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SIAM J. APPL. MATH. c 2011 Society for Industrial and Applied Mathematics Vol. 71, No. 2, pp. 605621
 

Summary: SIAM J. APPL. MATH. c 2011 Society for Industrial and Applied Mathematics
Vol. 71, No. 2, pp. 605­621
ELECTROMECHANICAL COUPLING IN CARDIAC DYNAMICS:
THE ACTIVE STRAIN APPROACH
D. AMBROSI, G. ARIOLI, F. NOBILE, AND A. QUARTERONI
Abstract. The coupling between cardiac mechanics and electric signaling is addressed in a
nonstandard framework in which the electrical potential dictates the active strain (not stress) of the
muscle. The physiological and mathematical motivations leading us to this choice are illustrated.
The propagation of the electric signal is assumed to be governed by the FitzHugh­Nagumo equations,
rewritten in material coordinates with a deforming substrate; the solution is compared with the rigid
case, and differences in celerity and width of a pulse are discussed. The role of viscoelasticity is
pointed out. We show that the stretching of coordinates is insufficient to originate electromechanical
feedback; nevertheless, it can increase the energy of a perturbation enough to produce a traveling
pulse: an energy estimate and numerical evidence are reported. To support these conclusions, numer-
ical simulations in two dimensions show the interplay between electric propagation and mechanical
strain.
Key words. elasticity, cardiac mechanics, electromechanical coupling, FitzHugh­Nagumo equa-
tions
AMS subject classifications. 74F, 92C10
DOI. 10.1137/100788379

  

Source: Ambrosi, Davide - Dipartimento di Matematica, Politecnico di Torino

 

Collections: Mathematics