93930 - Computational Cardiology

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Good health and well-being

Academic Year 2021/2022

Learning outcomes

The course will provide detailed insights in modeling approaches, which are applied to describe and reconstruct physical properties, physiology and pathologies of the cardiovascular system. In particular, the student will learn: - To critically analyse the scientific literature and the state of the art regarding computational cardiology. How to analyse existing models and simulations and their re-use for the solution of specific problems. - The main techniques, devices and protocols for cardiac electrophysiology measurements. - Mathematical models, which are used to quantify electrophysiology at the level of single channels, cells, tissue up to whole heart; through examples that illustrate how the model equations are derived, implemented and solved, and how numerical simulation is used to analyse the electrical activity and excitation-contraction coupling in cardiac cells. - How to interpret the cardiac physiology in terms of complex dynamics. - In-silico testing of therapeutic solutions. - To dialogue with both producers and end users of computational models, in order to obtain indications for the design and implementation of innovative solutions in the biomedical field.

Course contents

Basic elements of the structures and functions of cellular components

The main cellular components (membranes, nucleus, endoplasmic reticulum, ribosomes, nucleic acids and proteins). The fundamental processes underlying the cell function (duplication, transcription, protein synthesis, differentiation, transport, DNA repair). Homeostasis and signaling. Three-dimensional structure of a protein. Molecular dynamics.

Biochemical reactions

Mass action law. Polymerization and turnover. Enzyme reactions. Michaelis-Menten equations. Analytical solution in the hypothesis of substrate equilibrium and quasi-stationary conditions. Enzymatic kinetics and molecular transistors. Molecular basis of competitive inhibition. Bonding sites and catalysis control. Mathematical equations and their resolution. Allosteric control of an enzymatic reaction. Cooperative activation. Hill equation.

Intracellular calcium kinetics

Functions of intracellular calcium. L-type channels and activation of intracellular calcium. CICR mechanism. Ryanodine receptors and IP3 receptors. Derivation and analysis of a first order model. Analysis of the stability condition. Mechanism of calcium reabsorption (Calcium uptake). Calcium pumps. Model of reabsorption by algebraic linear retraction. Analytical solution. Linear dynamic model of calcium reabsorption. Search for eigenvalues. Parameter assignment and computer simulation.

Ion channels

The membrane proteins and ion channels. 3D structure of potassium channels. Heterologous expression systems. Recording techniques for ion currents. Kinetic models of membrane currents. Introduction to Markov models. Conformational states model. Relationship between kinetic models and models with gating variables. The Markov model for potassium current and sodium current. Membrane receptors and interaction: ligands, agonists and antagonists.

Cell excitability

Action potential. The Hodgking-Huxely experiments. Toxins and current blockers. Parallel conductance model structure. Model of the potassium and sodium conductance. Experimental protocols for the characterization of the ion currents. Techniques for the identification of model parameters.

Structure and function of cardiomyocyte.

Models of the cardiac action potentials. Biophysical properties of cardiac ion channels. Laboratory measurement of action potential and ionic currents. Computer simulation of the effects on the action potential of mutations in ion channels and of the effect of pharmacological blockers. Excitation-contraction coupling.

Multiscale cardiac models

Analysis of the genesis of arrhythmic phenomena in cardiac cells. Propagation in cardiac tissue. How the heart rate is generated and regulated. Computational analysis of atrial fibrillation.

Additional topics:

Elements of dynamical systems theory and bifurcation theory. Complexity and chaos


J. Keener and J. Sneyd, “Mathematical physiology”
Hille, “Ion Channels of Excitable Membranes”

Teaching methods

Lectures are scheduled in the classroom during which the teacher presents the topics of the program by integrating them with the graphic resolution of the equations to help the students to become familiar with the analysis tools. Lectures are integrated with computational biology laboratory activities that allow each student to acquire familiarity with numerical simulation. In addition, an activity in the Cellular and Molecular Bioengineering laboratory is planned, concerning the Dynamic Clamp technique, used to interface cardiomyocytes and numerical simulators. Some seminars on advanced research topics in the field of computational cardiology are also planned.

Assessment methods

Students will be assessed on the basis of a written assignment and an oral interview.

The written assignment contains about ten questions and / or short exercises concerning:
- nonlinear dynamic systems
- enzymatic kinetics
- mathematical models of cardiac action potentials and their numerical implementation
- measurement techniques in cardiac electrophysiology
- cardiac cell electrophysiology
- multiscale cardiac models

Passing the written test is strictly needed in order to access the oral interview. The final mark of the course is definde by overall evaluation of both the two tests, with no pre-defined constraints based on the grade obtained in the written test.

Teaching tools

Molecular and Cellular Engineering Lab.

Computational Biology Lab.


Office hours

See the website of Stefano Severi

See the website of Chiara Bartolucci