the workshop project
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The Workshop Project
Understanding Spiral Waves
The refractory period
• Excitable systems can sustain spiral waves as well as plain waves
• This is due to the refractory period– Three examples of the effect of the refractory peri
od
Induction of spiral waves
• Spiral waves can be initiated when tissue has repolarized nearly, but not fully, to the rest state.
• It’s all about timing!
Too late Too early Just right
Reentrant Spiral Waves: Simulation
Fenton FH et al. Chaos 2002; 12, 852-892.
Reentrant Spiral Waves: Simulation
Fenton FH et al. Chaos 2002; 12, 852-892.
Reentrant Spiral Waves: Simulation
Fenton FH et al. Chaos 2002; 12, 852-892.
Reentrant Spiral Waves: Simulation
Fenton FH et al. Chaos 2002; 12, 852-892.
Reentrant Spiral Waves: Simulation
Fenton FH et al. Chaos 2002; 12, 852-892.
Reentrant Spiral Waves: Simulation
Fenton FH et al. Chaos 2002; 12, 852-892.
Belusov-Zhabotinsky Reaction
Oliver Steinbock
Spiral Waves of Electrical Activity in the Heart(Arrhythmias)
Number one in industrialized countries
CDC/StatisticsNational Vital Statistics Report, Vol.49, No.11, October 12, 2006
Deaths and percent of total deaths for the 10 leading causes of death: United States
Rank Cause of death Total Deaths Percentage All causes ...........................................................2,391,399 100.0
1 Diseases of heart ................................................725,192 30.3 2 Malignant neoplasms ...........................................549,838 23.0 3 Cerebrovascular diseases .....................................167,366 7.0 4 Chronic lower respiratory diseases ......................124,181 5.2
etchttp://www.cdc.gov/nchs/data/nvsr/nvsr57/nvsr57_14.pdf
Heart diseases Heart disease is one of the leading causes of death in the world.
Many different types of cardiac arrhythmias• Heart disease is a broad term that includes:
– Coronary heart disease (arteries to heart blocked → heart attack).
– Stroke (arteries to brain blocked or burst).– Congestive heart failure (weakened pumping).– High blood pressure → all of the above.– Arrhythmias (disorders of regular rhythmic beating).
Types of Arrhythmias
• Can occur in upper chambers (atria) or lower chambers (ventricles) or both.
• Heart rate may be increased or decreased.• May be asymptomatic or immediately life-
threatening.• May result from pacemaker dysfunction or
breakdown of electrical activity (reentry)..
Main Types of Fibrillation
• Atrial fibrillation: – Not immediately life-threatening. – 2 million affected, influences lifestyle.– Responsible for 15-20% of all strokes (clotting).
• Ventricular fibrillation: – Contraction no longer coordinated: heart cannot
pump. – 340,000 deaths/year in US. – Tachycardia often immediately precedes fibrillation.
Your project
• Investigate spiral waves forming from the Tusscher-Noble-Noble-Panfilov model:
• For play, the simpler Fitzhugh-Nagumo model is helpful– Try altering the parameters a and b and see how
you can change the spiral tip pattern
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