Thom F. Oostendorp

The conductivity of the human skull: results of in vivo and in vitro measurements

The conductivity of the human skull was measured both in vitro and in vivo. The in vitro measurement was performed on a sample of fresh skull placed within a saline environment. For the in vivo measurement a small current was passed through the head by means of two electrodes placed on the scalp. The potential distribution thus generated on the scalp was measured in two subjects for two locations of the current injecting electrodes. Both methods revealed a skull conductivity of about 0.015 (1//spl Omega/)/m. For the conductivities of the brain, the skull and the scalp a ratio of 1:1/15:1 was found. This is consistent with some of the reports on conductivities found in the literature, but differs considerably from the ratio 1:1/80:1 commonly used in neural source localization. An explanation is provided for this discrepancy, indicating that the correct ratio is 1:1/15:1.

Source parameter estimation in inhomogeneous volume conductors of arbitrary shape

It is demonstrated that the use of a direct matrix inverse in the solution of the forward problem in volume conduction problems greatly facilitates the application of standard, nonlinear parameter estimation procedures for finding the strength as well as the location of the current source inside an inhomogeneous volume conductor of arbitrary shape from potential measurements at the outer surface (inverse procedure). This, in turn, facilitates the inclusion of a priori constraints. Where possible, the performance of the method is compared to that of the Gabor-Nelson method. Applications are in the field of bioelectricity (e.g. electrocardiography and electroencephalography).<<ETX>>

Validating the boundary element method for forward and inverse EEG computations in the presence of a hole in the skull.

Holes in the skull may have a large influence on the EEG and ERP. Inverse source modeling techniques such as dipole fitting require an accurate volume conductor model. This model should incorporate holes if present, especially when either a neuronal generator or the electrodes are close to the hole, e.g., in case of a trephine hole in the upper part of the skull. The boundary element method (BEM) is at present the preferred method for inverse computations using a realistic head model, because of its efficiency and availability. Using a simulation approach, we have studied the accuracy of the BEM by comparing it to the analytical solution for a volume conductor without a hole, and to the finite difference method (FDM) for one with a hole. Furthermore, we have evaluated the influence of holes on the results of forward and inverse computations using the BEM. Without a hole and compared to the analytical model, a three‐sphere BEM model was accurate up to 5–10%, while the corresponding FDM model had an error <0.5%. In the presence of a hole, the difference between the BEM and the FDM was, on average, 4% (1.3–11.4%). The FDM turned out to be very accurate if no hole is present. We believe that the difference between the BEM and the FDM represents the inaccuracy of the BEM. This inaccuracy in the BEM is very small compared to the effect that holes can have on the scalp potential (up to 450%). In regard to the large influence of holes on forward and inverse computations, we conclude that holes in the skull can be treated reliably by means of the BEM and should be incorporated in forward and inverse modeling. Hum. Brain Mapping 17:179–192, 2002.

ECGSIM: an interactive tool for studying the genesis of QRST waveforms

Background: Discussion about the selection of diagnostic features of the ECG and their possible interpretation would benefit from a model of the genesis of these signals that has a sound basis in electrophysiology as well as in physics. Recent advances in computer technology have made it possible to build a simulation package whereby the genesis of ECG signals can be studied interactively. Design: A numerical method was developed for computing ECG signals on the thorax, as well as electrograms on both endocardium and epicardium. The source representation of the myocardial electric activity is the equivalent double layer. The transfer factors between the electric sources and the resulting potentials on the heart surface as well as on the body surface were computed using a realistic thorax model. Results and conclusion: The resulting transfer factors were implemented in a simulation program. The program allows the user to make interactive changes in the timing of depolarisation and repolarisation on the ventricular surface, as well as changing the local source strength, and to inspect or document the effect of such changes instantaneously on electrograms and body surface potentials, visualised by waveforms as well as by potential maps and movies. The entire simulation package can be installed free of charge from www.ecgsim.org.

Non-Invasive Imaging of Cardiac Activation and Recovery

The sequences of activation and recovery of the heart have physiological and clinical relevance. We report on progress made over the last years in the method that images these timings based on an equivalent double layer on the myocardial surface serving as the equivalent source of cardiac activity, with local transmembrane potentials (TMP) acting as their strength. The TMP wave forms were described analytically by timing parameters, found by minimizing the difference between observed body surface potentials and those based on the source description. The parameter estimation procedure involved is non-linear, and consequently requires the specification of initial estimates of its solution. Those of the timing of depolarization were based on the fastest route algorithm, taking into account properties of anisotropic propagation inside the myocardium. Those of recovery were based on electrotonic effects. Body surface potentials and individual geometry were recorded on: a healthy subject, a WPW patient and a Brugada patient during an Ajmaline provocation test. In all three cases, the inversely estimated timing agreed entirely with available physiological knowledge. The improvements to the inverse procedure made are attributed to our use of initial estimates based on the general electrophysiology of propagation. The quality of the results and the required computation time permit the application of this inverse procedure in a clinical setting.

