Quantification of regional V/Q ratios in humans by use of PET. I. Theory

With positron emission tomography, quantitative measurements of regional alveolar and mixed venous concentrations of positron-emitting radioisotopes can be made within a transaxial section through the thorax. This allows the calculation of regional ventilation-to-perfusion (V/Q) ratios by use of established tracer dilution theory and the constant intravenous infusion of 13N. This paper considers the effect of the inspiration of dead-space gas on regional V/Q and investigates the relationship between the measured V/Q, physiological V/Q, and V/Q defined conventionally in terms of bulk gas flow (VA/Q). Ventilation has been described in terms of net gas transport, and the term effective ventilation has been introduced. A simple two-compartment model has been constructed to allow for the reinspiration of regional (or personal) and common dead-space gas. By use of this model, with parameters representative of normal lung the effective V/Q ratio for 13N [(VA/Q)eff(13N)] is shown to overestimate VA/Q by 18% when VA/Q = 0.1 but underestimate VA/Q by 68% when VA/Q = 10. For physiological gases, the model predicts that the behavior of O2 should be similar to that of 13N, so that, in terms of gas transport, V/Q ratios obtained using the infusion of 13N closely follow those for O2. Values of the effective V/Q ratio for CO2 [(VA/Q)eff(CO2)] lie approximately halfway between (VA/Q)eff(13N) and VA/Q. These results indicate that dead-space ventilation is far less a confounding issue when V/Q is considered in terms of net gas transport (VAeff), rather than bulk flow (VA).(ABSTRACT TRUNCATED AT 250 WORDS)     

Functional lung imaging with synchrotron radiation: Methods and preclinical applications

Many lung disease processes are characterized by structural and functional heterogeneity that is not directly appreciable with traditional physiological measurements. Experimental methods and lung function modeling to study regional lung function are crucial for better understanding of disease mechanisms and for targeting treatment. Synchrotron radiation offers useful properties to this end: coherence, utilized in phase-contrast imaging, and high flux and a wide energy spectrum which allow the selection of very narrow energy bands of radiation, thus allowing imaging at very specific energies. K-edge subtraction imaging (KES) has thus been developed at synchrotrons for both human and small animal imaging. The unique properties of synchrotron radiation extend X-ray computed tomography (CT) capabilities to quantitatively assess lung morphology, and also to map regional lung ventilation, perfusion, inflammation and biomechanical properties, with microscopic spatial resolution. Four-dimensional imaging, allows the investigation of the dynamics of regional lung functional parameters simultaneously with structural deformation of the lung as a function of time. This review summarizes synchrotron radiation imaging methods and overviews examples of its application in the study of disease mechanisms in preclinical animal models, as well as the potential for clinical translation both through the knowledge gained using these techniques and transfer of imaging technology to laboratory X-ray sources.     

Determination of regional ventilation and perfusion in the lung using xenon and computed tomography.

We propose a model to measure both regional ventilation (V) and perfusion (Q) in which the regional radiodensity (RD) in the lung during xenon (Xe) washin is a function of regional V (increasing RD) and Q (decreasing RD). We studied five anesthetized, paralyzed, mechanically ventilated, supine sheep. Four 2.5-mm-thick computed tomography (CT) images were simultaneously acquired immediately cephalad to the diaphragm at end inspiration for each breath during 3 min of Xe breathing. Observed changes in RD during Xe washin were used to determine regional V and Q. For 16 mm(3), Q displayed more variance than V: the coefficient of variance of Q (CV(Q)) = 1.58 +/- 0.23, the CV of V (CV(V)) = 0.46 +/- 0.07, and the ratio of CV(Q) to CV(V) = 3.5 +/- 1.1. CV(Q) (1.21 +/- 0.37) and the ratio of CV(Q) to CV(V) (2.4 +/- 1.2) were smaller at 1,000-mm(3) scale, but CV(V) (0.53 +/- 0.09) was not. V/Q distributions also displayed scale dependence: log SD of V and log SD of Q were 0.79 +/- 0.05 and 0.85 +/- 0.10 for 16-mm(3) and 0.69 +/- 0.20 and 0.67 +/- 0.10 for 1,000-mm(3) regions of lung, respectively. V and Q measurements made with CT and Xe also demonstrate vertically oriented and isogravitational heterogeneity, which are described using other methodologies. Sequential images acquired by CT during Xe breathing can be used to determine both regional V and Q noninvasively with high spatial resolution.     

