Heart rate variability biofeedback as a method for assessing baroreflex function: a preliminary study of resonance in the cardiovascular system

This study describes the use of a biofeedback method for the noninvasive study of baroreflex mechanisms. Five previously untrained healthy male participants learned to control oscillations in heart rate using biofeedback training to modify their heart rate variability at specific frequencies. They were instructed to match computer-generated sinusoidal oscillations with oscillations in heart rate at seven frequencies within the range of 0.01–0.14 Hz. All participants successfully produced high-amplitude target-frequency oscillations in both heart rate and blood pressure. Stable and predictable transfer functions between heart rate and blood pressure were obtained in all participants. The highest oscillation amplitudes were produced in the range of 0.055–0.11 Hz for heart rate and 0.02–0.055 Hz for blood pressure. Transfer functions were calculated among sinusoidal oscillations in the target stimuli, heart rate, blood pressure, and respiration for frequencies at which subjects received training. High and low target-frequency oscillation amplitudes at specific frequencies could be explained by resonance among various oscillatory processes in the cardiovascular system. The exact resonant frequencies differed among individuals. Changes in heart rate oscillations could not be completely explained by changes in breathing. The biofeedback method also allowed us to quantity characteristics of inertia, delay, and speed sensitivity in baroreflex system. We discuss the implications of these findings for using heart rate variability biofeedback as an aid in diagnosing various autonomic and cardiovascular system disorders and as a method for treating these disorders.     

Modeling baroreflex regulation of heart rate during orthostatic stress

During orthostatic stress, arterial and cardiopulmonary baroreflexes play a key role in maintaining arterial pressure by regulating heart rate. This study presents a mathematical model that can predict the dynamics of heart rate regulation in response to postural change from sitting to standing. The model uses blood pressure measured in the finger as an input to model heart rate dynamics in response to changes in baroreceptor nerve firing rate, sympathetic and parasympathetic responses, vestibulo-sympathetic reflex, and concentrations of norepinephrine and acetylcholine. We formulate an inverse least squares problem for parameter estimation and successfully demonstrate that our mathematical model can accurately predict heart rate dynamics observed in data obtained from healthy young, healthy elderly, and hypertensive elderly subjects. One of our key findings indicates that, to successfully validate our model against clinical data, it is necessary to include the vestibulo-sympathetic reflex. Furthermore, our model reveals that the transfer between the nerve firing and blood pressure is nonlinear and follows a hysteresis curve. In healthy young people, the hysteresis loop is wide, whereas, in healthy and hypertensive elderly people, the hysteresis loop shifts to higher blood pressure values, and its area is diminished. Finally, for hypertensive elderly people, the hysteresis loop is generally not closed, indicating that, during postural change from sitting to standing, baroreflex modulation does not return to steady state during the first minute of standing.     

Seidel–Herzel model of human baroreflex in cardiorespiratory system with stochastic delays

The stochastic versus deterministic solution of the Seidel–Herzel model describing the baroreceptor control loop (which regulates the short-time heart rate) are compared with the aim of exploring the heart rate variability. The deterministic model solutions are known to bifurcate from the stable to sustained oscillatory solutions if time delays in transfer of signals by sympathetic nervous system to the heart and vasculature are changed. Oscillations in the heart rate and blood pressure are physiologically crucial since they are recognized as Mayer waves. We test the role of delays of the sympathetic stimulation in reconstruction of the known features of the heart rate. It appears that realistic histograms and return plots are attainable if sympathetic time delays are stochastically perturbed, namely, we consider a perturbation by a white noise. Moreover, in the case of stochastic model the bifurcation points vanish and Mayer oscillations in heart period and blood pressure are observed for whole considered space of sympathetic time delays.      

Dynamic autoregulation of cutaneous circulation: differential control in glabrous versus nonglabrous skin

