Response functions for drift of spiral and scroll waves

Lead Research Organisation: University of Liverpool
Department Name: Computer Science

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.
 
Title 2D: Conversion of slow into fast spiral due to interaction with the boundary 
Description Illustration to A.J.Foulkes, D.Barkley, V.N.Biktashev and I.V.Biktasheva, "Alternative Stable Scroll Waves and Conversion of Autowave Turbulence", Chaos, 20, 043136, 2010 
Type Of Art Film/Video/Animation 
Year Produced 2010 
 
Title 3D: Conversion of negative filament tension turbulence into positive filament tension contraction, due to critical curvature of the filament 
Description Illustration to A.J.Foulkes, D.Barkley, V.N.Biktashev and I.V.Biktasheva, "Alternative Stable Scroll Waves and Conversion of Autowave Turbulence", Chaos, 20, 043136, 2010 
Type Of Art Film/Video/Animation 
Year Produced 2010 
 
Title Orbital motion 
Description An illustration to V.N.Biktashev, D.Barkley and I.V.Biktasheva, "Orbital motion of spiral waves in excitable media", Phys Rev Lett, 104(5): 058302, 2010 
Type Of Art Film/Video/Animation 
Year Produced 2010 
 
Description 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. Applicability of the universal asymptotic theory of drift caused by small perturbations was contingent on knowledge of so called response functions (RFs), in particular, the RFs being essentially non-zero only near the vortex core. As a result of this localization, spiral/scroll waves behave like point/string objects, despite being apparently non-local 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 the 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 proposal aimed to develop regular and generic methods of obtaining the RFs and thus to make the asymptotic theory into an actually working tool for understanding and controlling rotating waves in real systems.

In this project, we have:

- developed numerical methods of computing response functions in the FitzHugh-Nagumo and Barkley systems with high precision, sufficient for correct quantitative predictions of drift;

- studied the dependence of the response functions on parameters, particularly near boundaries in parameter regions where the spirals and scrolls are known to change their phenomenology, and confirmed the universality of the localization property of the spiral waves;

- verified predictions of the asymptotic theory, using the obtained response functions, for the drift of spiral waves in response to spatial gradients, time-periodic change of system parameters, localised inhomogeneities, and combinations thereof;

- verified the predictions of the asymptotic theory, using the obtained response functions, for the drift of scroll waves, including the transition from positive to negative tension of filaments of scrolls and its association with scroll wave turbulence;

- extended the developed technology from FitzHugh-Nagumo and Barkley to a Belousov-Zhabotinsky reaction model (Oregonator), and a physiologically detailed cardiac excitation model (Beeler-Reuter);

- applied the developed technology of predicting and studying the drift of spiral and scroll waves using the response functions, to various specific research problems.

- using the obtained response functions, made a novel prediction of spiral waves drift on thin layers caused by small variations of thickness of the layer. This novel prediction has been subsequently confirmed in experiments with BZ reaction medium by colleagues at Florida State University, USA.
Exploitation Route We see three sets of potential beneficiaries of our work:

- Nonlinear science: researchers working in the theory of spiral and scroll waves, which is a big and growing international community, and wider, in the theory of other nonlinear self-organized dissipative structures.

- Cardiac electrophysiology: researchers working in experimental studies of re-entrant arrhythmia and their mathematical modelling.

- Public health and wealth creation: long-term potential beneficiaries will be companies that manufacture pacemakers, operating theatre and implantable defibrillators and antiarrhythmic drugs, and hence eventually patients and general public.
Sectors Chemicals,Digital/Communication/Information Technologies (including Software),Education,Electronics,Environment,Healthcare,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology
URL http://cgi.csc.liv.ac.uk/~ivb/EPSRC_RFs.html
 
Description The RFs technology and the DXSpiral software has been used by researchers and research students from UK, Belgium, USA, and China for their research in dinamics of spiral waves, evidenced by a growing number of peer-reviewed publications.
First Year Of Impact 2012
Sector Digital/Communication/Information Technologies (including Software),Education,Pharmaceuticals and Medical Biotechnology
 
Description EPSRC Overseas Travel grant EP/P008690/1 "Research Collaboration Visit to the Auckland Bioengineering Institute, New Zealand."
Amount £15,890 (GBP)
Funding ID EP/P008690/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Academic/University
Country United Kingdom of Great Britain & Northern Ireland (UK)
Start 08/2016 
End 11/2016
 
