Modelling Cardiac Arrhythmia Due to Abnormal AV Function

Sean and Irene

Irene and Sean

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?

Heart Physiology

Heart Physiology Electrical Action Potentials

A simulated heartbeat

Analyzing the heartbeat

ElectrocardiogramNormal Heart

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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• 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

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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

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

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 doesn’t 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 3 rd SA

pulse arrives• 3rd cycle has no beat• 4th cycle returns to near normal behaviour

Demonstration

Run Model

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 1:1 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

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

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.

The End

Thanks for your attention!