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Transcript of Applications of Cellular Automata in Cardiac and Ecological Systems 國立東華大學物理系...
![Page 1: Applications of Cellular Automata in Cardiac and Ecological Systems 國立東華大學物理系 蕭又新 4/28/2006.](https://reader033.fdocument.pub/reader033/viewer/2022061502/56649e905503460f94b95682/html5/thumbnails/1.jpg)
Applications of Cellular Automata in Cardiac and Ecological Systems
國立東華大學物理系
蕭又新4/28/2006
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Outline: Cardiac Systems
Heart rate variability Action potential and Cardiac cells Arrhythmias and spiral waves Spiral waves described by partial differential
equations Cellular automata approach
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Cardiac activity and ECG
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正常人的心率及 R-R分佈圖
食用搖頭丸的女性患者
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Action Potential in a Ventricular Action Potential in a Ventricular Cell Cell
動作電位週期
動作電位週期
舒張區間
舒張區間
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APD versus DIAPD versus DI
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Restitution Curve by ExperimentRestitution Curve by Experiment
Restitution Curve in canine endocardial muscle
Koller, Marcus L. et al. Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation. Am. J. Physiol. 275(Heart Circ. Physiol. 44): H1635-H1642, 1998.
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APDAPD 、、 DI and T(CL)DI and T(CL)
TDA
DRA
nn
nn
)(1
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Restitution CurveRestitution Curve
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Conduction BlockConduction Block
Spatially distributed action potential dynamics in a canine cardiac Purkinje fiber
Jeffrey J. Fox et al. Spatiotemporal Transition to Conduction Block in Canine Ventricle. Circ Res. 2002;90:289-296
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Normal Rhythm and Arrhythmias
Normal sinus rhythm
60~100 beats per minute Ectopic rhythms
For examples : Ventricular tachycardia(心室頻脈 )
Ventricular fibrillation(心室顫動 )
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Ventricular Tachycardia (VT)
Ventricular tachycardia (VT) is a tachydysrhythmia originating from a ventricular ectopic focus, characterized by a rate typically greater than 120 beats per minute and wide QRS complexes.
VT may be monomorphic or polymorphic. Nonsustained VT is defined as a run of tachycardia of less than 30 seconds duration; a longer duration is considered sustained VT.
Referencehttp://www.emedicine.com/
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Ventricular Fibrillation (VF)
What is ventricular fibrillation? The heart beats when electrical signals move through it. Ventricular fibrillation is a condition in which the heart's electrical activity becomes disordered. When this happens, the heart's lower chambers contract in a rapid, unsynchronized way. The heart pumps little or no blood.
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VT and VF in Electrocardiogram
Reference: Chaos, Solitons and Fractals Vol.13 (2002) 1755.
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Normal Rhythm
ventricle cells 2.5 days in culture 8 day old embryo 0.8 ml plating density recorded temp: 36 deg.
C each frame is
approximately 1 cm square
Reference :Optical Mapping Image Database
http://www.cnd.mcgill.ca/bios/bub/imagebase.html
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Spiral Waves
ventricle cells 2 days in culture 8 day old embryo recorded temp: 36 deg
C. each frame is approxim
ately 1 cm square
Reference :Optical Mapping Image Database
http://www.cnd.mcgill.ca/bios/bub/imagebase.html
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Spiral Waves Breakup
ventricle cells 2 days in culture 8 day old embryo 0.4 ml plating density alphaGA acid 50ul recorded temp: 36 deg C. each frame is approximately
1 cm square
Reference :Optical Mapping Image Database
http://www.cnd.mcgill.ca/bios/bub/imagebase.html
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Experimental Results for Multi-armed Spirals in Cardiac Tissue
Reference: PNAS, vol. 101, p15530 (2004).
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Aliev-Panfilov Model
)1()(
)1)((
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2
2
2
2
bekere
r
t
r
ereaekey
e
x
ed
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e
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Cable TheoryCable Theory
)/(1
/
1
;
2
2
2
2
2
2
axialm
mion
ionmaxial
mcioncm
maxial
rCDx
VDCI
t
V
It
VC
x
V
r
dt
dVCIIII
Irx
V
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Normal Rhythm and Conduction Block
Simulation results of normal rhythm and conduction block
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Spiral Waves Formation and Breakup
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Action Potential in Cardiac Muscle
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Cellular Automata in Cardiac Tissue
Activation state (6 time units)
Refractory state (3 time units)
Rest state Nearest-neighbor
coupling
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Target Waves
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Spiral Waves Formation (I)
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Spiral Waves Formation (II)
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Wave Breaks by Considering Spatial-Modulation of the Refractory Period
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Wave Breaks Occurring by Heterogeneity :Alain Karma, PNAS 97, 5687 (2000)
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Simulated 3D Spirals Based on MRI Images
256X256 grids for each frame
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Enjoy Music Coming from Your Heart
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Outline: Ecological Systems
Complexity in laboratory insect populations Extinction in spatially structured populations Cellular automata approach in a modeling
ecology: grass, rabbit, and wolf Time-domain analysis: Hurst exponent Future works: computational epidemiology
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Laboratory Insect Populations
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Proc. R. Lond. B 264, 481 (1997)
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Food Chain
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Predator-Prey Mechanism
Species: grass, rabbit, and wolf
Season effect Nearest-neighbor
and next nearest-neighbor coupling: 8 cells
50x50 cells
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The frame of CA (50 X 50). The components of the ecosystem.
