Computational modeling of cardiac arrhytmia

Nele Vandersickel

Normal function of the heart

Normal rhythm 60 beats/min: determined by the SA node => 100.000 beats per day.

:delay of the signal

Normal function of the heart

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 different types of arrhtyhmia
Control of arrhythmia, how to remove it from the heart

Computer modeling can help with these questions!

Cardiac arrhythmia

Four major categories of cardiac arrhythmia

Regular

Irregular

Atrial Tachycardia

Atrial Fibrillation

Ventricular Fibrillation

Ventricular Tachycardia

Basic properties and computer modeling

1. Basic properties and computer modeling: single cell

The membrane: contains channels which can open and close

1. Basic properties and computer modeling: single cell

Nerst potential: 2 opposite forces:

diffusion
electrical force

You can find the equilibrium which gives you the Nerst potential

1. Basic properties and computer modeling: single cell

Nerst potential: 2 opposite forces:

diffusion
electrical force

You can find the equilibrium which gives you the Nerst potential

1. Basic properties and computer modeling: single cell

Most easy model: Hodgkin huxley (nerve cell)

1. Basic properties and computer modeling: single cell

Most easy model: Hodgkin huxley (nerve cell)

1. Basic properties and computer modeling: single cell

Most easy model: Hodgkin huxley (nerve cell)

1. Basic properties and computer modeling: single cell

The whole cell: many more channels

1. Basic properties and computer modeling: single cell

The whole cell: also internal dynamics

1. Basic properties and computer modeling: single cell

The whole cell: many more channels

1. Basic properties and computer modeling: single cell

The whole cell: many more channels

All the channels can be modeled as:

1. Basic properties and computer modeling: single cell

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...

1. Basic properties and computer modeling: single cell

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

Different cells are coupled

1. Basic properties and computer modeling: 2D modeling

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

Single cell

2D tissue

1. Basic properties and computer modeling: 2D modeling

Colliding waves annihilate

1. Basic properties and computer modeling: 2D modeling

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

1. Basic properties and computer modeling: 2D modeling

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

Anatomical reentry

Functional reentry

Period of rotation is usually close to refractoriness time

1. Basic properties and computer modeling: 2D modeling

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

1. Basic properties and computer modeling: 2D modeling - experimental evidence

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

--> First to record a real spiral wave

1. Basic properties and computer modeling: 2D modeling - experimental evidence

Cell cultures

(lab of L. Glass, neonatal rat cells)

1. Basic properties and computer modeling: 2D modeling - experimental evidence

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

1. Basic properties and computer modeling: 2D modeling - experimental evidence

Many other systems also have spiral waves!

1. Basic properties and computer modeling: 2D modeling - experimental evidence

Many other systems also have spiral waves!

1. Basic properties and computer modeling: 2D modeling - experimental evidence

Many other systems also have spiral waves!

Cable equation

1. Basic properties and computer modeling: 2D modeling

Cable equation

1. Basic properties and computer modeling: 2D modeling

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

1. Basic properties and computer modeling: whole heart modelling

Whole heart simulation: mesh of the heart + fiber orientation

1. Basic properties and computer modeling: whole heart modelling

Focale source

Functional reentry

= rotors

Anatomical reentry

-90

+30

Voltage (mV)

Mechanisms of arrhythmia

-------------------- Spiral waves --------------------

Types of arrhythmia and treatment

Four major categories of cardiac arrhythmia

Torsade de Pointes

Regular

Irregular

Atrial Tachycardia

Atrial Fibrillation

Ventricular Fibrillation

Ventricular Tachycardia

Regular

Irregular

Atrial Tachycardia

Atrial Fibrillation

Ventricular Fibrillation

Ventricular Tachycardia

2. Types of arrhythmia and treatmen: atrial tachycardia

In atria
Regular
Mechanism: anatomical reentry
No immediate risk of dying

Regular

Atrial Tachycardia

Multiple Hypothesis

1. Persistant AF is maintained by rotors

2. Multiple wavelets maintain AF

3. Double layer hypothesis

4. Mother rotor fibrillation

5. Atrial fibrillation driven by micro-anatomic intramural re-entry

2. Types of arrhythmia and treatment: atrial fibrillation

In atria
Irregular
Mechanism: unknown
No immediate risk of dying. high risk of stroke

Atrial Fibrillation

2. Types of arrhythmia and treatment: ventricular tachycardia

In ventricles
Regular
Mechanism: anatomical reentry in 3D
Risk of dying

Ventricular Tachycardia

2. Types of arrhythmia and treatment: ventricular fibrillation

In ventricles
Irregular
Mechanism: still no consensus
Dying within minutes

Ventricular Fibrillation

How to stop a reentry circuit?

