\% DOGS/bibtex/cardiac.bib [also copy this to CDI09/bibtex/cardiac.bib]
\% $Author: predrag $ $Date: 2013-11-06 12:16:54 -0500 (Wed, 06 Nov 2013) $
\% Predrag 2011-08-28
\% always edit DOGS/bibtex/cardiac.bib only
\% Predrag 2011-08-13
\% included Roman's CDI09/DOGS10/reports/nsf11rep.tex Bib files
\% see also zero:~garzon/thesis/cardiac.bib
\% Roman brutalized it with JabRef 2.7b. 2013-11-03
\% Enter entries alphabetically
@ARTICLE{ahuja_template-based_2007,
author = {S. Ahuja and I. G. Kevrekidis and C. W. Rowley},
title = {Template-based stabilization of relative equilibria in systems with
continuous symmetry},
journal = {J. Nonlin. Sci.},
year = {2007},
volume = {17},
pages = {109-143},
abstract = {We present an approach to the design of feedback control laws that
stabilize relative equilibria of general nonlinear systems with continuous
symmetry. Using a template-based method, we factor out the dynamics
associated with the symmetry variables and obtain evolution equations
in a reduced frame that evolves in the symmetry direction. The relative
equilibria of the original systems are fixed points of these reduced
equations. Our controller design methodology is based on the linearization
of the reduced equations about such fixed points. We present two
different approaches of control design. The first approach assumes
that the closed loop system is affine in the control and that the
actuation is equivariant. We derive feedback laws for the reduced
system that minimize a quadratic cost function. The second approach
is more general; here the actuation need not be equivariant, but
the actuators can be translated in the symmetry direction. The controller
resulting from this approach leaves the dynamics associated with
the symmetry variable unchanged. Both approaches are simple to implement,
as they use standard tools available from linear control theory.
We illustrate the approaches on three examples: a rotationally invariant
planar {ODE,} an inverted pendulum on a cart, and the {Kuramoto-Sivashinsky}
equation with periodic boundary conditions.}
}
@INPROCEEDINGS{sunil_ahuja_template-based_2006,
author = {S. Ahuja and I. G. Kevrekidis and C. W. Rowley},
title = {Template-based stabilization of relative equilibria},
booktitle = {2006 American Control Conference, 14-16 June 2006},
year = {2006},
pages = {6},
address = {Piscataway, NJ},
publisher = {{IEEE}},
abstract = {We present an approach to the design of feedback control laws that
stabilize the relative equilibria of general nonlinear systems with
continuous symmetry. Using a template-based method, we factor out
the dynamics associated with the symmetry variables and obtain evolution
equations in a reduced frame that evolves in the symmetry direction.
The relative equilibria of the original system are fixed points of
these reduced equations. Our controller design methodology is based
on the linearization of the reduced equations about such fixed points.
Assuming equivariant actuation, we derive feedback laws for the reduced
system that are optimal in the sense that they minimize a quadratic
cost function. We illustrate the method by stabilizing unstable traveling
waves of a dissipative {PDE} possessing translational invariance},
keywords = {control system synthesis, feedback, invariance, linearisation techniques,
nonlinear control systems, partial differential equations, stability}
}
@ARTICLE{alkhadra2000,
author = {A. Al-Khadra and V. Nikolski and I. R. Efimov},
title = {The role of electroporation in defibrillation},
journal = {Circ. Res.},
year = {2000},
volume = {87},
pages = {797-804}
}
@ARTICLE{AllCro13,
author = {Allen, J.-M. A. and Cross, M. C.},
title = {Frequency precision of two-dimensional lattices of coupled oscillators
with spiral patterns},
journal = {Phys. Rev. E},
year = {2013},
volume = {87},
pages = {052902},
note = {\arXiv{1303.1548}},
doi = {10.1103/PhysRevE.87.052902}
}
@ARTICLE{Otani2004,
author = {D. Allexandre and N. F. Otani},
title = {Preventing alternans-induced spiral wave breakup in cardiac tissue:
{An} ion-channel-based approach},
journal = {Phys. Rev. E},
year = {2004},
volume = {70},
pages = {061903}
}
@MISC{AMD_OpenCL_FFT,
author = {AMD.com},
title = {{AMD OpenCL Fast Fourier Transform}},
howpublished = {\url{http://developer.amd.com/appsdk}},
year = {2012}
}
@BOOK{anderson1990,
title = {Optimal control: linear quadratic methods},
publisher = {Prentice Hall},
year = {1990},
author = {B. D. O. Anderson and J. B. Moore},
address = {Englewood Cliffs, N.J.}
}
@BOOK{AnAr88,
title = {Dynamical systems {I}: {Ordinary} Differential Equations and Smooth
Dynamical Systems},
publisher = {Springer},
year = {1988},
author = {D. V. Anosov and V. I. Arnol'd}
}
@MISC{Apple_OpenCL_FFT,
author = {{Apple Inc.}},
title = {{OpenCL\_FFT}},
howpublished = {\url{http://developer.apple.com/library/mac/\#samplecode/OpenCL_FFT}},
year = {2012}
}
@UNPUBLISHED{BrCv12,
author = {S. Ortega Arango},
