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Simulations show possible new mechanism for heart failure

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  • medical research

Investigations of a new discrete heart model, which also takes modified cells or a disturbed cell-to-cell coupling into account, describe a possible new mechanism for severe cardiac arrhythmia and the resulting heart failure. In simulations, corresponding cardiac dynamics are caused by percolating pathologically modified cells within a sufficiently large area of tissue.

Comparison of re-entry phenomena in numerical simulations of the electrical activity (transmembrane potential, resting state black, excited state red to yellow) in a two-dimensional heart model. Computations in (a) a homogeneous medium and (b) a medium with a circular heterogeneity (bottom right).

The propagation of electrical signals in the heart of a mammal is usually modelled with reaction-diffusion equations. This opens up the possibility of realistically simulating biosignals such as the electrocardiogram (ECG) or the magnetocardiogram (MCG). On the other hand it is known that cardiac tissue is composed of relatively large muscle cells (length: approx. 0.1 mm) which are coupled to each other by so-called “gap junctions”. Electrical signals in the heart thus propagate in a coarse-grain discrete medium. A heterogeneous, discrete medium occurs if cells die or if their properties are modified with a pathological pattern. Simulations have provided PTB scientists with new findings concerning the influence of such heterogeneities on the occurrence of life-threatening cardiac arrhythmia.

Quantitatively speaking, continuum models describe the dynamics of non-linear waves correctly as long as the density of the heterogeneities is not too large. This density corresponds to the heart tissue, for example, to the part of the heart muscle cells showing pathologically modified activity or to the number of disturbed connections between adjacent cells. Numerical simulations have shown that the heterogeneities in the model have to be taken into account explicitly (multi-scale modelling) as soon as their density exceeds a critical value. This value lies roughly below the percolation threshold of the cell compound, which amounts to, e.g., 50 % of pathological cells for a square lattice and 66 % for a hexagonal one.

This finding is important to understand cardiac arrhythmia. Around the percolation threshold, the wave propagation is strongly disturbed, and due to the heterogeneities, a re-activation of the cells (also called “re-entry”) is triggered. It can lead to high-frequency activity of the heart tissue (tachycardia) or to irregular, chaotic activity (fibrillation). The re-entry phenomenon caused by heterogeneities (Figure b) looks very different to the well-known and thoroughly investigated phenomenon of the spiral re-entry dynamics in homogeneous media (Figure a). The irregular activity pattern of the cells leads to a loss of the synchronisation of the heart muscle cells – which is vital for the pumping function of the heart. If this condition is not suppressed early enough by massive intervention (defibrillation), sudden cardiac death becomes inevitable.


Sergio Alonso
Department 8.4 Mathematical Modelling and Data Analysis
Tel. +49(0)30 8481-7948
E-Mail: sergio.alonso(at)ptb.de

Scientific publications

Alonso, S.; Kapral, R.; Bär, M.: Effective medium theory for reaction rates and diffusion coefficients of heterogeneous systems. Phys. Rev. Lett. 102 (2009) 238302

Alonso, S.; Bär, M.; Panfilov, A.V.: Effects of reduced discrete coupling on filament tension in excitable media. Chaos (2011) 013118