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What is so scary about a perfectly uniform heartbeat?

What is so scary about a perfectly uniform heartbeat?. P G Vaidya Mathematical Modelling Unit National Institute of Advanced Studies Bangalore 560 012. International Biomedical Modeling School and Workshop NCBS, 2 March 2008. An ECG. Can Heart Attack be Predicted ?.

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What is so scary about a perfectly uniform heartbeat?

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  1. What is so scary about a perfectly uniform heartbeat? P G Vaidya Mathematical Modelling Unit National Institute of Advanced Studies Bangalore 560 012 International Biomedical Modeling School and Workshop NCBS, 2 March 2008

  2. An ECG Can Heart Attack be Predicted? Data Supplied by Dr. Pradhan of NIMHANS, Bangalore, Healthy Male, Age 36

  3. Phase distribution of the RR intervals of a healthy subject

  4. 3D state space picture of the ECG data using “Embedding” Can Heart Attack be Predicted?

  5. Can we synchronize them by givingthe same push to both ?

  6. Position and Velocity of the Swing

  7. State Space and Phase of Swing

  8. Portrait of a nonlinear autonomous system With the solitary exception of a trajectory starting at the origin, all others approach a limit cycle of unit radius :

  9. What is the phase outside of the limit cycle?

  10. Effect of Driving Force

  11. EFFECT of a single PULSE

  12. Change of Phase due to a Single Pulse

  13. Change in Phase due to single Pulse The graph and the equation shows that there is a fixed point at 0, which is stable and a fixed point at pi which is unstable. Therefore, multiple periodic pulses would lead to synchronization

  14. Example of ECG Data From a “normal” person’s data an approximate autonomous nonlinear equation was derived. (Experimental Chaos, Florence 2004)

  15. Two Stable and Two Unstable Fixed Points For this case, the before and after phase was determined by running several cases with different initial conditions. It can be seen from the map that now there are two stable and unstable fixed points.

  16. Change in Phase due to single Pulse

  17. Two Stable Rest Points GRAPHIC REPRESENTATION OF POSSIBLE PROBLEM S1 • • U2 • U1 • S2

  18. Multiple pulses .

  19. UNIFORM CASE

  20. Consequences Thus it is clear that it is possible that if two cells are nearly synchronized, chances are that they will continue to get closer. An occasional pulse which puts them on the wrong side would not cause lasting damage. But once they are farther, the chances of their drifting further increase.

  21. Pulses at a random interval from one another All drift, but together !

  22. PCEPHASE COHERNCE of an ENSEMBLE . PCE calculated in a manner similar to TSC (pl see poster) PCE=1 if all cells are in phase PCE=0 if phases are uniformly distributed across the circle

  23. PCE of RANDOM forcing vs. UNIFORM forcing

  24. A plausible Explanation of thedesirability of RR variability It does seem that Uniform Interval forcing, in most cases, could lead to more than one cluster of cells, each going at their own phases, well separated from each other A variable rate of pulsing, if with well distributed phases Could reduce this possibility Some theoretical justification based on Markov Modeling

  25. Special thanks are due to Professor V. Kannan, Univ. Hyderabad, Professor R. Narasimha, JNC, Professor Ivanov of Boston University and Dr. Kanters, University of Copenhagen and others

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