The effect of inspired oxygen concentration on the ventilation-perfusion distribution in inhomogeneous lungs

The coupled conservation of mass equations for oxygen, carbon dioxide and nitrogen are written down for a lung model consisting of two homogeneous alveolar compartments (with different ventilation-perfusion ratios) and a shunt compartment. As inspired oxygen concentration and oxygen consumption are varied, the flux of oxygen, carbon dioxide and nitrogen across the alveolar membrane in each compartment varies. The result of this is that the expired ventilation-perfusion ratio for each compartment becomes a function of inspired oxygen concentration and oxygen consumption as well as parameters such as inspired ventilation and alveolar perfusion. Another result is that the "inspired ventilation-perfusion ratio and the "expired ventilation-perfusion ratio differ significantly, under some conditions, for poorly ventilated lung compartments. As a consequence, we need to distinguish between the "inspired ventilation-perfusion distribution, which is independent of inspired oxygen concentration and oxygen consumption, and the "expired ventilation-perfusion distribution, which we now show to be strongly dependent on inspired oxygen concentration and less dependent oxygen consumption. Since the multiple inert gas elimination technique (MIGET) estimates the "expired ventilation-perfusion distribution, it follows that the distribution recovered by MIGET may be strongly dependent on inspired oxygen concentration.     

Characterizing airway and alveolar nitric oxide exchange during tidal breathing using a three-compartment model.

Exhaled nitric oxide (NO) may be a useful marker of lung inflammation, but the concentration is highly dependent on exhalation flow rate due to a significant airway source. Current methods for partitioning pulmonary NO gas exchange into airway and alveolar regions utilize multiple exhalation flow rates or a single-breath maneuver with a preexpiratory breath hold, which is cumbersome for children and individuals with compromised lung function. Analysis of tidal breathing data has the potential to overcome these limitations, while still identifying region-specific parameters. In six healthy adults, we utilized a three-compartment model (two airway compartments and one alveolar compartment) to identify two potential flow-independent parameters that represent the average volumetric airway flux (pl/s) and the time-averaged alveolar concentration (parts/billion). Significant background noise and distortion of the signal from the sampling system were compensated for by using a Gaussian wavelet filter and a series of convolution integrals. Mean values for average volumetric airway flux and time-averaged alveolar concentration were 2,500 +/- 2,700 pl/s and 3.2 +/- 3.4 parts/billion, respectively, and were strongly correlated with analogous parameters determined from vital capacity breathing maneuvers. Analysis of multiple tidal breaths significantly reduced the standard error of the parameter estimates relative to the single-breath technique. Our initial assessment demonstrates the potential of utilizing tidal breathing for noninvasive characterization of pulmonary NO exchange dynamics.     

Effect of airway closure on ventilation distribution

We examined the effect of airway closure on ventilation distribution during tidal breathing in six normal subjects. Each subject performed multiple-breath N2 washouts (MBNW) at tidal volumes of 1 liter over a range of preinspiratory lung volumes (PILV) from functional residual capacity (FRC) to just above residual volume. All subjects performed washouts at PILV below their measured closing capacity. In addition five of the subjects performed MBNW at PILV below closing capacity with end-inspiratory breath holds of 2 or 5 s. We measured the following two independent indexes of ventilation maldistribution: 1) the normalized phase III slope of the final breaths of the washout (Snf) and 2) the alveolar mixing efficiency of those breaths of the washout where 80-90% of the initial N2 had been cleared. Between a mean PILV of 0.28 liter above closing capacity and that 0.31 liter below closing capacity, mean Snf increased by 132% (P less than 0.005). Over the same volume range, mean alveolar mixing efficiency decreased by 3.3% (P less than 0.05). Breath holding at PILV below closing capacity resulted in marked and consistent decreases in Snf and increases in alveolar mixing efficiency. Whereas inhomogeneity of ventilation decreases with lung volume when all airways are patent (J. Appl. Physiol. 66: 2502-2510, 1989), airway closure increases ventilation inequality, and this is substantially reduced by short end-inspiratory breath holds. These findings suggest that the predominant determinant of ventilation distribution below closing capacity is the inhomogeneous closure of airways subtending regions in the lung periphery that are close together.     

