Models of the pressure-volume relationship of the human lung

Modeling the influence of gravity and the mechanical properties of elastin and collagen fibers on alveolar and lung pressure-volume curves

The relationship between pressure (P) and volume (V) in the human lung has been extensively studied. However, the combined effects of gravity and the mechanical properties of elastin and collagen on alveolar and lung P-V curves during breathing are not well understood. Here, we extended a previously established thick-walled spherical model of a single alveolus with wavy collagen fibers during positive pressure inflation. First, we updated the model for negative pressure-driven inflation that allowed incorporation of a gravity-induced pleural pressure gradient to predict how the static alveolar P-V relations vary spatially throughout an upright human lung. Second, by introducing dynamic surface tension and collagen viscoelasticity, we computed the hysteresis loop of the lung P-V curve. The model was tested by comparing its predicted regional ventilation to literature data, which offered insight into the effects of microgravity on ventilation. The model has also produced novel testable predictions for future experiments about the variation of mechanical stresses in the septal walls and the contribution of collagen and elastin fibers to the P-V curve and throughout the lung. The model may help us better understand how mechanical stresses arising from breathing and pleural pressure variations affect regional cellular mechanotransduction in the lung.

Airway occlusion assessed by single breath N2 test and lung P-V curve in healthy subjects and COPD patients

PURPOSE

To determine whether the analysis of the slow expiratory transpulmonary pressure-volume (P_L-V) curve provides an alternative to the single-breath nitrogen test (SBN) for the assessment of the closing volume (CV).

METHODS

SBN test and slow deflation P_L-V curve were simultaneously recorded in 40 healthy subjects and 43 COPD patients. Onset of phase IV identified CV in SBN test (CV_SBN), whereas in the P_L-V curve CV was identified by: a) deviation from the exponential fit (CV_exp), and b) inflection point of the interpolating sigmoid function (CV_sig).

RESULTS

In the absence of phase IV, COPD patients exhibited a clearly discernible inflection in the P_L-V curve. In the presence of phase IV, CV_SBN and CV_exp coincided (CV_SBN/CV_exp=1.04±0.04 SD), whereas CV_sig was systematically larger (CV_sig/CV_exp=2.1±0.86).

CONCLUSION

The coincidence between CV_SBN and CV_exp, and the presence of the inflection in the absence of phase IV indicate that the deviation of the P_L-V curve from the exponential fit reliably assesses CV.

Effects of superimposed tissue weight on regional compliance of injured lungs

Computed tomography (CT), together with image analysis technologies, enable the construction of regional volume (VREG) and local transpulmonary pressure (PTP,REG) maps of the lung. Purpose of this study is to assess the distribution of VREG vs PTP,REG along the gravitational axis in healthy (HL) and experimental acute lung injury conditions (eALI) at various positive end-expiratory pressures (PEEPs) and inflation volumes. Mechanically ventilated pigs underwent inspiratory hold maneuvers at increasing volumes simultaneously with lung CT scans. eALI was induced via the iv administration of oleic acid. We computed voxel-level VREG vs PTP,REG curves into eleven isogravitational planes by applying polynomial regressions. Via F-test, we determined that VREG vs PTP,REG curves derived from different anatomical planes (p-values<1.4E-3), exposed to different PEEPs (p-values<1.5E-5) or subtending different lung status (p-values<3E-3) were statistically different (except for two cases of adjacent planes). Lung parenchyma exhibits different elastic behaviors based on its position and the density of superimposed tissue which can increase during lung injury.

Relating indices of inert gas washout to localised bronchoconstriction

Asthma is typically characterised by increased ventilation heterogeneity. This can be directly inferred from the visualisation of ventilation defects in imaging studies, or indirectly inferred from indices derived from the multiple-breath nitrogen washout (MBNW). The basis for the understanding of the MBNW indices and their implication for changes in structure and function at the largest and smallest scales in the lung has been facilitated by mathematical models for inert gas transport. A new model is presented that couples airway resistance and regional tissue compliance, for simulation of the effect of 'patchy' bronchoconstriction - as inferred from imaging studies - on the Scond index of ventilation heterogeneity. Patches of reduced washin gas concentration can emerge by constricting only the terminal bronchioles within localised regions, however this pattern of constriction is insufficient to affect Scond; Scond from this model is only sensitive to constriction that occurs within entire contiguous regions. Furthermore the model illustrates the possibility that the MBNW may not detect gas trapped in ventilation defects.