Ablation: burning of tissue

2. Types of arrhythmia and treatment

More on Atrial Tachycardia

Four major categories of cardiac arrhythmia

Regular

Irregular

Atrial Tachycardia

Atrial Fibrillation

Ventricular Tachycardia

Ventricular Fibrillation

3. Atrial Tachycardia: a real case

Looks like typical case of flutter?

The atria form a closed surface

We can simplify the left atrium by deforming it to a sphere with 3 holes. While maintaining its topological properties!

3. Atrial Tachycardia: Anatomy of the left atrium: 3 natural holes

LPV

RPV

SVC

200 different simulations

All possible virtual ablation lines: 600 simulation

3. Atrial Tachycardia: Simulations

3. Atrial Tachycardia - 3 possible patterns

3 Patterns

Complete rotation

Incomplete rotation

Parallel activation

Good entrainment

Bad entrainment

3. Atrial Tachycardia - 3 possible patterns

3 Patterns

Complete rotation

Incomplete rotation

Parallel activation

3. Atrial Tachycardia - Ablation

Incomplete rotation becomes complete rotation, resulting in a slower AT

100% of simulations!

Index theorem

On a closed surface, the total number of clockwise and counterclockwise rotations must be equal.

1977, Glass. Science (limp generation)
1988, Winfree and Tyson. Physics Today (cardiac arrhythmia)
2004, Davidsen, Glass, Kapral. Physical Review E (cardiac arrhythmia)

Reentries can't be isolated entities. They must come in pairs!

Key insight 1: Reentries can't be isolated entities. They must come in pairs!

3. Atrial Tachycardia - Index Theorem > 20 years old!

Complete rotation

Parallel activation

Incomplete rotation

Critical Boundary

Non-Critical Boundary

CB: Santucci et al. JACC EP 2023

CB:

NCB: 0

Incomplete rotation becomes complete rotation, resulting in a slower AT

Loops come in pairs of 2: currently second loop is always missed

3. Atrial Tachycardia - Ablation: connect the critical boundaries!

3. Atrial Tachycardia - Ablation: Clinical cases

200 simulation with 2 boundaries

Clinical cases

3. Atrial Tachycardia - Ablation: Clinical cases

CB:

NCB: 0

Incomplete rotation becomes complete rotation, resulting in a slower AT

3. Atrial Tachycardia - Ablation: Clinical cases

LPV

RPV

3. Atrial Tachycardia: Scar creates additional holes

200 simulations with 4 boundaries

Clinical cases

3. Atrial Tachycardia: Scar creates additional holes

131 MRAT cases

3. Atrial Tachycardia: 131 clinical cases together!

3. Atrial Tachycardia: 20 detailed cases

20 detailed cases with slowing after ablation

Macro reentry

Localized reentry

Micro reentry

Focal

Rotor

Around anatomic obstacle, like valve or vessels.

Around non conducting area > 2-1.5cm, e.g. scar or functional block

Atypical Flutter (LA involving valves or vessels)
Atypical Flutter (RA involving valves or vessels)
Typical Flutter (clockwise and counter clockwise)
WPW

Atypical Flutter (LA with scar or previous ablation lines with gaps)
AVNRT (considering slow and fast pathway)

Around non conducting area < 1cm, e.g. scar or functional block

Atypical Flutter (LA with scar)
Atypical Flutter (RA crista terminalis region)

Ectopic AT

Spiral activation pattern with no scar in the core.

Focal activation from one single spot with centrifugal activation pattern

CL tends to be longer >350ms due to larger path

CL range varies and CL can shift around 20-40 ms during arrhythmia due to slight path variations

CL tends to be shorter due to short path, whole CL is covered by signals found in a small area like e.g. 4cm2 often a combination of double potentials in the „middle“ and very long fractionated signals surrounding

CL often not presented completely in one chamber

Focal activation patterns could also hint to epicardial entries – look for potential conducting structure like vein of Marshall, Bachmann´s etc. and exits that would fit a macro reentry with epicardial parts

We think non-existent in AT, especially as a stable configuration leading to a stable AT.

Maybe something close to a spiral pattern can exist in AF