title = {Towards reducing continuous symmetry of baroclinic flows},
note = {ChaosBook.org project, \\ \wwwcb{/projects/Ortega/BrCv12.pdf}},
year = {2012}
}
@BOOK{arnold92,
title = {Ordinary Differential Equations},
publisher = {Springer},
year = {1992},
author = {V. I. Arnol'd},
address = {New York}
}
@ARTICLE{arnold91k,
author = {V. I. Arnol'd},
title = {Kolmogorov's hydrodynamic attractors},
journal = {Proc. R. Soc. Lond. A},
year = {1991},
volume = {434},
pages = {19-22},
number = {1890},
abstract = {A review of Kolmogorov's efforts relating the Navier-Stokes equation
to the theory of dynamical system. Several interesting questions
regarding the connection are exposed.}
}
@BOOK{arnold89,
title = {Mathematical Methods for Classical Mechanics},
publisher = {Springer},
year = {1989},
author = {V. I. Arnol'd},
address = {New York}
}
@BOOK{ArKoNe88,
title = {Mathematical Aspects of Classical and Celestial Mechanics},
publisher = {Springer},
year = {1988},
author = {V. I. Arnol'd and V. V. Kozlov and A. I. Neishtadt},
address = {New York}
}
@PHDTHESIS{ashi2008numerical,
author = {H. Ashi},
title = {Numerical methods for stiff systems},
school = {Univ. of Nottingham},
year = {2008}
}
@ARTICLE{AshMe97,
author = {P. Ashwin and I. Melbourne},
title = {Noncompact drift for relative equilibria and relative periodic orbits},
journal = {Nonlinearity},
year = {1997},
volume = {10},
pages = {595},
url = {http://stacks.iop.org/0951-7715/10/i=3/a=002}
}
@ARTICLE{AshMeNi99,
author = {P. Ashwin and I. Melbourne and M. Nicol},
title = {Drift bifurcations of relative equilibria and transitions of spiral
waves},
journal = {Nonlinearity},
year = {1999},
volume = {12},
pages = {741},
abstract = {We consider dynamical systems that are equivariant under a noncompact
Lie group of symmetries and the drift of relative equilibria in such
systems. In particular, we investigate how the drift for a parametrized
family of normally hyperbolic relative equilibria can change character
at what we call a `drift bifurcation'. To do this, we use results
of Arnold to analyse parametrized families of elements in the Lie
algebra of the symmetry group. We examine effects in physical space
of such drift bifurcations for planar reaction-diffusion systems
and note that these effects can explain certain aspects of the transition
from rigidly rotating spirals to rigidly propagating `retracting
waves'. This is a bifurcation observed in numerical simulations of
excitable media where the rotation rate of a family of spirals slows
down and gives way to a semi-infinite translating wavefront.},
url = {http://stacks.iop.org/0951-7715/12/i=4/a=301}
}
@ARTICLE{Aslanidi2009,
author = {O. V. Aslanidi and P. Stewart and M. R. Boyett and H. Zhang},
title = {Optimal velocity and safety of discontinuous conduction through the
heterogeneous {Purkinje}-ventricular junction},
journal = {Biophys. J.},
year = {2009},
volume = {97},
pages = {20-39}
}
@ARTICLE{Aubry88,
author = {N. Aubry and P. Holmes and J.L. Lumley and E. Stone},
title = {The dynamics of coherent structures in the wall region of turbulent
boundary layer},
journal = {J. Fluid Mech.},
year = {1988},
volume = {192},
pages = {115-173}
}
@ARTICLE{pchaot,
author = {D. Auerbach and P. Cvitanovi{\'c} and J.-P. Eckmann and G. Gunaratne
and I. Procaccia},
title = {Exploring chaotic motion through periodic orbits},
journal = {Phys. Rev. Lett.},
year = {1987},
volume = {58},
pages = {23}
}
@MISC{Bealto_FFT,
author = {E. Bainville},
title = {{Bealto OpenCL Fast Fourier Transform}},
howpublished = {\url{http://www.bealto.com/gpu-fft.html}},
year = {2010}
}
@ARTICLE{BakasovAbraham93,
author = {A. A. Bakasov and N. B. Abraham},
title = {Laser second threshold: {Its} exact analytical dependence on detuning
and relaxation rates},
journal = {Phys. Rev. A},
year = {1993},
volume = {48},
pages = {1633-1660}
}
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author = {D. Barkley},
title = {Euclidean symmetry and the dynamics of rotating spiral waves},
journal = {Phys. Rev. Lett.},
year = {1994},
volume = {72},
pages = {164-167}
}
@TECHREPORT{EZRide,
author = {D. Barkley and V. N. Biktashev and A. J. Foulkes},
title = {{EZRide}: {A} code for simulating spiral waves in a comoving frame
of reference},
institution = {U. Liverpool},
year = {2010},
note = {www.maths.liv.ac.uk/$\sim$vadim/software/EZRide/},
publisher = {V. N. Biktashev}
}
@ARTICLE{BarKev94,
author = {Barkley, D. and Kevrekidis, I. G.},
title = {A dynamical systems approach to spiral wave dynamics},
journal = {Chaos},
year = {1994},
volume = {4},
pages = {453-460},
doi = {10.1063/1.166023}
}
@ARTICLE{BaKnTu90,
author = {D. Barkley and M. Kness and L. S. Tuckerman},
title = {Spiral wave dynamics in a simple model of excitable media: {Transition}
from simple to compound rotation},
journal = {Phys. Rev. A},
year = {1990},
volume = {42},
pages = {2489-2492}
}
@INPROCEEDINGS{bartocci2011toward,
author = {E. Bartocci and E. M. Cherry and J. Glimm and R. Grosu and S. A.
