A compartmental capillary, convolution integration model to investigate nutrient transport and metabolism in vivo from paired indicator/nutrient dilution curves.

Thirty-three paired indicator/nutrient dilution curves across the mammary glands of four cows were obtained after rapid injection of para-aminohippuric acid (PAH) plus glucose into the external iliac artery. For the measurement of extracellular volume and kinetics of nutrient uptake from indicator dilution curves, several models of solute dispersion and disappearance have been proposed. The Crone-Renkin models of exchange in a single capillary assume negligible washout of solutes from the extracellular space and do not describe entire dilution curves. The Goresky models include a distribution of capillary transit times to generate whole system outflow profiles but require two indicators to parametize extracellular behavior. A compartmental capillary, convolution integration model is proposed that uses one indicator to account for the extracellular behavior of the nutrient after a paired indicator/nutrient injection. With the use of an iterative approach to least squares, unique solutions for nonexchanging vessel transit time t(mu) and its variance sigma were obtained from all 33 PAH curves. The average of heterogeneous vascular transit times was approximated as 2sigma = 8.5 s. The remainder of indicator dispersion was considered to be due to washout from a well-mixed compartment representing extracellular space that had an estimated volume of 5.5 liters or 24% of mammary gland weight. More than 99% of the variation in the time course of venous PAH concentration after rapid injection into the arterial supply of the mammary glands was explained in an unbiased manner by partitioning the organ into a heterogeneous nonexchanging vessel subsystem and a well-mixed compartmental capillary subsystem.     

Physiological dead space during high-frequency ventilation in dogs

Tidal volumes used in high-frequency ventilation (HFV) may be smaller than anatomic dead space, but since gas exchange does take place, physiological dead space (VD) must be smaller than tidal volume (VT). We quantified changes in VD in three dogs at constant alveolar ventilation using the Bohr equation as VT was varied from 3 to 15 ml/kg and frequency (f) from 0.2 to 8 Hz, ranges that include normal as well as HFV. We found that VD was relatively constant at tidal volumes associated with normal ventilation (7-15 ml/kg) but fell sharply as VT was reduced further to tidal volumes associated with HFV (less than 7 ml/kg). The frequency required to maintain constant alveolar ventilation increased slowly as tidal volume was decreased from 15 to 7 ml/kg but rose sharply with attendant rapid increases in minute ventilation as tidal volumes were decreased to less than 7 ml/kg. At tidal volumes less than 7 ml/kg, the data deviated substantially from the conventional alveolar ventilation equation [f(VT - VD) = constant] but fit well a model derived previously for HFV. This model predicts that gas exchange with volumes smaller than dead space should vary approximately as the product of f and VT2.     

A model evaluation of estimates of breath-to-breath alveolar gas exchange

A mathematical model has been implemented for evaluation of methods for estimating breath-to-breath alveolar gas exchange during exercise in humans. This model includes a homogeneous alveolar gas exchange compartment, a dead space compartment, and tissue spaces for CO2 (alveolar and dead space). The dead space compartment includes a mixing portion surrounded by tissue and an unmixed (slug flow) portion which is partitioned between anatomical and apparatus contributions. A random sinusoidal flow pattern generates a breath-to-breath variation in pulmonary stores. The Auchincloss algorithm for estimating alveolar gas exchange (Auchincloss et al., J. Appl. Physiol. 21: 810-818, 1966) was applied to the model, and the results were compared with the simulated gas exchange. This comparison indicates that a compensation for changes in pulmonary stores must include factors for alveolar gas concentration change as well as alveolar volume change and thus implies the use of end-tidal measurements. Although this algorithm yields reasonable estimates of breath-to-breath alveolar gas exchange, it does not yield a "true" indirect measurement because of inherent error in the estimation of a homogeneous alveolar gas concentration at the end of expiration.     