Human variation in the peripheral air-space deposition of inhaled particles

Intersubject variability in both peripheral air-space dimensions and breathing pattern [tidal volume (VT) and respiratory frequency (f)] may play a role in determining intersubject variation in the fractional deposition of inhaled particles that primarily deposit in the lung periphery (i.e., distal to conducting airways). In healthy subjects breathing spontaneously at rest, we measured the deposition fraction (DF) of a 2.6-microns monodisperse aerosol by Tyndallometry while simultaneous measurement of VT and f were made. Under these conditions particle deposition occurs primarily in the peripheral air spaces of the lung. As an index of peripheral air-space size, we used measurements of aerosol recovery (RC) as a function of breath-hold time (t) (Gebhart et al. J. Appl. Physiol. 51: 465-476, 1981). In each subject, we measured RC (aerosol expired/aerosol inspired) of a 1.0-micron monodisperse aerosol as a function of breath-hold time for inspiratory capacity breaths of aerosol. The half time (t1/2) (the breath-hold time to reach 50% RC with no breath hold) is proportional to a mean diameter (D) of air spaces filled with aerosol. In the 10 subjects studied, we found a variable DF, range 0.04-0.44 [0.25 +/- 0.12 (SD)]. DF correlated most closely with 1/f, or the period of breathing (r = 0.96, P less than 0.01). There was no significant correlation between DF and t1/2 as an index of peripheral air-space size. In fact there was little deviation in t1/2 in these normal subjects [coefficient of variation (CV) = 0.12].(ABSTRACT TRUNCATED AT 250 WORDS)     

Alveolar pressure inhomogeneity during low-frequency oscillation of excised canine lobes

To quantify the inhomogeneity of alveolar pressures (PA) during cyclic changes in lung volume similar to those present during spontaneous breathing, inhomogeneity of PA was measured with an alveolar capsule technique in six excised canine lungs. The lungs were ventilated by a quasi-sinusoidal pump with a constant end-expiratory lung volume and tidal volumes of 10, 20, and 40% of vital capacity at breathing frequencies ranging from 5 to 45 breaths/min. Inhomogeneity of PA was quantified as the sample standard deviation of pressures measured in three capsules. A component of inhomogeneity in phase with flow and a smaller component out of phase with flow were present. The in-phase component increased approximately linearly with flow. The ratio of inhomogeneity to flow was smaller at large tidal volumes and, at the two higher tidal volumes studied, the ratio was greater during inspiration than during expiration. If these data are interpreted in terms of a simple circuit model, this degree of inhomogeneity implies an approximately twofold variation in regional time constants. Despite these considerable differences in time constants, the absolute amount of inhomogeneity as defined by the sample standard deviation of the three PA's was small (maximum 0.57 +/- 0.32 cmH2O at the highest breathing frequency and tidal volume) because airway resistance in the canine lung was small.     

Nonhomogeneity of lung response to inhaled histamine assessed with alveolar capsules

To assess the homogeneity of airway responses to inhaled histamine we examined regional alveolar pressure excursions (PA) arising from small-amplitude oscillations applied at the airway opening (Pao). In five anesthetized and vagotomized dogs the sternum was split and the anterior right lung field exposed. PA was sampled using four capsules affixed to the right apical and middle lobes while lung impedance (ZL) and airway impedances (Zaw) were measured during conventional tidal breathing and during forced oscillations (2-60 HZ at 10 cmH2O distending pressure). During tidal breathing after exposure to aerosol histamine regional PA's could be separated into three groups by plotting Lissajous figures of PA vs. Pao: PA in phase with Pao (no looping), PA lagging Pao (moderate looping), and PA decreasing while Pao was increasing and vice versa (paradoxical looping), suggesting unresponsive, responsive, and closed pathways, respectively, between the airway opening and specific alveolar zones. During high-frequency oscillation the corresponding PA spectra were markedly different from control spectra and revealed resonant amplification, overdamped resonance, and marked attenuation, respectively. With induced bronchospasm resonant amplification of PA was damped on average. However, the more obstructed and closed pathways were protected from resonant amplification, and the more open (nonlooping) pathways were subjected to resonant amplification greater than in the control state. In spite of this markedly nonhomogeneous behavior, frequency dependence of ZL was consistent with the model by Mead (J. Appl. Physiol. 26: 670-673, 1969), which ignores nonhomogeneity of peripheral compartments. These data demonstrate that the response of airways to inhaled histamine is nonhomogeneous but that frequency dependence of ZL above 2 Hz is not sufficient to characterize this nonhomogeneity.     

