On complex dynamics in a Purkinje and a ventricular cardiac cell model

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

On complex dynamics in a Purkinje and a ventricular cardiac cell model

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

Development of a Radioimmunoassay for Pig Pancreatic Kallikrein

Peer Reviewe

Global existence of solutions to Keller--Segel chemotaxis system with heterogeneous logistic source and nonlinear secretion

We study the following Keller-Segel chemotaxis system with logistic source and nonlinear secretion. For this system, we prove the global existence of solutions under suitable assumptions