Physiological dead space and effective parabronchial ventilation in ducks

Gas exchange in avian lungs is described by a cross-current model that has several differences from the alevolar model of mammalian gas exchange [e.g., end-expired PCO2 greater than arterial PCO2 (PaCO2)]. Consequently the methods available for estimating effective ventilation and physiological dead space (VDphys) in alveolar lungs are not suitable for an analysis of gas exchange in birds. We tested a method for measuring VDphys in birds that is functionally equivalent to the conventional alveolar VDphys. A cross-current O2-CO2 diagram was used to define the ideal expired point (PEi) and VDphys was calculated as from the equation, VDphys = [(PEiCO2--PECO2)/PEiCO2]. VT, where VT is tidal volume. In seven Pekin ducks VDphys was 13.8 ml greater than anatomic dead space and measured changes in the instrument dead space volume. VDphys also reflected changes in ventilation-perfusion inequality induced by temporary unilateral pulmonary arterial occlusion. Bohr dead space, calculated by substituting end-expired PCO2 for PEiCO2, was insensitive to such inhomogeneity. Enghoff dead space, calculated by substituting PaCO2 for PEiCO2, is theoretically incorrect for cross-current gas exchange and was often less than anatomic dead space. We conclude that VDphys is a useful index of avian gas exchange and propose a standard definition for effective parabronchial ventilation (VP) analogous to alveolar ventilation (i.e., VP = VE--VDphys, where VE is total ventilation).     

High-frequency ventilation of ducks and geese

We studied gas exchange in anesthetized ducks and geese artificially ventilated at normal tidal volumes (VT) and respiratory frequencies (fR) with a Harvard respirator (control ventilation, CV) or at low VT-high fR using an oscillating pump across a bias flow with mean airway opening pressure regulated at 0 cmH2O (high-frequency ventilation, HFV). VT was normalized to anatomic plus instrument dead space (VT/VD) for analysis. Arterial PCO2 was maintained at or below CV levels by HFV with VT/VD less than 0.5 and fR = 9 and 12 s-1 but not at fR = 6 s-1. For 0.4 less than or equal to VT/VD less than or equal to 0.85 and 3 s-1. less than or equal to fR less than or equal to 12 s-1, increased VT/VD was twice as effective as increased fR at decreasing arterial PCO2, consistent with oscillatory dispersion in a branching network being an important gas transport mechanism in birds on HFV. Ventilation of proximal exchange units with fresh gas due to laminar flow is not the necessary mechanism supporting gas exchange in HFV, since exchange could be maintained with VT/VD less than 0.5. Interclavicular and posterior thoracic air sac ventilation measured by helium washout did not change as much as expired minute ventilation during HFV. PCO2 was equal in both air sacs during HFV. These results could be explained by alterations in aerodynamic valving and flow patterns with HFV. Ventilation-perfusion distributions measured by the multiple inert gas elimination technique show increased inhomogeneity with HFV. Elimination of soluble gases was also enhanced in HFV as reported for mammals.(ABSTRACT TRUNCATED AT 250 WORDS)     

An assessment of dead space in pulmonary ventilation of the toad Bufo schneideri

The respiratory cycles of Rana and Bufo has been disputed in relation to flow patterns and to the respiratory dead-space of the buccal volume. A small tidal volume combined with a much larger buccal space motivated the "jet steam" model that predicts a coherent expired flow within the dorsal part of the buccal space. Some other studies indicate an extensive mixing of lung gas within the buccal volume. In Bufo schneideri, we measured arterial, end-tidal and intrapulmonary PCO(2) to evaluate dead-space by the Bohr equation. Dead-space was also estimated as: V(D)=(total ventilation-effective ventilation)/f(R), where total ventilation and f(R) were measured by pneumotachography, while effective ventilation was derived from the alveolar ventilation equation. These approaches were consistent with a dead space of 30-40% of tidal volume, which indicates a specific pathway for the expired lung gas.     

Effect of breath holding on ventilation maldistribution during tidal breathing in normal subjects

To test the hypothesis that during the course of a multiple-breath N2 washout (MBNW) diffusion-dependent ventilation maldistribution is more apparent in the early breaths, whereas convection-dependent maldistribution predominates in the later breaths, we performed MBNW with 0-, 1-, and 4-s end-inspiratory breath holds (BH0, BH1, BH4, respectively) in five normal subjects. Each subject breathed with a constant tidal volume of 1 liter, at 10-12 breaths/min and at constant flow rates. For each breath we computed the slope of the alveolar plateau normalized by the mean expired N2 concentration (Sn), the Bohr dead space (VDB), and an index analogous to the Fowler dead space (V50). In all five subjects, Sn, VDB, and V50 decreased with breath holding, indicating diffusion dependence of these indexes. Over the first five breaths the rate of increase of Sn as a function of cumulative expired volume (delta Sn/delta sigma VE) decreased by 29 and 54% during BH1 and BH4, respectively, compared with BH0. In contrast, from breath 5 to the end of the washout there was no significant change in delta Sn/delta sigma VE during BH1 and BH4 compared with BH0. Our results provide further experimental support for the hypothesis that the increase of Sn as a function of cumulative expired volume after the fifth breath constitutes a diffusion-independent index of ventilation inhomogeneity. It therefore reflects alveolar gas inequalities among larger units.(ABSTRACT TRUNCATED AT 250 WORDS)     