Description EPSRC POEMS Network Travel grant
Amount £750 (GBP)
Organisation University of Sheffield 
Sector Academic/University
Country United Kingdom of Great Britain & Northern Ireland (UK)
Start 08/2016 
End 09/2016
 
Description EPSRC POEMS Network Travel grant, University of Sheffield, UK 
Organisation University of Sheffield
Department Faculty of Engineering
Country United Kingdom of Great Britain & Northern Ireland (UK) 
Sector Academic/University 
PI Contribution Research visit to the Auckland Bioengineering Institute, University of Auckland, August- September 2016.
Collaborator Contribution £750 towards the cost of Research visit to the Auckland Bioengineering Institute, University of Auckland, August- September 2016.
Impact Research visit to the Auckland Bioengineering Institute, University of Auckland, August- September 2016.
Start Year 2016
 
Description Exeter 
Organisation University of Exeter
Country United Kingdom of Great Britain & Northern Ireland (UK) 
Sector Academic/University 
PI Contribution joint research, participation in and organisation of mini symposia, joint funding applications
Collaborator Contribution joint research, participation in and organisation of mini symposia, joint funding applications
Impact Grant applications 1. EPSRC Grant application EP/L005387/1 "Meander and drift of spiral and scroll waves", 2013. 2. EPSRC project EP/K038915/1"BeatBox - HPC Environment for Biophysically and Anatomically Realistic Cardiac Simulations", 2010. 3. BBSRC grant application "BB/L018349/1 "HPC simulation environment for high-resolution intracellular Ca dynamics", 2013. Papers I. V. Biktasheva, H. Dierckx, and V. N. Biktashev, "Drift of scroll waves in thin layers caused by thickness features", submitted to Phys Rev Lett, 2014. arXiv:1408.3654 [nlin.PS] 2. Sanjay R. Kharche, Irina V. Biktasheva, Gunnar Seemann, Henggui Zhang, and Vadim N. Biktashev, "Anatomy Induced Drift of Spiral Waves in the Human Atrium", submitted to BMRI, 2014. 3. Vadim N. Biktashev, Irina V. Biktasheva, "Dynamics of filaments of scroll waves", in Engineering of Chemical Complexity II, eds. A.S.Mikhailov and G.Ertl, pp 221-238, World Scientific, Singapore, 2014. arXiv:1403.6654v1 [nlin.PS] 4. S.R. Kharche, I.V. Biktasheva, H.G. Zhang, and V.N. Biktashev, "Simulating the Role of Anisotropy in Human Atrial Cardioversion", The 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC'13), Osaka, Japan, IEEE Engineering in Medicine and Biology Society, pp 6838-41, 2013. 5. S.R. Kharche, J. Beling, I.V. Biktasheva, H.G. Zhang, and V.N. Biktashev, "Simulating Cell Apoptosis Induced Sinus Node Dysfunction", The 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC'13), Osaka, Japan, IEEE Engineering in Medicine and Biology Society, pp 6842-5, 2013. 6. S.R. Kharche, T. Stary, I.V. Biktasheva, H. Zhang, and V.N. Biktashev, "Computer simulation of the role of fibre orientation in cardioversion of chronic atrial fibrillation", Journal of Electrocardiology 46(4), e6-e7I, 2013. 7. I.V. Biktasheva, N A. Sarvazyan, and V.N. Biktashev, "Dynamics of Scroll Waves of Excitation in a Mathematical Model of Ischaemic Border Zone" , COMPUTING IN CARDIOLOGY, 39:445-448, 2012. 8. S. Kharche, I. Biktasheva, G. Seemann, H. Zhang, and V. Biktashev, "Cardioversion Using Feedback Stimuli in Human Atria" , COMPUTING IN CARDIOLOGY, 39:133-136, 2012. Conference/Minisymposia 1. Mini symposium "Dynamics of Spiral Waves - Parts I and II", SIAM CONFERENCE ON APPLICATIONS OF DYNAMICAL SYSTEMS 2013 (DS13), Snow Bird, Utah, USA. 2. Minisymposium "Dynamics of Spiral and Scroll Waves in Cardiac Tissue", SIAM CONFERENCE ON Nonlinear Waves and Coherent Structures 2014 (DS14), Cambridge, UK.
Start Year 2012
 