Quantification of regional V/Q ratios in humans by use of PET. II. Procedure and normal values

Regional measurements of tissue isotope concentration, made using positron emission tomography (PET), allow tracer models to be used in a quantitative manner to provide topographic distributions of many structural and functional parameters, each derived for the same well-defined lung element. In this paper we describe a technique to measure regional ventilation-perfusion ratios (V/Q), in absolute units, by use of PET and the continuous intravenous infusion of an inert gas isotope, 13N, and report on measurements made in 12 normal subjects (4 smokers). Data were obtained from a single lung section (slice thickness, 1.7 cm full width at half-maximum response to a line source) at the level of the right ventricle in the supine posture during quiet breathing. For the 12 subjects, volume-weighted mean values of V/Q, averaged over individual right and left lung fields, ranged from 0.50 to 1.29. Analysis of these means showed no difference between lungs: right, 0.80 +/- 0.23 SD; left, 0.76 +/- 0.20 SD. Topographically, a systematic fall of V/Q in the ventrodorsal direction was observed in eight of the subjects (mean ventrodorsal difference 0.39, range 0.19-0.90), whereas two showed a clear increase toward dependent lung regions (range 0.16-0.26). Seven of the subjects with a falling ventrodorsal V/Q gradient also exhibited discrete regions of low V/Q at the dorsal lung border. We conclude that, in normal subjects, ventilation and perfusion are generally well matched in the supine posture, but isolated mismatching often occurs in dependent lung regions.     

Topographical distribution of pulmonary perfusion and ventilation, assessed by PET in supine and prone humans.

Using positron emission tomography (PET) and intravenously injected (13)N(2), we assessed the topographical distribution of pulmonary perfusion (Q) and ventilation (V) in six healthy, spontaneously breathing subjects in the supine and prone position. In this technique, the intrapulmonary distribution of (13)N(2), measured during a short apnea, is proportional to regional Q. After resumption of breathing, regional specific alveolar V (sVA, ventilation per unit of alveolar gas volume) can be calculated from the tracer washout rate. The PET scanner imaged 15 contiguous, 6-mm-thick, slices of lung. Vertical gradients of Q and sVA were computed by linear regression, and spatial heterogeneity was assessed from the squared coefficient of variation (CV(2)). Both CV and CV were corrected for the estimated contribution of random imaging noise. We found that 1) both Q and V had vertical gradients favoring dependent lung regions, 2) vertical gradients were similar in the supine and prone position and explained, on average, 24% of Q heterogeneity and 8% of V heterogeneity, 3) CV was similar in the supine and prone position, and 4) CV was lower in the prone position. We conclude that, in recumbent, spontaneously breathing humans, 1) vertical gradients favoring dependent lung regions explain a significant fraction of heterogeneity, especially of Q, and 2) although Q does not seem to be systematically more homogeneous in the prone position, differences in individual behaviors may make the prone position advantageous, in terms of V-to-Q matching, in selected subjects.     

Tracer kinetic model of regional pulmonary function using positron emission tomography.

To determine the spatial distributions of pulmonary perfusion, shunt, and ventilation, we developed a compartmental model of regional (13)N-labeled molecular nitrogen ((13)NN) kinetics measured from positron emission tomography (PET) images. The model features a compartment for right heart and pulmonary vasculature and two compartments for each region of interest: 1) aerated alveolar units and 2) alveolar units with no gas content (shunting). The model was tested on PET data from normal animals (dogs and sheep) and from animals with experimentally injured lungs simulating acute respiratory distress syndrome. The analysis yielded estimates of regional perfusion, shunt fraction, and specific ventilation with excellent goodness-of-fit to the data (R(2) > 0.99). Model parameters were estimated to within 10% accuracy in the presence of exaggerated levels of experimental noise by using a Monte Carlo sensitivity analysis. Main advantages of the present model are that 1) it separates intraregional blood flow to aerated alveolar units from that shunting across nonaerated units and 2) it accounts and corrects for intraregional tracer removal by shunting blood when estimating ventilation from subsequent washout of tracer. The model was thus found to provide estimates of regional parameters of pulmonary function in sizes of lung regions that could potentially approach the intrinsic resolution for PET images of (13)NN in lung (approximately 7.0 mm for a multiring PET camera).     

