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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Modeling the cardiac electromechanical function: A mathematical journey
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by Alfio Quarteroni, Luca Dedè and Francesco Regazzoni HTML | PDF
Bull. Amer. Math. Soc. 59 (2022), 371-403 Request permission


In this paper we introduce the electromechanical mathematical model of the human heart. After deriving it from physical first principles, we discuss its mathematical properties and the way numerical methods can be set up to obtain numerical approximations of the (otherwise unachievable) mathematical solutions. The major challenges that we need to face—e.g., possible lack of initial and boundary data, the trade off between increasing the accuracy of the numerical model and its computational complexity—are addressed. Numerical tests here presented have a twofold aim: to show that numerical solutions match the expected theoretical rate of convergence, and that our model can provide a preliminary valuable tool to face problems of clinical relevance.
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Additional Information
  • Alfio Quarteroni
  • Affiliation: MOX–Dipartimento di Matematica, Politecnico di Milano, Milano, Italy; and Mathematics Institute, École Polytechnique Fédérale de Lausanne, Switzerland
  • ORCID: 0000-0002-5947-6885
  • Email:
  • Luca Dedè
  • Affiliation: MOX–Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
  • MR Author ID: 771823
  • Email:
  • Francesco Regazzoni
  • Affiliation: MOX–Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
  • MR Author ID: 1096619
  • ORCID: 0000-0002-4207-1400
  • Email:
  • Received by editor(s): December 7, 2020
  • Published electronically: February 23, 2022
  • Additional Notes: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 740132, iHEART—An Integrated Heart Model for the simulation of the cardiac function, P.I., A. Quarteroni)
  • © Copyright 2022 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 59 (2022), 371-403
  • MSC (2020): Primary 65-02
  • DOI:
  • MathSciNet review: 4437802