Alternans and period-2 oscillatory cardiac spiral waves : properties - PDF document

Alternans and period-2 oscillatory cardiac spiral waves : properties and underlying mechanisms Kyoung Jin Lee Tae-yun Kim, Okyu Kwon, Jinhee Hong Center for Cell Dynamics & Dept. of Physics, Korea University (http://turing.korea.ac.kr) Center for Neurodynamics, 2008-07-08 1 Korea Univ. Collective spatiotemporal dynamics within cells & populations of cells 1) Social amoeba � development 2) Neurons � brain function 3) Glia � brain function? 4) Macrophage � immune system 5) Cadiac cells � heart function 5) Cadiac cells � heart function ..... many others Center for Neurodynamics, 2008-07-08 2 Korea Univ. Nonlinear dynamics in biological neural network 1

Dictyostelium discodium amoeba on a porous gel substrate Darkfield cell size image ∼ 10 μ m Center for Neurodynamics, 2008-07-08 3 Korea Univ. cAMP waves in signaling amoeba populations spiral wave circular waves 2.0x2.8 cm 2 Lee, Cox, & Goldstein, PRL (1996); PRL (2001); Nonlinearity (2002) Center for Neurodynamics, 2008-07-08 4 Korea Univ. Nonlinear dynamics in biological neural network 2

Waves, cytoplasmic flows & optimization in a social amoebae Physyrum polycephalum Toshiyuki NAKAGAKI (Hokkaido University) PRL 2008 Nature ( News & Views ) PRL 2008, Nature ( News & Views ) begin end Center for Neurodynamics, 2008-07-08 5 Korea Univ. Sychronized ‘bursts’ in coupled network of neurons (with glia) Jun Hwan Kim & Jun Ho Choi (Korea University) Center for Neurodynamics, 2008-07-08 6 Korea Univ. Nonlinear dynamics in biological neural network 3

Membrane potential and Hodgkin-Huxley Equation Center for Neurodynamics, 2008-07-08 7 Korea Univ. Multi-channel amplifying system Pre Amplifier, 64ch Pre Amplifier Differential Input, - CMRR > 60dB Gain : 10 ( at 900Hz ) - Filter : High pass @ - 100Hz, 1 pole Filter Amplifier Single-ended Input. - Gain : 1000 (3 stages, - Filter Amplifier, 64ch each 10x (at 900Hz ) Filter : Low pass @ - 5kHz, 6 poles 5kH 6 l High pass @ 100Hz, 3 poles Center for Neurodynamics, 2008-07-08 8 Korea Univ. Nonlinear dynamics in biological neural network 4

Calcium waves in confluent confluent layer of astroglia Jin Sung Park (Korea University) Center for Neurodynamics, 2008-07-08 9 Korea Univ. HEART - a complex functional system of cells: its hierarchical structure Center for Neurodynamics, 2008-07-08 10 Korea Univ. Nonlinear dynamics in biological neural network 5

Three important observables ( Δ V, Ca++, motion) Nature (2002) Center for Neurodynamics, 2008-07-08 11 Korea Univ. Excitation passage of a normal heart Ventricular Tachycardia (VT) VT 0 1 2 3 (sec) Ref> http://www.howstuffworks.com/heart.htm Nonlinear dynamics in biological neural network 6

A device for recording the activity of the heart Sir Thomas Lewis mastered the technology of the electrocardiogram in 1912 Center for Neurodynamics, 2008-07-08 13 Korea Univ. ECG trace of a patient having a cardiac arrest Center for Neurodynamics, 2008-07-08 14 Korea Univ. Nonlinear dynamics in biological neural network 7

Spiral wave p activities Cardiac fibrillations fibrillations Center for Neurodynamics, 2008-07-08 15 Korea Univ. VT � VF transition � Ventricular Tachycardia (VT): a bnormally fast b beating (usually > 150 bpm) independent of atrium ti ( ll > 150 b ) i d d t f t i contraction. In many cases, this is caused by the spontaneous creation of a (or a few) spiral wave on ventricle, which overrides the usual cue from the pacemaker (AV-node). � Ventricular Fibrillation (VF): fast irregular beating. It is the most common cause of sudden beating It i th t f dd VF cardiac death. Various instabilities of VT spiral waves are to initiate the VF. Center for Neurodynamics, 2008-07-08 16 Korea Univ. Nonlinear dynamics in biological neural network 8

Alternans: another precursor of VF Clusin’s review paper, Crit. Rev. Clin. Lab. Sci. 2003, 40(3):337-375 Center for Neurodynamics, 2008-07-08 17 Korea Univ. Cardiac cell culture at a high magnification Center for Neurodynamics, 2008-07-08 18 Korea Univ. Nonlinear dynamics in biological neural network 9

