Study plan


The Computational Cardiology (CC) elective subject provides a detailed review of the different phases and concepts required for modelling the cardiovascular system in a realistic way. Special emphasis will be given to the generation of 3D patient-specific multi-scale and multi-physic simulations in healthy and pathological conditions, as well as to the in-silico testing of different therapeutic solutions. Additionally, at the beginning of the course there will be an extensive review of cardiac physiology and morphology. Then, the focus will be on the generation of detailed meshes integrating multi-modal data provided by different sources, setting up the geometrical domain where simulations will be run. The remaining lectures will be devoted to the presentation of the state-of-the-art modelling approaches to simulate the most relevant physical phenomena in cardiology: electrophysiology, mechanics, and blood flow. Lectures of the CC subject will be given by researchers from Universitat Pompeu Fabra (UPF), all of them with a strong background and large experience on developing and investigating cardiac models.

The CC seminars will consist in lectures given by well-known researchers in the area of computational cardiology in different contexts and environments to give an overview on the interest, development and use of computational models in academic research. Additionally, if there is availability, we will visit the Mare Nostrum facilities at The Barcelona Supercomputing Centre (BSC), which is the largest High-Performance Computing (HPC) infrastructure in Spain and the 16th world-wide after the last update (, November 2017). Some researchers led by Dr. Mariano Vázquez, have developed during the last years efficient numerical solvers applied to biomedical applications, in particular for cardiovascular modelling. Assistance to the seminars is compulsory and some penalties will be applied in the final grades if some are missed without prior notice and reasonable justification.

The CC labs will be centred on a project where students will get familiar with computational tools to develop models of the cardiovascular system.


The theory of the course is designed such that students with any engineering bachelor degree can follow it. An extensive review on cardiac physiology is performed in some of the initial sessions to cover the most relevant information about heart functioning. The students should be familiar with fundamental concepts of physics and the use of mathematical equations to model physical phenomena. Prior knowledge about the main principles of meshing techniques and finite-element methods would be positive, but not necessary. The students will be asked to use different commercial or Open-Source engineering solvers (e.g. Ansys) to run the simulations, but tutorials and individual assistance will be given if required.


Module 1. Introduction to computational cardiology.

Introduction to the subject. Pipeline for cardiac modelling. Computational tools in cardiology: data processing, computational simulations. Presentation of projects.

Module 2. Cardiac morphology and physiology.

Cardiac macroscopic anatomy. Structure morphology in normal and pathological cases. Microscopic structure and molecular organization. Material properties of myocardium. Deformation. Stress-strain relations.

Module 3. Modelling of cardiac anatomy.

Patient-specific anatomical domains. Integration of multimodal information in the Digital Patient Avatar. Tetrahedral and hexahedral cardiac meshes. High-resolution sub-structural information (myofiber orientation, Purkinje system, scar tissue, trabeculations, outflow tracts). Simplified 2D representations.

Module 4. Mechanical modelling.

Passive mechanical properties of myocardium. Strain energy density functions. Stress-strain relationship. Active tension development. Boundary conditions. Numerical methods. Implementation in a High-Performance Computing facility. Open-Source and commercial cardiac modelling softwares.

Module 5. Cardiac electrophysiology and electromechanical modelling.

Cellular electrophysiology (experimental studies, cellular component modelling cardiac myocytes). Excitation-propagation, electrical current flow modelling (monodomain, bidomain). Phenomenological (e.g. Eikonal, reaction-diffusion, Mitchell-Schaeffer) vs detailed (e.g. Ten-Tusscher) models. Pathology simulations (dyssynchrony, arrhythmias). Electrical therapy modelling (drug therapy, pacemaker devices, radio-frequency ablation). Electro-mechanical and mechano-electrical feedback. Electromechanical coupling (weak and strong). Open-Source and commercial cardiac modelling softwares.

Module 6. Haemodynamics modelling.

Lumped models of haemodynamics. Analogies between electrical circuits and flow properties. Boundary conditions (Windkessel). Models of foetal circulation.


The labs will be organized in randomly chosen teams of 2-4 people. The teams will work on a heart modelling project during the whole trimester, using complex multi-dimensional cardiac models involving electrophysiology, mechanics, haemodynamics or a combination between them. Possible projects include: the use of mesh-less methods on detailed heart geometries with trabeculae or on a complete 4-chamber heart model; cardiac electromechanics with simplified or detailed models; and fluid simulations in the atria with rigid and flexible walls.

Each team will be asked to give a presentation / show a demo in the last week of the trimester, as well as to write a report in the form of a scientific paper (10 pages). All students will be asked to mainly work on the development of the model project outside classroom hours, having lab sessions as check-points to present intermediate results, questions, bottle-necks and re-orient objectives and strategies. During the course, there will be additional weekly short (around 5 min) telcos with a speaker of each team where a briefing of the work, difficulties, questions and plans will be exposed. These short telcos will take place in some afternoons in weeks without face-to-face lab sessions (i.e. week 3, 4 and 7 of the trimester). They are inspired by the synchronization meetings in the Scrum framework. The students are recommended to investigate the use of Scrum to organize the teamwork for the project during the trimester:

It is assumed then that within each team there is a laptop available where the required computational tools can be run and they are brought to each lab session. In case no laptop is available, one can be booked from the library.

  • Session 1 (Week 2) – Presentation of the project proposals.
  • Session 2 (Week 5) – Modelling pipeline.
  • Session 3 (Week 6) – Modelling experiments.
  • Session 4 (Week 8) – Presentation of preliminary simulation results (healthy and physiological conditions).
  • Session 5 (Week 9) – Final presentations.

Evaluation methods

  • Oral exam (30%)
    • Questions based on the concepts acquired during lectures and seminar sessions
    • Minimal mark of 5.0
  • Modelling project (70%)
  • Lab reports and work during the trimester (10%)
  • Oral presentation (30%)
  • Scientific article (30%)

Bibliography and information resources


  • F. Sachse. Computational cardiology. Modeling of Anatomy, Electrophysiology, and Mechanics. Springer, LNCS, vol. 2966. 2004.
  • Y. Zhang et al. Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention. Annals of Biomedical Engineering, Vol. 44, No. 9, September 2016
  • R. Chabiniok et al. Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics. Interface Focus, Royal Society Publishing, Vol 6, No. 2, February 2016
  • N. Westerhof, N. Stergiopulos, M.I.M. Noble, Snapshots of Hemodynamics. An Aid for Clinical Research and Graduate Education. Springer US, 2010.
  • Shi et al. Review of Zero-D and 1-D Models of Blood Flow in the Cardiovascular System. BioMedical Engineering OnLine, 2011.
  • Kokalari et al. Review on lumped parameter method for modeling the blood flow in systemic arteries. J. Biomedical Science and Engineering, 2013.


  • O. Nichols, M. Vlachopoulos. Blood Flow in Arteries Theoretical, Experimental and Clinical Principles, 6th Edition, Hodder Arnold, 2011.
  • V. Milisic, A. Quarteroni. Analysis of lumped parameter models for blood flow simulations and their relation with 1D models. ESAIM-Mathematical Modelling and Numerical Anslysis 2004.
  • L. Formaggia et al. One-dimensional models for blood flow in arteries. Journal of Engineering Mathematics 47: 251–276, 2003.
  • L. Formaggia et al. Reduced and multiscale models for the human cardiovascular system. Politecnico di Milano, 2003.