Smolka and F. H. Fenton},
title = {Toward real-time simulation of cardiac dynamics},
booktitle = {CMSB '11: Proceedings of the 9th International Conference on Computational
Methods in Systems Biology},
year = {2011},
editor = {F. Fages},
pages = {103-112},
address = {New York},
publisher = {ACM}
}
@ARTICLE{Baer2007,
author = {S. Bauer and G. Roeder and M. Baer},
title = {Alternans and the influence of ionic channel modifications: Cardiac
three-dimensional simulations and one-dimensional numerical bifurcation
analysis},
journal = {Chaos},
year = {2007},
volume = {17},
pages = {015104}
}
@INPROCEEDINGS{BayOrt04,
author = {E. Bayro-Corrochano and J. Ortegon-Aguilar},
title = {Lie algebra template tracking},
booktitle = {International Conference on Pattern Recognition},
year = {2004},
volume = {2},
pages = {56-59},
doi = {10.1109/ICPR.2004.1334036}
}
@ARTICLE{Beeler1977,
author = {G. W. Beeler and H. Reuter},
title = {Reconstruction of action potential of ventricular myocardial fibers},
journal = {J. Physiol.},
year = {1977},
volume = {268},
pages = {177-210}
}
@ARTICLE{Gauthier2007,
author = {C. M. Berger and J. W. Cain and J. E. S. Socolar and D. J. Gauthier},
title = {Control of electrical alternans in simulations of paced myocardium
using extended time-delay autosynchronization},
journal = {PHYS. REV. E},
year = {2007},
volume = {76},
pages = {041917}
}
@ARTICLE{berger2007,
author = {Carolyn M. Berger and Xiaopeng Zhao and David G. Schaeffer and Hana
M. Dobrovolny and Wanda Krassowska and Daniel J. Gauthier},
title = {Period-Doubling Bifurcation to Alternans in Paced Cardiac Tissue:
Crossover from Smooth to Border-Collision Characteristics},
journal = {Phys. Rev. Lett.},
year = {2007},
volume = {99},
pages = {058101}
}
@MISC{BeOttRott13,
author = {W.-J. Beyn and D. Otten and J. Rottmann-Matthes},
title = {Stability and computation of dynamic patterns in {PDEs}},
year = {2013}
}
@ARTICLE{BeTh04,
author = {W.-J. Beyn and V. Th{\"u}mmler},
title = {Freezing solutions of equivariant evolution equations},
journal = {SIAM J. Appl. Dyn. Syst.},
year = {2004},
volume = {3},
pages = {85-116}
}
@ARTICLE{Bikt07,
author = {V. N. Biktashev},
title = {Drift of spiral waves},
journal = {Scholarpedia},
year = {2007}
}
@ARTICLE{BiHoNi96,
author = {V. N. Biktashev and A. V. Holden and E. V. Nikolaev},
title = {Spiral wave meander and symmetry of the plane},
journal = {Int. J. Bifur. Chaos},
year = {1996},
volume = {6},
pages = {2433-2440}
}
@ARTICLE{BBBBF09,
author = {I. V. Biktasheva and D. Barkley and V. N. Biktashev and G. V. Bordyugov
and A. J. Foulkes},
title = {Computation of the response functions of spiral waves in active media},
journal = {Phys. Rev. E},
year = {2009},
volume = {79},
pages = {056702}
}
@ARTICLE{biktasheva2003wave,
author = {Biktasheva, I. V. and Biktashev, V. N.},
title = {Wave-particle dualism of spiral waves dynamics},
journal = {Phys. Rev. E},
year = {2003},
volume = {67},
pages = {026221}
}
@ARTICLE{Bondarenko2004,
author = {V. E. Bondarenko and G. P. Szigeti and G. C. Bett and S. J. Kim and
R. L. Rasmusson RL},
title = {Computer model of action potential of mouse ventricular myocytes},
journal = {Am. J. Physiol. Heart Circ. Physiol.},
year = {2004},
volume = {287},
pages = {H1378-H1403}
}
@BOOK{bowen,
title = {Equilibrium states and the ergodic theory of {Anosov} diffeomorphisms},
publisher = {Springer-Verlag},
year = {1975},
author = {R. Bowen},
volume = {470},
series = {Lecture Notes in Mathematics},
address = {New York}
}
@BOOK{boyce1969,
title = {Elementary differential equations and boundary value problems},
publisher = {Wiley},
year = {1969},
author = {W. E. Boyce and R. C. DiPrima},
address = {New York}
}
@article{Boyd07,
title={Why {Newton}'s method is hard for travelling waves:
small denominators, {KAM} theory, {Arnold}'s linear {Fourier} problem,
non-uniqueness, constraints and erratic failure},
author={Boyd, J. P.},
journal={Math. Comput. Simulation},
volume={74},
pages={72--81},
year={2007},
doi = "10.1016/j.matcom.2006.10.001",
}