Interpolation on a triangulated 3D surface

Abstract An interpolation method for scalar functions on a rectangular grid on a planar surface is extended to the interpolation function on a closed three-dimensional triangulated surface of arbitrary shape. Two variants are considered. The first one constrains the Laplacian of the function to be zero at points where the function values are unknown. The second one minimizes the Laplacian at all points of the surface considered. Some illustrative examples of both variants are given in applications to the display of potential distributions on the boundary surface of an electrical volume conductor.

The surface Laplacian of the potential: theory and application

The use of the surface Laplacian of the potential (L/sub s/) in bioelectricity is discussed. Different estimates of L/sub s/, in particular the field measured by coaxial electrodes, are compared to that of the true Laplacian. A method to compute L/sub s/ on the surface of an inhomogeneous volume conductor of arbitrary shape resulting from assumed electrical sources is introduced. In two applications the sensitivity of the body surface Laplacian is compared to that of body surface potentials. This comparison is carried out for dipolar sources within the human brain as well as for distributed sources within the heart.

Investigation of tDCS volume conduction effects in a highly realistic head model.

OBJECTIVE We investigate volume conduction effects in transcranial direct current stimulation (tDCS) and present a guideline for efficient and yet accurate volume conductor modeling in tDCS using our newly-developed finite element (FE) approach. APPROACH We developed a new, accurate and fast isoparametric FE approach for high-resolution geometry-adapted hexahedral meshes and tissue anisotropy. To attain a deeper insight into tDCS, we performed computer simulations, starting with a homogenized three-compartment head model and extending this step by step to a six-compartment anisotropic model. MAIN RESULTS We are able to demonstrate important tDCS effects. First, we find channeling effects of the skin, the skull spongiosa and the cerebrospinal fluid compartments. Second, current vectors tend to be oriented towards the closest higher conducting region. Third, anisotropic WM conductivity causes current flow in directions more parallel to the WM fiber tracts. Fourth, the highest cortical current magnitudes are not only found close to the stimulation sites. Fifth, the median brain current density decreases with increasing distance from the electrodes. SIGNIFICANCE Our results allow us to formulate a guideline for volume conductor modeling in tDCS. We recommend to accurately model the major tissues between the stimulating electrodes and the target areas, while for efficient yet accurate modeling, an exact representation of other tissues is less important. Because for the low-frequency regime in electrophysiology the quasi-static approach is justified, our results should also be valid for at least low-frequency (e.g., below 100 Hz) transcranial alternating current stimulation.

Simulating Transcranial Direct Current Stimulation With a Detailed Anisotropic Human Head Model

Transcranial direct current stimulation (tDCS) is a noninvasive brain stimulation technique able to induce long-lasting changes in cortical excitability that can benefit cognitive functioning and clinical treatment. In order to both better understand the mechanisms behind tDCS and possibly improve the technique, finite element models are used to simulate tDCS of the human brain. With the detailed anisotropic head model presented in this study, we provide accurate predictions of tDCS in the human brain for six of the practically most-used setups in clinical and cognitive research, targeting the primary motor cortex, dorsolateral prefrontal cortex, inferior frontal gyrus, occipital cortex, and cerebellum. We present the resulting electric field strengths in the complete brain and introduce new methods to evaluate the effectivity in the target area specifically, where we have analyzed both the strength and direction of the field. For all cerebral targets studied, the currently accepted configurations produced sub-optimal field strengths. The configuration for cerebellum stimulation produced relatively high field strengths in its target area, but it needs higher input currents than cerebral stimulation does. This study suggests that improvements in the effects of transcranial direct current stimulation are achievable.

Connecting Mean Field Models of Neural Activity to EEG and fMRI Data

Progress in functional neuroimaging of the brain increasingly relies on the integration of data from complementary imaging modalities in order to improve spatiotemporal resolution and interpretability. However, the usefulness of merely statistical combinations is limited, since neural signal sources differ between modalities and are related non-trivially. We demonstrate here that a mean field model of brain activity can simultaneously predict EEG and fMRI BOLD with proper signal generation and expression. Simulations are shown using a realistic head model based on structural MRI, which includes both dense short-range background connectivity and long-range specific connectivity between brain regions. The distribution of modeled neural masses is comparable to the spatial resolution of fMRI BOLD, and the temporal resolution of the modeled dynamics, importantly including activity conduction, matches the fastest known EEG phenomena. The creation of a cortical mean field model with anatomically sound geometry, extensive connectivity, and proper signal expression is an important first step towards the model-based integration of multimodal neuroimages.