Imaging Lung Function in Mice Using SPECT/CT and Per-Voxel Analysis

Chronic lung disease is a major worldwide health concern but better tools are required to understand the underlying pathologies. Ventilation/perfusion (V/Q) single photon emission computed tomography (SPECT) with per-voxel analysis allows for non-invasive measurement of regional lung function. A clinically adapted V/Q methodology was used in healthy mice to investigate V/Q relationships. Twelve week-old mice were imaged to describe normal lung function while 36 week-old mice were imaged to determine how age affects V/Q. Mice were ventilated with Technegas™ and injected with ^99mTc-macroaggregated albumin to trace ventilation and perfusion, respectively. For both processes, SPECT and CT images were acquired, co-registered, and quantitatively analyzed. On a per-voxel basis, ventilation and perfusion were moderately correlated (R = 0.58±0.03) in 12 week old animals and a mean log(V/Q) ratio of −0.07±0.01 and standard deviation of 0.36±0.02 were found, defining the extent of V/Q matching. In contrast, 36 week old animals had significantly increased levels of V/Q mismatching throughout the periphery of the lung. Measures of V/Q were consistent across healthy animals and differences were observed with age demonstrating the capability of this technique in quantifying lung function. Per-voxel analysis and the ability to non-invasively assess lung function will aid in the investigation of chronic lung disease models and drug efficacy studies.     

Microsphere maps of regional blood flow and regional ventilation.

Systematically mapped samples cut from lungs previously labeled with intravascular and aerosol microspheres can be used to create high-resolution maps of regional perfusion and regional ventilation. With multiple radioactive or fluorescent microsphere labels available, this methodology can compare regional flow responses to different interventions without partial volume effects or registration errors that complicate interpretation of in vivo imaging measurements. Microsphere blood flow maps examined at different levels of spatial resolution have revealed that regional flow heterogeneity increases progressively down to an acinar level of scale. This pattern of scale-dependent heterogeneity is characteristic of a fractal distribution network, and it suggests that the anatomic configuration of the pulmonary vascular tree is the primary determinant of high-resolution regional flow heterogeneity. At approximately 2-cm(3) resolution, the large-scale gravitational gradients of blood flow per unit weight of alveolar tissue account for <5% of the overall flow heterogeneity. Furthermore, regional blood flow per gram of alveolar tissue remains relatively constant with different body positions, gravitational stresses, and exercise. Regional alveolar ventilation is accurately represented by the deposition of inhaled 1.0-microm fluorescent microsphere aerosols, at least down to the approximately 2-cm(3) level of scale. Analysis of these ventilation maps has revealed the same scale-dependent property of regional alveolar ventilation heterogeneity, with a strong correlation between ventilation and blood flow maintained at all levels of scale. The ventilation-perfusion (VA/Q) distributions obtained from microsphere flow maps of normal animals agree with simultaneously acquired multiple inert-gas elimination technique VA/Q distributions, but they underestimate gas-exchange impairment in diffuse lung injury.     

Endotoxemia increases relative perfusion to dorsal-caudal lung regions.

Changes in the spatial distribution of perfusion during acute lung injury and their impact on gas exchange are poorly understood. We tested whether endotoxemia caused topographical differences in perfusion and whether these differences caused meaningful changes in regional ventilation-to-perfusion ratios and gas exchange. Regional ventilation and perfusion were measured in anesthetized, mechanically ventilated pigs in the prone position before and during endotoxemia with the use of aerosolized and intravenous fluorescent microspheres. On average, relative perfusion halved in ventral and cranial lung regions, doubled in caudal lung regions, and increased 1.5-fold in dorsal lung regions during endotoxemia. In contrast, there were no topographical differences in perfusion before endotoxemia and no topographical differences in ventilation at any time point. Consequently, endotoxemia increased regional ventilation-to-perfusion ratios in the caudal-to-cranial and dorsal-to-ventral directions, resulting in end-capillary PO2 values that were significantly lower in dorsal-caudal than ventral-cranial regions. We conclude that there are topographical differences in the pulmonary vascular response to endotoxin that may have important consequences for gas exchange in acute lung injury.     