Significance of airway resistance for the pattern of breathing and lung volumes in exercising humans

The effects of increased airway resistance on lung volumes and pattern of breathing were studied in eight subjects performing leg exercise on a cycle ergometer. Airway resistance was changed 1) by increasing the density (D) of the respired gas by a factor of 4.2 and changing the inspired gas from O2 at 1.3 bar to air at 6 bar and 2) by increasing airway flow rates by exposing the subjects to incremental work loads of 0-200 W. Increased gas D caused a slower and deeper respiration at rest and during exercise and, at work loads greater than 120 W, depressed the responses of ventilation and mean inspiratory flow. Raised airway resistance induced by increases in D and/or airway flow rates altered respiratory timing by increasing the ratio of inspiratory time (TI) to total breath duration. Furthermore, analyses of the relationships between tidal volume and TI and between end-inspiratory volume and TI revealed elevation of Hering-Breuer inspiratory volume thresholds. We propose that this elevation, and hence exercise-induced increases of tidal volume, can largely be explained by previous observations that the threshold of the inspiratory off-switch mechanisms depends on central inspiratory activity (cf. C. von Euler, J. Appl. Physiol. 55: 1647-1659, 1983), which in turn increases with airway resistance (Acta Physiol. Scand. 120: 557-565, 1984).     

Partitioning of pulmonary resistance in dogs: effect of tidal volume and frequency

To determine the sensitivity of pulmonary resistance (RL) to changes in breathing frequency and tidal volume, we measured RL in intact anesthetized dogs over a range of breathing frequencies and tidal volumes centering around those encountered during quiet breathing. To investigate mechanisms responsible for changes in RL, the relative contribution of airway resistance (Raw) and tissue resistance (Rti) to RL at similar breathing frequencies and tidal volumes was studied in six excised, exsanguinated canine left lungs. Lung volume was sinusoidally varied, with tidal volumes of 10, 20, and 40% of vital capacity. Pressures were measured at three alveolar sites (PA) with alveolar capsules and at the airway opening (Pao). Measurements were made during oscillation at five frequencies between 5 and 45 min-1 at each tidal volume. Resistances were calculated by assuming a linear equation of motion and submitting lung volume, flow, Pao, and PA to a multiple linear regression. RL decreased with increasing frequency and decreased with increasing tidal volume in both isolated and intact lungs. In isolated lungs, Rti decreased with increasing frequency but was independent of tidal volume. Raw was independent of frequency but decreased with tidal volume. The contribution of Rti to RL ranged from 93 +/- 4% (SD) with low frequency and large tidal volume to 41 +/- 24% at high frequency and small tidal volume. We conclude that the RL is highly dependent on breathing frequency and less dependent on tidal volume during conditions similar to quiet breathing and that these findings are explained by changes in the relative contributions of Raw and Rti to RL.     

Effect of volume history on changes in DLcoSB-3EQ with lung volume in normal subjects.

The purpose of this study was to determine the relationship between the three-equation diffusing capacity for carbon monoxide (DLcoSB-3EQ) and lung volume and to determine how this relationship was altered when maneuvers were immediately preceded by a deep breath. DLcoSB-3EQ maneuvers were performed in nine healthy subjects either immediately after a deep breath or after tidal breathing for 10 min. The maneuvers consisted of slow inhalation of test gas from functional residual capacity to 25, 50, 75, or 100% of the inspiratory capacity and, without breath holding, slow exhalation to residual volume. After either a deep breath or tidal breathing, we found that DLcoSB-3EQ decreased nonlinearly with decreasing lung volume. At all lung volumes, DLcoSB-3EQ was significantly greater when measured after a deep breath than after tidal breathing. This effect increased as lung volume decreased, so that the greatest difference between DLcoSB-3EQ after a deep breath and that after tidal breathing occurred at the lowest lung volume. We conclude that a deep breath or spontaneous sigh has a role in reestablishing the pathway for gas exchange during tidal breathing.     

Flow-independent nitric oxide exchange parameters in healthy adults.

