# ðŸ“’ Lopezperez 2015

Contents

Three-dimensional cardiac computational modelling: methods, features and applications

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## Introduction

- Nowadays, 3D cardiac models are becoming increasingly complex and are currently used in other areas such as cardiac image segmentation, statistical modelling of cardiac anatomy, patient risk stratification or surgical planning

## Evolution of 3D models of cardiac anatomy

### Generic models

- Geometric models
- anatomical models: the rabbit model from University of California San Diego and the canine model from University of Auckland
- computer-aided design (CAD) tools

### Medical image-based models

- CT / MRI images => patient-specific models
- Cardiac atlases
- highly-detailed bi-ventricular models built from very high resolution ex-vivo MRI datasets (~25 Î¼m per slice) from small mammalian hearts

## Elements of a 3D cardiac computational model

### Geometry

- completeness and the anatomical realism and accuracy required by a particular 3D cardiac model will strongly depend on its final application
- structurally simplified models (without endocardial details or vessels) are well suited for a large range of 3D cardiac modelling applications aimed at EP simulation
- Medical image-based models can include patient-specific details obtained from clinical imaging data and/or population-based properties collected from ex-vivo datasets
- Ex-vivo cardiac images can provide much higher spatial resolution than in-vivo datasets
- In-vivo images can provide both anatomical and temporal patient-specific information, thus enabling the characterisation of cardiac motion

### Meshing

- finite-element method (FEM) enabled the resolution of complex biophysical problems
- tetrahedral, hexahedral, cubic Hermite elements
- Spatial (ds) and temporal discretisation (dt) constraints are imposed when biophysical models are used, which are in the order of dsâ€‰=â€‰0.1-0.5 mm and dtâ€‰=â€‰0.05-0.005 ms
- For the case of phenomenological models, such as Eikonal ones, spatial and temporal discretisation is less demanding (order of dsâ€‰=â€‰0.5 mm, dtâ€‰=â€‰1 ms), resulting in faster computation times.

### Myocardial structure: fibre orientation

- rule-based algorithms
- measurements (histology, imaging)
- Diffusion tensor-MRI (DT-MRI), also called diffusion tensor imaging (DTI): diffusion of water molecules within the biological tissues

### Cardiac conduction system

### Electrophysiology

- cellular-level equations and the tissue-level equations
- Hodgkin and Huxley (HH) formalism vs Markov-type models (more mechanistic detailed)
- EP models are now highly specific and include human atrial, ventricular and Purkinje cells in normal or diseased conditions
- The number of state variables in the ionic AP models (and thus the number of ODEs) can be as high as 48

#### Electrophysiological heterogeneities

- The ventricular wall is not homogeneous, as cardiac myocytes in different portions of the ventricles exhibit different ionic currents and APs.
- epicardial-endocardial, apico-basal and left-right differences

#### Tissue level models

- bidomain model: extracellular and intracellular domains: two partial differential equations (PDEs) + a set of ODE systems
- equal anisotropy ratios are assumed in diffusion tensors: monodomain approach: one reaction-diffusion PDE plus a set of ODE systems
- Highly computationally demanding esp. using FEM
- Eikonal approximation, which replaces the reaction-diffusion equation with an eikonal equation that is simpler and based on a Huygens approach

#### Electromechanical coupling

- Ca2+ cycling => EC coupling => myocyte shortening
- Acute changes in ventricular mechanics can affect cardiac EP: stretch-activated ion channels, mechanical modulation of cell calcium handling

### Pathology

- functional remodelling: electrical / mechanical
- Chronic or healed ischaemic injuries resulting from myocardial infarctions (infarct
**scars**) - diffuse myocardial fibrosis

### Example of a 3D cardiac computational model

## Personalisation of 3D cardiac computational models

## Applications of 3D cardiac computational models

### Cardiac image segmentation

- model-based segmentation: in-vivo cardiac image segmentation and analysis
- The Cardiac Atlas Project: a wide database of cardiac images available online

### Simulation of acute ischaemia

### Ablation of chronic myocardial infarction

### Cardiac resynchronisation therapy

## Reference

Lopez-Perez A, Sebastian R, Ferrero JM. Three-dimensional cardiac computational modelling: methods, features and applications. Biomed Eng Online. 2015;14:35. Published 2015 Apr 17. doi:10.1186/s12938-015-0033-5. PMC4424572 ↩︎