P. Kuklik

Nonlinear oscillator model reproducing various phenomena in the dynamics of the conduction system of the heart.

A dedicated nonlinear oscillator model able to reproduce the pulse shape, refractory time, and phase sensitivity of the action potential of a natural pacemaker of the heart is developed. The phase space of the oscillator contains a stable node, a hyperbolic saddle, and an unstable focus. The model reproduces several phenomena well known in cardiology, such as certain properties of the sinus rhythm and heart block. In particular, the model reproduces the decrease of heart rate variability with an increase in sympathetic activity. A sinus pause occurs in the model due to a single, well-timed, external pulse just as it occurs in the heart, for example due to a single supraventricular ectopy. Several ways by which the oscillations cease in the system are obtained (models of the asystole). The model simulates properly the way vagal activity modulates the heart rate and reproduces the vagal paradox. Two such oscillators, coupled unidirectionally and asymmetrically, allow us to reproduce the properties of heart rate variability obtained from patients with different kinds of heart block including sino-atrial blocks of different degree and a complete AV block (third degree). Finally, we demonstrate the possibility of introducing into the model a spatial dimension that creates exciting possibilities of simulating in the future the SA the AV nodes and the atrium including their true anatomical structure.

The reconstruction, from a set of points, and analysis of the interior surface of the heart chamber.

Adequate description of heart muscle electrical activity is essential for the proper treatment of cardiac arrhythmias. Contemporary mapping and ablating systems allow a physician to introduce an electrode (catheter) into the human heart, to measure the position of the electrode in space and, simultaneously, the electrical activity timing and the bipolar and unipolar signal amplitudes--which correspond to the electrical viability of the heart muscle. If enough data points are collected, an approximate reconstruction of the heart chamber geometry (anatomy) is possible using also surface data such as the viability and local activity isochrones. Myocardial viability in patients after myocardial infarction is crucial for understanding and treating life threatening arrhythmias. Although there are commercial tools for heart chamber reconstruction, they lack the ability to quantitatively analyse the reconstructed data. Here, we show a method of reconstruction of the left ventricle of the heart from a measured set of data points and perform an interpolation of the measured voltages over the reconstructed surface. Next, we detect regions with voltage in a specified range and compute their areas and circumferences. Our methods allowed us to quantitatively describe the normal muscle, the damaged or scar areas and the border zones between healthy muscle and the scars. In particular, we are able to find geometries of the damaged muscle areas that may be dangerous, e.g. when two such areas lie close to each other creating an isthmus--a macroreentry arrhythmia substrate. This work was inspired by a clinical hypothesis that the size of the border zone corresponds to the rate of occurrence of ventricular arrhythmia in patients after myocardial infarction.

Reentry wave formation in excitable media with stochastically generated inhomogeneities

Clinical research shows that the frequency of arrhythmia events depends on the number and area of the border zones of infarct scars. We investigate the possibility that arrhythmia is initiated by reentry waves generated by the inhomogeneity of conduction velocity at the border zone. The interaction of a plane wave with a spatially extended inhomogeneity is simulated in the FitzHugh- Nagumo model. The inhomogeneity is introduced into the model by modifying the spatial dependence of the diffusion coefficient in a stochastic manner. This results in a rich variety of spatial distributions of conductivity. A plane wave propagating through such a system may break up on the regions with low conductivity and produce numerous spiral waves. The frequency of reentry wave formation is studied as a function of the parameters of the inhomogeneity generation algorithm. Three main scenarios of reentry wave formation were found: unidirectional block, main wave-wavelet collision, and wave break up during collision, on a region in which a conduction velocity gradient occurs. These scenarios are likely candidates for the mechanisms of arrhythmia initiation in a damaged tissue, e.g., the border zone of an infarct scar.

Integration of the data from electroanatomical mapping system and CT imaging modality

Heart mapping systems allow approximate reconstruction of the heart chamber geometry which is used as a base for the representation of the spatial distribution of electrophysiological parameters. Main limitation lies in the difficulty of the reconstruction of the geometry of more complicated areas of the heart. Here, we propose a new method of representation of the spatial distribution of the electrophysiological parameters—an integration of the data points collected by a classical mapping system with the geometry reconstructed from a computed tomography (CT) image. CARTO maps of activation and bipolar viability of seven patients undergoing atrial fibrillation ablation were integrated with the geometry of the left atria reconstructed from the CT image. In all cases, integration was successful with the registration error measured as the distance between objects equal to 2.52xa0±xa00.25xa0mm. Bipolar viability and activation maps were reconstructed on the CT geometry. Our method allowed us to create maps of electrophysiological parameters of anatomically complex structures without the need for their detailed mapping.

Spiral wave breakup in excitable media with an inhomogeneity of conduction anisotropy

Many conditions remodel the heart muscle such that it results in a perturbation of cells coupling. The effect of this perturbation on the stability of the spiral waves of electrochemical activity is not clear. We used the FitzHugh-Nagumo model of an excitable medium to model the conduction of the activation waves in a two-dimensional system with inhomogeneous anisotropy level. Inhomogeneity of the anisotropy level was modeled by adding Gaussian noise to diffusion coefficients corresponding with lateral coupling of the cells. Low noise levels resulted in a stable propagation of the spiral wave. For large noise level conduction was not possible due to insufficient coupling in direction perpendicular to fibers. For intermediate noise intensities, the initial wave broke up into several independent spiral waves or waves circulating around conduction obstacles. At an optimal noise intensity, the number of wavelets was maximized-a form of anti-coherent resonance was obtained. Our results suggest that the inhomogeneity of conduction anisotropy may promote wave breakup and hence play an important role in the initiation and perpetuation of the cardiac arrhythmias.

Causality in Atrial Fibrillation determined by transfer entropy

High level of complexity makes characterization of wave conduction during Atrial Fibrillation (AF) very difficult. Here we aim to use statistical approach characterizing AF as a system with determined information flow using a concept of transfer entropy. Left and right atrial 60 s electrograms were recorded at high right atrium (HRA), coronary sinus (CS) and Left Atrial Appendage (LAA) in 42 patients undergoing catheter ablation of AF. Transfer entropy (TE) was used to asses causality calculating direction and extent of information flow between neighboring sites in the atria. TE was calculated between electrograms recorded along each catheter. Additionally, numerical analysis were performed on a set of unidirectionally coupled stochastic signals modeling electrical activity during AF. We found an asymmetry in information flow along the catheters. In HRA catheter, in general, information flows from proximal to distal portion of the catheter and in CS from the distal towards the proximal portion. The dominant flow of information from the base into the LAA was the most pronounced and in agreement with believed passive role of LAA in maintenance of AF. Information flow in the atria during AF is asymmetric and it is possible to determine the direction of the flow using concept of entropy transfer.

Blood flow assessment in a heart with septal defect based on optical flow analysis of magnetic resonance images

This study describes an application based on the optical flow algorithm to construct a 2D velocity field plot. The estimated velocity field is used to track the movement of blood in real time. This methodology has been applied to medical images to quantify blood flow turbulence in the right atrium of the heart. Blood intensity fields that are obtained from clinical MRI scan sequences can be analyzed using this method. Septal defects and other heart diseases can be assessed for degrees of abnormality and post-surgical success can be evaluated. We have developed this technique specifically for characterizing the turbulence generated due to such heart abnormalities. The degree of turbulence and fluid shear stress can be determined from the measured flow field. The cardio dynamics information that is based on flow analysis and visualization of blood offers potential for the detection and quantification of myocardial malfunctioning.