Infant periodic breathing and apneic threshold.

A mathematical model was proposed to predict the role played by apneic threshold in periodic breathing in preterm infants. Prior models have mainly applied linear control theory which predicted instability but could not explain sustained periodic breathing. Apneic threshold to CO2 which has been postulated to play a major role in infant periodic breathing is a nonlinear effect and cannot be described by linear theory. Another previously unexplored nonlinear factor affecting instability is brain vascular volume change with CO2 which affects time delay to chemoreceptors. The current model explored the influences of apneic threshold, central and peripheral chemoreceptor gains, cardiac output, lung volume, and circulatory time delay on periodic breathing. Apneic threshold was found to play a major role in ventilatory responses to spontaneous sighs. Sighs led to apneic pauses followed by periods of periodic breathing with peripheral chemoreceptor CO2 gain, cardiac output, and lung volume were at reported normal levels. Apneic threshold when exceeded was observed to cause an asymmetry in the periodic breathing cycling and an increased periodic breathing frequency. Sighs in infants occur frequently enough to lead to repeated stimulation within the epoch duration of periodic breathing for a single sigh. Multiple sighs may then play a major role in promoting continuous periodic breathing in infants. Peripheral chemoreceptor gain estimated using endogenous CO2 led to validated predicted periodic breathing cycle duration as a function of age. Brain vascular volume increase with CO2 contributes to periodic breathing in very young (1-2 day old) preterm infants.

Modeling Long-Term Facilitation of Respiration During Interval Exercise in Humans.

Long-term facilitation (LTF) of respiration has been mainly initiated by intermittent hypoxia and resultant chemoreceptor stimulation in humans. Comparable levels of chemoreceptor stimulation can occur in combined exercise and carbon dioxide (CO2) inhalation and lead to LTF. This possibility was supported by data collected during combined interval exercise and 3% inhaled CO2 in seven normal subjects. These data were further analyzed based on the dynamics involved using mathematical models in this study. Previously estimated peripheral chemoreceptor sensitivity during light exercise (40 W) with air or 3% inhaled CO2 approximately doubled resting sensitivity. Ventilation after a delay increased by 17.0 ± 2.48 L/min (p < 0.001) during recovery following 45% maximal oxygen uptake ([Formula: see text] ) exercise consistent with LTF which exceeded what can be achieved with intermittent hypoxia. Model fitting of the dynamic responses was used to separate neural from chemoreceptor-mediated CO2 responses. Exercise of 45% [Formula: see text] was followed by ventilation augmentation following initial recovery. Augmentation of LTF developed slowly according to second-order dynamics in accordance with plasticity involving a balance between self-excitatory and self-inhibitory neuronal pools.

Altered chemosensitivity to CO2 during exercise.

The effect of exercise on chemosensitivity to carbon dioxide (CO2 ) has been controversial. Most studies have been based on rebreathing to alter inspired CO2 which is poorly tolerated in exercise. Instead, inhaling a fixed 3% CO2 from rest to moderate exercise was found to be well tolerated by seven normal subjects enabling CO2 chemosensitivity to be studied with minimal negative reaction. Results showed that chemosensitivity to CO2 following 5-6 min of stimulation was significantly enhanced during mild exercise (p < 0.01). This motivated exploring how much of the dynamic ventilatory response to mild exercise breathing air could be predicted by a model with central and peripheral chemosensitivity. Chemoreceptor stimulation combined with hypercapnia has been associated with long-term facilitation of ventilation (LTF). 3% CO2 inhalation during moderate exercise led to ventilation augmentation consistent with LTF following 6 min of exercise in seven normal human subjects (p < 0.01). Increased ventilation could not be attributed to hypercapnia or metabolic changes. Moderate exercise breathing air resulted in significantly less augmentation. In conclusion, both peripheral and central chemosensitivity to CO2 increased in exercise with the peripheral chemoreceptors playing a dominant role. This separation of central and peripheral contributions was not previously reported. This chemoreceptor stimulation can lead to augmented ventilation consistent with LTF.

Modeling cerebral blood flow and ventilation instability due to CO2.