@ARTICLE{Brandt2000,
author = {M. E. Brandt and G. Chen},
title = {Time-delay feedback control of complex pathological rhythms in an
atrioventricular conduction model},
journal = {Int. J. Bif. Chaos},
year = {2000},
volume = {10},
pages = {2781-2784}
}
@ARTICLE{BubShGl02,
author = {G. Bub and A. Shrier and L. Glass},
title = {Spiral wave generation in heterogeneous excitable media},
journal = {Phys. Rev. Lett.},
year = {2002},
volume = {88},
pages = {058101}
}
@ARTICLE{Bueno2008,
author = {Bueno-Orovio, A. and Cherry, E. M. and Fenton, F. H.},
title = {Minimal model for human ventricular action potentials in tissue},
journal = {J. Theor. Biol.},
year = {2008},
volume = {253},
pages = {544-560}
}
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author = {A. Bueno-Orovio and V. M. Perez-Garcia and F. H. Fenton},
title = {Spectral methods for partial differential equations in irregular
domains: The spectral smoothed boundary method},
journal = {SIAM J. Sci. Comp.},
year = {2006},
volume = {28},
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}
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author = {R. A. Burton and G. Plank and J. E. Schneider and V. Grau and H.
Ahammer and S. L. Keeling and J. Lee and N. P. Smith and D. Gavaghan
and N. Trayanova and P. Kohl},
title = {Three-dimensional models of individual cardiac histoanatomy: tools
and challenges},
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year = {2006},
volume = {1080},
pages = {301-319}
}
@ARTICLE{Cabo2003,
author = {C. Cabo and P. A. Boyden},
title = {Electrical remodeling of the epicardial border zone in the canine
infracted heart: a computational analysis},
journal = {Am. J. Physiol. Heart Circ. Physiol.},
year = {2003},
volume = {284},
pages = {H372-H384}
}
@ARTICLE{Cain2008,
author = {J. W. Cain and D. G. Schaeffer},
title = {Shortening of cardiac action potential duration near an insulating
boundary},
journal = {Math. Med. Biol.},
year = {2008},
volume = {25},
pages = {21-36}
}
@ARTICLE{Cain2006b,
author = {J. W. Cain and D. G. Schaeffer},
title = {Two-term asymptotic approximation of a cardiac restitution curve},
journal = {SIAM Review},
year = {2006},
volume = {48},
pages = {537-546}
}
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title = {Model predictive control},
publisher = {Springer-Verlag},
year = {2004},
author = {E. F. Camacho and C. Bordons},
address = {London}
}
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title = {La m{\'e}thode du rep{\`e}re mobile, la th{\'e}orie des groupes continus,
et les espaces g{\'e}n{\'e}ralis{\'e}s},
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series = {{Expos{\'e}s} de {G{\'e}om{\'e}trie}},
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}
@MISC{cns_teaching,
author = {{Center for Nonlinear Science}},
title = {nonlinear science courses},
howpublished = {{\tt cns.physics.gatech.edu/courses/index.html}}
}
@INPROCEEDINGS{ChaBliKie10,
author = {T. P. Chagas and P.-A. J. Bliman and K. H. Kienitz},
title = {New feedback laws for stabilization of unstable periodic orbits},
booktitle = {Nonlinear Control Systems},
year = {2010},
editor = {L. Marconi},
pages = {1005-1010},
doi = {10.3182/20100901-3-IT-2016.00139}
}
@INPROCEEDINGS{ChaBliKie12,
author = {T. P. Chagas and P.-A. J. Bliman and K. H. Kienitz},
title = {A new method for stabilizing unstable periodic orbits of continuous-time
systems. {Application} to control of chaos},
booktitle = {Decision and Control (CDC), 2012 IEEE 51st Annual Conference on},
year = {2012},
pages = {2146-2151},
organization = {IEEE}
}
@ARTICLE{ChaKer12,
author = {Chandler, G. J. and Kerswell, R. R.},
title = {Invariant recurrent solutions embedded in a turbulent two-dimensional
{Kolmogorov} flow},
journal = {J. Fluid M.},
year = {2013},
volume = {722},
pages = {554-595},
note = {\arXiv{1207.4682}},
doi = {10.1017/jfm.2013.122}
}
@ARTICLE{chen2003,
author = {P.-S. Chen and T.-J. Wu and C.-T. Ting and H. S. Karagueuzian and
A. Garfinkel and S.-F. Lin and J. N. Weiss},