Pulmonary gas-exchange analysis by using simultaneous deposition of aerosolized and injected microspheres

Numerical methods for determining end-capillarygas contents for ventilation-to-perfusion ratios were first developedin the late 1960s. In the 1970s these methods were applied to validate distributions of ventilation-to-perfusion ratios measured by the multiple inert-gas-elimination technique. We combined numerical gasanalysis and fluorescent-microsphere measurements of ventilation andperfusion to predict gas exchange at a resolution of~2.0-cm³ lung volume in pigs.Oxygen, carbon dioxide, and inert gas exchange were calculated in551-845 compartments/animal before and after pulmonaryembolization with 780-µm beads. Whole lung gas exchange was estimatedfrom the perfusion- and ventilation-weighted end-capillary gascontents. Before lung injury, no significant difference existed betweenmicrosphere-estimated arterial PO₂and PCO₂ and measured values. Afterlung injury, the microsphere method predicted a decrease in arterialPO₂ but consistently underestimatedits magnitude. Correlation between predicted and measured inert gasretentions was 0.99. Overestimation of low-solubility inert gasretentions suggests underestimation of areas with low ventilation-to-perfusion ratios by microspheres after lung injury. Regional deposition of aerosolized and injected microspheres is a validmethod for investigating regional gas exchange with high spatial resolution.

     

Ventilation and perfusion distribution during altered PEEP in the left lung in the left lateral decubitus posture with unchanged tidal volume in dogs

Previous studies in anesthetized humans positioned in the left lateral decubitus (LLD) posture have shown that unilateral positive end-expiratory pressure (PEEP) to the dependent lung produce a more even ventilation distribution and improves gas exchange. Unilateral PEEP to the dependent lung may offer special advantages during LLD surgery by reducing the alveolar-to-arterial oxygen pressure difference {(A-a)PO2 or venous admixture} in patients with thoracic trauma or unilateral lung injury. We measured the effects of unilateral PEEP on regional distribution of blood flow (Q) and ventilation (V(A)) using fluorescent microspheres in pentobarbital anesthetized and air ventilation dogs in left lateral decubitus posture with synchronous lung inflation. Tidal volume to left and right lung is maintained constant to permit the effect on gas exchange to be examined. The addition of unilateral PEEP to the left lung increased its FRC with no change in left-right blood flow distribution or venous admixture. The overall lung V(A)/Q distribution remained relatively constant with increasing unilateral PEEP. Bilateral PEEP disproportionately increased FRC in the right lung but again produced no significant changes in venous admixture or V(A)/Q distribution. We conclude that the reduced dependent lung blood flow observed without PEEP occurs secondary to a reduction in lung volume. When tidal volume is maintained, unilateral PEEP increases dependent lung volume with little effect of perfusion distribution maintaining gas exchange.     

Physiological imaging of the lung: single-photon-emission computed tomography (SPECT).

Emission tomography provides three-dimensional, quantitative images of the distribution of radiotracers used to mark physiological, metabolic, or pathological processes. Quantitative single photon emission computed tomography (SPECT) requires correction for the image-degrading effects due to photon attenuation and scatter. Phantom experiments have shown that radioactive concentrations can be assessed within some percentage of the true value when relevant corrections are applied. SPECT is widely spread, and radiotracers are available that are easy to use and comparably inexpensive. Compared with other methods, SPECT suffers from a lower spatial resolution, and the time required for image acquisition is longer than for some alternative methods. In contrast to some other methods, SPECT allows simultaneous imaging of more than one process, e.g., both regional blood flow and ventilation, for the whole lung. SPECT has been used to explore the influence of posture and clinical interventions on the spatial distribution of lung blood flow and ventilation. Lung blood flow is typically imaged using macroaggregates of albumin. Both radioactive gases and particulate aerosols labeled with radioactivity have been used for imaging of regional ventilation. However, all radiotracers are not equally suited for quantitative measurements; all have specific advantages and limitations. With SPECT, both blood flow and ventilation can be marked with radiotracers that remain fixed in the lung tissue, which allows tracer administration during conditions different from those at image registration. All SPECT methods have specific features that result from the used radiotracer, the manner in which it is administered, and how images are registered and analyzed.     

Fractal nature of regional ventilation distribution.

