An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

Elena Beretta, Cecilia Cavaterra, M. Cristina Cerutti, Andrea Manzoni, Luca Ratti

    Research output: Contribution to journalArticle

    Abstract

    In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity ω∈ (where the coefficients of the equation are altered) located inside a domain φ starting from observations of the potential on the boundary ∂φ. Such a problem is related to the detection of myocardial ischemic regions, characterized by severely reduced blood perfusion and consequent lack of electric conductivity. In the first part of the paper we provide an asymptotic formula for electric potential perturbations caused by internal conductivity inhomogeneities of low volume fraction in the case of three-dimensional, parabolic problems. In the second part we implement a reconstruction procedure based on the topological gradient of a suitable cost functional. Numerical results obtained on an idealized three-dimensional left ventricle geometry for different measurement settings assess the feasibility and robustness of the algorithm.

    Original languageEnglish (US)
    Article number105008
    JournalInverse Problems
    Volume33
    Issue number10
    DOIs
    StatePublished - Sep 20 2017

    Fingerprint

    Cardiac Electrophysiology
    Semilinear Parabolic Equation
    Electric Potential
    Inverse problems
    Inhomogeneity
    Conductivity
    Inverse Problem
    Inverse Boundary Value Problem
    Three-dimensional
    Left Ventricle
    Electric potential
    Parabolic Problems
    Asymptotic Formula
    Volume Fraction
    Boundary value problems
    Blood
    Volume fraction
    Theoretical Analysis
    Tissue
    Gradient

    Keywords

    • cardiac electrophysiology
    • inverse boundary value problem
    • semilinear parabolic equation

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Signal Processing
    • Mathematical Physics
    • Computer Science Applications
    • Applied Mathematics

    Cite this

    An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology. / Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca.

    In: Inverse Problems, Vol. 33, No. 10, 105008, 20.09.2017.

    Research output: Contribution to journalArticle

    Beretta, Elena ; Cavaterra, Cecilia ; Cerutti, M. Cristina ; Manzoni, Andrea ; Ratti, Luca. / An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology. In: Inverse Problems. 2017 ; Vol. 33, No. 10.
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