On the complex dynamics of intracellular ganglion cell light responses in the cat retina

We recorded intracellular responses from cat retinal ganglion cells to sinusoidal flickering lights and compared the response dynamics to a theoretical model based on coupled nonlinear oscillators. Flicker responses for several different spot sizes were separated in a 'smooth' generator (G) potential and eorresponding spike trains. We have previously shown that the G-potential reveals complex, stimulus dependent, oscillatory behavior in response to sinusoidally flickering lights. Such behavior could be simulated by a modified van der Pol oscillator. In this paper, we extend the model to account for spike generation as well, by including extended Hodgkin-Huxley equations describing local membrane properties. We quantified spike responses by several parameters describing the mean and standard deviation of spike burst duration, timing (phase shift) of bursts, and the number of spikes in a burst. The dependence of these response parameters on stimulus frequency and spot size could be reproduced in great detail by coupling the van der Pol oscillator, and Hodgkin-Huxley equations. The model mimics many experimentally observed response patterns, including non-phase-locked irregular oscillations. Our findings suggest that the information in the ganglion cell spike train reflects both intraretinal processing, simulated by the van der Pol oscillator) and local membrane properties described by Hodgkin-Huxley equations. The interplay between these complex processes can be simulated by changing the coupling coefficients between the two oscillators. Our simulations therefore show that irregularities in spike trains, which normally are considered to be noise, may be interpreted as complex oscillations that might earry information.Whitehall Foundation (S93-24

Numerical Simulations of Dynamics Behaviour of the Action Potential of the Human Heart\u27s Conduction System

A proposed model consisting of two coupled van der Pol models is considered as a description of the heart action potential. A system of ordinary differential equations is used to recreate pathological behaviour in the conducting system of the heart such as Wolff-Parkinson-White (WPW) syndrome and the most common tachycardia: atrioventricular nodal reentrant tachycardia (AVNRT). Part of the population has abnormal accessory pathways: fast and slow. These pathways in the atrioventricular node (AV node) are anatomical and functional excipients of supraventricular tachycardia. However, the appearance of two pathways in the AV node may be an excipient of arrhythmia—the WPW syndrome. The difference in the conduction time between these pathways is the most important factor. This is the reason to introduce three types of couplings and delay to our system in order to reproduce different types of the AVNRT. In our research, the result of introducing the feedback loops and couplings entails the creation of waves which can correspond to the re-entry waves which occur in the AVNRT. Our main aim is to study solutions of the equations of the system and to take into consideration the influence of feedback and delays which occur in the pathological modes. The proposed models made it possible to reproduce the most important physiological properties of the discussed pathologies. Since the model is phenomenological, the results are accurate as far as a simple model can describe the potential found in one of the more complex oscillators found in biology

三次元心臓モデルと不均一振動モデルによる心臓活動電位のコンピュータシミュレーション

Tohoku University西條芳文論

A wire transducer in a system with a van der Pol oscillator and velocity feedback

The work concerns wire transducers, which use a system with a van der Pol oscillator, with the aim of maintaining non-decreasing natural vibrations in the wire. As opposed to classical solutions, in which the feedback signal of the oscillator contains the course of displacement and velocity of the vibrating mass, a simple solution based only on the course of velocity is used. Such a solution is more advantageous from a practical perspective as regards to physical systems, because in the case of velocity transducers it eliminates the need to integrate the signal and the problems connected with it.Particular places for this solution may be found in wire tensometer systems designated for the long-term constant measurement, as well as for the measurement of time-variable courses, including those of a chaotic character.In the work, analysis was conducted on a modified van der Pol equation adapted for the movement of a discrete mass for the determination conditions of the existence of a limit cycle, the vibration course as well as the definition of the capabilities of adapting the results in the case of a wire transducer.The results of theoretical analysis were confirmed by the results of the experimental tests conducted on a laboratory model constructed for this purpose

Heart rate variability study using phase response curve

A noninvasive phase resetting experiment on human subjects was investigated. The phase response curve was estimated and was used to demonstrate cardiac phase resetting due to a vagal input. The estimated running phase response curve showed that the cardiac cycle resetting depended on the time and the amplitude of the vagal stimulation. The phase response curve was then studied using time circle analysis, topological analysis and nonlinear dynamics analysis. Also phase entrainment and stimulus frequency dependence of the phase response were evaluated. Further, the Van Der Pol model, Generalized Additive model and Knight and Peskin\u27s model were used to simulate the phase resetting process so that the characteristics of the phase resetting can be better understood

A STUDY ON DYNAMIC SYSTEMS RESPONSE OF THE PERFORMANCE CHARACTERISTICS OF SOME MAJOR BIOPHYSICAL SYSTEMS

Dynamic responses of biophysical systems - performance characteristic

Numerical Analysis of the Coupled Modified van der Pol Equations in a Model of Heart Action

In this paper, a modified van der Pol equations are considered as a description of the heart action. Wide ranges of the model parameters yield interesting qualitative results, e.g. Hopf bifurcation, Bogdanov-Takens bifurcation, transcritical and pitchfork bifurcations but also some stable solutions can be found. The physiological model works in the narrowest range of parameters which allows to obtain a stable behaviour what is important in biological problem. When some kinds of pathologies appear in the heart, it is possible to obtain chaotic behaviour. My aim is to compare the influence of these two types of coupling (unidirectional and bidirectional) on the behaviour of the van der Pol system. The coupling takes place in a system with healthy conductivity, between two nodes: SA and AV, but in some circumstances, a pathological coupling may occur in the heart. The van der Pol oscillator is a type of relaxation oscillator which can be synchronized. In this paper, synchronization properties of such a system are studied as well. For the purpose of a numerical analysis of the system in question, a numerical model was created

Relationship between Mathematical Parameters of Modified Van der Pol Oscillator Model and ECG Morphological Features

The mathematical model describes the electrical and mechanical activity of the cardiac conduction system thought set of differential equations. By changing the value of parameters included in these equations, it is possible to change the amplitude and the period of ECG waves. Although this model is a powerful tool for modeling the electrical activity of the heart, its use is often limited to those familiar with the differential equations that describe the system. The purpose of this work is to provide a system that allows generating an ECG signal using Ryzhii model without knowing the details of differential equations. First, we provide the relationships between the ECG wave features and the model parameters; then we generalize them through fitting neural networks. Finally, putting in series fitting neural network and heart model, we provide a system that allows generating a synthetic signal by setting as input only the morphological ECG feature. We computed numerical simulation in Simulink environment and implemented the fitting neural networks in Matlab. Results show that non-linear trends characterize the correlation functions between ECG morphological features and model parameters and that the fitting neural networks can generalized this trend by providing the model parameters given in input the respectively ECG feature

Embodied Cognitive Science of Music. Modeling Experience and Behavior in Musical Contexts

Recently, the role of corporeal interaction has gained wide recognition within cognitive musicology. This thesis reviews evidence from different directions in music research supporting the importance of body-based processes for the understanding of music-related experience and behaviour. Stressing the synthetic focus of cognitive science, cognitive science of music is discussed as a modeling approach that takes these processes into account and may theoretically be embedded within the theory of dynamic systems. In particular, arguments are presented for the use of robotic devices as tools for the investigation of processes underlying human music-related capabilities (musical robotics)