Non-linear dynamics of human periodic breathing and implications for sleep apnea therapy.

A mathematical model of non-obstructive human periodic breathing (Cheyne-Stokes respiration) or central sleep apnea (CSA) is described which focused on explaining recently reported non-linear behavior. Evidence was presented that CHF (chronic heart failure)-CSA and ICSA (idiopathic central sleep apnea) both involved limit cycle oscillations. The validity of applying linear control theory for stabilization must then be re-examined. Critical threshold values and ranges of parameters were predicted which caused a change (bifurcation) from limit cycle periodic breathing to stable breathing. Changes in lung volume were predicted to form a bifurcation during CHF-CSA where stability and instability can involve a lung volume change as small as 0.1 l. CSA therapy based on reducing control loop gain was predicted to be relatively ineffective during stable limit cycle oscillation. The relative ratios of durations of ventilation to apnea (T(v)/T(a)) during periodic breathing were primarily determined by peripheral chemoreceptor dynamics during crescendo, de-crescendo, and apnea phases of CSA.

Separation of cardiac conduction system and atrial activities by spatial regression.

Multiple channel magnetocardiography is potentially useful for the study of the cardiac conduction system. However, normal atrial repolarization occurs simultaneously and obscures the interpretation of the net signal. Magnetocardiographic data in four normal subjects at rest and mild exercise were found to exhibit high spatial correlation during atrial activation. Based on measured channel-to-channel covariances, the atrial repolarization signals as measured in channels in the null zone of conduction system activity were used to estimate atrial repolarization in all channels. A linear prediction method was used which based on the "kriging" estimator of geostatistical theory. Due to high spatial correlations in the limited thoracic region studied, predictions based on a single null channel were found to be adequate. Removal of the atrial component facilitates the beat-by-beat estimation of conduction system changes during rest and exercise using the multiple channel biomagnetometer.

Uniqueness of optimal controllers during exercise.

The optimization hypothesis of respiratory control during exercise is based on the minimization of a function reflecting both chemical and mechanical costs. Both additive and multiplicative controllers have been derived as optimal from similar cost functions. The purpose of the present study was to explore the uniqueness of such predictions. Various formulations of controllers compatible with isocapnia were found to yield identical costs as controllers predicted to be optimal. It was concluded that controller predictions based on optimization theory are not unique. Optimization can occur with either an additive or multiplicative controller or any combination of the two which satisfies an isocapnic constraint. A general form of a combined additive-multiplicative controller was derived which was found to be compatible with previously reported experimental data collected during combined CO2 inhalation and exercise.

Minimization of lung pressure swings during high-frequency ventilation: a model.

The goal of this theoretical study was to develop a simple computational model for determining the lung pressure excursions that accompany the maintenance of adequate gas transport through high-frequency airway oscillations applied via the trachea (HFAO) and by transthoracic means (HFTO). Respiratory mechanics and gas transport parameters estimated from the preceding companion study (J. Appl. Physiol. 67: 985-992, 1989) were used in the model for computing tracheal, alveolar, pleural, and transpulmonary pressure swings. Comparison of model predictions with corresponding data obtained in dogs showed close agreement. The specification of eucapnia as a constraint led to results that were significantly different from previous findings which had assumed constant airflow. We used the model to identify "quasi-optimal" strategies for HFAO and HFTO application in which all pressure excursions were kept below the corresponding levels produced by conventional mechanical ventilation operating at 15 breaths/min. The model suggests the application of both HFAO and HFTO at frequencies substantially lower than the settings commonly employed in high-frequency ventilation. Application of HFAO at frequencies ranging from 1 to 4 Hz is recommended, whereas for HFTO the quasi-optimal range lies between 1 and 1.7 Hz. In patients with chronic obstructive pulmonary disease, pressure costs during HFAO or HFTO are minimized in the vicinity of 1 Hz.

Lung hyperinflation in isolated dog lungs during high-frequency oscillation.

To study the phenomenon of lung hyperinflation (LHI), i.e., an increase in lung volume without a concomitant rise in airway pressure, we measured lung volume changes in isolated dog lungs during high-frequency oscillation (HFO) with air, He, and SF6 and with mean tracheal pressure controlled at 2.5, 5.0, and 7.5 cmH2O. The tidal volume and frequency used were 1.5 ml/kg body wt and 20 Hz, respectively. LHI was observed during HFO in all cases except for a few trials with He. The degree of LHI was inversely related to mean tracheal pressure and varied directly with gas density. Maximum expiratory flow rate (Vmax) was measured during forced expiration induced by a vacuum source (-150 cmH2O) at the trachea. Vmax was consistently higher than the peak oscillatory flow rate (Vosc) during HFO, demonstrating that overall expiratory flow limitation did not cause LHI in isolated dog lungs. Asymmetry of inspiratory and expiratory impedances seems to be one cause of LHI, although other factors are involved.