Currently accepted techniques utilize the plateau concentration of nitric oxide (NO) at a constant exhalation flow rate to characterize NO exchange, which cannot sufficiently distinguish airway and alveolar sources. Using nonlinear least squares regression and a two-compartment model, we recently described a new technique (Tsoukias et al. J Appl Physiol 91: 477-487, 2001), which utilizes a preexpiratory breath hold followed by a decreasing flow rate maneuver, to estimate three flow-independent NO parameters: maximum flux of NO from the airways (J(NO,max), pl/s), diffusing capacity of NO in the airways (D(NO,air), pl x s(-1) x ppb(-1)), and steady-state alveolar concentration (C(alv,ss), ppb). In healthy adults (n = 10), the optimal breath-hold time was 20 s, and the mean (95% intramaneuver, intrasubject, and intrapopulation confidence interval) J(NO,max), D(NO,air), and C(alv,ss) are 640 (26, 20, and 15%) pl/s, 4.2 (168, 87, and 37%) pl x s(-1) x ppb(-1), and 2.5 (81, 59, and 21%) ppb, respectively. J(NO,max) can be estimated with the greatest certainty, and the variability of all the parameters within the population of healthy adults is significant. There is no correlation between the flow-independent NO parameters and forced vital capacity or the ratio of forced expiratory volume in 1 s to forced vital capacity. With the use of these parameters, the two-compartment model can accurately predict experimentally measured plateau NO concentrations at a constant flow rate. We conclude that this new technique is simple to perform and can simultaneously characterize airway and alveolar NO exchange in healthy adults with the use of a single breathing maneuver.     

Breath-by-breath alveolar gas exchange

A method is described for breath-by-breath measurement of alveolar gas exchange corrected for changes of lung gas stores. In practice, the subject inspires from a spirometer, and each expired tidal volume is collected into a rubber bag placed inside a rigid box connected to the same spirometer. During the inspiration following any given expiration the bag is emptied by a vacuum pump. A computer monitors inspiratory and expiratory tidal volumes, drives four solenoid valves allowing appropriate operation of the system, and memorizes end-tidal gas fractions as well as mixed expired gas composition analyzed by mass spectrometer. Thus all variables for calculating alveolar gas exchange, based on the theory developed by Auchincloss et al. (J. Appl. Physiol. 21: 810-818, 1966), are obtained on a single-breath basis. Mean resting and steady-state exercise gas exchange data are equal to those obtained by conventional open-circuit measurements. Breathing rates up to 30 X min-1 can be followed. The breath-to-breath variability of O2 uptake at the alveolar level is less (25-35%) than that measured at the mouth as the difference between the inspired and expired volumes, both at rest and during exercise up to 0.7 of maximum O2 consumption.     

Breath-by-breath measurement of the volume displaced by diaphragm motion.

To develop an accurate method to measure the volume displaced by diaphragm motion (DeltaVdi) breath by breath, we compared DeltaVdi measured by a previously evaluated biplanar radiographic method (Singh B, Eastwood PR, and Finucane KE. J Appl Physiol 91: 1913-1923, 2001) at several lung volumes during vital capacity inspirations in 10 healthy and nine hyperinflated subjects with 1) DeltaVdi measured from the same chest X-rays by two previously described uniplanar methods (Petroll WM, Knight H, and Rochester DF. J Appl Physiol 69: 2175-2182, 1990; Verschakelen JA, Deschepper K, and Demendts M. J Appl Physiol 72: 1536-1540, 1992) and a proposed method that considered actual cross-sectional shape of the rib cage and spinal volume (DeltaVdi(S)); and 2) DeltaVdi(S) measured by lateral fluoroscopy in the same 10 healthy subjects. Relative to biplanar DeltaVdi, DeltaVdi(S) values from lateral chest X-rays and fluoroscopy were not different, whereas DeltaVdi values of Petroll et al. and Verschakelen et al. were increased by (means +/- SD) 1.98 +/- 1.59 and 1.16 +/- 0.82 liters, respectively (both P < 0.001). During quiet breathing, DeltaVdi(S) by lateral fluoroscopy was 66 +/- 16% of tidal volume and similar to that between functional residual capacity and one-half inspiratory capacity by the biplanar radiographic method. We conclude that accurate breath-by-breath measurements of DeltaVdi can be made by using lateral fluoroscopy.     