title = {A Tale of Two Fibrillations},
journal = {Circulation},
year = {2003},
volume = {108},
pages = {2298},
owner = {roman},
timestamp = {2013.11.03}
}
@MISC{award_04,
author = {E. M. Cherry and F. H. Fenton},
howpublished = {One of five finalists for the Golden Polygon award in 2004 in the
Simulation/Industry/e-learning/Science category}
}
@MISC{award_05,
author = {E. M. Cherry and F. H. Fenton},
howpublished = {One of five finalists for the Golden Polygon award in 2005 in the
Simulation/Industry/e-learning/Science category}
}
@MISC{award_06,
author = {E. M. Cherry and F. H. Fenton},
howpublished = {An honorable mention in the 2006 NSF and Science Scientific Visualization
Challenge in the Interactive Media category, available at\\ {\tt
www.vet.cornell.edu/news/FentonCherry/Media/main.html}}
}
@ARTICLE{Cherry08,
author = {E. M. Cherry and F. H. Fenton},
title = {Visualization of spiral and scroll waves in simulated and experimental
cardiac tissue},
journal = {New J. Phys.},
year = {2008},
volume = {10},
pages = {125016}
}
@ARTICLE{CheFen07,
author = {E. M. Cherry and F. H. Fenton},
title = {A tale of two dogs: {A}nalyzing two models of canine ventricular
electrophysiology},
journal = {Am. J. Physiol. Heart Circ. Physiol.},
year = {2007},
volume = {292},
pages = {H43-55}
}
@ARTICLE{Cherry2004,
author = {E. M. Cherry and F. H. Fenton},
title = {Suppression of alternans and conduction blocks despite steep APD
restitution: Electrotonic, memory and conduction velocity restitution
effects},
journal = {Am. J. Physiol. Heart Circ. Physiol.},
year = {2004},
volume = {286},
pages = {H2332-H2341}
}
@ARTICLE{ChGrHe03,
author = {E. M. Cherry and H. S. Greenside and C. S. Henriquez},
title = {Efficient simulation of three-dimensional anisotropic cardiac tissue
using an adaptive mesh refinement method},
journal = {Chaos},
year = {2003},
volume = {13},
pages = {853}
}
@ARTICLE{ChGrHe00,
author = {E. M. Cherry and H. S. Greenside and C. S. Henriquez},
title = {A space-time adaptive method for simulating complex cardiac dynamics},
journal = {Phys. Rev. Lett.},
year = {2000},
volume = {84},
pages = {1343-1346}
}
@UNPUBLISHED{Cherry2010,
author = {E. M. Cherry and R. F. Gilmour Jr. and F. H. Fenton},
title = {Characterization of the bifurcation to alternans in canine cardiac
tissue},
note = {In preparation},
year = {2010}
}
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author = {D. R. Chialvo and J. Jalife},
title = {Non-linear dynamics of cardiac excitation and impulse propagation},
journal = {Nature},
year = {1987},
volume = {330},
pages = {749-752}
}
@ARTICLE{BumRak,
author = {B. R. Choi and W. Jang. and G. Salama},
title = {Spatially discordant voltage alternans cause wavebreaks in ventricular
fibrillation},
journal = {Heart Rhythm},
year = {2007},
volume = {4},
pages = {1057},
}
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author = {P. Chossat},
title = {The reduction of equivariant dynamics to the orbit space for compact
group actions},
journal = {Acta Appl. Math.},
year = {2002},
volume = {70},
pages = {71-94}
}
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title = {The {Taylor-Couette} Problem},
publisher = {Springer},
year = {1994},
author = {P. Chossat and G. Iooss},
address = {New York}
}
@BOOK{ChossLaut00,
title = {Methods in Equivariant Bifurcations and Dynamical Systems},
publisher = {World Scientific},
year = {2000},
author = {P. Chossat and R. Lauterbach},
address = {Singapore}
}
@ARTICLE{Christini2006,
author = {D. J. Christini and M. L. Riccio and C. A. Culianu and J. J. Fox
and A. Karma and R. F. Gilmour},
title = {Control of electrical alternans in canine cardiac {Purkinje} fibers},
journal = {Phys. Rev. Lett.},
year = {2006},
volume = {96},
pages = {104101}
}
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author = {C. E. Clancy and Y. Rudy},
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year = {1999},
volume = {400},
pages = {566-569}
}
@UNPUBLISHED{Clayton2010,
author = {R. H. Clayton and O. Bernus and E. M. Cherry and H. Dierckx and F.