A minimal model of cerebral blood flow and respiratory control was developed to describe hypocapnic and hypercapnic responses. Important nonlinear properties such as cerebral blood flow changes with arterial partial pressure of carbon dioxide ([Formula: see text]) and associated time-dependent circulatory time delays were included. It was also necessary to vary cerebral metabolic rate as a function of [Formula: see text]. The cerebral blood flow model was added to a previously developed respiratory control model to simulate central and peripheral controller dynamics for humans. Model validation was based on previously collected data. The variable time delay due to brain blood flow changes in hypercapnia was an important determinant of predicted instability due to nonlinear interaction in addition to linear loop gain considerations. Peripheral chemoreceptor gains above a critical level, but within normal limits, were necessary to produce instability. Instability was observed in recovery from hypercapnia and hypocapnia. The 20-s breath-hold test appears to be a simple test of brain blood flow-mediated instability in hypercapnia. Brain blood flow was predicted to play an important role with nonlinear properties. There is an important interaction predicted by the current model between central and peripheral control mechanisms related to instability in hypercapnia recovery. Posthyperventilation breathing pattern can also reveal instability tied to brain blood flow. Previous data collected in patients with chronic obstructive lung disease were closely fitted with the current model and instability predicted. Brain vascular volume was proposed as a potential cause of instability despite cerebral autoregulation promoting constant brain flow.NEW & NOTEWORTHY Prior models of brain blood flow and respiratory control have not focused on instability. Time varying time delay resulting from brain blood flow changes due to carbon dioxide (CO2) and peripheral chemoreceptor gain were predicted to be important determinants of instability due to nonlinear interaction in addition to linear control loop gain. Time delay was assumed to be set by the ratio of brain arterial vascular volume and blood flow. This vascular volume was predicted to also significantly change with CO2.

Effect of 3% CO2 inhalation on respiratory exchange ratio and cardiac output during constant work-rate exercise.

BACKGROUND: The aim of this study was to examine whether the decrease in respiratory exchange ratio (RER) during constant work-rate exercise (CWE) with 3% carbon dioxide (CO2) inhalation could be caused by the combination of the decrease in CO2 output (V̇CO2) and the increase in oxygen uptake (V̇O2). In addition, we investigated the effect of 3% CO2 inhalation on cardiac output (Q̇) during CWE. METHODS: Seven males (V̇O2max: 44.1±6.4 mL/min/kg) carried out transitions from low-load cycling (baseline; 40w) to light intensity exercise (45% V̇O2 max; 89.3±12.5 W) and heavy intensity exercise (80% V̇O2max; 186.5±20.2 W) while inhaling normal air (Air) or an enriched CO2 gas (3% CO2, 21% O2, balance N2). Each exercise session was 6 min, and respiratory responses by Douglas bag technique and cardiac responses by thoracic bio-impedance method were measured during the experiment. RESULTS: Ventilation for 3% CO2 was higher than for air through the experiment (P<0.05). Steady and non-steady state RER and V̇CO2 for 3% CO2 were less than for air in both light and heavy intensities (P<0.05), but V̇O2 and Q̇ did not differ between the two conditions. CONCLUSIONS: 3% CO2 inhalation induced the decrease in RER during CWE at light and heavy intensities, which was due to the decrease in V̇CO2. The promoted ventilation with 3% CO2 did not lead to the increase in V̇O2. Moreover, 3% CO2 inhalation did not affect Q̇ during CWE at light and heavy intensities.

Nonparametric Model of Smooth Muscle Force Production During Electrical Stimulation.

A nonparametric model of smooth muscle tension response to electrical stimulation was estimated using the Laguerre expansion technique of nonlinear system kernel estimation. The experimental data consisted of force responses of smooth muscle to energy-matched alternating single pulse and burst current stimuli. The burst stimuli led to at least a 10-fold increase in peak force in smooth muscle from Mytilus edulis, despite the constant energy constraint. A linear model did not fit the data. However, a second-order model fit the data accurately, so the higher-order models were not required to fit the data. Results showed that smooth muscle force response is not linearly related to the stimulation power.

Modeling rate sensitivity of exercise transient responses to limb motion.

Transient responses of ventilation (V̇e) to limb motion can exhibit predictive characteristics. In response to a change in limb motion, a rapid change in V̇e is commonly observed with characteristics different than during a change in workload. This rapid change has been attributed to a feed-forward or adaptive response. Rate sensitivity was explored as a specific hypothesis to explain predictive V̇e responses to limb motion. A simple model assuming an additive feed-forward summation of V̇e proportional to the rate of change of limb motion was studied. This model was able to successfully account for the adaptive phase correction observed during human sinusoidal changes in limb motion. Adaptation of rate sensitivity might also explain the reduction of the fast component of V̇e responses previously reported following sudden exercise termination. Adaptation of the fast component of V̇e response could occur by reduction of rate sensitivity. Rate sensitivity of limb motion was predicted by the model to reduce the phase delay between limb motion and V̇e response without changing the steady-state response to exercise load. In this way, V̇e can respond more quickly to an exercise change without interfering with overall feedback control. The asymmetry between responses to an incremental and decremental ramp change in exercise can also be accounted for by the proposed model. Rate sensitivity leads to predicted behavior, which resembles responses observed in exercise tied to expiratory reserve volume.