The purpose of this project was to test the hypothesis that, independent of neural control, glabrous and nonglabrous cutaneous vasculature is capable of autoregulating blood flow. In 10 subjects, spectral and transfer function analyses of arterial pressure and skin blood flow (laser-Doppler flowmetry) from glabrous (palm) and nonglabrous (forearm) regions were performed under three conditions: baseline, ganglionic blockade via intravenous trimethaphan administration, and trimethaphan plus oscillatory lower body negative pressure (LBNP; -5 to -10 mmHg) from 0.05 to 0.07 Hz. Oscillatory LBNP was applied to regenerate mean arterial pressure variability that was abolished by ganglionic blockade. Ganglionic blockade was verified by an absence of a heart rate response to a Valsalva maneuver. Spectral power and transfer function gain between blood pressure and skin blood flow were calculated in this oscillatory frequency range (0.05-0.07 Hz). Within this frequency range, ganglionic blockade significantly decreased spectral power of blood flow in both the forearm and palm, whereas regeneration of arterial blood pressure oscillations significantly increased spectral power of forearm blood flow but not palm blood flow. During oscillatory LBNP, transfer function gain between blood pressure and skin blood flow was significantly elevated at the forearm (0.28 +/- 0.03 to 0.53 +/- 0.02 flux units/mmHg; P < 0.05) but was reduced at the palm (4.7 +/- 0.5 to 1.2 +/- 0.1 flux units/mmHg; P < 0.05). These data show that independent of neural control of blood flow, glabrous skin has the ability to buffer blood pressure oscillations and demonstrates a degree of dynamic autoregulation. Conversely, these data suggest that nonglabrous skin has diminished dynamic autoregulatory capabilities.     

Sustained oscillations generated by mutually inhibiting neurons with adaptation

Autonomic oscillatory activities exist in almost every living thing and most of them are produced by rhythmic activities of the corresponding neural systems (locomotion, respiration, heart beat, etc.). This paper mathematically discusses sustained oscillations generated by mutual inhibition of the neurons which are represented by a continuous-variable model with a kind of fatigue or adaptation effect. If the neural network has no stable stationary state for constant input stimuli, it will generate and sustain some oscillation for any initial state and for any disturbance. Some sufficient conditions for that are given to three types of neural networks: lateral inhibition networks of linearly arrayed neurons, symmetric inhibition networks and cyclic inhibition networks. The result suggests that the adaptation of the neurons plays a very important role for the appearance of the oscillations. Some computer simulations of rhythic activities are also presented for cyclic inhibition networks consisting of a few neurons.     

Pulmonary vascular impedance and wave reflections in the hypoxic calf.

The alterations in pulsatile hemodynamics that occur during hypoxic pulmonary vasoconstriction have not been well characterized. Changes in oscillatory hemodynamics, however, may affect right ventricular-pulmonary vascular coupling and the dissipation of energy within the lung vasculature. To better define hypoxic pulsatile hemodynamics, we measured main pulmonary artery proximal and distal micromanometric pressures and ultrasonic flow in four open-chest calves during progressive hypoxia. Main pulmonary artery impedance and pressure transmission spectra were calculated using spectral analysis methods. Measured pressure and flow signals were separated in the time domain into forward and backward components. Hypoxia increased pulmonary blood pressure and resistance and produced multiple modifications in the impedance and pressure transmission spectra that indicated increased wave reflections and elasticity. The impedance and apparent phase velocity first-harmonic values were increased in amplitude, and the pressure transmission modulus plot showed an increased peak value. In addition, the impedance modulus plot demonstrated a rightward shift and increased oscillation in the mid- to high-frequency range. The time domain analysis also confirmed increased wave reflections and elasticity. Hypoxia produced large backward-traveling (reflected) pressure and flow waves. The initial portions of these waves arrived at the heart during systole, producing characteristic changes in the measured pressure and flow waveforms. With prolonged hypoxia, main pulmonary artery pulse wave velocity increased by 30%. Thus, hypoxia is associated with complex alterations in pulmonary artery elasticity and wave reflections that act to increase the oscillatory afterload of the right ventricle.     

Efficient “Communication through Coherence” Requires Oscillations Structured to Minimize Interference between Signals

The ‘communication through coherence’ (CTC) hypothesis proposes that selective communication among neural networks is achieved by coherence between firing rate oscillation in a sending region and gain modulation in a receiving region. Although this hypothesis has stimulated extensive work, it remains unclear whether the mechanism can in principle allow reliable and selective information transfer. Here we use a simple mathematical model to investigate how accurately coherent gain modulation can filter a population-coded target signal from task-irrelevant distracting inputs. We show that selective communication can indeed be achieved, although the structure of oscillatory activity in the target and distracting networks must satisfy certain previously unrecognized constraints. Firstly, the target input must be differentiated from distractors by the amplitude, phase or frequency of its oscillatory modulation. When distracting inputs oscillate incoherently in the same frequency band as the target, communication accuracy is severely degraded because of varying overlap between the firing rate oscillations of distracting inputs and the gain modulation in the receiving region. Secondly, the oscillatory modulation of the target input must be strong in order to achieve a high signal-to-noise ratio relative to stochastic spiking of individual neurons. Thus, whilst providing a quantitative demonstration of the power of coherent oscillatory gain modulation to flexibly control information flow, our results identify constraints imposed by the need to avoid interference between signals, and reveal a likely organizing principle for the structure of neural oscillations in the brain.     