Description Gent University 
Organisation University of Ghent
Country Belgium, Kingdom of 
Sector Academic/University 
PI Contribution joint research and joint research outputs, joint funding application
Collaborator Contribution joint research and joint research outputs, joint funding application, provision of research advice and software
Impact 1. I. V. Biktasheva, H. Dierckx, and V. N. Biktashev, "Drift of scroll waves in thin layers caused by thickness features", submitted to Phys Rev Lett, 2014. arXiv:1408.3654 [nlin.PS] 2.EPSRC Grant application EP/L005387/1 "Meander and drift of spiral and scroll waves", 2013. 3. Mini symposium "Dynamics of Spiral Waves - Parts I and II", SIAM CONFERENCE ON APPLICATIONS OF DYNAMICAL SYSTEMS 2013 (DS13), Snow Bird, Utah, USA. 4. Mini symposium "Dynamics of Spiral and Scroll Waves in Cardiac Tissue", CONFERENCE ON NONLINEAR WAVES AND COHERENT STRUCTURES 2014 (NW14), Cambridge, UK.
Start Year 2008
 
Description Manchester 
Organisation University of Manchester
Department School of Physics and Astronomy Manchester
Country United Kingdom of Great Britain & Northern Ireland (UK) 
Sector Academic/University 
PI Contribution Joint research and joint research outputs
Collaborator Contribution Joint research and joint research outputs
Impact Software 1. BeatBox - HPC Environment for Biophysically and Anatomically Realistic Cardiac Simulations Publications 1. S.R. Kharche, T. Stary, I. V. Biktasheva, A. J. Workman, A. C.Rankin, A. V. Holden and H. Zhang, "Computer Simulation of the Anti-arrhythmic Effects of Chronic ß-blocker Treatment on Human Atrial Electrophysiology", submitted to Europace journal. Presentations 1. S. Kharche, I. Biktasheva, G. Seemann, H.G. Zhang, V. Biktashev, "Cardioversion Using Feedback Stimuli in Human Atria", CMMB meeting "Multiscale Modelling in Medicine and Biology", September 3-5, 2012, Nottinham, UK 2. S. Kharche, I. Biktasheva, G. Seemann, H. Zhang, and V. Biktashev, "Cardioversion Using Feedback Stimuli in Human Atria", 39th Annual Conference on Computing in Cardiology, , September 9-12, 2012, Krakow, Poland; Computing in Cardiology 39:133-136, 2012. 3. S. Kharche, I. Biktasheva, G. Seemann, H. Zhang, V. Biktashev "Low Energy Cardioversion Using Feedback Stimuli in Human Atria", Multiscale Modelling in Medicine and Biology: 3-5 September 2012, Centre for Mathematical Medicine and Biology, University of Nottingham. 4. S. R. Kharche, T. Stary, I. V. Biktasheva, H. Zhang and V. N. Biktashev, "The role of fibre orientation in cardioversion of chronic atrial fibrillation: a simulation study", Proc 37th IUPS (2013) 5. S. R. Kharche1, T. Stary, I. V. Biktasheva, H. Zhang and V. Biktashev, "Simulating cell apoptosis induced sinus node dysfunction", Proc 37th IUPS (2013) 6. S. R. Kharche, T. Stary, I. V. Biktasheva, A. J. Workman, A. C. Rankin, A. V. Holden and H. Zhang, "Effects of human atrial ionic remodelling by ß-blocker therapy on mechanisms of atrial fibrillation: a computer simulation" Journal of Electrocardiology, Volume 46, Issue 4 , Page e6, July 2013 7. S. R. Kharche, T. Stary, I. V. Biktasheva, H. Zhang, V. N. Biktashev "Computer simulation of the role of fibre orientation in cardioversion of chronic atrial fibrillation" Journal of Electrocardiology, Volume 46, Issue 4 , Pages e6-e7, July 2013 Workshop 1. BeatBox users workshop took place in Manchester on June 24-25, 2013. See the Workshop materials at http://wiener.ex.ac.uk/~vadim/projects/BeatBox/workshop/ Scalability studies 1. The presentation at the users' workshop (PDF, 1.2M) http://wiener.ex.ac.uk/~vadim/projects/BeatBox/workshop/beatbox-scalability-profiling.pdf 2. A more recent study http://empslocal.ex.ac.uk/people/staff/vnb262/projects/BeatBox/scalability/index.html
Start Year 2006
 
