1. Modelling Cardiac Arrhythmia Due to Abnormal AV Function Sean and Irene Irene and Sean

2. Cardiac Arrhythmia Means irregular heartbeat Condition can be benign to fatal Several causes of arrhythmia due to abnormal functioning at various locations within the heart Statement of the Problem –What are the causes of different types of arrhythmia? –How can we model those arrhythmias caused by malfunctions of the AV-node?

3. Heart Physiology

4. Heart Physiology Electrical Action Potentials A simulated heartbeat Analyzing the heartbeat

5. Electrocardiogram Normal Heart

6. Electrocardiogram Arrhythmias

7. Mathematizing the Physiological Process Modelling One AV Potential Cycle: –Three Phases: Resting Rise Post-Peak Plateau & Decay –Two thresholds: Resting Potential Peak Potential –Two Triggers: Start Cycle (From SA Node) Trigger Heartbeat (Peak Potential is Reached in AV Node)

8. Modelling Multiple Heartbeats: Check the AV Node Potential at the time the pulse from the SA Node arrives (typically about 200 msec delay) Mathematizing the Physiological Process ? If the AV Node is Refractory (above Resting Potential)  Reject the Action Potential and Skip a Beat If the AV Node is at Resting Potential  Accept the Pulse and Produce a Beat

9. Model Simple discrete-time model with geometric increase or decrease: Potential ( t + 1 ) = Potential ( t ) * ( Time Constant ) When TC > 1  Rising When TC = 1  Stable Plateau or Resting When TC < 1  Decaying Using modular arithmetic to generate each cycle and keep track of parameters. Assumptions: –Every component other than the AV node functions correctly –Based on patterns observed in EKG’s, AV Block results from a longer Rise- &/or Decay-time of AV Potential  plateau duration was not modified at this stage –Threshold Criterion: The Threshold Potential is the Resting Potential –Threshold Timing: The AV cannot be refractory when the AP arrives at the AV node. –A Heartbeat is generated at the peak of the AV Node Potential –Constant heart rate of 1 beat per second

10. Implementation Coded in Excel VB –The mathematical representation is simple, but implementation in Excel is not a pretty sight –Two bright spots: Using Subroutines in Visual Basic Putting Macro Buttons into the Excel Spreadsheet Normal Heartbeat –Using fast Rise and Decay Times; Node is quickly back to Resting Potential 1 st Degree AV Block –Using slower Rise of AV Node Potential; heartbeat occurs later after SA Pulse than in a normal heartbeat, but beat is regular. 2 nd Degree Type 1 (Wenckebach) AV Block –The AV Node fatigues with successive cycles and doesn’t respond as quickly to the pulse from the SA Node 1 st cycle is near normal 2 nd cycle uses slower Rise and Decay Times; the node is refractory when the 3 rd SA pulse arrives 3 rd cycle has no beat 4 th cycle returns to near normal behaviour

11. Demonstration Run Model

12. Interpretation We are able to model all of the known Arrhythmia patterns caused directly by AV Node Heart Block –Normal  1 st Degree by increasing the Rise Time a constant amount –Can induce 1:1 skipped beats (mathematically) with the 1 st Degree model by using large enough Rise/Decay Time (maybe unphysically!) –1 st Degree  2 nd Degree (Wenckebach) by progressively increasing Rise/Decay Time from one cycle to the next (AV node fatigues) The important factor is the AV Node Response, modeled by parameters which control the Rise/Decay times

13. Critique of the Model We are modeling the patterns, not the physiological process We had to force the 2:1 Wenckebach cycle with two specified Rise/Decay times Captures periodicity but not necessarily true pulse shape, thresholds, scaling of rise and decay Could account for other (non-AV) arrhythmias with a better understand of which mathematical parameters relate to other heart malfunctions Code would benefit from cleaning up multiple/nested loops with subroutines but it was not done for this beta version

14. Answer the Questions What causes arrhythmia? –AV Node block; blocks before and after AV node How to mathematically model the heart rhythms? –Empirically using approximated threshold criteria rather than physics In particular, can one model account for all observed arrhythmia? –Our model accounts for arrhythmia caused by malfunction of the AV node only –How would we adapt this model to describe more or all arrhythmias? Need to mathematically add in malfunctions of other heart components –This is not impossible, just requires even more variable parameters, program subroutines etc.

15. The End Thanks for your attention!