scholarly journals The Dynamics of Coupled  Oscillators

2021 ◽  
Author(s):  
◽  
Nigel Lawrence Holland
Keyword(s):  
Heart Rate ◽  
Differential Equations ◽  
Cardiovascular System ◽  
Coupled Oscillators ◽  
Dynamical Process ◽  
Coupled Oscillator ◽  
Sinus Arrhythmia ◽  
Oscillator System ◽  
Respiration Frequency ◽  
Human Cardiovascular System

<p>The subject is introduced by considering the treatment of oscillators in Mathematics from the simple Poincar´e oscillator, a single variable dynamical process defined on a circle, to the oscillatory dynamics of systems of differential equations. Some models of real oscillator systems are considered. Noise processes are included in the dynamics of the system. Coupling between oscillators is investigated both in terms of analytical systems and as coupled oscillator models. It is seen that driven oscillators can be used as a model of 2 coupled oscillators in 2 and 3 dimensions due to the dependence of the dynamics on the phase difference of the oscillators. This means that the dynamics are easily able to be modelled by a 1D or 2D map. The analysis of N coupled oscillator systems is also described. The human cardiovascular system is studied as an example of a coupled oscillator system. The heart oscillator system is described by a system of delay differential equations and the dynamics characterised. The mechanics of the coupling with the respiration is described. In particular the model of the heart oscillator includes the baroreceptor reflex with time delay whereby the aortic fluid pressure influences the heart rate and the peripheral resistance. Respiration is modelled as forcing the heart oscillator system. Locking zones caused by respiratory sinus arrhythmia (RSA), the synchronisation of the heart with respiration, are found by plotting the rotation number against respiration frequency. These are seen to be relatively narrow for typical physiological parameters and only occur for low ratios of heart rate to respiration frequency. Plots of the diastolic pressure and heart interval in terms of respiration phase parameterised by respiration frequency illustrate the dynamics of synchronisation in the human cardiovascular system.</p>

scholarly journals The Dynamics of Coupled  Oscillators

2021 ◽  
Author(s):  
◽  
Nigel Lawrence Holland
Keyword(s):  
Heart Rate ◽  
Differential Equations ◽  
Cardiovascular System ◽  
Coupled Oscillators ◽  
Dynamical Process ◽  
Coupled Oscillator ◽  
Sinus Arrhythmia ◽  
Oscillator System ◽  
Respiration Frequency ◽  
Human Cardiovascular System

<p>The subject is introduced by considering the treatment of oscillators in Mathematics from the simple Poincar´e oscillator, a single variable dynamical process defined on a circle, to the oscillatory dynamics of systems of differential equations. Some models of real oscillator systems are considered. Noise processes are included in the dynamics of the system. Coupling between oscillators is investigated both in terms of analytical systems and as coupled oscillator models. It is seen that driven oscillators can be used as a model of 2 coupled oscillators in 2 and 3 dimensions due to the dependence of the dynamics on the phase difference of the oscillators. This means that the dynamics are easily able to be modelled by a 1D or 2D map. The analysis of N coupled oscillator systems is also described. The human cardiovascular system is studied as an example of a coupled oscillator system. The heart oscillator system is described by a system of delay differential equations and the dynamics characterised. The mechanics of the coupling with the respiration is described. In particular the model of the heart oscillator includes the baroreceptor reflex with time delay whereby the aortic fluid pressure influences the heart rate and the peripheral resistance. Respiration is modelled as forcing the heart oscillator system. Locking zones caused by respiratory sinus arrhythmia (RSA), the synchronisation of the heart with respiration, are found by plotting the rotation number against respiration frequency. These are seen to be relatively narrow for typical physiological parameters and only occur for low ratios of heart rate to respiration frequency. Plots of the diastolic pressure and heart interval in terms of respiration phase parameterised by respiration frequency illustrate the dynamics of synchronisation in the human cardiovascular system.</p>

Bifurcation in a Simple Model of the Cardiovascular System

2000 ◽  
Vol 39 (02) ◽  
pp. 118-121 ◽  
Author(s):  
S. Akselrod ◽  
S. Eyal
Keyword(s):  
Nonlinear Dynamics ◽  
Blood Pressure ◽  
Heart Rate ◽  
Fixed Point ◽  
Cardiovascular System ◽  
Modified Model ◽  
Mayer Waves ◽  
Sustained Oscillations ◽  
Human Cardiovascular System ◽  
Physiological Values