Brownian particles on periodically beating cardiac tissue unfixed μ m fixed μ m Center for Neurodynamics, 2008-07-08 19 Korea Univ. Cardiac cells on a MEA plate (a) (b) (c) (a) ITO MEA : (electrode diameter 30 μ m; lattice (a) ITO MEA : (electrode diameter 30 μ m; lattice constant 150 μ m), only 3 x 3 grids are shown. (b) Platinized ITO MEA (c) cultured cardiac cells on a platinized MEA. Center for Neurodynamics, 2008-07-08 20 Korea Univ. Nonlinear dynamics in biological neural network 10

MEA data acquisition system Center for Neurodynamics, 2008-07-08 21 Korea Univ. Case #1 Case #2 Unusual IBI time series IBI (ms) recorded 1.4 mm through MEA electrodes Event No. Case #3 Case #4 Case #5 ms) IBI (m Event No. Glass Substrate Center for Neurodynamics, 2008-07-08 22 Korea Univ. Nonlinear dynamics in biological neural network 11

Propagation induced phase contrast MACROscope Center for Neurodynamics, 2008-07-08 23 Korea Univ. Rotating spiral wave in confluent layer of rat ventricular cells Optical system & culture chamber S. Hwang, K. Yea, & K. Lee PRL (2004) ( ) raw image w/ collagen coating; Density= 2.0 x 10 3 6 mm (cells/ mm 2 ); 70-hr old culture Time- difference image Center for Neurodynamics, 2008-07-08 24 Korea Univ. Nonlinear dynamics in biological neural network 12

Regular cardiac spiral wave Raw image LAT image Time-diff. image 18 mm Local Activation Time: S. Hwang, K. Yea, & K. Lee, PRL (2004) LAT(t) = t – t n Center for Neurodynamics, 2008-07-08 25 Korea Univ. P-2 oscillatory cardiac spiral wave 6 mm having a static line defect Kim et al., PNAS (2007) τ 1 ∫ = + − + − τ V ( x , t ) [ G ( x , t t ' ) G ( x , t t ' )] dt ' τ 0 Center for Neurodynamics, 2008-07-08 26 Korea Univ. Nonlinear dynamics in biological neural network 13

Rotating line-defect & quasi- periodic local time series 114 hr i in vitro it space 30 min later Center for Neurodynamics, 2008-07-08 27 Korea Univ. Kinks in oscillated granular layers h=Acos(2 π ft) Melo, Umbanhowar & Swinney, PRL1995 Sand grains can exhibit discordant alternans! L-s-L-s-L-s- s-L-s-L-s-L- Nonlinear dynamics in biological neural network 14

Complex-periodic c x = -c y -c z oscillations in a c y =c x +Ac y Roessler system c z =c z c x -Cc z +B C z period-1 cycle (C=C 1 ) C y period-2 C x cycle (C C 2 ) (C=C 2 ) C x period-4 cycle (C=C 3 ) time Center for Neurodynamics, 2008-07-08 29 Korea Univ. Period-2 spiral wave with one line-defect in a R ö ssler system line-defect line defect Period 2 spiral Period-2 spiral Parameters: A=0.2, B=0.2, C=3.84, D Δ t/( Δ r) 2 =1.6x10 -2 τ 1 ∫ = + − + − τ V ( x , t ) [ G ( x , t t ' ) G ( x , t t ' )] dt ' τ 0 [ References] Center for Neurodynamics, 2008-07-08 30 Goryachev et al., Chaos 10 (2000); PRL(1999), PRL(1998), PRL(1996) Korea Univ. Nonlinear dynamics in biological neural network 15

Periodically forced excitable cell picture: Action potential duration (APD) vs. Diastolic interval (DI) restitution APD n APD n + DI n = τ APD n DI n APD n+1 0 0 DI n Center for Neurodynamics, 2008-07-08 31 Korea Univ. Transition to a line-defect mediated “turbulent” state (BZ experiment) - ] = 0.106 M [BrO 3 0.124 M [H + ]=2.12M, 0.132 M [Br - ]=1.25M 2008-07-08 Center for Neurodynamics, 32 Korea Univ. Nonlinear dynamics in biological neural network 16

Summary � Alternans (i.e., P-2 dynamics) can be viewed as a temporal (ECG) manifestation of P-2 oscillatory spiral waves. � Complex oscillatory spiral reentries can be also caused by some localized inhomogeneities [Hwang et al., PNAS 2005]. � Cardiac fibrillation via a “ line defect- mediated spatio-temporal chaos ” ? [yet to be seen]. � Similar problems in neuroscience? Center for Neurodynamics, 2008-07-08 33 Korea Univ. Complex- periodic oscillations driven by a d iven by a meandering spiral core S. Hwang, T. Kim & K Lee PNAS (cover 2005) K. Lee, PNAS (cover, 2005) 5 Days in Vitro Center for Neurodynamics, 2008-07-08 34 Korea Univ. Nonlinear dynamics in biological neural network 17