Ventilatory responses to increased blood flow and decreased lung volume in awake dogs.

The effect of decreased lung volume on ventilatory responses to arteriovenous fistula-induced increased cardiac output was studied in four chronic awake dogs. Lung volume decreases were imposed by application of continuous negative-pressure breathing of -10 cmH2O to the trachea. The animals were surgically prepared with chronic tracheostomy, indwelling carotid artery catheter, and bilateral arteriovenous femoral shunts. Control arteriovenous blood flow was 0.5 l/min, and test flow level was 2.0 l/min. Arterial blood CO2 tension (PaCO2) was continuously monitored using an indwelling Teflon membrane mass spectrometer catheter, and inhaled CO2 was given to maintain isocapnia throughout. Increased fistula flow alone led to a mean 52% increase in cardiac output (CO), whereas mean systemic arterial blood pressure (Psa) fell 4% (P less than 0.01). Negative-pressure breathing alone raised Psa by 3% (P less than 0.005) without a significant change in CO. Expired minute ventilation (VE) increased by 27% (P less than 0.005) from control in both of these conditions separately. Combined increased flow and negative pressure led to a 50% increase in CO and 56% increase in VE (P less than 0.0025) without any significant change in Psa. Effects of decreased lung volume and increased CO appeared to be additive with respect to ventilation and to occur under conditions of constant PaCO2 and Psa. Because both decreased lung volume and increased CO occur during normal exercise, these results suggest that mechanisms other than chemical regulation may play an important role in the control of breathing and contribute new insights into the isocapnic exercise hyperpnea phenomenon.

Ventilatory response to CO2 and O2 near eupnea in awake dogs.

The problem faced in determining the ventilatory response to CO2 near eupnea has been the difficulty of unloading metabolically produced CO2 from the subject in the steady state. Previous methods using extracorporeal circuits to unload CO2 are technically difficult and provide a limited number of experimental states per experiment. Using the method of high-frequency ventilation to unload CO2, we were able to obtain a large number of determinations in the same subject under conditions of hypoxia, normoxia, and hyperoxia. Data collected in five awake dogs show that the ventilatory response to CO2 is linear down to apnea during normoxic conditions but exhibits nonlinear behavior dependent on the level of arterial O2 tension. During hyperoxic conditions, the response was concave curvilinear, with a statistically significant decrease in slope near apnea. In contrast, mild hypoxia led to a convex curvilinear response with an increased slope near apnea.

Automated temperature control system for vagal cooling.

An automated cooling system for vagal cold blockade was developed. A simple electronic circuit is described that enabled regulation of the steady-state nerve or circulant temperature to within +/- 0.1 degree C by alternating the cold circulant between low and high flows (10 and 350 ml/min, respectively). The 90% rise time ranged from 15 to 40 s depending on the desired steady state and the surrounding temperatures. The present apparatus can be conveniently and safely used, especially for differential vagal cold blockade.

Changes in lung volume and breathing pattern during exercise and CO2 inhalation in humans.

Lung volume changes during CO2 inhalation and exercise were compared in seven human subjects. Expiratory reserve volume (ERV) normalized by vital capacity (VC) was used as an index of end-expiratory lung volume (EELV). Work loads tried were 30, 60, and 90 W and inspired CO2 concentrations were 3.5 and 5.0%. Exercise at 30 W led to a significant decrease in EELV, by 7% VC (P less than 0.005), with no further change at higher levels of exercise (P greater than 0.1). Both 3.5 and 5.0% CO2 inhalation resulted in an increase in EELV that was not statistically significant (3% VC, P greater than 0.1). A possible linkage of this different EELV behavior to breathing pattern was tested. The tidal volume-inspiratory duration curve shifted to a higher volume region during exercise compared with CO2 inhalation. Consequently, the volume-time threshold characteristic was better described by an end-inspiratory lung volume-inspiratory duration plot, resulting in a common relationship under these two different stimuli. These results suggest that the depth and rate of breathing in humans can be affected by not only phasic but also tonic components. A decrease in functional residual capacity or EELV was peculiar to exercise and should be associated with increased mechanical efficiency compared with CO2 inhalation. Theoretical predictions based on work of breathing optimization via a decreased EELV seemed to be capable of explaining isocapnic exercise hyperpnea in conjunction with proportional control of arterial CO2 tension.