Mechanisms of blood pressure and heart rate variability: an insight from low-level paraplegia

It is still unclear whether the low-frequency oscillation in heart rate is generated by an endogenous neural oscillator or by a baroreflex resonance. Our aim was to investigate this issue by analyzing blood pressure and heart rate variability and the baroreflex function in paraplegic subjects with spinal cord injury below the fourth thoracic vertebra. These subjects were selected because they represent a model of intact central neural drive to the heart, with a partially impaired autonomic control of the vessels. In our study, arterial blood pressure and ECG were recorded in 33 able-bodied controls and in 33 subjects with spinal cord lesions between the fifth thoracic and the fourth lumbar vertebra 1) during supine rest (lowest sympathetic activation), 2) sitting on a wheelchair (light sympathetic activation), and 3) during exercise (moderate sympathetic activation). Blood pressure and heart rate spectra, coherence, and baroreflex function (sequence technique) were estimated in each condition. Compared with controls, paraplegic subjects showed a reduction of the low-frequency power of blood pressure and heart rate, and, unlike controls, a 0.1-Hz peak did not appear in their spectra. Sympathetic activation increased the 0.1-Hz peak of blood pressure and heart rate and the coherence at 0.1 Hz in controls only. Paraplegic subjects also had significantly lower baroreflex effectiveness and greater blood pressure variability. In conclusion, the disappearance of the 10-s oscillation of heart rate and blood pressure in subjects with spinal cord lesion supports the hypothesis of the baroreflex nature of this phenomenon.     

Control of blood pressure oscillation elicited by bleeding.

1) A control objective regarding the blood pressure oscillation is to decrease the heart rate. 2) The transfusion of a small amount of blood at the bottom of a cycle in the oscillation is usually useful as a control plan for the blood pressure oscillation. 3) A partial occlusion of the abdominal aorta is effective in arresting the oscillation, but the oscillation starts again after releasing the abdominal aorta from the partial occlusion.     

Modelling of the control of heart rate by breathing using a kernel method

The process of the breathing (input) to the heart rate (output) of man is considered for system identification by the input-output relationship, using a mathematical model expressed as integral equations. The integral equation is considered and fixed so that the identification method reduces to the determination of the values within the integral, called kernels, resulting in an integral equation whose input-output behaviour is nearly identical to that of the system. This paper uses an algorithm of kernel identification of the Volterra series which greatly reduces the computational burden and eliminates the restriction of using white Gaussian input as a test signal. A second-order model is the most appropriate for a good estimate of the system dynamics. The model contains the linear part (first-order kernel) and quadratic part (second-order kernel) in parallel, and so allows for the possibility of separation between the linear and non-linear elements of the process. The response of the linear term exhibits the oscillatory input and underdamped nature of the system. The application of breathing as input to the system produces an oscillatory term which may be attributed to the nature of sinus node of the heart being sensitive to the modulating signal the breathing wave. The negative-on diagonal seems to cause the dynamic asymmetry of the total response of the system which opposes the oscillatory nature of the first kernel related to the restraining force present in the respiratory heart rate system. The presence of the positive-off diagonal of the second-order kernel of respiratory control of heart rate is an indication of an escape-like phenomenon in the system.     

Nonlinear control of bioreactors with input multiplicities—an experimental work

The phrase input multiplicities means that an input variable with more than one value produces the same output value as if there were a single input–single output process. With input multiplicities, the value of the process gain changes as the manipulated variable changes, and beyond a certain input value, the sign of the gain also changes. A conventional PI controller for processes with input multiplicities may give unstable, less economical, or oscillatory responses. In the present work, control problems of a continuous bioreactor exhibiting two input multiplicities in the dilution rate on productivity were experimentally analyzed. A regulatory problem for the evaluation of controllers was taken up, i.e. a step change was made in the feed substrate concentration from 20 to 25 g/l at steady state conduction at lower (0.09386 h⁻¹) and higher (0.2278 h⁻¹) dilution rates for the same productivity of 2.9 g/l h. The nonlinear PI controller gave a more stable and fast response at both input dilution rates. The linear PI controller designed for a lower input dilution rate was stable, with some oscillations at the lower dilution rate, but the response was unstable at a higher dilution rate due to the input multiplicity behaviour of the process. Thus, nonlinear PI controller performance was found to be superior to that of the linear controller, and earlier reported theoretical results have been validated by the present experimental work.     

