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Author: Erhardt, André H. × Type: Article ×

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    Editorial: Dynamical systems, PDEs and networks for biomedical applications: Mathematical modeling, analysis and simulations
    (Lausanne : Frontiers Media, 2023) Erhardt, André H.; Tsaneva-Atanasova, Krasimira; Lines, Glenn Terje; Martens, Erik Andreas
    [No abstract available]
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    On complex dynamics in a Purkinje and a ventricular cardiac cell model
    (Amsterdam [u.a.] : Elsevier, 2020) Erhardt, André H.; Solem, Susanne
    Cardiac muscle cells can exhibit complex patterns including irregular behaviour such as chaos or (chaotic) early afterdepolarisations (EADs), which can lead to sudden cardiac death. Suitable mathematical models and their analysis help to predict the occurrence of such phenomena and to decode their mechanisms. The focus of this paper is the investigation of dynamics of cardiac muscle cells described by systems of ordinary differential equations. This is generically performed by studying a Purkinje cell model and a modified ventricular cell model. We find chaotic dynamics with respect to the leak current in the Purkinje cell model, and EADs and chaos with respect to a reduced fast potassium current and an enhanced calcium current in the ventricular cell model — features that have been experimentally observed and are known to exist in some models, but are new to the models under present consideration. We also investigate the related monodomain models of both systems to study synchronisation and the behaviour of the cells on macro-scale in connection with the discovered features. The models show qualitatively the same behaviour to what has been experimentally observed. However, for certain parameter settings the dynamics occur within a non-physiological range.
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    Stability of Weak Solutions to Parabolic Problems with Nonstandard Growth and Cross–Diffusion
    (Basel : MDPI, 2021) Erhardt, André H.
    We study the stability of a unique weak solution to certain parabolic systems with nonstandard growth condition, which are additionally dependent on a cross-diffusion term. More precisely, we show that two unique weak solutions of the considered system with different initial values are controlled by their initial values.