Abstract:A simple nonlinear beat-to-beat model of the human cardiovascular system has been studied. The model, introduced by DeBoer et al. was a simplified linearized version. We present a modified model which allows to investigate the nonlinear dynamics of the cardiovascular system. We found that an increase in the -sympathetic gain, via a Hopf bifurcation, leads to sustained oscillations both in heart rate and blood pressure variables at about 0.1 Hz (Mayer waves). Similar oscillations were observed when increasing the -sympathetic gain or decreasing the vagal gain. Further changes of the gains, even beyond reasonable physiological values, did not reveal another bifurcation. The dynamics observed were thus either fixed point or limit cycle. Introducing respiration into the model showed entrainment between the respiration frequency and the Mayer waves.

Respiratory sinus arrhythmia: laws derived from computer simulation

1960 ◽  
Vol 15 (5) ◽  
pp. 863-874 ◽  
Author(s):  
Manfred Clynes
Keyword(s):  
Heart Rate ◽  
Computer Simulation ◽  
Differential Equations ◽  
Respiratory Sinus Arrhythmia ◽  
Nonlinear Differential Equations ◽  
Analogue Computer ◽  
Sinus Arrhythmia ◽  
Respiratory Effects ◽  
Rate Effects ◽  
Mathematical Relations

Dynamic mathematical relations describing respiratory sinus arrhythmia were derived through analogue computer simulation. If a signal proportional to thorax circumference is fed into the analogue computer, it calculates with differential equations the complex heart rate changes in real time and records them along with those of the real heart. Close correspondence of the predicted and actual changes of heart rate for a wide variety of modes of breathing, and for different individuals, proves the validity of the nonlinear differential equations describing the phenomenon. The respiratory effects are shown to be caused by two separate reflexes each producing biphasic heart rate transients in the same directions. The observed effects are the result of superposition of those transients. Previous paradoxical results in attempting to relate heart rate to respiration on a steady-state, nondynamic basis are thus explained. The laws indicate that stretch receptors and not hemodynamic or central nervous factors initiate the changes in heart rate. The analysis also allows heart rate effects of exercise and emotional stresses to be more precisely perceived, as clearly separated from respiratory effects. Submitted on June 16, 1959

Effects of peptide YY on the human cardiovascular system: reversal of responses to vasoactive intestinal peptide

1992 ◽  
Vol 263 (4) ◽  
pp. E740-E747 ◽  
Author(s):  
R. J. Playford ◽  
M. A. Benito-Orfila ◽  
P. Nihoyannopoulos ◽  
K. A. Nandha ◽  
J. Cockcroft ◽  
...  
Keyword(s):  
Heart Rate ◽  
Blood Flow ◽  
Cardiac Output ◽  
Cardiovascular System ◽  
Vasoactive Intestinal Peptide ◽  
Brachial Artery ◽  
Peptide Yy ◽  
Intestinal Secretion ◽  
Venous Occlusion ◽  
Human Cardiovascular System

Peptide YY (PYY) reverses the increased intestinal secretion stimulated by vasoactive intestinal peptide (VIP) in humans. VIP also dilates blood vessels, so we investigated the effect of PYY on the cardiovascular system. Six volunteers received PYY, 0.4 and 1.2 pmol.kg-1 x min-1 i.v. for 2 h, reproducing plasma levels seen postprandially and during a diarrheal illness, respectively. Cardiac function was assessed by echocardiography. PYY infused at 0.4 pmol.kg-1 x min-1 had no effect on cardiovascular parameters. PYY infused at 1.2 pmol.kg-1 x min-1 caused a fall in both stroke volume from 128 +/- 8 to 110 +/- 8 ml/beat (mean +/- 95 confidence interval, P < 0.01) and cardiac output from 7.2 +/- 0.4 to 6.1 +/- 0.4 l/min (P < 0.01). Effects of infusion of PYY into the brachial artery at doses of 0-16 pmol/min were assessed using venous occlusion plethysmography in six subjects. PYY infusion caused a dose-dependent fall in forearm blood flow. Six subjects received VIP, 5 pmol.kg-1 x min-1 i.v., causing a rise in heart rate from 55 +/- 3 to 70 +/- 3 beats/min and increased cardiac output from 7.3 +/- 1.1 to 13.1 +/- 1.1 l/min. The addition of PYY, 0.4 pmol.kg-1 x min-1 i.v., did not affect the heart rate significantly but decreased the cardiac output to 10.4 +/- 1.1 l/min (P < 0.01). Infusions of PYY into the brachial artery at 5 pmol/min decreased local vasodilation induced by VIP infused at 2 pmol/min at the same site by 40% (P < 0.01), even though this dose of PYY had no significant effect on local blood flow when given alone.(ABSTRACT TRUNCATED AT 250 WORDS)

scholarly journals A computational physiology approach to personalized treatment models: the beneficial effects of slow breathing on the human cardiovascular system