Mechanics of the lung in the 20th century

Major advances in respiratory mechanics occurred primarily in the latter half of the 20th century, and this is when much of our current understanding was secured. The earliest and ancient investigations involving respiratory physiology and mechanics were frequently done in conjunction with other scientific activities and often lacked the ability to make quantitative measurements. This situation changed rapidly in the 20th century, and this relatively recent history of lung mechanics has been greatly influenced by critical technological advances and applications, which have made quantitative experimental testing of ideas possible. From the spirometer of Hutchinson, to the pneumotachograph of Fleisch, to the measurement of esophageal pressure, to the use of the Wilhelmy balance by Clements, and to the unassuming strain gauges for measuring pressure and rapid paper and electronic chart recorders, these enabling devices have generated numerous quantitative experimental studies with greatly increased physiologic understanding and validation of mechanistic theories of lung function in health and disease.

Lung regional stress and strain as a function of posture and ventilatory mode

During positive-pressure ventilation parenchymal deformation can be assessed as strain (volume increase above functional residual capacity) in response to stress (transpulmonary pressure). The aim of this study was to explore the relationship between stress and strain on the regional level using computed tomography in anesthetized healthy pigs in two postures and two patterns of breathing. Airway opening and esophageal pressures were used to calculate stress; change of gas content as assessed from computed tomography was used to calculate strain. Static stress-strain curves and dynamic strain-time curves were constructed, the latter during the inspiratory phase of volume and pressure-controlled ventilation, both in supine and prone position. The lung was divided into nondependent, intermediate, dependent, and central regions: their curves were modeled by exponential regression and examined for statistically significant differences. In all the examined regions, there were strong but different exponential relations between stress and strain. During mechanical ventilation, the end-inspiratory strain was higher in the dependent than in the nondependent regions. No differences between volume- and pressure-controlled ventilation were found. However, during volume control ventilation, prone positioning decreased the end-inspiratory strain of dependent regions and increased it in nondependent regions, resulting in reduced strain gradient. Strain is inhomogeneously distributed within the healthy lung. Prone positioning attenuates differences between dependent and nondependent regions. The regional effects of ventilatory mode and body positioning should be further explored in patients with acute lung injury.

Non lineal respiratory systems mechanics simulation of acute respiratory distress syndrome during mechanical ventilation

Model and simulation of biological systems help to better understand these systems. In ICUs patients often reach a complex situation where supportive maneuvers require special expertise. Among them, mechanical ventilation in patients suffering from acuter respiratory distress syndrome (ARDS) is specially challenging. This work presents a model which can be simulated and use to help in training of physicians and respiratory therapists to analyze the respiratory mechanics in this kind of patients. We validated the model in 2 ARDS patients.

Simulation of pulmonary pathophysiology during spontaneous breathing

This paper presents a functional model of lung mechanics including a non-linear alveolar pressure volume curve and representation of the work of respiratory muscles during breathing. The model is used to simulate the response to forced inspiration and expiration, and these simulations compared to the standard results of lung function tests routinely performed in departments of lung medicine. The model can simulate the characteristics of inspiratory and expiratory flow profiles seen in normal subjects, and in patients with obstructive or restrictive diseases.

Respiratory System Model for Quasistatic Pulmonary Pressure-Volume (P-V) Curve: Inflation-Deflation Loop Analyses

A respiratory system model (RSM) is developed for the deflation process of a quasistatic pressure-volume (P-V) curve, following the model for the inflation process reported earlier. In the RSM of both the inflation and the deflation limb, a respiratory system consists of a large population of basic alveolar elements, each consisting of a piston-spring-cylinder subsystem. A normal distribution of the basic elements is derived from Boltzmann statistical model with the alveolar closing (opening) pressure as the distribution parameter for the deflation (inflation) process. An error minimization by the method of least squares applied to existing P-V loop data from two different data sources confirms that a simultaneous inflation-deflation analysis is required for an accurate determination of RSM parameters. Commonly used terms such as lower inflection point, upper inflection point, and compliance are examined based on the P-V equations, on the distribution function, as well as on the geometric and physical properties of the basic alveolar element.

