was introduced in the model. Spatial gradient of transmembrane potential, which is defined by APA and AT distributed in the ventricular wall, is used for the computation of a current source distribution. Based on this source model, the distributions of APA and AT are inversely reconstructed from the QRS interval of magnetocardiogram (MCG) utilizing a maximum a posteriori approach. The proposed reconstruction method was tested through computer simulations. Stability of the methods with respect to measurement noise was demonstrated. When reference APA was provided as a uniform distribution, root-mean-square errors of estimated APA were below 10 mV for MCG signal-to-noise ratios greater than, or equal to, 20 dB. Low-amplitude regions located at several sites in reference APA distributions were correctly reproduced in reconstructed APA distributions. The goal of our study is to develop a method for detecting myocardial ischemia through the depression of reconstructed APA distributions.

Generator mechanisms of epileptic potentials analyzed by dipole tracing method

A new dipole tracing method, based on a realistic head model, was used to determine dipole locations and vector moments of interictal convexity sharp waves recorded (with conventional EEG technique) from the right fronto-temporal region in a patient with partial complex seizures. When the dipole locations in the head model were compared to MRI scans, the majority of the sharp wave dipoles were found to be located in the right hippocampal area. For individual sharp waves, the hippocampal dipoles moved along tracks corresponding to the vector moment directions, suggesting that the electrical sources of the convexity sharp waves were somato-dendritic currents which spread rapidly from one neuron group to the next in the hippocampal area. Previous long-term subdural recording had shown seizure onset in this area. After right-sided anterior temporal lobectomy including the hippocampus the patient has been seizure-free for three months.

EEG Markers for Characterizing Anomalous Activities of Cerebral Neurons in NAT (Neuronal Activity Topography) Method

A pair of markers, sNAT and vNAT, is derived from the electroencephalogram (EEG) power spectra (PS) recorded for 5 min with 21 electrodes (4-20 Hz) arranged according to the 10-20 standard. These markers form a new diagnosis tool “NAT” aiming at characterizing various brain disorders. Each signal sequence is divided into segments of 0.64 s and its discrete PS consists of eleven frequency components from 4.68 (3 × 1.56) Hz through 20.34 (13 × 1.56) Hz. PS is normalized to its mean and the bias of PS components on each frequency component across the 21 signal channels is reset to zero. The marker sNAT consists often frequency components on 21 channels, characterizing neuronal hyperactivity or hypoactivity as compared with NLc (normal controls). The marker vNAT consists of ten ratios between adjacent PS components denoting the over- or undersynchrony of collective neuronal activities as compared with NLc. The likelihood of a test subject to a specified brain disease is defined in terms of the normalized distance to the template NAT state of the disease in the NAT space. Separation of MCI-AD patients (developing AD in 12-18 months) from NLc is made with a false alarm rate of 15%. Locations with neuronal hypoactivity and undersynchrony of AD patients agree with locations of rCBF reduction measured by SPECT. The 2D diagram composed of the binary likelihoods between ADc and NLc in the two representations of sNAT and vNAT enables tracing the NAT state of a test subject approaching the AD area, and the follow-up of the treatment effects.

Body Surface Laplacian Mapping in Patients with Left or Right Ventricular Bundle Branch Block

Body surface Laplacian maps (BSLMs) have been previously reported to provide enhanced capability in localizing and resolving multiple spatially separate myocardial events. However, only a few studies have been reported on the clinical applications of BSLM. To test the clinical utility of BSLMs, BSLMs and body surface potential maps (BSPMs) during ventricular depolarization for complete right or left ventricular bundle branch block (CRBBB or CLBBB) were studied in ten patients in each group. As a control group, ten healthy subjects were also studied using the same procedure. One hundred and twenty‐eight electrodes were placed uniformly over the entire chest and back of the subjects. BSLMs were computed from recorded potentials, using a numerical algorithm. The BSLMs showed multiple and more localized positive and negative activities compared with the BSPMs. In healthy subjects, the BSLMs showed multiple areas of positive activity overlying the RV, LV, and the RV outflow, and negative activity corresponding to RV free‐wall breakthrough and LV anterolateral breakthrough sites, whereas the BSPMs could not separate RV and LV activities. In the patients with CRRRR, the BSLMs showed more localized areas of activity corresponding to the LV apex breakthrough and LV lateral breakthrough, and separated LV lateral and posterior activation. In the patients with CLBBB, the BSLMs showed multiple RV activation, and propagating activation of LV from lateral to posterior. The BSLMs appear to provide enhanced capability in detecting multiple ventricular electrical events associated with normal and abnormal conduction and a more detailed activation sequence of both ventricles in healthy subjects and in the patients with CRBBB and CLBBB. BSLM may provide an important alternative to other imaging modalities in localizing cardiac electrical activity noninvasively.