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

Nonlinear dynamics in biological neural network 1

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

2008-07-08 Center for Neurodynamics, Korea Univ. 1

Physics, Korea University (http://turing.korea.ac.kr)

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

2008-07-08 Center for Neurodynamics, Korea Univ. 2

5) Cadiac cells heart function ..... many others

Nonlinear dynamics in biological neural network 2

Dictyostelium discodium amoeba on a porous gel substrate

2008-07-08 Center for Neurodynamics, Korea Univ. 3

cell size ∼ 10 μm Darkfield image

cAMP waves in signaling amoeba populations

spiral wave circular waves

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Lee, Cox, & Goldstein, PRL (1996); PRL (2001); Nonlinearity (2002)

2.0x2.8 cm2

Nonlinear dynamics in biological neural network 3

Waves, cytoplasmic flows &

• ptimization in a social amoebae

Physyrum polycephalum

Toshiyuki NAKAGAKI (Hokkaido University) PRL 2008 Nature (News & Views) begin end PRL 2008, Nature (News & Views)

2008-07-08 Center for Neurodynamics, Korea Univ. 5

Sychronized ‘bursts’ in coupled network of neurons (with glia)

Jun Hwan Kim & Jun Ho Choi (Korea University)

2008-07-08 Center for Neurodynamics, Korea Univ. 6

Nonlinear dynamics in biological neural network 4

Membrane potential and Hodgkin-Huxley Equation

2008-07-08 Center for Neurodynamics, Korea Univ. 7

Multi-channel amplifying system

Pre Amplifier, 64ch

Pre Amplifier

• Differential Input,

CMRR > 60dB

• Gain : 10 ( at 900Hz )

Filter Amplifier, 64ch

• Filter : High pass @

100Hz, 1 pole Filter Amplifier

• Single-ended Input.
• Gain : 1000 (3 stages,

each 10x (at 900Hz )

• Filter : Low pass @

5kH 6 l

2008-07-08 Center for Neurodynamics, Korea Univ. 8

5kHz, 6 poles High pass @ 100Hz, 3 poles

Nonlinear dynamics in biological neural network 5

Calcium waves in confluent confluent layer

• f

astroglia

2008-07-08 Center for Neurodynamics, Korea Univ. 9

Jin Sung Park (Korea University)

HEART - a complex functional system

• f cells: its hierarchical structure

2008-07-08 Center for Neurodynamics, Korea Univ. 10

Nonlinear dynamics in biological neural network 6

Three important observables (ΔV, Ca++, motion)

2008-07-08 Center for Neurodynamics, Korea Univ. 11 Nature (2002)

Excitation passage

• f a normal heart

Ref> http://www.howstuffworks.com/heart.htm

1 2 3 (sec) VT

Ventricular Tachycardia (VT)

Nonlinear dynamics in biological neural network 7

A device for recording the activity of the heart

Sir Thomas Lewis mastered the technology of the electrocardiogram in 1912

2008-07-08 Center for Neurodynamics, Korea Univ. 13

ECG trace of a patient having a cardiac arrest

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Nonlinear dynamics in biological neural network 8

Spiral wave p activities

Cardiac fibrillations

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fibrillations

VT VF transition

Ventricular Tachycardia (VT): abnormally fast

b ti ( ll > 150 b ) i d d t f t i beating (usually > 150 bpm) independent of atrium

• 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 i th t f dd

2008-07-08 Center for Neurodynamics, Korea Univ. 16

• beating. It is the most common cause of sudden

cardiac death. Various instabilities of VT spiral waves are to initiate the VF.

VF

Nonlinear dynamics in biological neural network 9

Alternans: another precursor of VF

Clusin’s review paper, Crit. Rev. Clin. Lab. Sci. 2003, 40(3):337-375

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Cardiac cell culture at a high magnification

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Nonlinear dynamics in biological neural network 10

Brownian particles on periodically beating cardiac tissue

μm

fixed unfixed

2008-07-08 Center for Neurodynamics, Korea Univ. 19

μm

Cardiac cells on a MEA plate

(a) (b) (c)

(a) ITO MEA : (electrode diameter 30μm; lattice

2008-07-08 Center for Neurodynamics, Korea Univ. 20

(a) ITO MEA : (electrode diameter 30μm; lattice constant 150μm), only 3 x 3 grids are shown. (b) Platinized ITO MEA (c) cultured cardiac cells on a platinized MEA.

