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Ronald L. Westra Department of Mathematics Maastricht University Complex Pattern Formation in Electrophysiological Wave Propagation on Cardiac Walls

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Problem formulation Outline of proposed research Empirical observations and experimental equipment Theoretical framework and complex behavior Spatiotemporal analysis with wavelets Multidisciplinary approach Relation to other research Items in this Presentation

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Question: Can complex spatiotemporal patterns in electrophysiological waves be related to a pathological condition of the heart? Problem formulation

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Question: Can complex spatiotemporal patterns in electrophysiological waves be related to a pathological condition of the heart? Answer: yes, if the substrate is damaged Problem formulation

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Question: Can complex spatiotemporal patterns in electrophysiological waves be related to a pathological condition of the heart? Answer: yes, if the substrate is damaged Question 2: What about complex patterns if the substrate is not damaged? Problem formulation

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Question: Can complex spatiotemporal patterns in electrophysiological waves be related to a pathological condition of the heart? Answer: yes, if the substrate is damaged Question 2: What about complex patterns if the substrate is not damaged? Q3: In what language should we characterize these patterns? Problem formulation

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Question: Can complex spatiotemporal patterns in electrophysiological waves be related to a pathological condition of the heart? Answer: yes, if the substrate is damaged Question 2: What about complex patterns if the substrate is not damaged? Q3: In what language should we characterize these patterns? Q4: How to associate them with pathological conditions? Problem formulation

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Question: Can complex spatiotemporal patterns in electrophysiological waves be related to a pathological condition of the heart? Answer: yes, if the substrate is damaged Question 2: What about complex patterns if the substrate is not damaged? Q3: In what language should we characterize these patterns? Q4: How to associate them with pathological conditions? Q5: What are the driving parameters and their critical values? Problem formulation

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Question: Can complex spatiotemporal patterns in electrophysiological waves be related to a pathological condition of the heart? Answer: yes, if the substrate is damaged Question 2: What about complex patterns if the substrate is not damaged? Q3: In what language should we characterize these patterns? Q4: How to associate them with pathological conditions? Q5: What are the driving parameters and their critical values? Problem formulation Q6: Can the dynamical systems approach and wavelet analysis be useful?

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* Mathematical framework for modelling of electrophysiological wave propagation and analysis of the resulting patterns * Analysis of annotated empirical spatiotemporal data * Identification of abnormal substrate * Dynamic analysis of complex behavior Outline of proposed research

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Spatiotemporal annotated data from in-vivo experiments Dynamical systems approach Fractal wavelet analysis Identification techniques Methodology andamp; approach

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Background: 1D-pattern analysis The ECG with the characteristic P,Q,R,S,T components (van Einthoven, 1936)

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1D-Morphological analysis : Traditionally, ECG-signal analysis is focussed on the single R-wave event signaling the occurrence of cardiac depolarization, morphological attributes of the electrogram are not taken into account.

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1D-Morphological analysis : Relation between the shape of the part and possible cardiopathologies

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1D-Morphological analysis : Wavelets are superior in identifying the characteristic parts of the signal.

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Direct observation of electrophysiological waves on cardiac walls, using MRI or array of electrodes Regular behavior in case of normal substrate and normal pacing Complex behavior in case of damaged substrate , fast pacing (Wenkebach), and e.g. some types of atrium fibrilation (afib III) 2D-spatiotemporal pattern analysis

‘Spoon’ of about 3 cm2 with matrix ofelectrodes with grid spacing 0.2 mm and sampling frequency of > 1 kHz: 

‘Spoon’ of about 3 cm2 with matrix of electrodes with grid spacing 0.2 mm and sampling frequency of andgt; 1 kHz 2D-spatiotemporal pattern analysis

Spoon is positioned on the cardiac wall: 

Spoon is positioned on the cardiac wall 2D-spatiotemporal pattern analysis

Electrostatic potential is measured: 

Electrostatic potential is measured 2D-spatiotemporal pattern analysis electrostatic field fractal wave type

Normal: 

Normal Empirical Observations Regular, quasi-periodic, soliton-like wave fronts

Atrium fibrilation type III: 

Atrium fibrilation type III Empirical Observations ‘Figure 8’ re-entry ‘spiral-wave’ re-entry Wave annihilation