Micron-sized intrapulmonary particle deposition in the developing rat lung

Little is known about the effects of postnatal developmental changes in lung architecture and breathing patterns on intrapulmonary particle deposition. We measured deposition in the developing Wistar-Kyoto rat, whose lung development largely parallels that of humans. Deposition of 2-μm sebacate particles was determined in anesthetized, intubated, spontaneously breathing rats on postnatal days (P) 7 to 90 by aerosol photometry (Karrasch S, Eder G, Bolle I, Tsuda A, Schulz H. J Appl Physiol 107: 1293-1299, 2009). Respiratory parameters were determined by body plethysmography. Tidal volume increased substantially from P7 (0.19 ml) to P90 (2.1 ml) while respiratory rate declined from 182 to 107/min. Breath-specific deposition was lowest (9%) at P7 and P90 and markedly higher at P35 (almost 16%). Structural changes of the alveolar region include a ninefold increase in surface area (Bolle I, Eder G, Takenaka S, Ganguly K, Karrasch S, Zeller C, Neuner M, Kreyling WG, Tsuda A, Schulz H. J Appl Physiol 104: 1167-1176, 2008). Particle deposition per unit of time and surface area peaked at P35 and showed a minimum at P90. At an inhaled particle number concentration of 10(5)/cm(3), there was an estimated 450, 690, and 330 particles/(min × cm(2)) at P7, P35, and P90, respectively. Multiple regression models showed that deposition depends on the mean linear intercept as structural component and the breathing parameters, tidal volume, and respiratory rate (r(2) > 0.9). In conclusion, micron-sized particle deposition was dependent on the stage of postnatal lung development. A maximum was observed during late alveolarization (P35), which corresponds to human lungs of about eight years of age. Children at this age may therefore be more susceptible to micron-sized airborne environmental health hazards.     

Alveolar dead space does not affect indirect Fick cardiac output determinations

We examined the influence of three variables (different breathing circuits, breath selected for analysis, and alveolar dead space ventilation) on the accuracy of noninvasive cardiac output determinations with the Fick CO2 (indirect) equation. We compared noninvasive determinations with invasive thermodilution measurements over a wide range of cardiac outputs in 17 2-mo-old pigs anesthetized with halothane and nitrous oxide and paralyzed with either pancuronium or d-tubocurare. We found that rebreathing and nonrebreathing circuits provide accurate cardiac output determinations and that the optimal breath for analysis with either the rebreathing or nonrebreathing technique appears to depend on the cardiac output. When alveolar dead space was increased by using positional changes and the intracardiac administration of glass beads, there was still a good correlation between noninvasive and invasive cardiac output determinations. We conclude that both rebreathing and nonrebreathing techniques of indirect Fick cardiac output determinations correlate well with thermodilution measures over a wide range of cardiac outputs and alveolar dead space/tidal volume fractions.     

Analysis of diaphragm movement during tidal breathing and during its activation while breath holding using MRI synchronized with spirometry

Using magnetic resonance imaging (MRI) in conjunction with synchronized spirometry we analyzed and compared diaphragm movement during tidal breathing and voluntary movement of the diaphragm while breath holding. Breathing cycles of 16 healthy subjects were examined using a dynamic sequence (77 slices in sagittal plane during 20 s, 1NSA, 240x256, TR4.48, TE2.24, FA90, TSE1, FOV 328). The amplitude of movement of the apex and dorsal costophrenic angle of the diaphragm were measured for two test conditions: tidal breathing and voluntary breath holding. The maximal inferior and superior positions of the diaphragm were subtracted from the corresponding positions during voluntary movements while breath holding. The average amplitude of inferio-superior movement of the diaphragm apex during tidal breathing was 27.3+/-10.2 mm (mean +/- SD), and during voluntary movement while breath holding was 32.5+/-16.2 mm. Movement of the costophrenic angle was 39+/-17.6 mm during tidal breathing and 45.5+/-21.2 mm during voluntary movement while breath holding. The inferior position of the diaphragm was lower in 11 of 16 subjects (68.75 %) and identical in 2 of 16 (12.5 %) subjects during voluntary movement compared to the breath holding. Pearson's correlation coefficient was used to demonstrate that movement of the costophrenic angle and apex of the diaphragm had a linear relationship in both examined situations (r=0.876). A correlation was found between the amplitude of diaphragm movement during tidal breathing and lung volume (r=0.876). The amplitude of movement of the diaphragm with or without breathing showed no correlation to each other (r=0.074). The movement during tidal breathing shows a correlation with the changes in lung volumes. Dynamic MRI demonstrated that individuals are capable of moving their diaphragm voluntarily, but the amplitude of movement differs from person to person. In this study, the movements of the diaphragm apex and the costophrenic angle were synchronous during voluntary movement of the diaphragm while breath holding. Although the sample is small, this study confirms that the function of the diaphragm is not only respiratory but also postural and can be voluntarily controlled.     

