Computational modeling of cardiac arrhythmias

Normal function of the heart

Normal function of the heart

Normal function of the heart

Normal rhythm 60 beats/min: determined by the SA node

=> 100.000 beats per day.

:delay of the signal

Cardiac arrhythmia

  • Ischaemic heart disease: Ventricular arrhythmias remain the leading cause of death from coronary artery disease
  • Stroke can also be caused by cardiac arrhythmia: e.g. atrial fibrillation

Cardiac arrhythmia

Main questions

 

- Mechanisms of the initiation of arrhythmias

 

- Transition of arrhythmia (tachycardia) into more

  dangerous arrhythmia (fibrillation)


- Control of arrhythmia, how to remove it from the heart

 

Computer modeling help with these questions!

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
    - 3D dynamics of filaments
    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
    - 3D dynamics of filaments
    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
    - 3D dynamics of filaments
    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

Single cell

The membrane: contains channels which can open and close

Nerst potential: 2 opposite forces:

  • diffusion
  • electrical force

You can find the equilibrium which gives you the Nerst potential

 

 

 

 

 

 

 

 

 

 

Nerst potential: 2 opposite forces:

  • diffusion
  • electrical force

You can find the equilibrium which gives you the Nerst potential

 

 

 

 

 

 

 

 

 

 

Most easy model: Hodgkin huxley (nerve cell)

Most easy model: Hodgkin huxley (nerve cell)

Most easy model: Hodgkin huxley (nerve cell)

The whole cell: many more channels

The whole cell: also internal dynamics

The whole cell: many more channels

The whole cell: many more channels

The whole cell: many more channels

All the channels can be modeled as:

The whole cell: many more channels

- Only the most simple model (HH) can be solved analytically

 

- All other models have to be solved numerically with the

  computer:

 

  At each timestep you can output any variable that you want,
  voltage, currents, concentration...

 

The whole cell: many more channels

  • There exist many different different models: for the ventricles 3 major models, more than 10 other models

 

  • The ORD model is being used to test the effect of drugs: ’Comprehensive in-vitro Pro-arrhythmia Assay (CiPA) initiative www.cipaproject.org. CiPA aims to replace the existing pro-arrhythmic safety testing and Thorough QT Study with a combination of ion channel screening, mathematical modelling, stem-cell derived myocyte experiments and more lightweight Phase I ECG monitoring’

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
    - 3D dynamics of filaments
    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

Different cells are coupled

  • conduction of a wavefront
  • refraction: during the wavefront: no new wave can be excited
  • resting state: new wave can arrive

Single cell

2D tissue

Colliding waves annihilate

Wave can rotate in a ring, rotation is possible if the length of a ring (L) is longer than the product of the refractory period and the velocity of the wave: L > Rv

 

 

 

 

 

 

 

 

 

 

Wave can rotate around an obstacle/Wave can rotate around itself

Anatomical reentry

Functional reentry

Period of rotation is usually close to refractoriness time

Experimental evidence

In a rabbit heart (Allessie 1973):

  • first to record it
  • not big enough preparation, called it a leading circle
  • wrong idea still exists up today

Experimental evidence

In a sheep and dog epicardial muscle (Davidenko, Jalife 1973):

--> First to record a real spiral wave

Experimental evidence

Cell cultures (lab of L. Glass, neonatal rat cells)

Experimental evidence

Whole heart of guinea pig (lab of J. Jalife, 2002)

Many other systems also have spiral waves!

Many other systems also have spiral waves!

Many other systems also have spiral waves!

Cable equation

Cable equation

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
    - 3D dynamics of filaments
    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

A spiral wave becomes a scroll wave: it can be open or closed

Whole heart simulation: mesh of the heart + fiber orientation

Whole heart simulation: scroll wave leads to an arrhythmia

Spiral waves have many different names

1. anatomical reentry -> around obstacle

2. functional reentry = rotor -> around itself

Tachycardia

Fibrillation

Spiral waves have many different names

1. anatomical reentry -> around obstacle

2. functional reentry = rotor -> around itself

Still a lot of discussion in the medical world what is the role of spiral waves!

How to stop a reentry circuit?