* The electrostatic field propagates in soliton-like, well-localized shockfront waves* A normal heart exhibits regular quasi-periodic waves seemingly without dispersion or dissipation* Damaged substrate causes irregular behavior like re-entry phenomena * Re-entry phenomena can also be caused by refractory substrate* Other complex patterns like wave-annihilation or breathers not-related to substrate* Some parameters drive complex behavior like period of sinus rhythm and the Wenkebach-effect : 

* The electrostatic field propagates in soliton-like, well-localized shockfront waves * A normal heart exhibits regular quasi-periodic waves seemingly without dispersion or dissipation * Damaged substrate causes irregular behavior like re-entry phenomena * Re-entry phenomena can also be caused by refractory substrate * Other complex patterns like wave-annihilation or breathers not-related to substrate * Some parameters drive complex behavior like period of sinus rhythm and the Wenkebach-effect Empirical Observations

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Propagation of electrostatic potential over cardiac substrate * substrate properties: capacity , conductivity , and parameters * diffusion-like equation causing dispersion and exponential extinction * extinction is prevented by active ion-currents exhibiting a refractory period in substrate Microscopic Equations

Propagation of electrophysiological waves [1]: 

electrostatic potential scalar capacity density scalar 1st order approximation conductivity tensor 1st order approximation (Ohm) model parameter vectors Propagation of electrophysiological waves [1]

Propagation of electrophysiological waves [2]: 

food supply/inhibition scalar Ion reaction currents Phenomenological models Propagation of electrophysiological waves [2]

Propagation of electrophysiological waves [3]: 

* Ion reaction current involves many terms: * These terms are individually modeled empirically by piecewise-linear equations * Iion can also be modeled phenomenologically, as by Luo-Rudy and Fitzhugh-Nagumo, e.g. : * The food supply/inhibition scalar f can also be phenomenological entity, e.g. Fitzhugh-Nagumo: Propagation of electrophysiological waves [3]

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Parametrized PDE models like Fitzhugh-Nagumo allow for the identification of damaged substrate from empirical spatiotemporal data using e.g. nonlinear least-squares methods Westra R.L., Haldermans Ph., Peeters R.L.M., 2004 Identification of damaged substrate

Normal: data substrate identified from data: 

Identification of damaged substrate Normal: data substrate identified from data

Afib III: data substrate identified from data: 

Identification of damaged substrate Afib III: data substrate identified from data

Complex patterns need not associate with damaged substrate:Hoekstra (2000) calls atrium fibrillation a ‘dynamical disease’Aliev, Panfilov (1998): period of sinus rhythm drives the Wenkebach-effect, Sidorov, Aliev, et al. (2003), Spatiotemporal Dynamics of Damped Propagation in Excitable Cardiac Tissue, Phys. Rev. Letters 2003Gray RA, et al., Nonstationary vortexlike reentrant activity as a mechanism of polymorphic ventricular tachycardia. Circulation 1995: 

Complex patterns need not associate with damaged substrate: Hoekstra (2000) calls atrium fibrillation a ‘dynamical disease’ Aliev, Panfilov (1998): period of sinus rhythm drives the Wenkebach-effect, Sidorov, Aliev, et al. (2003), Spatiotemporal Dynamics of Damped Propagation in Excitable Cardiac Tissue, Phys. Rev. Letters 2003 Gray RA, et al., Nonstationary vortexlike reentrant activity as a mechanism of polymorphic ventricular tachycardia. Circulation 1995 Pattern Formation and the Emergence of Complexity

Propagation models like Fitzhugh-Nagumo exhibit realistic features observed in empirical data* complex re-entry phenomena like figure-8 and spirals* exhibits soliton-like and breather-like solutions * complex wave interactions like annihilation* Fitzhugh-Nagumo ion-currents a bit like phi-four potential: 

Propagation models like Fitzhugh-Nagumo exhibit realistic features observed in empirical data * complex re-entry phenomena like figure-8 and spirals * exhibits soliton-like and breather-like solutions * complex wave interactions like annihilation * Fitzhugh-Nagumo ion-currents a bit like phi-four potential Complex Patterns from Fitzhugh-Nagumo models

What drives pattern formation?* sinus rhythm → Wenkebach effect* damaged substrate → re-entry* feed-back mechanism to sinus node drives atrium fibrilation: 

