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Why Is Alternans Indeterminate?

Why Is Alternans Indeterminate?. cell. tissue. Xiaopeng Zhao Mechanical, Aerospace and Biomedical Engineering University of Tennessee Xzhao9@utk.edu. Ventricular Fibrillation. ECG. Courtesy of Flavio H. Fenton, Cornell University. stroke 167,000. sudden cardiac arrest 350,000.

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Why Is Alternans Indeterminate?

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  1. Why Is Alternans Indeterminate? cell tissue Xiaopeng Zhao Mechanical, Aerospace and Biomedical Engineering University of Tennessee Xzhao9@utk.edu

  2. Ventricular Fibrillation ECG Courtesy of Flavio H. Fenton, Cornell University

  3. stroke 167,000 sudden cardiac arrest 350,000 lung cancer 160,000 Death in the US Ventricular Fibrillation Leads to SCA http://www.wrongdiagnosis.com

  4. Basic Physiology Calcium Contraction -- Action Potential Duration-- Diastolic Interval-- Basic Cycle Length

  5. Alternans: period doubling Slow pacing 1:1 response Rapid pacing 2:2 response (alternans)

  6. Model Fox et al., Am J Physiol, 2002 Shiferaw et al., Biophy, 2003

  7. Alternans in Single Cells Simulation of the Shiferaw-Fox Model

  8. Alternans in Fibers

  9. Alternans in Fibers A “fiber” of Two Cells desynchronized synchronized

  10. D.M. Bers, 2001 Influence of Junctional Diffusion

  11. Spatial Pattern of Alternans • Existing theory: • Pattern determined by length of fiber;short fibers: spatially concordant;long fibers: spatially discordant • Shiferaw-Fox model: • Pattern determined by initial condition;spatial concordance independent of length of fiber

  12. Voltage/Calcium Coupling A Single Cell

  13. Voltage/Calcium Coupling Two Coupled Cells

  14. Eigenvalues

  15. Coupled Cells Stability Boundary Single Cell

  16. Eigenvectors: Spatial Synchrony

  17. Diaz et al., Circ Res, 2002 Shiferaw et al, Biophy, 2003 Calcium Dynamics

  18. Coupled Cells Border-collision Bifurcation Single Cell

  19. Simulation of Mapping Bifurcation Diagram a single cell two coupled cells

  20. Simulation of Mapping

  21. Future Work Coupled Oscillators Open questions: stability, synchronization, … experiments, prediction, control, …

  22. Take-home Message The spatiotemporal pattern of calcium-driven alternans is indeterminate.

  23. Acknowledgement • Code of the Shi-Fox model, courtesy of Yohannes Shiferaw • Useful discussion with Wanda Krassowska, David Schaeffer, Daniel Gauthier, Daisuke Sato, and Alain Karma

  24. Positive Vm/Ca Coupling

  25. Summary In tissue, spatial coupling in APD is strong whereas the coupling in Ca is weak Multiple alternans (period-2) solutions coexist if alternans is induced by instability in calcium dynamics At a first approximation, the phenomenon occurs through a border-collision bifurcation.

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