Computer simulation of human breath-hold diving: cardiovascular adjustments

The world record for a sled-assisted human breath-hold dive has surpassed 200 m. Lung compression during descent draws blood from the peripheral circulation into the thorax causing engorgement of pulmonary vessels that might impose a physiological limitation due to capillary stress failure. A computer model was developed to investigate cardiopulmonary interactions during immersion, apnea, and compression to elucidate hemodynamic responses and estimate vascular stresses in deep human breath-hold diving. The model simulates active and passive cardiovascular adjustments involving blood volumes, flows, and pressures during apnea at diving depths up to 200 m. Redistribution of blood volume from peripheral to central compartments increases with depth. Pulmonary capillary transmural pressures in the model exceed 50 mm Hg at record depth, producing stresses in the range known to cause alveolar capillary damage in animals. Capillary pressures are partially attenuated by blood redistribution to compliant extra-pulmonary vascular compartments. The capillary pressure differential is due mainly to a large drop in alveolar air pressure from outward elastic chest wall recoil. Autonomic diving reflexes are shown to influence systemic blood pressures, but have relatively little effect on pulmonary vascular pressures. Increases in pulmonary capillary stresses are gradual beyond record depth.

A Mechanistic Model for Quasistatic Pulmonary Pressure-Volume Curves for Inflation

A mechanistic model of the respiratory system is proposed to understand differences in quasistatic pressure-volume (p-V) curves of the inflation process in terms of the alveolar recruitment and the elastic distension of the wall tissues. In the model, a total respiratory system consists of a large number of elements, each of which is a subsystem of a cylindrical chamber fitted with a piston attached to a spring. The alveolar recruitment is simulated by allowing a distribution of the critical pressure at which an element opens; while the wall distension is represented by the piston displacement. Relations are derived between parameters in the error-function p-V model equation and properties of the mechanistic model. The parameters of the model-based p-V equation are determined for clinical data sets of patients with acute respiratory distress syndrome.

General characteristics of the sigmoidal model equation representing quasi-static pulmonary P-V curves

A pulmonary pressure-volume (P-V) curve represented by a sigmoidal model equation with four parameters, V(P) = a + b[1 + exp[-(P - c)/d]](-1), has been demonstrated to fit inflation and deflation data obtained under a variety of conditions extremely well. In the present report, a differential equation on V(P) is identified, thus relating the fourth parameter, d, to the difference between the upper and the lower asymptotes of the volume, b, through a proportionality constant, alpha, with its order of magnitude of 10(-4) to 10(-5) (in ml(-1). cmH(2)O(-1)). When the model equation is normalized using a nondimensional volume, (-1 < < 1), and a nondimensional pressure, (=(p/c) - 1), the resulting - curve depends on a single nondimensional parameter, Lambda = alphabc. A nondimensional work of expansion/compression, (1-2), is also obtained along the quasi-static sigmoidal P-V curve between an initial volume (at 1) and a final volume (at 2). Six sets of P-V data available in the literature are used to show the changes that occur in these two parameters (Lambda defining the shape of the sigmoidal curve and (1-2) accounting for the range of clinical data) with different conditions of the total respiratory system. The clinical usefulness of these parameters requires further study.

Effects of recruitment of collapsed lung units on the elastic pressure-volume relationship in anaesthetised healthy adults

BACKGROUND

The elastic pressure-volume (Pel-V) curve of the respiratory system can be used as a guide for improved ventilator management. The understanding of curves recorded for sick patients can be improved with better knowledge of the Pel-V relationship observed in healthy humans. Dynamic Pel-V curves were determined over an extended volume range in 15 anaesthetised and muscle-relaxed healthy humans. The influence of a recruitment manoeuvre was studied.

METHODS

Dynamic Pel-V curves were determined during a single prolonged insufflation before and after the recruitment manoeuvre. A mathematical three-segment model of the curve including a linear intermediate segment, delineated by the lower (LIP) and upper (UIP) inflection points, was used for characterisation of the recorded curves.

RESULTS

The model gave an adequate description of the recorded Pel-V curves. Before the recruitment manoeuvre, compliance increased until the LIP was reached at 20 cm H2O (1.9 L). Then followed a long linear segment. After the recruitment manoeuvre, compliance increased during insufflation until a LIP was reached at 13 cm H2O (1.2 L). Above the LIP followed a shorter linear segment (compliance = 140 mL/cm H2O) and then an upper segment with decreasing compliance.

CONCLUSION

Pel-V curves recorded before and after the recruitment manoeuvre show that large lung compartments close during anaesthesia and that high pressures are needed to achieve recruitment even in the normal lung. Accordingly, the LIP does not define the end of recruitment during insufflation.