High-resolution measurements of pulmonary perfusion reveal substantial spatial heterogeneity that is fractally distributed. This observation led to the hypothesis that the vascular tree is the principal determinant of regional blood flow. Recent studies using aerosol deposition show similar ventilation heterogeneity that is closely correlated with perfusion. We hypothesize that ventilation has fractal characteristics similar to blood flow. We measured regional ventilation and perfusion with aerosolized and injected fluorescent microspheres in six anesthetized, mechanically ventilated pigs in both prone and supine postures. Adjacent regions were clustered into progressively larger groups. Coefficients of variation were calculated for each cluster size to determine fractal dimensions. At the smallest size lung piece, local ventilation and perfusion are highly correlated, with no significant difference between ventilation and perfusion heterogeneity. On average, the fractal dimension of ventilation is 1.16 in the prone posture and 1. 09 in the supine posture. Ventilation has fractal properties similar to perfusion. Efficient gas exchange is preserved, despite ventilation and perfusion heterogeneity, through close correlation. One potential explanation is the similar geometry of bronchial and vascular structures.     

Spatial distribution of ventilation and perfusion in anesthetized dogs in lateral postures.

We aimed to assess the influence of lateral decubitus postures and positive end-expiratory pressure (PEEP) on the regional distribution of ventilation and perfusion. We measured regional ventilation (VA) and regional blood flow (Q) in six anesthetized, mechanically ventilated dogs in the left (LLD) and right lateral decubitus (RLD) postures with and without 10 cmH(2)O PEEP. Q was measured by use of intravenously injected 15-microm fluorescent microspheres, and VA was measured by aerosolized 1-microm fluorescent microspheres. Fluorescence was analyzed in lung pieces approximately 1.7 cm(3) in volume. Multiple linear regression analysis was used to evaluate three-dimensional spatial gradients of Q, VA, the ratio VA/Q, and regional PO(2) (Pr(O(2))) in both lungs. In the LLD posture, a gravity-dependent vertical gradient in Q was observed in both lungs in conjunction with a reduced blood flow and Pr(O(2)) to the dependent left lung. Change from the LLD to the RLD or 10 cmH(2)O PEEP increased local VA/Q and Pr(O(2)) in the left lung and minimized any role of hypoxia. The greatest reduction in individual lung volume occurred to the left lung in the LLD posture. We conclude that lung distortion caused by the weight of the heart and abdomen is greater in the LLD posture and influences both Q and VA, and ultimately gas exchange. In this respect, the smaller left lung was the most susceptible to impaired gas exchange in the LLD posture.     

Advances in magnetic resonance imaging of lung physiology.

This review presents an overview of some recent magnetic resonance imaging (MRI) techniques for measuring aspects of local physiology in the lung. MRI is noninvasive, relatively high resolution, and does not expose subjects to ionizing radiation. Conventional MRI of the lung suffers from low signal intensity caused by the low proton density and the large degree of microscopic field inhomogeneity that degrades the magnetic resonance signal and interferes with image acquisition. However, in recent years, there have been rapid advances in both hardware and software design, allowing these difficulties to be minimized. This review focuses on some newer techniques that measure regional perfusion, ventilation, gas diffusion, ventilation-to-perfusion ratio, partial pressure of oxygen, and lung water. These techniques include contrast-enhanced and arterial spin-labeling techniques for measuring perfusion, hyperpolarized gas techniques for measuring regional ventilation, and apparent diffusion coefficient and multiecho and gradient echo techniques for measuring proton density and lung water. Some of the major advantages and disadvantages of each technique are discussed. In addition, some of the physiological issues associated with making measurements are discussed, along with strategies for understanding large and complex data sets.     

Physiological evaluation of a new quantitative SPECT method measuring regional ventilation and perfusion.

We have developed a new quantitative single-photon-emission computed tomography (SPECT) method that uses (113m)In-labeled albumin macroaggregates and Technegas ((99m)Tc) to estimate the distributions of regional ventilation and perfusion for the whole lung. The multiple inert-gas elimination technique (MIGET) and whole lung respiratory gas exchange were used as physiological evaluations of the SPECT method. Regional ventilation and perfusion were estimated by SPECT in nine healthy volunteers during awake, spontaneous breathing. Radiotracers were administered with subjects sitting upright, and SPECT images were acquired with subjects supine. Whole lung gas exchange of MIGET gases and arterial Po(2) and Pco(2) gases was predicted from estimates of regional ventilation and perfusion. We found a good agreement between measured and SPECT-predicted exchange of MIGET and respiratory gases. Correlations (r(2)) between SPECT-predicted and measured inert-gas excretions and retentions were 0.99. The method offers a new tool for measuring regional ventilation and perfusion in humans.     

