Dataset Information

Early Afterdepolarizations with Growing Amplitudes via Delayed Subcritical Hopf Bifurcations and Unstable Manifolds of Saddle Foci in Cardiac Action Potential Dynamics.

ABSTRACT: Early afterdepolarizations (EADs) are pathological oscillations in cardiac action potentials during the repolarization phase and may be caused by drug side effects, ion channel disease or oxidative stress. The most widely observed EAD pattern is characterized by oscillations with growing amplitudes. So far, its occurence has been explained in terms of a supercritical Hopf bifurcation in the fast subsystem of the action potential dynamics from which stable limit cycles with growing amplitudes emerge. The novel contribution of this article is the introduction of two alternative explanations of EAD genesis with growing amplitudes that do not involve stable limit cycles in fast subsystems. In particular, we demonstrate that EAD patterns with growing amplitudes may alternatively arise due to a delayed subcritical Hopf bifurcation or an unstable manifold of a saddle focus fixed point in the full fast-slow system modelling the action potential. Our work extends the list of possible dynamical EAD mechanisms and may contribute to a classification of drug effects in preclinical cardiotoxicity testing.

SUBMITTER: Kugler P

PROVIDER: S-EPMC4792449 | biostudies-literature | 2016

REPOSITORIES: biostudies-literature

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Publications

Early Afterdepolarizations with Growing Amplitudes via Delayed Subcritical Hopf Bifurcations and Unstable Manifolds of Saddle Foci in Cardiac Action Potential Dynamics.

Kügler Philipp P

PloS one 20160315 3

Early afterdepolarizations (EADs) are pathological oscillations in cardiac action potentials during the repolarization phase and may be caused by drug side effects, ion channel disease or oxidative stress. The most widely observed EAD pattern is characterized by oscillations with growing amplitudes. So far, its occurence has been explained in terms of a supercritical Hopf bifurcation in the fast subsystem of the action potential dynamics from which stable limit cycles with growing amplitudes eme ...[more]

PMID: 26977805

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Project description:Stability of human gait is the ability to maintain upright posture during walking against external perturbations. It is a complex process determined by a number of cross-related factors, including gait trajectory, joint impedance and neural control strategies. Here, we consider a control strategy that can achieve stable steady-state periodic gait while maintaining joint flexibility with the lowest possible joint impedance. To this end, we carried out a simulation study of a heel-toe footed biped model with hip, knee and ankle joints and a heavy head-arms-trunk element, working in the sagittal plane. For simplicity, the model assumes a periodic desired joint angle trajectory and joint torques generated by a set of feed-forward and proportional-derivative feedback controllers, whereby the joint impedance is parametrized by the feedback gains. We could show that a desired steady-state gait accompanied by the desired joint angle trajectory can be established as a stable limit cycle (LC) for the feedback controller with an appropriate set of large feedback gains. Moreover, as the feedback gains are decreased for lowering the joint stiffness, stability of the LC is lost only in a few dimensions, while leaving the remaining large number of dimensions quite stable: this means that the LC becomes saddle-type, with a low-dimensional unstable manifold and a high-dimensional stable manifold. Remarkably, the unstable manifold remains of low dimensionality even when the feedback gains are decreased far below the instability point. We then developed an intermittent neural feedback controller that is activated only for short periods of time at an optimal phase of each gait stride. We characterized the robustness of this design by showing that it can better stabilize the unstable LC with small feedback gains, leading to a flexible gait, and in particular we demonstrated that such an intermittent controller performs better if it drives the state point to the stable manifold, rather than directly to the LC. The proposed intermittent control strategy might have a high affinity for the inverted pendulum analogy of biped gait, providing a dynamic view of how the step-to-step transition from one pendular stance to the next can be achieved stably in a robust manner by a well-timed neural intervention that exploits the stable modes embedded in the unstable dynamics.

Dataset Information

Early Afterdepolarizations with Growing Amplitudes via Delayed Subcritical Hopf Bifurcations and Unstable Manifolds of Saddle Foci in Cardiac Action Potential Dynamics.

Publications

Early Afterdepolarizations with Growing Amplitudes via Delayed Subcritical Hopf Bifurcations and Unstable Manifolds of Saddle Foci in Cardiac Action Potential Dynamics.

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