A comprehensive equation for the pulmonary pressure-volume curve

Quantification of pulmonary pressure-volume (P-V) curves is often limited to calculation of specific compliance at a given pressure or the recoil pressure (P) at a given volume (V). These parameters can be substantially different depending on the arbitrary pressure or volume used in the comparison and may lead to erroneous conclusions. We evaluated a sigmoidal equation of the form, V = a + b[1 - e-(P-c)/d]-1, for its ability to characterize lung and respiratory system P-V curves obtained under a variety of conditions including normal and hypocapnic pneumoconstricted dog lungs (n = 9), oleic acid-induced acute respiratory distress syndrome (n = 2), and mechanically ventilated patients with acute respiratory distress syndrome (n = 10). In this equation, a corresponds to the V of a lower asymptote, b to the V difference between upper and lower asymptotes, c to the P at the true inflection point of the curve, and d to a width parameter proportional to the P range within which most of the V change occurs. The equation fitted equally well inflation and deflation limbs of P-V curves with a mean goodness-of-fit coefficient (R2) of 0.997 +/- 0.02 (SD). When the data from all analyzed P-V curves were normalized by the best-fit parameters and plotted as (V-a)/b vs. (P-c)/d, they collapsed into a single and tight relationship (R2 = 0.997). These results demonstrate that this sigmoidal equation can fit with excellent precision inflation and deflation P-V curves of normal lungs and of lungs with alveolar derecruitment and/or a region of gas trapping while yielding robust and physiologically useful parameters.

Respiratory mechanics in rabbits ventilated with different tidal volumes

Respiratory mechanics was studied in 11 rabbits at tidal volumes (VT) of 6.7, 10, and 20 ml/kg. Flow interruptions were performed during the full respiratory cycle. The viscoelastic pressure (Pve) was measured as the dynamic elastic pressure (Pel(dyn)) after flow cessation minus the static elastic pressure (Pel(st)). Static elastic and viscoelastic parameters were determined with numerical technique. Static hysteresis was minimal even at large VT. The Pel(st)-V curve was linear at small VT and in 6 animals at moderate VT. In 5 animals at moderate VT and in all animals at large VT, a linear segment with constant compliance was followed by a segment with decreasing compliance. The Pve-V curve could be described with a linear model only at small VT. A non-linear model was needed at increased VT. Compliance increased with VT. Both static and viscoelastic behaviours were linear up to larger volume ranges at large VT compared to moderate VT.

Computer-controlled mechanical lung model for application in pulmonary function studies

A computer controlled mechanical lung model has been developed for testing lung function equipment, validation of computer programs and simulation of impaired pulmonary mechanics. The construction, function and some applications are described. The physical model is constructed from two bellows and a pipe system representing the alveolar lung compartments of both lungs and airways, respectively. The bellows are surrounded by water simulating pleural and interstitial space. Volume changes of the bellows are accomplished via the fluid by a piston. The piston is driven by a servo-controlled electrical motor whose input is generated by a microcomputer. A wide range of breathing patterns can be simulated. The pipe system representing the trachea connects both bellows to the ambient air and is provided with exchangeable parts with known resistance. A compressible element (CE) can be inserted into the pipe system. The fluid-filled space around the CE is connected with the water compartment around the bellows; The CE is made from a stretched Penrose drain. The outlet of the pipe system can be interrupted at the command of an external microcomputer system. An automatic sequence of measurements can be programmed and is executed without the interaction of a technician.

Exponential analysis of the pressure-volume characteristics of ovine lungs

Static pressure-volume curves were generated from data obtained from 18 normal anaesthetized adult sheep. Lung volumes were determined by helium dilution. An exponential curve of the form V = Vmax - Ae-KP was fitted to the pressure-volume data from each sheep where P is the static recoil pressure, Vmax represents the volume asymptote, A is the difference between Vmax and the intercept on the volume axis and K defines the slope and hence the shape of the P-V curve. Quality of fit of the data was assessed visually, by means of a sign test and a runs test and by the coefficient of determination (r2). Exponential equations were found to adequately describe the shape of the pressure-volume curve in sheep. The exponent K was not correlated with effective alveolar volume (VAeff) (rs = 0.183; P > 0.05). Static lung compliance was determined over a volume range from the end-expiratory level (VEEL) to VEEL plus 400 ml. Measurements of static lung compliance were significantly correlated with measurements of effective alveolar volume (VAeff) (rs = 0.505; P < 0.025). In the ovine, the exponent K, an index of distensibility, is independent of lung volume and offers a means of assessing lung distensibility in this species.

