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A modified van der Pol equation with delay in a description of the heart action

Beata Zduniak, Marek Bodnar, Urszula Foryś (2014)

International Journal of Applied Mathematics and Computer Science

In this paper, a modified van der Pol equation is considered as a description of the heart action. This model has a number of interesting properties allowing reconstruction of phenomena observed in physiological experiments as well as in Holter electrocardiographic recordings. Our aim is to study periodic solutions of the modified van der Pol equation and take into consideration the influence of feedback and delay which occur in the normal heart action mode as well as in pathological modes. Usage...

Asymptotic analysis of blood flow in stented arteries: time dependency and direct simulations***

Vuk Milišić, Amélie Rambaud, Kirill Pichon Gostaf (2010)

ESAIM: Proceedings

This work aims to extend in two distinct directions results recently obtained in [10]. In a first step we focus on the possible extension of our results to the time dependent case. Whereas in the second part some preliminary numerical simulations aim to give orders of magnitudes in terms of numerical costs of direct 3D simulations. We consider, in the first part, the time dependent rough problem for a simplified heat equation in a straight channel that mimics the axial...

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