Medical background information

Human heart

In its function as a pump the heart drives the cardiovascular system. A single working cycle of the heart consists of the contraction of both atria followed by that of the ventricles, where blood is pressed towards the lung and into the systemic circulation by the right and left ventricle respectively. The heart rhytm is controlled by several interacting systems: through the autonomous heart-internal excitation-conduction-system, via Vagus and Sympathicus through various specialized brain regions, finally through several hormonal systems.

Schrittmacher- und Erregungsleitungsystem

Arrhythmias in most cases are caused by malfunctions of the excitation-conduction-system, that one one hand comprises the primary impulse generator - the so-called sine node -, and on the other hand embodies the HIS-bundle, which is responsible for the correct timing of the contractions of the different parts of the heart muscle. The whole system works on an electro-physiological basis. Arrhythmias can be harmless, but they can also increase the risk to come down with certain other diseases like e.g. stroke. In the case of the Sudden Cardiac Death (SCD) they can even be letal. Frequently arrhythmias are a consequence of organic heart diseases like e.g. the myocard infraction.
The electrocardiogram (ECG) is a standard instrument for the diagnosis of arrhythmias. Usually it is visually inspected by the physician, but it is also used to calculate numerical quantities, that are presumed to be indicators for certain diseases or the risk to fall ill with them in the future.

Electrocardiogram

Amongst other things the ECG is utilized to comprehend the so-called heart rate variability (HRV), i.e. the time- and exposure-dependent variation of the heart rate. The quantification of the HRV and the formulation of criteria for the estimation of the risk to fall ill with a certain heart disease is a difficult task investigated by many researchers. It involves a variety of mathematical techniques.

 

Lorenzplots: ECGs of a healthy individual (left) and a person that died of SCD some time after the measurement (right)

Approach

Within the project the time intervals between successive heart beats - so-called RR-intervals - as extracted from an ECG are investigated using methods from non-linear time series analysis as well as methods of pattern recognition. In doing so two intentions are followed up: the discovery of new risk parameter for the appearance of SCD and the automatic detection of Atrial Fibrillation utilizing ECGs of less than one hour in length. .

In the case of the SCD-risk parameter the time series constituted by the RR-intervals extracted from 24-hour-electrocardiograms are investigated. They typically contain 100 000 values, and on the basis of known facts from biology and anatomy it is most likely that the stochastic process underlying this time series is non-linear.
The time series are visualized using so-called Lorenz plots: By always grouping three successive RR-intervals together and viewing this triple as a point in 3-dimensional euclidean space the whole time series of RR-intervals appears as a structured cloud of points in space. Obviously in doing so one has dropped a lot of the dynamical information contained in the sequence of RR-intervals. However it turns out that there are significant differences between the shapes of Lorenz plots of healthy individuals and such with some kind of heart disease. The RR-intervals of a healthy person appear as a characteristic club-shaped structure of a size within a specific range. Structures appearing beside the club-shape, or deformations of this form correspond to pathologies in the heart rhythm. These pathologies may be so dominant that the normal club-shape completely disappears.

Morphological classification of Lorenplots is performed using two different methods: One approach utilizes local dimension numbers, similiar to the Hausdorff dimension known in Topology. The distribution of these numbers is characterized through numerical parameters, which are in this way used as quantities to classify Lorenzplots. The relevance of the classification thus obtained is validated using ECGs classified by a physician. The second method of morphological classification is based on a clustering algorithm, that reduces the original step by step to a simple easy to characterize shape. Again the correlation between the appearing simple shapes and the SCD-risk must be evaluated by comparison with classified ECGs.

The implementation of the morphological classification of 3-dimensional Lorenz plots utilizing topological dimensions by order of the project partner Ganimed ECG Laboratory led to the software coRRida. It is used for ECG-analysis for medical and research purposes.