Key result
A global Carleman-type estimate established the uniqueness and a Lipschitz stability estimate of the ion channels conductance parameters in a bidomain model of cardiac electrophysiology.
Provides a mathematical proof for the uniqueness and stability of identifying ion channel conductance parameters in cardiac electrophysiology models using Carleman estimates.
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Advances inverse modeling in cardiac electrophysiology; extends theoretical tools but leaves clinical translation open.
In this paper, we consider an inverse problem of determining multiple ionic parameters of a 2 × 2 strongly coupled parabolic–elliptic reaction–diffusion system arising in cardiac electrophysiology modeling. We use the bidomain model coupled to an ordinary differential equation (ODE) system and we consider a general formalism of physiologically detailed cellular membrane models to describe the ionic exchanges at the microscopic level. Our main result is the uniqueness and a Lipschitz stability estimate of the ion channels conductance parameters of the model using subboundary observations over an interval of time. The key ingredients are a global Carleman-type estimate with a suitable observations acting on a part of the boundary.
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Abidi et al. (2019) studied cardiac electrophysiology modeling. Carleman estimates was evaluated on uniqueness and Lipschitz stability estimate of ion channels conductance parameters. A global Carleman-type estimate established the uniqueness and a Lipschitz stability estimate of the ion channels conductance parameters in a bidomain model of cardiac electrophysiology.
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