Pulmonary ventilation/perfusion ratio

The ratios of ventilatory (V) and perfusion (Q) flow rates in the lung are to a large extent responsible for the efficiency of gas exchange. In a simplified monocompartmental model of the lung, the arterial partial pressure of a given gas (Pa) is a function of several factors: the solubility of this gas in blood, its venous and inspired partial pressures and the V/Q ratio. In a multicompartemental model, the mean arterial partial pressure of the gas is a function of the individual values of Pa in each compartment as well as the distribution of V/Q ratios in the lung and the relationship between the concentration and the partial pressure of the gas. The heterogeneity of the distribution of V/Q results from those of both V and Q. Two factors are mainly responsible for this heterogeneity: the gravity and the morphometric characteristics of bronchi and vessels. V/Q ratios are partially controlled at least in low V/Q compartments since hypoxia in these compartments leads to pulmonary arteriolar vasoconstriction. However lungs V/Q ratios range from 0.1 to 10 with a mode around 1. Age, muscular exercise, posture, accelerations, anesthesia, O2 breathing, pulmonary pathology are factors which may alter the distribution of V/Q ratios.     

Ventilation-perfusion distribution in normal subjects

Functional values of LogSD of the ventilation distribution (σ(V)) have been reported previously, but functional values of LogSD of the perfusion distribution (σ(q)) and the coefficient of correlation between ventilation and perfusion (ρ) have not been measured in humans. Here, we report values for σ(V), σ(q), and ρ obtained from wash-in data for three gases, helium and two soluble gases, acetylene and dimethyl ether. Normal subjects inspired gas containing the test gases, and the concentrations of the gases at end-expiration during the first 10 breaths were measured with the subjects at rest and at increasing levels of exercise. The regional distribution of ventilation and perfusion was described by a bivariate log-normal distribution with parameters σ(V), σ(q), and ρ, and these parameters were evaluated by matching the values of expired gas concentrations calculated for this distribution to the measured values. Values of cardiac output and LogSD ventilation/perfusion (Va/Q) were obtained. At rest, σ(q) is high (1.08 ± 0.12). With the onset of ventilation, σ(q) decreases to 0.85 ± 0.09 but remains higher than σ(V) (0.43 ± 0.09) at all exercise levels. Rho increases to 0.87 ± 0.07, and the value of LogSD Va/Q for light and moderate exercise is primarily the result of the difference between the magnitudes of σ(q) and σ(V). With known values for the parameters, the bivariate distribution describes the comprehensive distribution of ventilation and perfusion that underlies the distribution of the Va/Q ratio.     

Ventilation-perfusion relationships in isolated blood-free perfused rabbit lungs.

The multiple inert gas elimination technique (MIGET) was applied to blood-free perfused isolated rabbit lungs. Commonly accepted criteria for reliability of the method were found to be fulfilled in this model. Ventilation-perfusion (VA/Q) distributions in isolated control lungs corresponded to those repeatedly detected under physiological conditions. In particular, a narrow unimodal dispersion of perfusate flow was observed: perfusion of low-VA/Q areas ranged below 1% and shunt flow approximately 2-3%; perfusion of high-VA/Q regions was not detected. Gas flow was characterized by narrow dispersion in the midrange-VA/Q areas. Application of a low level of PEEP (1 cmH2O) reduced shunt flow to less than 1%, and low-VA/Q areas were no longer noted. By using this PEEP-level, stable gas exchange conditions were maintained for greater than 5 h of extracorporeal perfusion. Graded embolization with small air bubbles caused a typical rightward shift (to higher VA/Q ratios) of mean ventilation, associated with the appearance of high-VA/Q regions and an increase in dead space ventilation. Mean perfusion was shifted leftward, and shunt flow was approximately doubled. Whole lung lavage with saline for washout of surfactant evoked a progressive manifold increase in shunt flow, accompanied by a moderate rise of perfusate flow to low-VA/Q areas. We conclude that the MIGET can be applied to isolated blood-free perfused rabbit lungs for assessment of gas exchange and that typical patterns of VA/Q mismatch are reproduced in this model.