Bonhoeffer-van der Pol Oscillator Model of the Sino-Atrial Node: A Possible Mechanism of Heart Rate Regulation

1994 ◽  
Vol 33 (01) ◽  
pp. 116-119 ◽  
Author(s):  
S. Sato ◽  
S. Doi ◽  
T. Nomura
Keyword(s):  
Heart Rate ◽  
Stable Limit Cycle ◽  
Nonlinear Dynamic System ◽  
Van Der Pol Oscillator ◽  
Transition Curve ◽  
Stable Limit ◽  
Van Der Pol ◽  
Rate Regulation ◽  
Dynamic System Theory ◽  
Heart Rate Regulation

Abstract:A Bonhoeffer-van der Pol equation with a stable limit cycle is proposed as a model of the pacemaker in the sino-atrial node to exptain heart rate regulation. Standard tools, such as the phase transition curve in nonlinear dynamic system theory, are used to analyze the model and results are compared with other studies on experiments with dogs.

Developing a Reduced-Order Model to Understand Non-Synchronous Vibration (NSV) in Turbomachinery

2012 ◽  
Author(s):  
Stephen T. Clark ◽  
Robert E. Kielb ◽  
Kenneth C. Hall
Keyword(s):  
Stable Limit Cycle ◽  
Forced Response ◽  
Van Der Pol Oscillator ◽  
Future Research ◽  
Limit Cycle Oscillation ◽  
Preliminary Design ◽  
Stable Limit ◽  
Van Der Pol ◽  
Reduced Order ◽  
Van Der Pol Model

This paper demonstrates the potential of using a multi-degree-of-freedom, traditional van der Pol oscillator to model Non-Synchronous Vibration (NSV) in turbomachinery. It is shown that the two main characteristics of NSV are captured by the reduced-order, van der Pol model. First, a stable limit cycle oscillation (LCO) is maintained for various conditions. Second, the lock-in phenomenon typical of NSV is captured for various fluid-structure frequency ratios. The results also show the maximum amplitude of the LCO occurs at an off-resonant condition, i.e., when the natural shedding frequency of the aerodynamic instability is not coincident with the natural modal frequency of the structure. This conclusion is especially relevant in preliminary design in industry because it suggests that design engineers cannot treat NSV as a normal Campbell-diagram crossing as they would for preliminary design for forced response; it is possible that by redesigning the blade, the response amplitude of the blade may actually be higher. The goal of future research will be to identify values and significance of the coupling parameters used in the van der Pol model, to match these coefficients with confirmed instances of experimental NSV, and to develop a preliminary design tool that engineers can use to better design turbomachinery for NSV. Proper Orthogonal Decomposition (POD) CFD techniques and coefficient tuning from experimental instances of NSV have been considered to identify the unknown coupling coefficients in the van der Pol model. Both the modeling of experimental NSV and preliminary design development will occur in future research.

scholarly journals Design of a New Chaotic System Based on Van Der Pol Oscillator and Its Encryption Application

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 743 ◽  
Author(s):  
Jianbin He ◽  
Jianping Cai
Keyword(s):  
Control Method ◽  
Variable Parameter ◽  
Stable Limit Cycle ◽  
Simple Algorithm ◽  
Van Der Pol Oscillator ◽  
Stable Limit ◽  
Van Der Pol ◽  
Dynamical Characteristics ◽  
New Chaotic System ◽  
Exclusive Or

The Van der Pol oscillator is investigated by the parameter control method. This method only needs to control one parameter of the Van der Pol oscillator by a simple periodic function; then, the Van der Pol oscillator can behave chaotically from the stable limit cycle. Based on the new Van der Pol oscillator with variable parameter (VdPVP), some dynamical characteristics are discussed by numerical simulations, such as the Lyapunov exponents and bifurcation diagrams. The numerical results show that there exists a positive Lyapunov exponent in the VdPVP. Therefore, an encryption algorithm is designed by the pseudo-random sequences generated from the VdPVP. This simple algorithm consists of chaos scrambling and chaos XOR (exclusive-or) operation, and the statistical analyses show that it has good security and encryption effectiveness. Finally, the feasibility and validity are verified by simulation experiments of image encryption.

Heart Rate Regulation During Exercise with Various Loads: Identification and Nonlinear H∞ Control

2008 ◽  
Vol 41 (2) ◽  
pp. 11618-11623 ◽  
Author(s):  
Teddy M. Cheng ◽  
Andrey V. Savkin ◽  
Branko G. Celler ◽  
Steven W. Su ◽  
Lu Wang
Keyword(s):  
Heart Rate ◽  
Rate Regulation ◽  
Heart Rate Regulation

Reduced capacity of heart rate regulation in response to mild hypoglycemia induced by glibenclamide and physical exercise in type 2 diabetes

Metabolism ◽  
2013 ◽  
Vol 62 (5) ◽  
pp. 717-724 ◽  
Author(s):  
Nedim Soydan ◽  
Reinhard G. Bretzel ◽  
Britta Fischer ◽  
Florian Wagenlehner ◽  
Adrian Pilatz ◽  
...  
Keyword(s):  
Type 2 Diabetes ◽  
Heart Rate ◽  
Physical Exercise ◽  
Rate Regulation ◽  
Heart Rate Regulation

scholarly journals Features of heart rate variability in patients with takotsubo syndrome

2021 ◽  
Vol 10 (Supplement_1) ◽  
Author(s):  
D Evdokimov ◽  
SA Boldueva ◽  
VS Feoktistova ◽  
TA Baeva
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Sinus Rhythm ◽  
Autonomic Regulation ◽  
Deep Breathing ◽  
Takotsubo Syndrome ◽  
Orthostatic Test ◽  
Rate Regulation ◽  
Heart Rate Regulation ◽  
Deep Breathing Test