Use of a random forcing for high-frequency ventilation.

Previous applications of high-frequency oscillatory ventilation (HFOV) have used cyclic forcings with the frequency of oscillation considered to be a fundamental parameter. A question that is addressed in the present study is whether or not periodicity is an essential requirement for this mode of ventilation to occur. It was found possible to adequately ventilate anesthetized and paralyzed cats with volume excursions below the dead-space level using a random band-limited forcing. Experimental conditions were close to a constant flow variance (VARF) state, and arterial CO2 tension varied linearly as a function of the ratio of noise bandwidth and VARF. Periodicity per se did not appear to be a requirement for HFOV to occur, a result consistent with predictions of Taylor dispersion theory.

Analysis of the gas exchange system dynamics during high-frequency ventilation.

High-frequency ventilation (HFV) as a form of artificial respiration has attracted interest in recent years as a means of reducing the risk of barotrauma in clinical applications. This paper explores the high-frequency dynamics of the gas exchange system in order to obtain mathematical models that allow optimization studies aimed at answering the question: What is the optimum ventilatory waveform that secures a certain level of gas exchange while minimizing the resulting fluctuations in pleural or alveolar pressure? Two classes of input are considered: sinusoids and band-limited white noise. A model for the dynamic relation between tracheal flow and CO2 tension is obtained from experimental data which, in combination with existing models relating tracheal flow to pleural or alveolar pressure, allows optimization of the input flow waveform for a given level of CO2 elimination rate. The developed relation between CO2 elimination rate and input was verified by experimentally measured arterial CO2 tension.

Ventilatory CO2 responses during hypocapnia in anesthetized cats.

CO2 response curves were measured in six anesthetized cats under open-loop conditions in both hyperoxia and hypoxia. Markedly nonlinear characteristics were observed with CO2 response slopes below the normal operating level almost three times that above the normal operating level. In all animals, complete apnea was observed when CO2 was reduced sufficiently. The zero ventilation intercept averaged 23.5 +/- 5.6 (SD) Torr in hyperoxia (arterial PO2 greater than 400 Torr) and 21.0 +/- 5.4 Torr in hypoxia (arterial PO2 = 52.7 Torr). These results suggest that an increased tendency for periodic breathing in hypocapnia could be due to the higher CO2 response slope.

Bilateral reflex effects on phrenic nerve activity in response to single-shock vagal stimulation.

The bilateral reflex actions of vagus nerve afferent signals on phrenic efferent activity have been tested by unilateral graded single shock electrical stimulation. An early excitation (latency 3-5 msec) was more prominent in the phrenic nerve contralateral to the stimulated vagus. Spinal cord hemisection at C3 eliminated both contralateral and ipsilateral responses: thus, both were mediated via descending tracts in the contralateral cord. A bilaterally symmetrical early inhibition (latency 8-12 msec) followed the early excitation. The electrical thresholds for evoking the early responses and the temperature for blocking these responses during graded vagal cooling were closely similar to the threshold and blocking temperature for pulmonary stretch receptor afferents. Higher stimulus strengths evoked a strong, bilaterally similar, late excitation (latency 12-20 msec) followed by a late inhibition. At very high stimulus strengths a third excitation (latency 25-30 msec) could appear. Sometimes these responses were followed by lowered phrenic activity for the remainder of inspiration. Single shock stimulation of the intact vagus nerve or of the peripheral end of the cut recurrent laryngeal nerve provoked, by the contraction of laryngeal muscles, a strong, short latency (12 msec) inhibition of phrenic activity mediated by superior laryngeal nerve afferents. The implications of these results with respect to the reflex pathways of the different responses and their possible integration in the central respiratory control mechanisms are discussed.

Dynamics of ventilatory response to exercise in humans.

The dynamics of the ventilatory response to moderate exercise on a bicycle ergometer have been studied in humans. The work load was varied between 25 and 100 W as a pseudorandom binary sequence (PRBS) that enabled the impulse responses to be calculated by cross-correlation techniques. The response of all five subjects exhibited a bimodal response, i.e., a fast component that was followed after a delay by a slow component. The fast component accounted for a relatively small proportion of the total response. Also, it was demonstrated that to identify the rapid component it was necessary to excite the respiratory system with an input containing highfrequency components; this result was used to reconcile the findings from this study with those of previous investigation.

