G. Huiskamp

The depolarization sequence of the human heart surface computed from measured body surface potentials

A method for computing the activation sequence at the ventricular surface from body surface potentials, has been adapted to handle measured data. By using measured anatomical data together with a 64-channel ECG (electrocardiogram) recording of the same subject for three subjects, it is shown that the model is able to determine activation sequences on the heart surface which closely resemble similar data obtained through invasive measurement as reported in literature.<<ETX>>

Difference formulas for the surface Laplacian on a triangulated surface

Abstract Different approximating expressions for the surface Laplacian operator on a triangulated surface are derived. They are evaluated on a triangulated spherical surface for which the analytical expression of the surface Laplacian is known. It is shown that in order to obtain accurate results, due care has to be taken of irregularities present in the triangulation grid. If this is done, the approximation will equal the performance of an expression based on least squares which can be derived. Next the different approximations obtained are used as a regularization operator in the solution of an ill-posed inverse problem in electrical volume conduction. It is shown that in this application a crude approximation to the surface Laplacian suffices.

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.

Tailored versus realistic geometry in the inverse problem of electrocardiography

The stability and applicability of a previously developed inverse procedure for the noninvasive determination of the activation sequence of the human heart has been evaluated. In particular, the possibility of using a standard geometrical configuration representing the heart and the inhomogeneous volume conductor in this procedure has been tested. Results show that in order to obtain reliable inverse solutions, true tailored geometry should be used.<<ETX>>

Heart position and orientation in forward and inverse electrocardiography.

A study has been made of the influence of the position and orientation of the heart within the thorax on computed ECG waveforms (forward model) and on computed activation sequences (inverse model) in three normal cases. Results show that differences in heart position and orientation, associated with shifts relative to the precordium of the order of 0·5 cm, may result in amplitude differences or QRS waveforms of typically tenths or millivolts, which consistute part of the observed interindividual variability of the ECG. The inverse study shows that, in spite of similar errors in estimated heart position and orientation, stable solutions of the ventricular activation sequence can still be found. However, in the case where the heart is very close to precordial leads, the stability of the inverse solution is found to be intrinsically poor.

New quantitative and qualitative approaches to the inverse problem of electrocardiology : their theoretical relationship and experimental consistency

In addition to formidable theoretical obstacles that a proposed solution to the inverse electrocardiology problem must overcome, there are great practical difficulties in establishing its accuracy in actual clinical application. However, the recent appearance of two fundamentally independent treatments of the inverse problem raises the possibility that they may be used in tandem to help establish their individual accuracy. Thus, if the two methods give incompatible results in application then one of the methods must be inaccurate. Conversely, if the two methods give compatible results then the accuracy of both methods is supported (for the particular quantities measured) subject only to the validity of the assumptions common to both methods. We have compared results from the application of a quantitative integral equations based method with that of a qualitative differential topology inspired approach in three healthy volunteers. The output examined consists of measurements of the times of appearance of epicardial sources (depolarization wavefront breakthroughs) and sinks of the ventricular surface activation map. The extent of agreement on source/sink times between the methods was consistent with the resolution limits imposed by noise and discrete sampling on derivatives of the electrocardiogram. When events defined by the integral method occurring within 2 ms of each other are grouped together (and their times averaged), the two methods agreed on source/sink times to within 3 ms except in two instances where they differed by 5 ms. The measurements made by the two methods were found to be highly correlated (R = 0.95). While the quantitative method alone rests on a variety of modeling and procedural assumptions, the only assumption common to both methods is the uniform dipole layer hypothesis. Thus, subject to this single assumption, one may infer the accuracy of the quantitative method in healthy individuals for epicardial source/sink times. On the other hand, coupling with the far more detailed quantitative method allows further useful characterization of the output of the qualitative method. In particular, this study provides convincing evidence that the major deflections of the spatial velocity electrocardiogram are coupled to particular epicardial sources and sinks, as has been previously conjectured on theoretical grounds. This raises the possibility of bedside evaluation of these epicardial events.

Invasive confirmation of the human ventricular activation sequence as computed from body surface potentials

The authors recorded body surface potential maps (BSPMs) of a patient undergoing a catheterization. During this catheterization the heart was paced on a fixed location in the right ventricle. They then used an inverse procedure, which was developed previously, to determine the isochrones of ventricular activation noninvasively, from the measured BSPMs. The computed activation sequence for the paced heartbeat was in complete accordance with what was known invasively. It reflected the spreading of a single wavefront starting at the exact site of pacing in the right ventricle.<<ETX>>

Physiologically based constraints in the inverse problem of electrocardiography

Two formulations of the inverse problem of electrocardiography are presented which implicitly contain physiologically based spatio-temporal constraints. One formulation is based on the UDL model of ventricular activation, the other on a new, well posed formulation of the inverse problem. When applied to data of a WPW patient, results show agreement with invasive information regarding the site of pre-excitation, right ventricular epicardial breakthrough and termination of activation.

Implicit and explicit constraints in inverse electrocardiography

This paper reviews the major distributed source models that have been postulated over the years to support the interpretation of observed body surface potentials: double-layer models, the source description in terms of epicardial (ie, pericardial) potentials, and its equivalent: the distributed monolayer. This includes a presentation and discussion of a source model that has been developed over the past decade: the uniform double-layer model. The properties of this model are contrasted to those of other distributed source models from the perspective of their inherent capacity for imposing the constraints that are essential for regularizing the involved inverse problem.

Spatio-Temporal Constraints in Inverse Electrocardiography

One cannot uniquely determine the bioelectric sources in the heart solely from the observed potentials on the body surface [1] without first postulating models of cardiac electric sources and of a volume conductor that characterizes the torso’s passive electric properties. With both models in place, one can solve the forward problem by computing the potential distribution on the body surface from the given sources [2], and the inverse problem [3] by estimating source-model parameters from the observed body-surface potentials (given the restrictions implied by the source model).The inverse problem can, therefore, be viewed as a parameter-estimation problem.