Computational modeling of cardiac arrhythmias

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

3. The real world: clinical research

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

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)

The whole cell: many more channels

The whole cell: also internal dynamics

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

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!

Cable equation

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

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

Spiral waves have many different names

1. anatomical reentry -> around obstacle

Spiral waves have many different names

1. anatomical reentry -> around obstacle

Spiral waves have many different names

1. anatomical reentry -> around obstacle

2. functional reentry -> around itself

How to stop a reentry circuit?

Ablation: burning of tissue

Atrial fibrillation

Atrial tachycardia

Ventricular tachycardia

Ventricular fibrillation

Torsade de Pointes

Atrial Tachycardia

LPV

RPV

Anatomy of the left atrium: 3 natural holes

3 possible patterns

True loop

Suppressed loop

Fork

LPV

RPV

3 possible patterns

True loop

Suppressed loop

Fork

Classification in case of three holes with at least one reentry

Ablation

Clinical example

LPV

RPV

Scar creates additional holes

Classification in case of four holes with at least one reentry

Clinical example

Scar tissue at the anterior wall.

LPV

RPV

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

3. The real world: clinical research

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

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

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

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

3. The real world: clinical research

Restitution curve

Restitution curve

Break-up of a spiral due to restitution

Atrial fibrillation

Atrial tachycardia

Ventricular tachycardia

Ventricular fibrillation

Torsade de Pointes

Very dangerous!!!!

Hypothesis:

different types of spirals give rise to different arrhythmias

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

3. The real world: clinical research

3D dynamics of filaments

There is a filament present!

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

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

3. The real world: clinical research

Typical in aging heart: more myofibroblast = 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

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

Atrial fibrillation

Atrial tachycardia

Ventricular tachycardia

Ventricular fibrillation

Torsade de Pointes

Atrial Fibrillation

Atrial fibrillation

Hypothesis 1: Persistant AF is maintained by rotors

Hypothesis 2: Multiple wavelets maintain AF

Hypothesis 3: Double layer hypothesis

Hypothesis 4: Mother rotor fibrillation

Many of the clinical methods use phase mapping to determine rotational activity

Which one is correct?

Maybe there are many different types of AF?

Hypothesis 5: Atrial fibrillation driven by micro-anatomic intramural re-entry

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

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

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

Operator independent and in some cases better than the operator: DG-mapping removes intuition, is thus very robust
Can limit the amount of scar
Added value for complex cases
Can be used for training of fellows
faster: DG-mapping is instantaneous
no more entrainment mapping which is an extra technique usually performed

DG-mapping

Modeling can cover even more scales...