Optimal control evaluation of left ventricular systolic dynamics.

A model of the contracting left ventricle was developed, in which the left ventricle was represented as a time-varying compliance. The vascular load included the nonlinear (Bernoulli) resistance of the aortic valve, blood inertance, and a Windkessel model of the arterial tree. Owing to the obligatory aerobic nature of the heart, oxygen consumption can be used to characterize the energy utilized by the myocardium. An adaptive control law was developed for determining the systolic time course of ventricular pressure and volume that minimizes cardiac oxygen consumption. Three main determinants of myocardial oxygen consumption were included in the integral criterion function: developed wall tension, inotropic state, and external (mechanical) work. The optimal control problem was solved using the Pontryagin maximum principle. The model could predict, in good agreement with experimentally obtained data, systolic time course of ventricular pressure and volume, as well as directional changes in the duration of isovolumic contraction and ejection phase under various conditions of end-diastolic volume, mean aortic pressure, and inotropic state.

Pseudorandom testing of ventilatory response to inspired carbon dioxide in man.

A new method of testing the transient ventilatory response to inspired CO2 in humans has been developed in an attempt to improve the resolution and reproducibility of measures of peripheral chemoreceptor-mediated dynamics. The test input consisted of varying the level of inspired CO2 between 0 and 6-8% on a pseudorandom breath-by-breath basis. Cross-correlating this input with responses of end-tidal CO2, tidal volume, durations of inspiration and expiration, and respiratory rate yielded estimates of impulse responses. Computer simulation results and data collected in two subjects showed that reliable estimates of circulatory time lags and rapid dynamics are possible with this method. In one subject, the response dynamics observed were consistent with peripheral chemoreceptor rate sensitivity or adaptation. The rapid changes in inspiratory and expiratory durations also observed are probably mediated by peripheral chemoreceptors and appear to depend on the phase of the breathing cycle at which the CO2 stimulus arrives.

Hemodynamic parameters of the isolated dog kidney as determined by a frequency response method.

The isolated kidney of the dog was perfused with autologous blood through an oxygenator. Responses of arterial input pressure (PI), venous pressure (PV), and venous flow (UV) were measured during sinusoidal forcing of arterial inflow (UA) at 5 to 1,000 cpm superimposed on a steady-state flow level. Pre- (RA) and postglomerular (REV) resistances, and compliances of artery (CA) and glomeruli (CG) were estimated based on a network model and using the Bode diagram of gains PI/UA, UV/UA. The data were evaluated by the least square method with a digital computer. The mean values of the parameters normalized for the average weight of the kidney (64.5g) were: CA = 0.0027 ml/mmHg, CG = 0.088, RA = 0.45 mmHg . min/ml, and REV = 0.35. Mean arterial pressure (PA) and glomerular pressure (PG) were 111 and 50 mmHg, respectively. The regression lines of PG against PA were significantly different at high and low PA, this being taken as a manifestation of autoregulation of the renal circulation. PG values were less than those given by the classical study of Winton but close to those recently obtained on mutants rats with a direct puncture method by Brenner et al. It is concluded that the present study has given an experimental background with which we may continuously estimate, under more intact conditions, circulatory parameter values by monitoring pressures and flows which respond to external perturbations.

Dynamic analysis of gravimetric response of isolated dog hindlimb.

Previous gravimetric studies of transcapillary fluid movement have been based on capillary filtration coefficient (CFC) estimates. In these studies only a single CFC value is estimated for the entire isolated vascular bed. We have analyzed the dynamic gravimetric responses of isolated dog hindlimb to venous pressure steps and found it possible to estimate two different CFC values. Under control conditions, one CFC value averaged .0049 ml/mmHg min per 100g tissue wt, whichagrees with results of previous investigators. The other CFC value averaged 90304, which is very close to estimates we have previously made by an independent frequency-response methods. Changes in hindlimb properties to intra-arterial infusions of acetylcholine, papaverine, isoproterenol, and norepinephrine were also studied. Drug infusion results and the presence of similar dynamic components in experiments on gracilis muscle support the existence of inhomogeneous pathwaysin tissue, which lead to fluid-exchange nonuniformity.