Modeling the heart contraction leads to the solution of a coupled problem between the electrical model, which describes the propagation of the electrical signal that triggers the heart contraction, and the mechanical model, that describes the cardiac deformations.
Beside the direct effect of the electrical activity in the mechanics, it is relevant to model also the feedback of the mechanics in the propagation of the electrical signal. The main components of this feedback are:
- Domain deformation: The deformations of the heart during the contraction alter the conduction velocity of the electrical signal;
- Stretch activated ion channels: Ion channels which open in response to a mechanical deformation, modifying the electrical behavior of the cell.
The research focused on the study of stable numerical schemes for the solution of the coupled problem with the aim of describing the heart contraction in real geometries.
- D. Ambrosi, G. Arioli, F. Nobile and A. Quarteroni, Electromechanical Coupling in Cardiac Dynamics: The Active Strain Approach,SIAM J. Appl. Math., 71(2), 605–621, 2011
- F. Nobile, A. Quarteroni and R. Ruiz-Baier, An active strain electromechanical model for cardiac tissue, Numerical Methods in Biomedical Engineering, 28(1) , pp 52-71, 2012
- S. Rossi, T. Lassila, R. Ruiz-Baier, A. Sequeira and A. Quarteroni, Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics, European journal of mechanics, in press, 2013
- Mathematical modelling of active contraction in isolated cardiomyocytes, in Mathematical Medicine And Biology-A Journal Of The Ima, vol. 31, num. 3, p. 259-283, 2014. .
- Solvability analysis and numerical approximation of linearized cardiac electromechanics, Mathematical Models and Methods in Applied Sciences, vol. 25, num. 05, p. 959-993, 2015. .
A.Quarteroni, T. Lassila, S. Rossi, R. Ruiz Baier, Integrated Heart Coupling multiscale and multiphysics models for the simulation of the cardiac function, Comput. Methods Appl. Mech. Engrg., 2016
- Quarteroni A., Manzoni A., Vergara C., The Cardiovascular System: Mathematical Modeling, Numerical Algorithms, Clinical Applications. MOX Report n. 38/2016.