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  1. The Workshop Project Understanding Spiral Waves

  2. 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 period

  3. 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

  4. Reentrant Spiral Waves: Simulation Fenton FH et al. Chaos 2002; 12, 852-892.

  5. Reentrant Spiral Waves: Simulation Fenton FH et al. Chaos 2002; 12, 852-892.

  6. Reentrant Spiral Waves: Simulation Fenton FH et al. Chaos 2002; 12, 852-892.

  7. Reentrant Spiral Waves: Simulation Fenton FH et al. Chaos 2002; 12, 852-892.

  8. Reentrant Spiral Waves: Simulation Fenton FH et al. Chaos 2002; 12, 852-892.

  9. Reentrant Spiral Waves: Simulation Fenton FH et al. Chaos 2002; 12, 852-892.

  10. Belusov-Zhabotinsky Reaction Oliver Steinbock

  11. Spiral Waves of Electrical Activity in the Heart(Arrhythmias)

  12. Heart diseases Heart disease is one of the leading causes of death in the world. Number one in industrialized countries CDC/Statistics National 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 etc http://www.cdc.gov/nchs/data/nvsr/nvsr57/nvsr57_14.pdf

  13. 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).

  14. 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). .

  15. 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.

  16. 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