Description Research Collaboration Visit to the Auckland Bioengineering Institute, New Zealand. 
Organisation University of Auckland
Department Auckland Bioengineering Institute (ABI)
Country New Zealand 
Sector Academic/University 
PI Contribution Research Collaboration Visit to the Auckland Bioengineering Institute, New Zealand.
Collaborator Contribution host for Research Collaboration Visit to the Auckland Bioengineering Institute, New Zealand.
Impact Invited Lecture "Wave-particle duality of dissipative vortices and implications for cardiology" (Video http://www.abi.auckland.ac.nz/en/about/events/2016/wave-particle-duality-of-dissipative-vortices-and-implications-f.html) , in Auckland Bioengineering Institute seminar series , 30 August 2016, University of Auckland, New Zealand.
Start Year 2016
 
Description The George Washington University 
Organisation George Washington University
Country United States of America 
Sector Academic/University 
PI Contribution Joint research and joint research output
Collaborator Contribution Joint research and joint research output
Impact 1. I.V. Biktasheva, N A. Sarvazyan, and V.N. Biktashev, "Dynamics of Scroll Waves of Excitation in a Mathematical Model of Ischaemic Border Zone" , COMPUTING IN CARDIOLOGY, 39:445-448, 2012. 2. V.N. Biktashev, I.V. Biktasheva and N A. Sarvazyan, "Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone", PLoS ONE 6(9): e24388, 2011. doi:10.1371/journal.pone.0024388
Start Year 2011
 
Description Warwick 
Organisation University of Warwick
Department Mathematics Institute Warwick
Country United Kingdom of Great Britain & Northern Ireland (UK) 
Sector Academic/University 
PI Contribution Joint externally funded collaboration, joint research and research output.
Collaborator Contribution joint research and research output.
Impact Peer-reviewed papers: 1. I.V.Biktasheva, D.Barkley, V.N.Biktashev, G.V.Bordyugov and A.J.Foulkes, "Computation of the response functions of spiral waves in active media", Phys Rev E, 79(5): 056702, 2009 2. V.N.Biktashev, D.Barkley and I.V.Biktasheva, "Orbital motion of spiral waves in excitable media", Phys Rev Lett, 104(5): 058302, 2010 3. I.V.Biktasheva, D.Barkley, V.N.Biktashev and A.J.Foulkes, "Computation of the Drift Velocity of Spiral Waves using Response Functions", Phys Rev E, 81(6): 066202, 2010 5. A.J.Foulkes, D.Barkley, V.N.Biktashev and I.V.Biktasheva, "Alternative Stable Scroll Waves and Conversion of Autowave Turbulence", Chaos, 20, 043136, 2010 6. J. Langham, I. Biktasheva, and D. Barkley, "Asymptotic theory for spiral wave reflections", Phys Rev E, accepted, 2014. arXiv:1401.7626 [nlin.PS] Software 1. D.Barkley, V.N.Biktashev, I.V.Biktasheva, G.V.Bordyugov, and A.J.Foulkes, "DXSpiral: a code to study the Response Functions of spiral waves, to predict the slow dynamics of the vortices"
Start Year 2006
 
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
 
Title EZRide: A Code for Simulating Spiral Waves in Comoving Frame of Reference 
Description EZRide: A Code for Simulating Spiral Waves in Comoving Frame of Reference 
Type Of Technology Software 
Year Produced 2010 
Open Source License? Yes  
Impact
URL http://empslocal.ex.ac.uk/people/staff/vnb262/software/EZRide/
 
Description Lecture "Wave-particle duality of dissipative vortices and implications for cardiology", in Auckland Bioengineering Institute seminar series , 30 August 2016, University of Auckland, New Zealand. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact Invited Lecture "Wave-particle duality of dissipative vortices and implications for cardiology" (Video http://www.abi.auckland.ac.nz/en/about/events/2016/wave-particle-duality-of-dissipative-vortices-and-implications-f.html) ,
in Auckland Bioengineering Institute seminar series , 30 August 2016, University of Auckland, New Zealand.
Year(s) Of Engagement Activity 2016
URL http://www.abi.auckland.ac.nz/en/about/events/2016/wave-particle-duality-of-dissipative-vortices-and...