H. Fenton and L. Mirabella and A. V. Panfilov and F. B. Sachse and
G. Seemann and H. Zhang},
title = {Models of cardiac tissue electrophysiology: {Progress}, challenges
and open questions},
note = {Submitted to Prog. Biophys. Mol. Biol.},
year = {2010}
}
@ARTICLE{Clayton2005,
author = {R. H. Clayton and P. Taggart},
title = {Regional differences in APD restitution can initiate wavebreak and
re-entry in cardiac tissue: A computational study},
journal = {BioMedical Engineering OnLine},
year = {2005},
volume = {4},
pages = {54}
}
@phdthesis{Coff76,
Author = {Coffee, T. P.},
School = {City Univ.~of New York, N.Y.},
Title = {The stability of plane {Couette} flow},
Year = 1976}
}
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institution = {U. New Hempshire},
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note = {{\tt {Channelflow.org}}},
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note = {\arXiv{0808.3375}}
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the vulnerable period or to defibrillate, an extracellular electric
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to initiate fibrillation or to defibrillate is much greater than
six times the diastolic pacing threshold. The ventricular fibrillation
threshold is typically 40 times greater than the diastolic pacing
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in terms of current is typically thousands of times greater than
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vary so much more in terms of stimulus current than in terms of extracellular
potential gradient is that each of the three thresholds requires
creation of the required potential gradient at different distances
from the stimulating electrode. Pacing requires a potential gradient
of approximately 1 V/cm only in a small liminal volume of tissue
immediately adjacent to the electrode. Initiation of ventricular
fibrillation by premature stimulation during the vulnerable period
requires a potential gradient of approximately 6 V/cm about 1 cm
away from the stimulating electrode to allow sufficient space for
the central common pathway of a figure-eight reentrant circuit to
form. Since the potential gradient falls off rapidly with distance
from the stimulating electrode, a stimulating current about 40 times
greater than the diastolic pacing threshold is required to generate
an electric field of 6 V/cm approximately 1 cm away from the stimulating
electrode. Defibrillation requires an electric field of approximately
6 V/cm throughout all or almost all of the ventricular myocardium.
Since some portions of the ventricles can be more than 10cm away
from the defibrillation electrodes, a shock of several amps is required
to create this field, a current thousands of times greater than the
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pages = {241},
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timestamp = {2013.11.03}
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timestamp = {2013.11.03}
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year = {2001},
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pages = {291-300},
abstract = {Two time-periodic solutions are found in a 3-d constrained plane Couette
flow, multishooting method being used. The turbulent state mainly
follows the periodic orbit with strong variations. The gentle one
is related to the bursting behavior of the system. Heteroclinic orbits
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and practical question is what range of shock energies is most likely
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is most difficult to answer in the pre-hospital defibrillation setting
where the patients’ size and shape vary, placement of the defibrillation
patches vary, and the etiology of their arrhythmia varies. Unlike
internal defibrillators, which are tested at implantation, efficacy
of an external defibrillator is determined only once, when it is
most needed. This review discusses shock damage and dysfunction caused
by monophasic waveforms as well as biphasic waveforms. Evidence is
presented suggesting that for perfused hearts, the threshold for
damage is well above any shock size delivered clinically. For non-perfused
hearts, both in humans and animals, evidence is presented that monophasic
shocks of up to 5 J/kg do not cause any more cardiac damage/dysfunction
than that associated with smaller shocks and that much of this damage
is caused by the ischemic period itself rather than the shock. Although
many patients can be defibrillated with 150 J (2.2 J/kg) biphasic
shocks, some patients may require biphasic shocks up to 360 J (5
J/kg) to be defibrillated. Studies still need to be performed comparing
the efficacy and damaging effects of 360 J biphasic shocks to 150
J biphasic shocks. Until those studies are completed, it seems reasonable
