A minimal mathematical model of human periodic breathing

Numerous mathematical models of periodic breathing (PB) currently exist. These models suggest mechanisms that may underlie many known causes of PB. However, each model that has been shown to simulate PB under reasonable conditions contains greater than 15 physiological parameters. Because some parameters exhibit a wide range of values in a population, such simulations cannot test a model's ability to account for the breathing patterns of individuals. Furthermore it is impractical to perform a direct experimental validation study that would require the estimation of each of 15 or more parameters for each subject. A minimal model of PB is presented that is suitable for direct validation. Analytic expressions are given that define the conditions for PB in terms of the following: 1) CO2 sensitivity, 2) Cardiac output, 3) Mixed venous CO2, 4) Circulation time, and 5) Mean lung volume for CO2. This model is shown to be consistent with previous models and experimental data regarding the degree of hypoxia or congestive heart failure required to produce PB. A quantitative measure of relative stability is defined as a metric of comparison to the human studies described in the accompanying paper (J. Appl. Physiol. 65: 1389-1399, 1988).     

Mechanical work of breathing during maximal voluntary ventilation

With the use of the esophageal balloon technique, the workingcapacity of the respiratory muscles was assessed in four normal subjects by measuring the work per breath (W) and respiratory power() during maximal voluntary ventilationwith imposed respiratory frequencies (f) ranging from 20 to 273 cycles/min. Measurements were made in a body plethysmograph to assessthe work wasted as a result of alveolar gas compressibility(Wg'). In line with other types of human voluntary muscleactivity, W decreased with increasing f, whereas exhibited a maximum at f of ~100cycles/min. Up to this f value, Wg' was small relative to W. Withfurther increase in f, the Wg'/W ratio increased progressively,amounting to 8-22% of at f of 200 cycles/min.

     

Diaphragmatic work of breathing in premature human infants

Present methods of assessing the work of breathing in human infants do not account for the added load when intercostal muscle activity is lost and rib cage distortion occurs. We have developed a technique for assessing diaphragmatic work in this circumstance utilizing measurements of transdiaphragmatic pressure and abdominal volume displacement. Eleven preterm infants without evidence of lung disease were studied. During periods of minimal rib cage distortion, inspiratory diaphragmatic work averaged 5.9 g X cm X ml-1, increasing to an average of 12.4 g X cm X ml-1 with periods of paradoxical rib cage motion (P less than 0.01). Inspiratory work was strongly correlated with the electrical activity of the diaphragm as measured from its moving time average (P less than 0.05). Assuming a mechanical efficiency of 4% in these infants, the caloric cost of diaphragmatic work may reach 10% of their basal metabolic rate in periods with rib cage distortion. When lung disease is superimposed, the increased metabolic demands of the diaphragm may predispose preterm infants to fatigue and may contribute to a failure to grow.     

Total work rate of breathing optimization in CO-2 inhalation and exercise.

The hypothesis that respiratory frequency and the relative durations of inspiration and expiration are regulated according to a total cycle work rate minimization criterion was explored. Effects of negative work performed by the respiratory muscles and dead space variation as a function of tidal volume were included in a formulation which yielded a theoretically predictable optimal frequency and relative duration of inspiration and expiration at all levels of ventilation. Predicted cycle characteristics based on measured mechanical parameters were compared with data taken during CO-2 inhalation (3 and 5%) and moderate exercise (MRR = 3 and 6) in three normal human subjects. No major difference in breathing pattern was observed between CO-2 inhalation and exercise. Results suggest that conditions for minimization of total cycle work rate are achieved asympototically as the level of ventilation rises above the resting level. At rest and at low levels of hyperpnea complete work rate optimization is not achieved.     

Effect of bronchomotor tone on work rate of breathing

We studied the optimal airway caliber for minimizing the work rate of breathing in the lung (W) with different bronchomotor tones in six normal subjects. The inhalation of methacholine contracted airway smooth muscle, and the inhalation of salbutamol relaxed it. To calculate W at a given alveolar ventilation (VA), anatomical dead space (VDanat), pulmonary resistance (RL), and dynamic compliance were measured simultaneously, breath by breath, during various breathing maneuvers. VDanat increased and RL decreased with both increased breathing frequency and tidal volume, even at a given airway tone. This suggests that the airway caliber varied even at a given bronchomotor tone. The minimum W at a given VA increased in constricted airways, but there was no significant difference between control airways after saline inhalation and relaxed airways. It has been suggested that airway smooth muscle tones at both control and relaxed conditions bring W to a minimum and that the airway smooth muscle tone existing in the control state acts to keep the airway caliber optimal in order to minimize the W and stabilize the airway mechanics.     

Airway caliber and the work of breathing in humans

Mechanical work rate of breathing was measured in five normal subjects during voluntary eucapnic hyperventilation at rates of approximately 10, 20, 40, 60, and 80 l/min before and after inhalation of 1 mg of ipratropium bromide, an anticholinergic agent. Chest wall recoil pressure was measured over a range of lung volumes in each subject and was used as the reference pressure in the calculation of work rate. There was little change in elastic or resistive work rate at rest when vagal tone was reduced by ipratropium. The mean work at 40, 60, and 80 l/min was 8.9, 17.2, and 34.0 cmH2O.l-1.s before and 5.6, 12.4 and 25.8 cmH2O.l-1.s after ipratropium. This suggests that vagal tone significantly influences the work of breathing at high ventilatory rates, such as occur during strenuous exercise.     