Ablation: burning of tissue

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
    - 3D dynamics of filaments
    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
    - 3D dynamics of filaments
    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

Excitability important for creation of a spiral wave: properties of the single cell!

very low excitability

low excitability

INa

INa

low excitability

  • circular rotation
  • the period is longer to the refractory period
  • Substantial excitable gap

INa

high excitability

  • instantaneous rotation
  • the period is close to the refractory period
  • There is a small excitable gap

INa

very high excitability

INa

If wavefront cannot make a complete turn without interaction with the tail of the wave, there will be interaction and thus meandering.

long refractory tail

Ik

Stable spiral

Meandering spiral

Hypothesis:

different types of spirals give rise to different arrhythmias

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
    - 3D dynamics of filaments
    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

Restitution curve

Restitution curve

Restitution curve

Restitution curve

Break-up of a spiral due to restitution

Hypothesis:

different types of spirals give rise to different arrhythmias

Very dangerous!!!!

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
   
- 3D dynamics of filaments
    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

3D dynamics of filaments

There is a filament present!

3D dynamics of filaments

This filament has dynamics:

- closed ring:

Scroll ring grows: low excitability
Scroll ring shrinks: high excitability

 

 

 

 

- Filament attached to two boundaries

 

 

 

 

 

3D dynamics of filaments

Example: filament with negative tension: possible mechanism of VF (Alonso, Panfilov)

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
    - 3D dynamics of filaments

    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

Steep APD gradient in the Mcell region of a non failing human heart

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
    - 3D dynamics of filaments

    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

Typical in aging heart: more myofibroblast = fibrotic tissue

Spiral waves are attracted by fibrotic tissue

Spiral waves are attracted by fibrotic tissue

In clinic: spiral waves are often found close to fibrotic tissue

Currently, electrophysiologists are already ablating based on computer modeling

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
    - 3D dynamics of filaments

    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

Single cells can have early afterdepolarizations when channels properties are changed

Regions of EAD sensitive cells can cause focal beats = extra beats

These extra beats can also cause spiral waves

1. Basic properties and computer modeling
    - Single cell
    - 2D modeling
    - Whole heart modeling

2. The study of spiral waves by computer modeling
    - Dynamics of spiral waves in homogeneous media
    - Breakup of a spiral
    - 3D dynamics of filaments

    - Influence of a spiral wave by a heterogeneity
    - Influence of fibrosis on spiral waves
    - EADs, spiral waves and ectopic activity

3. The real world: clinical research

 

Computer modeling is useful to understand arrhythmias, however, only one group in the world (Baltimore) uses modeling to actually treat patients. Still a long way to go...

Computer modeling can however also be used to test new techniques

Cardiac arrhythmias: 3 main different types of mechanisms

2. Anatomical reentry

1. Rotors or functional reentry

3. Focal sources

Therefore, we developed a methodology to determine these sources automatically: we describe the electrical propagation in the heart as a directed network: 

DG-mapping

Huge field of applications

Brain

Facebook

Search algorithm

Network theory

Network theory on the excitation of the heart: concept

1. rotors or functional reentry

2. anatomical reentry

3. focal sources

DG-mapping on clinical AT cases

Optimization protocols

DG-mapping on clinical AT - DG GUI

In collaboration with  the AZ-sint Jan Bruges (in collaboration with Prof. Dr. MD. Mattias Duytschaever, Prof. Dr. MD. Sebastian Knecht, Dr. Jan de Pooter, Dr Rene Tavernier)

 

DG-mapping on tested on clinical AT cases

# Setting Expert + latest mapping system Junior +  latest mapping system DG-mapping ablation endpoint (with entrainment)
43 Real time  72% 48% 88% 100 %
# Setting Ablation target DG
31 Post ablation 100 % 100 %

DG-mapping can automatically find the mechanism of an AT without manual interpretation of the colormap of the atrium

  1. ​Operator independent and in some cases better than the operator: DG-mapping removes intuition, is thus very robust

  2. Can limit the amount of scar

  3. Added value for complex cases

  4. Can be used for training of fellows

  5. faster: DG-mapping is instantaneous

  6. no more entrainment mapping which is an extra technique usually performed  

​             

DG-mapping

Modeling can cover even more scales...

Computational modeling of cardiac arrhythmia

By Nele Vandersickel

Computational modeling of cardiac arrhythmia

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