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 invitro Proarrhythmia Assay (CiPA) initiative www.cipaproject.org. CiPA aims to replace the existing proarrhythmic safety testing and Thorough QT Study with a combination of ion channel screening, mathematical modelling, stemcell 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
Breakup 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:
DGmapping
Huge field of applications
Brain
Search algorithm
Network theory
Network theory on the excitation of the heart: concept
1. rotors or functional reentry
2. anatomical reentry
3. focal sources
DGmapping on clinical AT cases
Optimization protocols
DGmapping on clinical AT  DG GUI
In collaboration with the AZsint Jan Bruges (in collaboration with Prof. Dr. MD. Mattias Duytschaever, Prof. Dr. MD. Sebastian Knecht, Dr. Jan de Pooter, Dr Rene Tavernier)
DGmapping on tested on clinical AT cases
#  Setting  Expert + latest mapping system  Junior + latest mapping system  DGmapping  ablation endpoint (with entrainment) 

43  Real time  72%  48%  88%  100 % 
#  Setting  Ablation target  DG 

31  Post ablation  100 %  100 % 
DGmapping 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: DGmapping 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: DGmapping is instantaneous

no more entrainment mapping which is an extra technique usually performed
DGmapping
Modeling can cover even more scales...
Biomedical students: Computational modeling of cardiac arrhythmia
By Nele Vandersickel
Biomedical students: Computational modeling of cardiac arrhythmia
 123