Stress-strain characteristics of normal and emphysematous hamster lung strips

A simple mathematical model of the one dimensional, stress-strain behavior of hamster lung tissue based on strain energy considerations was tested in degassed, uniaxially stretched strips obtained from normal and emphysematous hamster lungs cycled in saline. The relationship between Eulerian stress (sigma) and extension ratio (lambda) was found to take the form sigma = (lambda 2-1/lambda) x f(lambda) where the function f(lambda) was experimentally determined. Stress in six normal and five emphysematous strips was calculated by dividing the tension at each stretch increment by the strip cross-sectional area. Plotting sigma lambda/(lambda 2-1) versus a function of the form e eta lambda yielded a linear expression for f(lambda), me eta lambda + b, where n = 2. The complete stress-strain behavior of hamster lung strip tissue could then be expressed as a simple function of lambda over a range of lambda = 1.0-2.0: sigma = (lambda 2-1/lambda)(me2 lambda+b) The values of the constants m and b depend solely upon the mechanical properties of the elastic and collagen fiber networks in these atelectatic, saline cycled lung strips. The slope m = 0.151, and the intercept b = 0.416 in normal strips (r = 0.98). In emphysematous strips m = 0.016 and b = -0.199 (r = 0.82). Given the smaller m found for emphysematous strips, less strain energy accumulated with increasing stretch and did not even begin in these strips until lambda = 1.3. Further, the fit of the equation to the data was not as good for emphysematous as for normal strips. We conclude that the above equation adequately describes the stress-strain properties of normal hamster lung strips tissue but is not as good in emphysematous strips where the disease is patchy.

Effects of positive end-expiratory pressure on alveolar recruitment and gas exchange in patients with the adult respiratory distress syndrome

The effects of different levels of positive end-expiratory pressure (PEEP) (zero to 15 cm H2O) on the static inflation volume-pressure (V-P) curve of the respiratory system and on gas exchange were studied in eight patients with the adult respiratory distress syndrome (ARDS). Alveolar recruitment with PEEP was quantified in terms of recruited volume, i.e., as difference in lung volume between PEEP and zero end-expiratory pressure (ZEEP) for the same static inflation pressure (20 cm H2O) from the V-P curves obtained at the different PEEP levels. In addition, static compliance of the respiratory system at fixed tidal volume (0.7 L) was determined at the different PEEP levels. The results suggest that: (1) in some patients with ARDS the V-P curves determined on ZEEP exhibit an upward concavity reflecting progressive alveolar recruitment with increasing inflation volume, and PEEP results in alveolar recruitment (range of recruited volume at 15 cm H2O of PEEP: 0.11 to 0.36 L); (2) in other patients with ARDS the V-P curves on ZEEP are characterized by an upward convexity, and PEEP results in a volume displacement along this curve without alveolar recruitment and with enhanced risk of barotrauma; (3) the PEEP-induced increase in arterial oxygenation is significantly correlated to the recruited volume but not to the changes in static compliance. The shape of the static inflation V-P curves on ZEEP allows the prediction of alveolar recruitment with PEEP.

Comparison of five methods of analyzing respiratory pressure-volume curves

Five methods of analyzing the deflation limb of respiratory pressure-volume (PV) curves obtained from seven groups of rats that had undergone various treatments were compared. The five methods utilized measurements of: y intercept and slope with simple exponential curve fitting; area under the curve; volumes at fixed pressures; shape constant, k, of the sigmoid curve described by Paiva et al. (Respir. Physiol. 23:317, 1975); and quasi-static compliance. The seven groups of rats were treated as follows: control (n = 10); high tar/nicotine cigarette smoke exposure (n = 10); low tar/nicotine cigarette smoke exposure (n = 9); intratracheal elastase (n = 10); intratracheal elastase plus sham smoke exposure (n = 10); intratracheal elastase plus high tar/nicotine cigarette smoke exposure (n = 9); and intratracheal elastase plus low tar/nicotine cigarette smoke exposure (n = 10). Elastase treatment caused a leftward and upward shift of the PV curve and this shift was augmented by exposure to either high tar/nicotine or low tar/nicotine cigarette smoke. Using Duncan's multiple range test, we found that the y-intercept measurement of method 1, the area under the curve, volumes at fixed pressures, and quasi-static compliance methods were better able to differentiate PV curves between groups than were the slope measurement of method 1 and the shape constant measurement of method 4.