to use the same 360 J (5 J/kg) energy limit for biphasic shocks as
for monophasic shocks.},
doi = {10.1016/S0300-9572(03)00161-8}
}
@ARTICLE{W97,
author = {F. Waleffe},
title = {On a self-sustaining process in shear flows},
journal = {Phys. Fluids},
year = {1997},
volume = {9},
pages = {883-900}
}
@ARTICLE{W95a,
author = {F. Waleffe},
title = {Hydrodynamic Stability and Turbulence: Beyond transients to a self-sustaining
process },
journal = {Stud.\ Applied Math.},
year = {1995},
volume = {95},
pages = {319-343}
}
@ARTICLE{walker2003,
author = {M. L. Walker and D. S. Rosenbaum},
title = {Repolarization alternans: implications for the mechanism and prevention
of sudden cardiac death},
journal = {Cardiovasc. Res.},
year = {2003},
volume = {57},
pages = {599},
owner = {roman},
timestamp = {2013.11.03}
}
@ARTICLE{Wang2008,
author = {L. J. Wang and E. A. Sobie},
title = {Mathematical model of the neonatal mouse ventricular action potential},
journal = {Am. J. Physiol. Heart Circ. Physiol.},
year = {2008},
volume = {294},
pages = {H2565-H2575}
}
@INPROCEEDINGS{Wardetzky:2007:DLO:1281991.1281995,
author = {Max Wardetzky and Saurabh Mathur and Felix K{\"a}lberer and Eitan
Grinspun},
title = {Discrete {Laplace operators}: no free lunch},
booktitle = {Proceedings of the fifth Eurographics symposium on Geometry processing},
year = {2007},
series = {SGP '07},
pages = {33-37},
address = {Aire-la-Ville, Switzerland, Switzerland},
publisher = {Eurographics Association},
acmid = {1281995},
isbn = {978-3-905673-46-3},
location = {Barcelona, Spain},
numpages = {5},
url = {http://dl.acm.org/citation.cfm?id=1281991.1281995}
}
@ARTICLE{Watanabe2001,
author = {M. A. Watanabe and F. H. Fenton and S. J. Evans and H. M. Hastings
and A. Karma},
title = {Mechanisms for discordant alternans},
journal = {J. Cardiovasc. Electrophysiol.},
year = {2001},
volume = {12},
pages = {196-206}
}
@ARTICLE{MaWa95,
author = {M. Watanabe and N. F. Otani and R. F. Jr. Gilmour},
title = {Biphasic restitution of action potential duration and complex dynamics
in ventricular myocardium},
journal = {Circ. Res.},
year = {1995},
volume = {76},
pages = {915-921},
abstract = {The purpose of this study was to determine whether biphasic restitution
of action potential duration (APD) in ventricular muscle permits
the development of complex dynamic behavior. Such behavior is expected
because of the steep ascending slope of restitution and the presence
of a maximum. Action potentials recorded from strips of epicardial
muscle in which biphasic APD restitution occurred demonstrated a
characteristic pattern of phase locking during progressive shortening
of the pacing cycle length. 1:1 locking was replaced by irregular
dynamics, which in turn was replaced by higher order periodic behavior
(eg, 8:8 locking), then by 2:2 locking, and finally by 2:1 locking.
Similar patterns of dynamic behavior were produced in a computer
model by using a piecewise linear approximation of biphasic APD restitution.
Features of APD restitution that were critical determinants of irregular
dynamics included the slopes of the ascending and the nonmonotonic
regions. These results suggest that rate-related alterations of APD
and refractoriness may be affected significantly by small nonmonotonicities
in APD restitution. }
}
@BOOK{Wat07,
title = {The Matrix Eigenvalue Problem: {GR} and {Krylov} Subspace Methods},
publisher = {SIAM},
year = {2007},
author = {Watkins, D. S.},
address = {Philadelphia}
}
@UNPUBLISHED{Wilczak09,
author = {R. Wilczak},
title = {Reducing the state-space of the complex {L}orenz flow},
note = {{NSF REU} summer 2009 project, {U. of Chicago}, \\ \wwwcb{/projects/Wilczak/blog.pdf}},
year = {2009}
}
@ARTICLE{ACHKW11,
author = {Willis, A. P. and Cvitanovi{\'c}, P. and Avila, M.},
title = {Revealing the state space of turbulent pipe flow by symmetry reduction},
journal = {J. Fluid Mech.},
year = {2013},
volume = {721},
pages = {514-540},
note = {\arXiv{1203.3701}}
}
@ARTICLE{Winfree1997,
author = {A. T. Winfree},
title = {Heart muscle as a reaction-diffusion medium: The roles of electric
potential diffusion, activation front curvature, and anisotropy},
journal = {Int. J. Bif. Chaos},
year = {1997},
volume = {7},
pages = {487-526}
}
@ARTICLE{Winfree91,
author = {A. T. Winfree},
title = {Varieties of spiral wave behavior: {An} experimentalist's approach
to the theory of excitable media},
journal = {CHAOS},
year = {1991},
volume = {1},
pages = {303-334}
}
@BOOK{Winfree1980,
title = {The Geometry of Biological Time},
publisher = {Springer},
year = {1980},
author = {A. T. Winfree},
address = {New York}
}
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author = {A. T. Winfree},
title = {Scroll-shaped Waves of Chemical Activity in 3 Dimensions},
journal = {Science},
year = {1973},
volume = {181},