Resonance in a mathematical model of baroreflex control: arterial blood pressure waves accompanying postural stress

A mathematical model of the arterial baroreflex was developed and used to assess the stability of the reflex and its potential role in producing the low-frequency arterial blood pressure oscillations called Mayer waves that are commonly seen in humans and animals in response to decreased central blood volume. The model consists of an arrangement of discrete-time filters derived from published physiological studies, which is reduced to a numerical expression for the baroreflex open-loop frequency response. Model stability was assessed for two states: normal and decreased central blood volume. The state of decreased central blood volume was simulated by decreasing baroreflex parasympathetic heart rate gain and by increasing baroreflex sympathetic vaso/venomotor gains as occurs with the unloading of cardiopulmonary baroreceptors. For the normal state, the feedback system was stable by the Nyquist criterion (gain margin = 0.6), but in the hypovolemic state, the gain margin was small (0.07), and the closed-loop frequency response exhibited a sharp peak (gain of 11) at 0.07 Hz, the same frequency as that observed for arterial pressure fluctuations in a group of healthy standing subjects. These findings support the theory that stresses affecting central blood volume, including upright posture, can reduce the stability of the normally stable arterial baroreflex feedback, leading to resonance and low-frequency blood pressure waves.     

Renal SNA as the primary mediator of slow oscillations in blood pressure during hemorrhage

Blood pressure contains a distinct low-frequency oscillation often termed the Mayer wave. This oscillation is caused by the action of the sympathetic nervous system on the vasculature and results from time delays in the baroreflex feedback loop for the control of sympathetic nerve activity (SNA) in response to changes in blood pressure. In this study, we used bilateral renal denervation to test the hypothesis that it is SNA to the kidney that contributes a large portion of the vascular resistance associated with changes in the strength of the slow oscillation in blood pressure. In conscious rabbits, SNA and blood pressure were measured during hemorrhage (blood withdrawal at 1.35 ml. min(-1). kg(-1) for 20 min). Spectral analysis identified a strong increase in power at 0.3 Hz in SNA and blood pressure in the initial compensatory phase of hemorrhage before blood pressure started to fall. However, in a separate group of renal denervated rabbits, although the power of the 0.3-Hz oscillation under control conditions in blood pressure was similar, it was not altered during hemorrhage. Wavelet analysis revealed the development of low-frequency oscillations at 0.1 Hz in both intact and denervated animals. In conclusion, we propose that changes in the strength of the oscillation at 0.3 Hz in arterial pressure during hemorrhage are primarily mediated by sympathetic activity directed to the kidney.     

安定对家兔呼吸的作用

在切断迷走神经和局部麻醉的家兔中观察了静脉注射安定(2mg/kg)对呼吸和循环的影响。在动物进行自然呼吸的条件下,安定使每分通气量减少,心率变慢和血压降低。在将动物肌肉麻痹并进行正压人工呼吸的条件下,安定使呼吸频率加快,吸气时程和呼气时程缩短,即呼吸周期缩短。此外,膈神经放电的高频振荡频率增高而电位的幅度变小,动物的血压也降低。在桥脑头端去大脑而表现长吸式呼吸,以及在延體髓纹水平横断脑干而表观喘息式呼吸的动物中,安定亦使膈神经放电的幅度减小,呼吸周期延长和血压降低。以上结果表明安定可使呼吸抑制、血压降低,而其作用的基本部位可能主要在延髓。     

Pressure dependence of the carotid sinus elastic modulus in the dog.

The effect of the mean intrasinusal pressure upon the dynamic elastic modulus of the carotid sinus was examined in seven dogs. In all dogs the carotid sinus elastic modulus was a direct function of the mean intrasinusal pressure, measured at the lingual artery. The carotid sinus thus appears to become progressively stiffer with increasing pressure with a consequent reduction in oscillatory strain. This reduction of oscillatory stimulation of the carotid sinus mechanoreceptors acts so as to limit the maximum gain of the carotid sinus reflex to the region of the closed loop operating pressure.     

A blood pressure-regulating device for inducing hemorrhagic shock.

An instrument for producing closely controlled and repeatable hemorrhagic shock in laboratory animals is described. A Sarns roller pump, controlled by an electronic device, is used to pump blood in and out of the animal at a constant rate. Photoelectric cells are used to sense pressure changes and depending on their configuration, the pump runs forward or backward or stops. Pressures are accurately maintained, bleeding and reinfusion rates are controlled, and a record of bleeding patterns is provided.     

