📒 Lopezperez 2015

Three-dimensional cardiac computational modelling: methods, features and applications1



  • 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 μm per slice) from small mammalian hearts

Elements of a 3D cardiac computational model


  • 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
    3D cardiac geometry generation stage
  • 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


  • 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 ds = 0.1-0.5 mm and dt = 0.05-0.005 ms
  • For the case of phenomenological models, such as Eikonal ones, spatial and temporal discretisation is less demanding (order of ds = 0.5 mm, dt = 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 h

Cardiac conduction system


  • 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


  • 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


  1. 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 ↩︎