Exponential analysis of the lung pressure-volume curve in newborn mammals

The compliance of the lung (per unit of lung weight) is less in newborn mammals than in adults. This could result from a smaller volume of airspaces per unit weight and/or a lower lung distensibility. The isolated role of lung distensibility was evaluated by using a mathematical description of the pressure-volume (P-V) curve during lung deflation. Deflation limbs of static P-V curves in newborns of six species (four experimentally obtained and two taken from the literature) ranging from total lung capacity to the resting volume (Vr) were fitted by a monoexponential function of the type V = B - Ae-KP, where B equals Vmax at infinite P, A equals the difference between Vmax and V at P = O, and K is a constant representing lung distensibility. Unlike in adults, in newborns the monoexponential fitting provided an adequate description of the P-V curve for only a relatively small range of transpulmonary pressure (from P at Vr to 10-15 cm H2O). The K value of this portion of the curve was similar among species but higher than in adult mammals, averaging 0.240 cm H2O-1. This suggests a similar lung structure in the different species. Since lung distensibility in newborns is larger than in adults, the fact that a unit mass of lung in the newborn is less compliant should be due to the smaller volume of its airspaces.

Analysis of the pressure-volume relationship of excised lungs

The pressure-volume relationship of excised lungs is explicitly defined in the form of a mathematical model. In the model, lung volume (V) is given by the function V = VmaxF(Ptp,T*)H(Ptp). Vmax is maximum lung volume. F, which describes the recruitment of air-filled units, is a function of transpulmonary pressure (Ptp) and surface tension (T*), whereas H, which is also a function of transpulmonary pressure, describes the expansion of recruited units against tissue forces. F is shown to be the integral of the normalized distribution function of the lung units and remains constant so long as the number of air-filled units does not change. H, on the other hand, is shown to be the product of the elastic properties of the tissues and is responsible for the characteristic non-linear sigmoid shape of lung deflation curves. Results obtained with the model are consistent with the hypothesis that tissue elasticity, tissue hysteresis, area dependent surface tension, and recruitment share responsibility for the characteristic hysteresis of excised lungs.

Elastic behavior of the lungs in healthy children determined by means of an exponential function

In order to evaluate the elastic properties of the lungs in children, a new exponential sigmoid curve fitting model was developed with the function VL = Vm + (Vm/1 + b X e-K X Pst), where VL is the lung volume, Pst the static recoil pressure, VM and Vm the upper and the lower asymptotes (limits of lung volume) and K and b are specific constants. Pressure-volume (PV) data obtained from tidal breathing cycles at different inflation and deflation levels from functional residual capacity (FRC) up to approximately 90% total lung capacity (TLC) in 16 healthy children have been evaluated by this model. K in relation to age, calculated by the least square nonlinear regression analysis decreased during childhood, whereas in b increased. It seems that K (a volume-independent index of compliance and alveolar distensibility) is influenced by the increasing number of elastic fiber bundles, changes in the surface/volume ratio and finally by changes in the composition of the surfactant. It can be seen that this model is not only restricted to higher lung volumes, the lower limb of the S-shaped curve is also represented.

Effects of unequal pressure swings and different waveforms on distribution of ventilation: a non-linear model simulation

In an attempt to understand the role of unequal pleural pressure swings and of different waveforms of pleural pressure variation in the distribution of ventilation during cyclic breathing, a mathematical model simulation was performed. The computer model which incorporates non-linear resistances and compliances as well as sinusoidal, square, and triangular waveforms of pleural pressure variations indicates that the distribution of ventilation is insensitive to the waveform of the pleural pressure. The distribution is also little changed by the depth of breathing (amplitude), but it is affected significantly by the pattern of different pressures over the regions of the model. For sinusoidal, triangular, and low amplitude square wave pleural pressures with equal amplitudes on both compartments, air was distributed preferentially to the lower compartment under the influence of the static pressure difference. With unequal amplitudes, more air flowed to the compartment experiencing the larger pressure swing. This was virtually independent of the waveform and of the amplitudes of the pleural pressure variation. Comparison of the present results with a constant flow model reveals that the overall distribution of tidal air during cyclic breathing is very different from the results obtained in constant rate inspiration experiments or in bolus distribution experiments. New experiments performed under cyclic breathing conditions are thus indicated.

Quantitative comparisons of mammalian lung pressure volume curves

The deflation pressure-volume curves of the lungs of a wide range of mammalian species were studied to compare their mechanical properties. A monoexponential mathematical function of the form V = Vmax - (Vmax - Vo)e - kp was fitted to the deflation data. It was found that the bulk stiffness index k (approximately 0.12 cm H2O-1) varied little over the 10(5) fold range of animal body weight. This range of k was far smaller than found in man in the presence of pulmonary parenchymal disease. It was concluded that the intrinsic stiffness characteristics of most mammalian lungs are similar.