Modelling Cardiac Arrhythmia Due to Abnormal AV Function

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Modelling Cardiac Arrhythmia Due to Abnormal AV
Function

• Sean and Irene
• Irene and Sean

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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?

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Heart Physiology
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Heart Physiology Electrical Action Potentials
A simulated heartbeat Analyzing the heartbeat
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ElectrocardiogramNormal Heart
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ElectrocardiogramArrhythmias
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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)

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Mathematizing the Physiological Process

• Modelling Multiple Heartbeats
• Check the AV Node Potential at the time the
  pulse from the SA Node arrives (typically about
  200 msec delay)

If the AV Node is at Resting Potential? Accept
the Pulse and Produce a Beat
If the AV Node is Refractory (above Resting
Potential) ? Reject the Action Potential and Skip
a Beat
?
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Model

• Simple discrete-time model with geometric
  increase or decrease
• Potential ( t 1 ) Potential ( t ) ( Time
  Constant )
• When TC gt 1 ? Rising
• When TC 1 ? Stable Plateau or Resting
• When TC lt 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 EKGs, 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

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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
• 1st 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.
• 2nd Degree Type 1 (Wenckebach) AV Block
• The AV Node fatigues with successive cycles and
  doesnt respond as quickly to the pulse from the
  SA Node
• 1st cycle is near normal
• 2nd cycle uses slower Rise and Decay Times the
  node is refractory when the 3rd SA pulse arrives
• 3rd cycle has no beat
• 4th cycle returns to near normal behaviour

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Demonstration

• Run Model

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Interpretation

• We are able to model all of the known Arrhythmia
  patterns caused directly by AV Node Heart Block
• Normal ? 1st Degree by increasing the Rise Time a
  constant amount
• Can induce 11 skipped beats (mathematically)
  with the 1st Degree model by using large enough
  Rise/Decay Time (maybe unphysically!)
• 1st Degree ? 2nd 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

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Critique of the Model

• We are modeling the patterns, not the
  physiological process
• We had to force the 21 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

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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.

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The End

• Thanks for your attention!