2014 ◽  
Vol 307 (7) ◽  
pp. H1073-H1091 ◽  
Author(s):  
Maria Fonoberova ◽  
Igor Mezić ◽  
Jennifer F. Buckman ◽  
Vladimir A. Fonoberov ◽  
Adriana Mezić ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Heart Rate ◽  
Heart Rate Variability ◽  
Cardiovascular System ◽  
Empirical Support ◽  
System Level ◽  
Heart Period ◽  
Heart Rate Variability Biofeedback ◽  
Human Cardiovascular System ◽  
Slow Breathing

Heart rate variability biofeedback intervention involves slow breathing at a rate of ∼6 breaths/min (resonance breathing) to maximize respiratory and baroreflex effects on heart period oscillations. This intervention has wide-ranging clinical benefits and is gaining empirical support as an adjunct therapy for biobehavioral disorders, including asthma and depression. Yet, little is known about the system-level cardiovascular changes that occur during resonance breathing or the extent to which individuals differ in cardiovascular benefit. This study used a computational physiology approach to dynamically model the human cardiovascular system at rest and during resonance breathing. Noninvasive measurements of heart period, beat-to-beat systolic and diastolic blood pressure, and respiration period were obtained from 24 healthy young men and women. A model with respiration as input was parameterized to better understand how the cardiovascular processes that control variability in heart period and blood pressure change from rest to resonance breathing. The cost function used in model calibration corresponded to the difference between the experimental data and model outputs. A good match was observed between the data and model outputs (heart period, blood pressure, and corresponding power spectral densities). Significant improvements in several modeled cardiovascular functions (e.g., blood flow to internal organs, sensitivity of the sympathetic component of the baroreflex, ventricular elastance) were observed during resonance breathing. Individual differences in the magnitude and nature of these dynamic responses suggest that computational physiology may be clinically useful for tailoring heart rate variability biofeedback interventions for the needs of individual patients.

How Does Heart Rate Variability Biofeedback Work? Resonance, the Baroreflex, and Other Mechanisms

Biofeedback ◽  
2013 ◽  
Vol 41 (1) ◽  
pp. 26-31 ◽  
Author(s):  
Paul Lehrer
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Cardiovascular System ◽  
Vascular Tone ◽  
Emotional Reactivity ◽  
Clinical Applications ◽  
Direct Effects ◽  
Sinus Arrhythmia ◽  
Heart Rate Variability Biofeedback ◽  
Resonance Effects

Heart rate variability biofeedback is known to have multiple effects on the cardiovascular system, the respiratory system, and emotional reactivity. This paper reviews the origins of work on heart rate variability biofeedback, and mechanisms for its various effects, including direct effects on the baroreflex system and gas exchange efficiency, as well as indirect effects on emotional reactivity and possibly inflammatory activity. Resonance in the cardiovascular system is explained, as well as ways that heart rate variability biofeedback stimulates these resonance effects, through interactions between respiratory sinus arrhythmia and the baroreflex system. Relationships of these mechanisms to various clinical applications of heart rate variability biofeedback are explored, as are future extensions of biofeedback to the vascular tone baroreflex.

scholarly journals Numerical study of coupled oscillator system using the classical Euler-Lagrange equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
H. Shanak ◽  
H. Khalilia ◽  
R. Jarrar ◽  
J. Asad
Keyword(s):  
Coupled Oscillators ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Lagrangian Method ◽  
Order Equation ◽  
Kutta Method ◽  
Lagrange Equations ◽  
Coupled Oscillator ◽  
Oscillator System ◽  
Runge Kutta Method

Abstract Problems involving vibrations (mechanical or electrical) can be reduced to problems of coupled oscillators. For this, we consider the motion of coupled oscillators system using Lagrangian method. The Lagrangian of the system was initially constructed, and then the Euler-Lagrange equations (i.e., equations of motion of the system) have been obtained. The obtained equations of motion are a homogenous second-order equation. These equations were solved numerically using the ode45 code, which is based on Runge-Kutta method.