Nonlinear dynamics in biological neural network 11

MEA data acquisition system

2008-07-08 Center for Neurodynamics, Korea Univ. 21

Unusual IBI time series recorded through MEA electrodes

1.4 mm

IBI (ms) Case #1 Case #2 ms) Event No. Case #3 Case #4 Case #5

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Glass Substrate

Event No. IBI (m

Nonlinear dynamics in biological neural network 12

Propagation induced phase contrast MACROscope

2008-07-08 Center for Neurodynamics, Korea Univ. 23

Rotating spiral wave in confluent layer of rat ventricular cells

Optical system & culture chamber

• S. Hwang, K. Yea, &
• K. Lee PRL (2004)

raw image

6 mm w/ collagen coating; Density= 2.0 x 103 (cells/ mm 2); 70-hr old culture

( )

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Time- difference image

Nonlinear dynamics in biological neural network 13

Regular cardiac spiral wave

Raw image LAT image Time-diff. image

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Local Activation Time: LAT(t) = t – tn 18 mm

• S. Hwang, K. Yea, &
• K. Lee, PRL (2004)

P-2 oscillatory cardiac spiral wave

6 mm

having a static line defect

Kim et al., PNAS (2007)

2008-07-08 Center for Neurodynamics, Korea Univ. 26

' )] ' , ( ) ' , ( [ 1 ) , ( dt t t x G t t x G t x V

∫

− + − + =

τ

τ τ

Nonlinear dynamics in biological neural network 14

Rotating line-defect & quasi- periodic local time series

114 hr i it in vitro

space

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30 min later

Kinks in oscillated granular layers

Melo, Umbanhowar & Swinney, PRL1995

h=Acos(2πft)

L-s-L-s-L-s-

Sand grains can exhibit discordant alternans!

s-L-s-L-s-L-

Nonlinear dynamics in biological neural network 15

Complex-periodic

• scillations in a

Roessler system

cx= -cy-cz cy=cx+Acy cz=czcx-Ccz+B

period-1 cycle period-2 cycle Cx Cz Cy (C=C1) (C=C2)

2008-07-08 Center for Neurodynamics, Korea Univ. 29

period-4 cycle

time

Cx (C C2) (C=C3) Period 2 spiral line-defect

Period-2 spiral wave with one line-defect in a Rössler system

Period-2 spiral line defect

Parameters: A=0.2, B=0.2, C=3.84, DΔt/(Δr)2=1.6x10-2

2008-07-08 Center for Neurodynamics, Korea Univ. 30

' )] ' , ( ) ' , ( [ 1 ) , ( dt t t x G t t x G t x V

∫

− + − + =

τ

τ τ

[References] Goryachev et al., Chaos 10 (2000); PRL(1999), PRL(1998), PRL(1996)

Nonlinear dynamics in biological neural network 16

Periodically forced excitable cell picture: Action potential duration (APD) vs.

Diastolic interval (DI) restitution APDn

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APDn DIn APDn+1

DIn

0 0

APDn + DIn = τ

Transition to a line-defect mediated “turbulent” state (BZ experiment)

[BrO3

• ] = 0.106 M

0.124 M

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[H+]=2.12M, [Br-]=1.25M 0.132 M

Nonlinear dynamics in biological neural network 17

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-

2008-07-08 Center for Neurodynamics, Korea Univ. 33

mediated spatio-temporal chaos”? [yet to be seen].

Similar problems in neuroscience?

Complex- periodic

• scillations

driven by a d iven by a meandering spiral core

• S. Hwang, T. Kim &

K Lee PNAS (cover 2005)

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5 Days in Vitro

• K. Lee, PNAS (cover, 2005)