Wave-particle duality of dissipative vortices and implications for cardiology (Video) Event as iCalendar


30 August 2016

4 - 5pm

Venue: Ground Floor Seminar Room (G10)

Location: 70 Symonds St, Auckland Central

An ABI seminar by Dr. Irina Biktasheva, Department of Computer Science, University of Liverpool


Spiral and scroll waves are nonlinear dissipative patterns occurring in 2- and 3-dimensional excitable and oscillatory media, where they act as organizing centers. Although the vortices become of increasing interest of their own as regimes of self-organisation and transition to chaos, important motivation to study dynamics of dissipative vortices has been, and is, better control of cardiac re-entry underlying dangerous arrhythmias and fatal fibrillation. Recent advances in experimental, theoretical and computer simulation techniques brought the studies closer to practical applications than ever before.

In the simplest 2D case a spiral wave rotates around rotation center R with angular velocity omega. A 3D vortex will rotate around an “organising filament”. Thus, a homogeneous system spontaneously divides into the core, defined by the centre of rotation in 2D or by the organising filament in 3D, and the periphery synchronised by signals from the core, while location of the core is defined by initial conditions, not due to properties of the medium. In presence of a small perturbation, vortex preserves the pattern and slowly changes its frequency and location of the core. Although the regime appears non-localised, as it fills up and synchronises all available space, it behaves as a localised object, only sensitive to perturbations affecting the core. This macroscopic dissipative wave-particle duality is due to localisation of the vortex's Response Functions (RFs) in the immediate vicinity of the core. Knowledge of the response functions allows quantitative prediction of spiral waves’ drift due to small perturbations of any nature, which makes the RFs as fundamental characteristics for spiral waves as mass is for the matter.

We use asymptotics based on cardiac re-entry response functions to predict its dynamics in a moving border zone of recovering ischaemic tissue, due to gradients of cell excitability and cell-to-cell coupling, and heterogeneity of individual cells. In three spatial dimensions, theory predicts conditions for scroll waves to escape into the recovered tissue, where they either collapse or develop fibrillation-like state, depending on filament tension. We confirm these predictions by direct simulations.

In biophysically and anatomically realistic model of human atrium, we demonstrate functional effects of atrial anatomical structures on reentrant wave’s spontaneous drift. Spiral waves drift from thicker to thinner regions, along ridge-like structures of pectinate muscles (PM) and crista terminalis, anchor to PM-atrial wall junctions or to some locations with no obvious anatomical features. The insight can be used to improve low-voltage defibrillation protocols, and predict atrial arrhythmia evolution given a patient specific atrial anatomy.