pages = {937-939}
}
@ARTICLE{Winfree1988,
author = {A. T. Winfree and J. J. Tyson},
title = {When time breaks down: The three-dimensional dynamics of electrochemical
waves and cardiac arrhythmias},
journal = {Physics Today},
year = {1988},
volume = {41},
pages = {107}
}
@ARTICLE{Winslow1999,
author = {R. L. Winslow and J. Rice and S. Jafri and E. Marban and B. ORourke},
title = {Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced
heart failure. II. Model studies},
journal = {Circ. Res.},
year = {1999},
volume = {84},
pages = {571-586}
}
@ARTICLE{Wu2002,
author = {T J Wu and S F Lin and J N Weiss and C T Ting and P.-S. Chen},
title = {Two types of ventricular fibrillation in isolated rabbit hearts},
journal = {Circulation},
year = {2002},
volume = {106},
pages = {1859},
owner = {roman},
timestamp = {2013.11.03}
}
@InProceedings{ Wardetzky:2007:DLO:1281991.1281995,
author = {M. Wardetzky and S. Mathur and F. K{\"a}lberer and E. Grinspun},
title = "Discrete {Laplace operators}: no free lunch",
booktitle = "Proceedings of the fifth Eurographics symposium on Geometry processing",
series = "SGP '07",
year = "2007",
isbn = "978-3-905673-46-3",
location = "Barcelona, Spain",
pages = "33--37",
numpages = "5",
url = "http://dl.acm.org/citation.cfm?id=1281991.1281995",
publisher = "Eurographics Assoc.",
address = "Aire-la-Ville, Switzerland"
}
@ARTICLE{ZaZha70,
author = {A. N. Zaikin and A. M. Zhabotinsky},
title = {Concentration wave propagation in 2-dimensional liquid-phase self-oscillating
system},
journal = {Nature},
year = {1970},
volume = {225},
pages = {535-537}
}
@BOOK{zak2003,
title = {Systems and control},
publisher = {Oxford University Press},
year = {2003},
author = {S. H. Zak},
address = {New York},
owner = {roman},
timestamp = {2013.11.03}
}
@Article{ ZDZDXZ13,
title = "Theoretical investigation of the mechanism of heart
failure using a canine ventricular cell model: {Especially} the role
of up-regulated {CaMKII and $SR Ca^{2+}$} leak",
journal = "J. Molecular and Cellular Cardiology",
volume = "56",
pages = "34--43",
year = "2013",
doi = "10.1016/j.yjmcc.2012.11.020",
author = "Y. Zang and L. Dai and H. Zhan and J. Dou and L. Xia and H. Zhang",
abstract = "Abstract Heart failure (HF) is associated with
susceptibility to sudden cardiac death. However, the underlying
mechanism of electrical instability and mechanical dysfunction
associated with HF remains poorly understood. In this study, a new
canine ventricular cell model based on the Hund--Rudy dynamic (HRd)
model and recently published experimental data was developed to
investigate the electrical changes and calcium handling dysfunction
in HF. Simulation results suggest that: 1) acute
$Ca^{2+}$/calmodulin-dependent protein kinase II (CaMKII)
over-expression (CaMKII-OE) affects the action potential (AP)
profile, while AP prolongation is mainly caused by the
down-regulation of K+ currents; 2) enhanced late Na+ current (INaL)
alone cannot adequately lead to [Na+] elevation in HF; 3) enhanced
sarcoplasmic reticulum (SR) leak current (Ileak) causes disturbed
$Ca^{2+}$;+ handling and there is little contribution from Na+/$SR
Ca^{2+}$ exchanger (NCX); 4) at high $SR Ca^{2+}$ load, a steeper
fractional $SR Ca^{2+}$;+ release is observed in HF than that in
control, causing alternans to occur more easily; and 5) Ileak block
restores the contraction and relaxation function, but cannot
eliminate alternans. By inhibiting CaMKII, alternans is eliminated,
but contractility is not improved. Partial CaMKII inhibition in
combination with Ileak block could augment mechanical function and
depress alternans, suggesting a new possible therapeutic target for
HF treatment."
}
@ARTICLE{ZhoSalWu99,
author = {Zhou, K. and Salomon, G. and Wu, E.},
title = {Balanced realization and model reduction for unstable systems},
journal = {Int. J. Robust and Nonlin. Contr.},
year = {1999},
volume = {9},
pages = {183-198}
}
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author = {X. Zhou and L. Sirovich},
title = {Coherence and Chaos in a model of turbulent boundary layer},
journal = {Phys. Fluids A},
year = {1992},
volume = {4},
pages = {2855-2874}
}
@ARTICLE{Zhukov2003,
author = {L. Zhukov and A. H. Barr},
title = {Heart-muscle fiber reconstruction from diffusion tensor MRI},
journal = {Proc. IEEE Visualization},
year = {2003}
}
@ARTICLE{zykov1994external,
author = {Zykov, V. S. and Steinbock, O. and M{\"u}ller, S. C.},
title = {External forcing of spiral waves},
journal = {Chaos},
year = {1994},
volume = {4},
pages = {509-518}
}
@BOOK{Zipes2009,
title = {Cardiac Electrophysiology: From Cell to Bedside, 5th Edition},
publisher = {Saunders},
year = {2009},
editor = {D. P. Zipes and J. Jalife},
address = {Philadelphia}
}
@MISC{CDSNS,
note = {Center for Dynamical Systems \& Nonlinear Studies, {\tt www.math.gatech.edu/cdsns}}
}