High-cut characteristics of the baroreflex neural arc preserve baroreflex gain against pulsatile pressure

A transfer function from baroreceptor pressure input to sympathetic nerve activity (SNA) shows derivative characteristics in the frequency range below 0.8 Hz in rabbits. These derivative characteristics contribute to a quick and stable arterial pressure (AP) regulation. However, if the derivative characteristics hold up to heart rate frequency, the pulsatile pressure input will yield a markedly augmented SNA signal. Such a signal would saturate the baroreflex signal transduction, thereby disabling the baroreflex regulation of AP. We hypothesized that the transfer gain at heart rate frequency would be much smaller than that predicted from extrapolating the derivative characteristics. In anesthetized rabbits (n = 6), we estimated the neural arc transfer function in the frequency range up to 10 Hz. The transfer gain was lost at a rate of -20 dB/decade when the input frequency exceeded 0.8 Hz. A numerical simulation indicated that the high-cut characteristics above 0.8 Hz were effective to attenuate the pulsatile signal and preserve the open-loop gain when the baroreflex dynamic range was finite.     

Mechanisms of Periodic Heart Rate Oscillations: A Study Using Controlled Breathing Tests

An orthostatic test with frequency-controlled breathing (with periods of 4, 6, 8, 10, and 12 s) was used to analyze frequency estimates of the heart rate variability (HRV) spectrum in the low frequency (LF) and high frequency (HF) ranges in 36 volunteers (26 men and 10 women) aged 19–21 years without signs of heart or respiratory pathology. The subjects took a breath at the moment of an auditory signal. There were no other requirements for the respiration rhythm. Variables were compared using Wilcoxon’s test for pairwise comparisons; correlations were estimated by Spearman’s rank correlation R test. The sensitivities of the LF and HF ranges of the HRV spectrum to periodic respiratory perturbations at different frequencies were demonstrated to differ from each other. Autonomous 0.10- and 0.25-Hz circuits of oscillatory processes were found in HRV. The transition zone of influence of these circuits was located in the region around 0.125 Hz. The characteristics of the 0.10- and 0.25-Hz oscillations in HRV were studied. It was demonstrated that the 0.10-Hz oscillatory process is a potent mechanism of heart rate control, is affected by external factors, and determines the dynamics of the autonomic nervous state of the body, while the 0.25-Hz process is a regulatory mechanism of medium strength, is resistant to external factors, and characterizes the adaptation reserve of the autonomic nervous control of the heart rate, as well as the autonomic nervous state of the body. Resonance responses in the HRV spec-trum can be used for studying the characteristics of the 0.10- and 0.25-Hz oscillations.__________Translated from Fiziologiya Cheloveka, Vol. 31, No. 3, 2005, pp. 76–83.Original Russian Text Copyright © 2005 by Kiselev, Kirichuk, Posnenkova, Gridnev.     

Oscillations,clocks and segmentation

Notch signalling molecules, such as the basic helix-loop-helix factors Hes1 and Hes7, periodically change their expression in the presomitic mesoderm, and each cycle of gene expression is associated with somite formation (every two hours in mouse). This cyclic expression is the manifestation of an intrinsic mechanism, called the segmentation clock, which is essential for coordinated somite segmentation. Interestingly, the oscillatory expression of Hes1 is observed in many cell types after serum stimulation, suggesting that this ultradian clock is not unique to presomitic mesoderm cells but widely distributed. This oscillation depends on the negative feedback loop, and once its promoter is constitutively activated, Hes1 seems to start oscillatory gene expression autonomously. Thus, Hes1 acts as a device that transduces a direct current of input into an alternating current, which ticks the hours in many biological systems.     

Diversity of Intrinsic Frequency Encoding Patterns in Rat Cortical Neurons—Mechanisms and Possible Functions

Extracellular recordings of single neurons in primary and secondary somatosensory cortices of monkeys in vivo have shown that their firing rate can increase, decrease, or remain constant in different cells, as the external stimulus frequency increases. We observed similar intrinsic firing patterns (increasing, decreasing or constant) in rat somatosensory cortex in vitro, when stimulated with oscillatory input using conductance injection (dynamic clamp). The underlying mechanism of this observation is not obvious, and presents a challenge for mathematical modelling. We propose a simple principle for describing this phenomenon using a leaky integrate-and-fire model with sinusoidal input, an intrinsic oscillation and Poisson noise. Additional enhancement of the gain of encoding could be achieved by local network connections amongst diverse intrinsic response patterns. Our work sheds light on the possible cellular and network mechanisms underlying these opposing neuronal responses, which serve to enhance signal detection.