0 ~ Carnivores ~ 10 ~ Carnivores ~ 1
0 ~ Herbivores ~ 30 ~ Herbivores ~ 3
0 ~ Plants ~ 90 ~ Plants ~ 9
Rules of Cellular Automata
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The next population in a cell. Time step = 1.
Value(next) = Value = Value(now)(now) + Changes + Changes
nownow nextnext
Update the Population
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Plants dominated by season and herbivores. Roughly separating the season into two parts.
Pla.Pla.(next)(next) = Pla. = Pla.(now)(now) + Changes + Changes
{Changes Changes Summer +1 –Her.Summer +1 –Her.
Winter –Her. Winter –Her.
The Rules of Plants
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The affection coming from neighboring cells. Define the local sum (L) of the population
densities.
Eight Eight NeighborsNeighbors
L(i)L(i) = Value(i) + = Value(i) + Value(j)Value(j)
j = Neiborsj = Neibors
The Neighbors of a Fixed Cell
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Her.Her.(next)(next) = Her. = Her.(now)(now) + Changes + Changes
If Pla. GE. Her. If Pla. GE. Her.
{Changes Changes
Car. = 0 ; HCar. = 0 ; H00~L(H)~H~L(H)~H11 +1 +1
Otherwise -1Otherwise -1
The Rules of Herbivores
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Her.Her.(next)(next) = Her. = Her.(now)(now) + Changes + Changes
If Pla. LT. Her. If Pla. LT. Her.
{Changes Changes -(Her. – Pla.) – Car.-(Her. – Pla.) – Car.
The Rules of Herbivores
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Her.Her.(next)(next) = Her. = Her.(now)(now) + Changes + Changes
{Changes Changes Her. > 0 ; CHer. > 0 ; C00~L(C)~C~L(C)~C11 +1 +1
Otherwise -1Otherwise -1
The Rules of Carnivores
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No wolf Summer period Complicated
fluctuations Anti-correlation in
between grass and rabbit
No extinction
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Spatiotemporal Plot for Grass Evolution
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Considering wolf Summer period Complicated
fluctuations Positive correlation in
between rabbit and wolf
No extinction
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Spatiotemporal Plots for Grass Evolution
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No wolf Considering winter
effect (W=1, S+W=10) Complicated
fluctuations No extinction Anti-correlation in
between grass and rabbit
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Spatiotemporal Plots for Grass Evolution
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Considering wolf Considering longer winter
(W=3, S+W=10) Complicated fluctuations Wolf extinction Anti-correlation in between
grass and rabbit Complicated correlation in
between wolf and rabbit
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Spatiotemporal Evolution of Grass
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No wolf Considering spatial
effect: uniformly distributed rabbit (R=1)
Summer period Complicated fluctuations In early stage rabbits
increase fast Rabbit extinction Anti-correlation in
between grass and rabbit
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Spatiotemporal Plots for Grass Evolution
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No wolf Considering spatial effect:
uniformly distributed rabbit (R=3)
Considering winter effect (W=1, S+W=10)
Complicated fluctuations Surprise! slow down rabbit
extinction Anti-correlation in between
grass and rabbit
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Spatiotemporal Plots for Grass Evolution
It might be a good way to design tiles as well as carpets!
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Spiral Waves in Ecology: SURPRISE!
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Random Noise and Brownian Diffusion
-4
-3
-2
-1
0
1
2
3
4
0 500 1000 1500 2000 2500 3000
-20
-10
0
10
20
30
40
50
60
0 500 1000 1500 2000 2500 3000
2
2
2exp
2
1),(
t
xx
ttxp
Gaussian random noise
Brownian trajectory
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Hurst Exponent (I)
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Hurst Exponent (II)
H=0.8
H=0.6
H=0.4
H=0.2
Persistent noise: H>0.5Random noise: H=0.5Anti-persistent noise: H<0.5S(f) ~ f-b, b = 2H – 1
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Extinction Characterized by H: OK
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Extinction Characterized by H: NOT OK
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Computational Epidemiology
S: susceptible state (latent period)
I: Infectious state (infectious period)
R: recovery period
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Measles and Vaccination
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