Abstract Funding Acknowledgements Type of funding sources: None. Main funding source(s): North-Western State Medical University named after I.I. Mechnikov Objective to study the features of autonomic regulation of sinus rhythm features of autonomic regulation of cardiac sinus rhythm in patients with Takotsubo syndrome (TTS) during inpatient stay in hospital. Materials and methods. The study included 25 female patients (the median age 57.5 ± 28.5 years) with TTS, diagnosis was based on the InterTAK criteria. On the 5-7th day after admission, the heart rate variability (HRV) was assessed both at rest and cardiac autonomic function tests: the deep breathing test (DBT) and active orthostatic test (AOT) with the usage of a computer diagnostic system «Valenta». RESULTS According to HRV data, initially at rest, the majority of the studied patients predominantly had a parasympathetic impact on the heart rate regulation: in 70% - increased parasympathetic influence, in 17% - increased sympathetic influence, in 13% - a balanced heart rate regulation. When performing a DBT, the predominance of the parasympathetic influence on the heart rate was noted both in spectral parameters and according to the data of time analysis (HF  during DBT  increased 1.8 times  up to  489.6 ± 114.2 ms2 (p <0.05) ; LF  decreased 1.7 times  up to 254.1 ± 70.3 ms2 (p <0.05); VLF  increased 2.8 times up to 402.3 ± 101.8 ms2 (p <0, 05); TP  increased 1.4 times up to 1145.9 ± 251.3 ms2; CV increased 1.3 times up to 6.5 ± 0.7% (p <0.05); SDNN increased 1.3 times up to - 58.7 ± 6.6 ms (p <0.05). HRV measured during an AOT  showed a paradoxical  evaluation  in the parasympathetic impact on the heart rate (HF increased by 1.8 times and reached - 488.0 ± 104.7 ms2 (p <0.05); LF decreased by 1.1 times up to  408 , 4 ± 103.6 ms2; VLF increased 1.2 times  up to  166.4 ± 52.2 ms2; TP increased 1.3 times  up to 1062.8 ± 181.1 ms2 (p <0.05); CV increased 1.6 times  up to 8.0 ± 0.9% (p <0.05); SDNN increased 1.4 times  up to 62.6 ± 7.5 ms (p <0.05)). Conclusions During the index hospital inpatient stays the majority of patients with TTS have a vegetative imbalance due to increased parasympathetic influence on the heart rate, both at rest and  during a deep breathing test and an active orthostatic test. This fact is quite unexpected and requires further study.

Implementation of RSA-BFB Therapy in Students with Various Types of Autonomic Heart Rate Regulation in the Process of Adaptation to Learning Activity

2020 ◽  
Vol 46 (6) ◽  
pp. 663-670
Author(s):  
P. U. Zarchenko ◽  
E. M. Kazin ◽  
N. G. Blinova ◽  
L. A. Varich ◽  
I. L. Vasilchenko
Keyword(s):  
Heart Rate ◽  
Learning Activity ◽  
Rate Regulation ◽  
Heart Rate Regulation

Extending a Van der Pol Based Reduced-Order Model for Fluid-Structure Interaction Applied to Non-Synchronous Vibrations in Turbomachinery

2021 ◽  
Author(s):  
Richard Hollenbach ◽  
Robert Kielb ◽  
Kenneth Hall
Keyword(s):  
Fluid Structure Interaction ◽  
Reduced Order Model ◽  
Van Der Pol Oscillator ◽  
Previous Model ◽  
Stable Limit ◽  
Order Model ◽  
Van Der Pol ◽  
Fluid Structure ◽  
Reduced Order ◽  
Structure Interaction

Abstract This paper expands upon a multi-degree-of-freedom, Van der Pol oscillator used to model buffet and Nonsynchronous Vibrations (NSV) in turbines. Two degrees-of-freedom are used, a fluid tracking variable incorporating a Van der Pol oscillator and a classic spring, mass, damper mounted cylinder variable; thus, this model is one of fluid-structure interaction. This model has been previously shown to exhibit the two main aspects of NSV. The first is the lock-in or entrainment phenomenon of the fluid shedding frequency jumping onto the natural frequency of the oscillator, while the second is a stable limit cycle oscillation (LCO) once the transient solution disappears. Improvements are made to the previous model to better understand this aeroelastic phenomenon. First, an error minimizing technique through a system identification method is used to tune the coefficients in the Reduced Order Model (ROM) to improve the accuracy in comparison to experimental data. Secondly, a cubic stiffness term is added to the fluid equation; this term is often seen in the Duffing Oscillator equation, which allows this ROM to capture the experimental behavior more accurately, seen in previous literature. The finalized model captures the experimental cylinder data found in literature much better than the previous model. These improvements also open the door for future models, such as that of a pitching airfoil or a turbomachinery blade, to create a preliminary design tool for studying NSV in turbomachinery.

scholarly journals β3 Adrenergic Receptors in the Sinoatrial Node for Heart Rate Regulation

2021 ◽  
Vol 16 ◽  
Author(s):  
Shu Nakao ◽  
Kazuki Yanagisawa ◽  
Tomoe Ueyama ◽  
Koji Hasegawa ◽  
Teruhisa Kawamura
Keyword(s):  
Heart Rate ◽  
Adrenergic Receptors ◽  
Sinoatrial Node ◽  
Rate Regulation ◽  
Heart Rate Regulation
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