What drives pattern formation? * sinus rhythm → Wenkebach effect * damaged substrate → re-entry * feed-back mechanism to sinus node drives atrium fibrilation Complex Patterns from Fitzhugh- Nagumo class models

Which parameters drive complex pattern formation, e.g. afib?* extension to sinus node uSN(t)* feed-back mechanism to sinus node drives atrium fibrilation* model parameters and critical bifurcations : 

Which parameters drive complex pattern formation, e.g. afib? * extension to sinus node uSN(t) * feed-back mechanism to sinus node drives atrium fibrilation * model parameters and critical bifurcations Complex Patterns from Fitzhugh- Nagumo class models

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* 2D Multifractal wavelet analysis of patterns and turbulence * Wavelet formulation and analysis of shockwaves Spatiotemporal Analysis with Wavelets

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2D Fractal wavelet analysis of turbulence, A. Arneodo, 2003 Wavelet analysis of blood flow singularities by using ultrasound data, Ph. May, 2002 Multifractal wavelet analysis of 2D-rheological patterns, R.L. Westra, 2001 2D Multifractal analysis of turbulence with wavelets

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Wavelet formulation of PDEs and analysis of shockwaves Cheng, H.K., Lee, C.J. and Edwards, J., 2001, Sonic Boom Noise Penetration Under a Wavy Ocean, Fatkullin I. and Hesthaven J. S., Adaptive High-Order Finite-Difference Method for Nonlinear Wave Problems, J. Scientific Computation., 2001 Vasilyev, O. V., and Paolucci, S. A dynamically adaptive multilevel wavelet collocation method for solving partial differential equations in a finite domain. J. Comput. Phys., 1996. Wavelet and multiscale techniques for the Numerical Analysis of PDEs, Kunoth, A, SIAM J. on Num. Analysis, 2002 Shockwaves Analysis with Wavelets

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UM Department of cardiology/CARIM: generation of annotated spatiotemporal data interpretation of theoretic findings validation of theoretic predictions (e.g. damaged substrate) UM Department of mathematics: Analysis of empirical data Prediction of behavior Multidisciplinary approach

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UM Department of cardiology/CARIM: UM Department of mathematics: Multidisciplinary approach No funding requested in this proposal Requests funding in this proposal

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Consortium and links Maastricht Instruments Medtronic Bakken Research UM mathematics UM Physiology, UM Cardiology, CARIM

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Relation with other internal research * Nationally STW research project BIOSENS DTC.6418 Biosens - the relation between ECG morphological analysis and the pathological condition of the heart - partner: tech. university Delft (Nl), co-funder: Medtronic (USA) - start: March 2004, end: March 2008 - proposer and local project leader: R.L. Westra * European Union research project NiSIS FP6-013569 - Mathematical modeling, analysis and identification of gene regulatory networks - direct partners: universities of Vienna (Au) and Jena (Ger) - start: February 2005, end: February 2008 - co-proposer and local project leader: R.L. Westra

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Affiliation with other research groups * UM\math is member of the Dutch Institute of Systems and Control (DISC) research school of the KNAW (Royal Dutch Academy of Sciences). * Close co-operation with Technical University Delft and the Delft Institute of Microelectronics and Submicron Technology DIMES through BIOSENS. * Close co-operation with University of Aachen and Jena (GER) and Vienna (AU) through NiSIS. * Numerous contacts with other groups in and outside the Netherlands

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BIOSENS = BIOmedical Signal Processing Platform for Low-Power Real- Time SENSing of Cardiac Signals NWO/STW

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BIOSENS Objective Utilizing morphological features of ECGs in novel prototypes of pacemaker and ICD front-ends.

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TU Delft microelectronics Low-voltage low-power analog electronics for biomedical radio-frequency applications UM mathematics – Systems Theory Group Signal analysis, mathematical morphology , clustering and classification Research Objectives

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BIOSENS support group Substantial support of : Medtronic Bakken Research Center World leader in medical implantable technology. Other biotechnology partners are: Maastricht Instruments, SystematIC Design, Twente Medical Systems International. Vitatron, Weijand Randamp;D Consultancy

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Complex Pattern Formation in Electrophysiological Wave Propagation on Cardiac Walls 