A model of the spontaneously breathing patient: applications to intrinsic PEEP and work of breathing

Schuessler, Thomas F., Stewart B. Gottfried, and Jason H. T. Bates. A model of the spontaneously breathing patient: applications to intrinsic PEEP and work of breathing.J. Appl. Physiol. 82(5):1694-1703, 1997.Intrinsic positive end-expiratory pressure(PEEP_i) and inspiratory work ofbreathing (WI) are important factors in the management of severe obstructive respiratory disease. Weused a computer model of spontaneously breathing patients with chronicobstructive pulmonary disease to assess the sensitivity of measurementtechniques for dynamic PEEP_i(PEEP_{i dyn}) andWI to expiratory muscle activity(EMA) and cardiogenic oscillations (CGO) on esophageal pressure.Without EMA and CGO, bothPEEP_{i dyn} andWI were accurately estimated(r = 0.999 and 0.95, respectively). Addition of moderate EMA causedPEEP_{i dyn} andWI to be systematically overestimated by 141 and 52%, respectively. Furthermore, CGOintroduced large random errors, obliterating the correlation betweenthe true and estimated values for bothPEEP_{i dyn}(r = 0.29) andWI (r = 0.38). Thus the accurateestimation of PEEP_{i dyn} andWI requires steps to be taken toameliorate the adverse effects of both EMA and CGO. Taking advantage ofour simulations, we also investigated the relationship betweenPEEP_{i dyn} and staticPEEP_i(PEEP_{i stat}). ThePEEP_{i dyn}/PEEP_{i stat}ratio decreased as stress adaptation in the lung was increased,suggesting that heterogeneity of expiratory flow limitation isresponsible for the discrepancies betweenPEEP_{i dyn} andPEEP_{i stat} thathave been reported in patients with severe airwayobstruction.

     

In-vivo analysis of sternal angle,sternal and sternocostal kinematics in supine humans during breathing

This paper aims at contributing to the understanding of the combination of in vivo sternum displacement, sternal angle variations and sternocostal joints (SCJ) kinematics of the seven first rib pairs over the inspiratory capacity (IC). Retrospective codified spiral-CT data obtained at total lung capacity (TLC), middle of inspiratory capacity (MIC) and at functional residual capacity (FRC) were used to compute kinematic parameters of the bones and joints of interest in a sample of 12 asymptomatic subjects. 3D models of rib, thoracic vertebra, manubrium and sternum were processed to determine anatomical landmarks (ALs) on each bone. These ALs were used to create local coordinate system and compute spatial transformation of ribs and manubrium relative to sternum, and sternum relative to thoracic vertebra. The rib angular displacements and associated orientation of rotation axes and joint pivot points (JPP), the sternal angle variations and the associated displacement of the sternum relative to vertebra were computed between each breathing pose at the three lung volumes. Results can be summarized as following: (1) sternum cephalic displacement ranged between 17.8 and 19.2 mm over the IC; (2) the sternal angle showed a mean variation of 4.4° ± 2.7° over the IC; (3) ranges of rib rotation relative to sternum decreased gradually with increasing rib level; (4) axes of rotation were similarly oriented at each SCJ; (5) JPP spatial displacements showed less variations at first SCJ compared to levels underneath; (6) linear relation was demonstrated between SCJ ROMs and sternum cephalic displacement over the IC.     

Muscle mass as a factor limiting physical work

Maximal exercise has been performed by eight men and eight women, using four types of ergometer (2-leg, 1-leg, arm + shoulder, and arm) while breathing room air and while breathing 12% O2. Results have been related to anthropometric estimates of muscle mass in the active limbs. Although significant sex differences of O2 transfer and power output are shown, the sex-specific aerobic performance was roughly proportional to active muscle volume (both when comparing individuals on a given type of ergometer and when comparing average scores of the several types of ergometer). However, the relationship was closer for steady power output than for peak O2 intake (where the scores for arm work were boosted by the use of accessory muscles and by hyperventilation). When breathing 12% O2, the 2-leg performance was substantially reduced (an average of 28.7% for O2 transport and 19.2% for power output). This effect dropped to 9.1% for O2 transport and 12% for power output in one-leg ergometry and was negligible for arm or arm plus shoulder work. It is argued that because of difficulty in perfusing small muscles, arm work is limited largely by the intrinsic power of the active muscles, that single-leg ergometry is limited rather equally by central circulatory and muscular factors, and that two-leg ergometry is almost entirely dependent on the central circulatory transport of O2.     

Effects of industrial respirators on breathing pattern at different work levels

The effects of a filtering device and an air-line apparatus on breathing pattern were studied in healthy men with different physical characteristics and work capacity. The subjects comprised nine construction workers aged 35-44, and nine firemen aged 21-35. The construction workers' mean maximal oxygen consumption (VO2max) was 34.5 ml min-1 kg-1, the firemen's 66.9 ml min-1 kg-1. Breathing pattern was analyzed for its components, inspiratory time, expiratory time, breathing frequency, tidal volume, and pulmonary ventilation at rest, during two submaximal treadmill walks when the subjects' absolute work load was equal, and during recovery. Neither the filtering device nor the air-line apparatus had a significant effect on breathing pattern when compared with the control values measured twice with a low-resistance breathing valve. A significantly longer expiratory time, lower breathing frequency, and smaller pulmonary ventilation were found for the firemen with the breathing valve and the industrial respirators. The breathing pattern of the construction workers and the firemen differed, but the alterations were not induced by the use of the filtering device or the air-line apparatus when studied at aerobic work levels up to 60% VO2max.