Response functions for drift of spiral and scroll waves
Lead Research Organisation:
University of Warwick
Department Name: Mathematics
Abstract
Rotating spiral waves (in two dimensions) and scroll waves (in three dimensions) are a form of self-organization observed in numerous spatially extended systems of physical, chemical and biological nature. The most important of these is heart muscle where rotating waves are responsible for re-entrant arrhythmias, including the most lethal one, the ventricular fibrillation. Under ideal conditions, a spiral/scroll wave commonly rotates steadily around a nonmoving center/filament. However, any symmetry-breaking perturbation, always present in reality, causes a gradual change in rotation frequency and in spatial location of the centre/filament, i.e. a drift. Understanding this drift is vitally important for applications. While drift may be observed in direct numerical simulations, these computations are often expensive and lack generality. There exists a universal asymptotic theory of drift caused by small perturbations. Its applicability is contingent on knowledge of so called response functions (RFs). In a few known cases, the RFs are essentially nonzero only near the core. As a result of this localization, spiral/scroll waves behave like point/string objects, despite being apparently nonlocal regimes. This unique kind of wave-particle duality is directly related to the remarkable stability of spiral/scroll waves. The asymptotic theory exploits this property and allows, in principle, a much simpler and orders of magnitude more efficient prediction of their drift than direct numerical simulations. Once found, RFs of a particular model allow one to predict the drift of spirals and scrolls in response to arbitrary perturbations. The current proposal aims to develop regular and generic methods of obtaining the RFs and then to make the asymptotic theory into an actually working tool for understanding and controlling rotating waves in real systems.
People |
ORCID iD |
Dwight Barkley (Principal Investigator) |
Publications
Andrew Foulkes (Co-Author)
(2010)
Alternative Stable Scroll Waves and Conversion of Autowave Turbulence
Barkley, D.
(2010)
DXSpiral: code for studying spiral waves on a disk
Biktashev V
(2011)
Evolution of Spiral and Scroll Waves of Excitation in a Mathematical Model of Ischaemic Border Zone
in PLoS ONE
Biktashev VN
(2010)
Orbital motion of spiral waves in excitable media.
in Physical review letters
Biktasheva I
(2009)
Computation of the Drift Velocity of Spiral Waves using Response Functions
Biktasheva I
(2010)
Computation of the drift velocity of spiral waves using response functions
in Physical Review E
Biktasheva IV
(2009)
Computation of the response functions of spiral waves in active media.
in Physical review. E, Statistical, nonlinear, and soft matter physics
Foulkes AJ
(2010)
Alternative stable scroll waves and conversion of autowave turbulence.
in Chaos (Woodbury, N.Y.)
Langham J
(2014)
Asymptotic dynamics of reflecting spiral waves.
in Physical review. E, Statistical, nonlinear, and soft matter physics
Title | spiral pinballs |
Description | Video showing spiral waves in excitable media illustrating wave-particle duality. |
Type Of Art | Film/Video/Animation |
Year Produced | 2011 |
Impact | Shown at several public presentations. Has 4 likes on Youtube. |
URL | https://www.youtube.com/watch?v=YGVvZVD_ddo |
Description | The first achievement was a suite of numerical tools for computing Response Functions (RFs) for the types of spiral and scrolls associated with cardiac arrhythmias. The tools are sufficiently general that they can be applied to almost any model/numerical system. This resulted in a number of subsequent studies on the dynamics of spiral and scroll waves. Quite unexpectedly we discovered that the de-pinning of spiral waves from obstacles is far more complex than was believed at the time, and that methods that were thought to de-pin waves would in fact fail in many cases. We provided a mathematical foundation for the newly discovered effect. |
Exploitation Route | The most important next steps are in addressing the behaviour of spiral and scroll waves in complex geometries. One could use our results and our numerical algorithms to address realistic geometries of the heart for example. |
Sectors | Healthcare |
URL | http://repository.liv.ac.uk/1393215/ |
Description | Exeter |
Organisation | University of Exeter |
Department | School of Mathematics |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | Applied for joint Leverhulme Grant (unsuccessful). Scientific discussions. |
Collaborator Contribution | Applied for joint Leverhulme Grant (unsuccessful). Scientific discussions. |
Impact | None. |
Start Year | 2014 |
Title | DXSpiral: a code to study the Response Functions of spiral waves, to predict the slow dynamics of the vortices |
Description | DXSpiral: a code to study the Response Functions of spiral waves, to predict the slow dynamics of the vortices |
Type Of Technology | Software |
Year Produced | 2010 |
Open Source License? | Yes |
Impact | . |
URL | http://www.csc.liv.ac.uk/%7Eivb/SOFTware/DXSpiral.html |