Effects of inspired CO2, hyperventilation, and time on VA/Q inequality in the dog.

In a recent study by Tsukimoto et al. (J. Appl. Physiol. 68: 2488-2493, 1990), CO2 inhalation appeared to reduce the size of the high ventilation-perfusion ratio (VA/Q) mode commonly observed in anesthetized mechanically air-ventilated dogs. In that study, large tidal volumes (VT) were used during CO2 inhalation to preserve normocapnia. To separate the influences of CO2 and high VT on the VA/Q distribution in the present study, we examined the effect of inspired CO2 on the high VA/Q mode using eight mechanically ventilated dogs (4 given CO2, 4 controls). The VA/Q distribution was measured first with normal VT and then with increased VT. In the CO2 group at high VT, data were collected before, during, and after CO2 inhalation. With normal VT, there was no difference in the size of the high VA/Q mode between groups [10.5 +/- 3.5% (SE) of ventilation in the CO2 group, 11.8 +/- 5.2% in the control group]. Unexpectedly, the size of the high VA/Q mode decreased similarly in both groups over time, independently of the inspired PCO2, at a rate similar to the fall in cardiac output over time. The reduction in the high VA/Q mode together with a simultaneous increase in alveolar dead space (estimated by the difference between inert gas dead space and Fowler dead space) suggests that poorly perfused high VA/Q areas became unperfused over time. A possible mechanism is that elevated alveolar pressure and decreased cardiac output eliminate blood flow from corner vessels in nondependent high VA/Q regions.     

A model for determining alveolar and small airway dimensions from aerosol recovery data

A mathematical model is presented that allows the determination of alveolar and small airway dimensions from a series of aerosol recovery measurements performed at different inspiration volumes. The model assumes 1) a symmetric dichotomous lung, 2) representation of airway and alveoli as ensembles of straight tubes, and 3) Gaussian dispersion of the aerosol bolus. Calculations with this model using dimensions given by Weibel show general agreement with experimental data on six human subjects obtained by Palmes et al. (J. Appl. Physiol. 34: 356-360, 1973). Close agreement is found by varying two parameters describing alveolar size and airway size to obtain the best fit. The resulting estimates of size are almost independent of the choice of the dispersion coefficient; however, the estimate of alveolar size is quite dependent on the form of settling assumed during breath holding. The values of alveolar diameter in the six subjects, determined under the assumption of stirred settling, ranged from 0.13 to 0.33 mm, whereas under the assumption of still settling the range was 0.24-0.65 mm. Small airway (generations 18-24) dimensions ranged from 0.41 to 0.66 mm under the still-settling assumption and 0.39 to 0.63 mm under the stirred-settling assumption. With the assumption of an intermediate (partially stirred) form of settling, the alveolar diameter in the six subjects is 0.28 +/- 0.02 mm, in close agreement with morphometric measurements by other investigators. A partially stirred form of settling is also consistent with model predictions of recovery vs. breath-holding time and with cardiogenic gas mixing in the lung.     

A Simple Dynamic Model of Respiratory Pump

To study the interaction of forces that produce chest wall motion, we propose a model based on the lever system of Hillman and Finucane (J Appl Physiol 63(3):951–961, 1987) and introduce some dynamic properties of the respiratory system. The passive elements (rib cage and abdomen) are considered as elastic compartments linked to the open air via a resistive tube, an image of airways. The respiratory muscles (active) force is applied to both compartments. Parameters of the model are identified in using experimental data of airflow signal measured by pneumotachography and rib cage and abdomen signals measured by respiratory inductive plethysmography on eleven healthy volunteers in five conditions: at rest and with four level of added loads. A breath by breath analysis showed, whatever the individual and the condition are, that there are several breaths on which the airflow simulated by our model is well fitted to the airflow measured by pneumotachography as estimated by a determination coefficient R ² ≥ 0.70. This very simple model may well represent the behaviour of the chest wall and thus may be useful to interpret the relative motion of rib cage and abdomen during quiet breathing.