scholarly journals Emotion, Respiration, and Heart Rate Variability: A Mathematical Model and Simulation Analyses

2019 ◽  
Vol 9 (23) ◽  
pp. 5008
Author(s):  
Satoko Hirabayashi ◽  
Masami Iwamoto
Keyword(s):  
Mathematical Model ◽  
Heart Rate ◽  
Heart Rate Variability ◽  
Simulation Analysis ◽  
Total Power ◽  
Potential Candidate ◽  
Sinus Arrhythmia ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Respiration Frequency

Although the generation mechanism of the low-frequency (LF) component of heart rate variability (HRV) is controversial, HRV is a potential candidate in designing objective measurement methodologies for emotions. These methodologies could be valuable for several biosignal applications. Here, we have conducted a simulation analysis using a novel mathematical model that integrates emotion, respiration, the nervous system, and the cardiovascular system. Our model has well reproduced experimental results, specifically concerning HRV with respiratory sinus arrhythmia and LF, the relation between HRV total power and the respiration frequency, and the homeostatic maintenance by the baroreflex. Our model indicates the following possibilities: (i) The delay in the heart rate control process of the parasympathetic activity works as a low-pass filter and the HRV total power decreases with a higher respiration frequency; (ii) the LF component of HRV and the Mayer wave are generated as transient responses of the baroreflex feedback control to perturbations induced by an emotional stimulus; and (iii) concentration on breathing to reduce the respiration frequency can reduce LF/HF and the reduction can be fed back to the emotional status.

Model-based sensor fusion of multimodal cardiorespiratory signals using an unscented Kalman filter

2020 ◽  
Vol 68 (11) ◽  
pp. 933-940
Author(s):  
Onno Linschmann ◽  
Steffen Leonhardt ◽  
Christoph Hoog Antink
Keyword(s):  
Heart Rate ◽  
Kalman Filter ◽  
Sensor Fusion ◽  
Coupled Oscillators ◽  
Unscented Kalman Filter ◽  
Real Data ◽  
Sinus Arrhythmia ◽  
Data Errors ◽  
Sensor Signals ◽  
Mean Heart Rate

AbstractBased on a model of three coupled oscillators describing the influence of respiration, namely respiratory sinus arrhythmia (RSA), and so-called Mayer waves on the heart rate, an unscented Kalman filter (UKF) is designed to perform sensor fusion of multimodal cardiorespiratory sensor signals. The aim is to implicitly use redundancy between the sensor signals to improve the estimated heart rate while utilising model knowledge. The effectiveness of the approach is shown by estimations of the heart rate on synthesised data as well as patient data from the Fantasia dataset and a Sleep laboratory which provide two, three or six sensor channels for resting individuals. It could be shown that the approach is able to fuse multimodal sensor signals on signal level to achieve more accurate estimations. For real data, errors in mean heart rate as small as 1.56 % were achieved.

Measures of RSA Suppression, Attentional Control, and Negative Affect Predict Self-Ratings of Executive Functions

2011 ◽  
Vol 25 (4) ◽  
pp. 164-173 ◽  
Author(s):  
Brian Healy ◽  
Aaron Treadwell ◽  
Mandy Reagan
Keyword(s):  
College Students ◽  
Heart Rate ◽  
Regression Analysis ◽  
Individual Differences ◽  
Negative Affect ◽  
Respiratory Sinus Arrhythmia ◽  
Attentional Control ◽  
Executive Processes ◽  
Sinus Arrhythmia ◽  
Low Levels

The current study was an attempt to determine the degree to which the suppression of respiratory sinus arrhythmia (RSA) and attentional control were influential in the ability to engage various executive processes under high and low levels of negative affect. Ninety-four college students completed the Stroop Test while heart rate was being recorded. Estimates of the suppression of RSA were calculated from each participant in response to this test. The participants then completed self-ratings of attentional control, negative affect, and executive functioning. Regression analysis indicated that individual differences in estimates of the suppression of RSA, and ratings of attentional control were associated with the ability to employ executive processes but only when self-ratings of negative affect were low. An increase in negative affect compromised the ability to employ these strategies in the majority of participants. The data also suggest that high attentional control in conjunction with attenuated estimates of RSA suppression may increase the ability to use executive processes as negative affect increases.

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