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