Xenon kinetics in muscle are not explained by a model of parallel perfusion-limited compartments

Experimental tissue gas kinetics do not follow the prediction for a single stirred perfusion-limited compartment. One hypothesis proposes that the kinetics might be explained by considering the tissue as a collection of parallel compartments, each with its own flow, reflecting the tissue microcirculatory flow heterogeneity. In this study, observed tissue gas kinetics were compared with the kinetics predicted by a model of multiple parallel compartments. Gas exchange curves were generated by recording the time course of tissue radioactivity in the intact calf muscles of anesthetized ventilated dogs exposed to step function changes of 133Xe in the inspired air for 5-h periods. Microcirculatory flow heterogeneity in the same tissue was determined by the radioactive microsphere method. Observed mean tissue transit times were on average longer than predicted by a factor of 6.7. Observed means averaged 52.1 min compared with 8.3 min predicted by the perfusion-limited model. Relative dispersions of tissue transit times were also uniformly larger than predicted. We conclude that Xe gas kinetics in intact canine skeletal muscle are not explained by a model of multiple parallel perfusion-limited compartments. Countercurrent exchange of gas between vessels is a possible explanation.     

Pulmonary function of the green sea turtle, Chelonia mydas

Lung volumes, oxygen uptake (VO2), end-tidal PO2, and PCO2, diffusing capacity of the lungs for CO (DLCO), pulmonary blood flow (QL) and respiratory frequency were measured in the green sea turtle (Chelonia mydas) (49-127 kg body wt). Mean lung volume (VL) determined from helium dilution was 57 ml/kg and physiological dead space volume (VD) was about 3.6 ml/kg. QL, determined from acetylene uptake during rebreathing, increased in proportion to VO2 with temperature. Therefore, constant O2 content difference was maintained between pulmonary arterial and venous blood. DLCO, measured using a rebreathing technique, was 0.04 ml X kg-1 X min-1 X Torr-1 at 25 degrees C. Several cardiopulmonary characteristics in C. mydas are advantageous to diving: large tidal volume relative to functional residual capacity promotes fast exchange of the alveolar gas when the turtle surfaces for breathing: and the concomitant rise of pulmonary blood flow and O2 uptake with temperature assures efficient O2 transport regardless of wide temperature variations encountered during migrations.     

CO2 elimination as a function of frequency and tidal volume in rabbits during HFO

CO2 elimination (VCO2) was monitored during high-frequency oscillation (HFO) over a frequency (f) range of 2-30 Hz in anesthetized and paralyzed rabbits to determine whether effective gas exchange could be achieved in this species, to determine the f and tidal volume (VT) dependence of gas exchange in this species, and to compare these results with those from dog and human studies. We were able to produce VCO2 levels during HFO that exceeded normal steady-state levels of CO2 production with VT's less than the total dead space volume. VCO2 was related to f in a curvilinear fashion, whereas in some rabbits VCO2 became independent of f at higher frequencies. This curvilinear relationship between f and VCO2 is similar to data from humans but contrasts with the linear relationship found in dogs. Evidence is presented indicating frequency-dependent behavior of gas exchange is correlated with a frequency-dependent decrease in respiratory system resistance. We propose that the frequency-dependent mechanical properties of the rabbit lung may also account for the species differences in HFO gas exchange.     

Effect of breathing pattern on gas mixing in a model with asymmetrical alveolar ducts

A model of the pulmonary airways was used to study three single-breath indices of gas mixing, dead space (VD), slope of the alveolar plateau, and alveolar mixing inefficiency (AMI). In the model, discrete elements of airway volume were represented by nodes. Using a finite difference technique the differential equation for simultaneous convection and diffusion was solved for the nodal network. Conducting airways and respiratory bronchioles were modeled symmetrically, but alveolar ducts asymmetrically, permitting interaction between convection and diffusion. VD, alveolar slope, and AMI increased with increasing flow. Similar trends were seen with inspired volume, although slope decreased at high inspired volumes with constant flow. VD was affected most by inspiratory flow and AMI and alveolar slope by expiratory time. VD fell approximately exponentially with time of breath holding. Eight different breathing patterns were compared. They had a small effect on alveolar slope and AMI and a greater effect on VD. The model shows how series and parallel inhomogeneity occur together and interact in asymmetrical systems: the old argument as to which is the more important should be abandoned.     

Ventilation by external high-frequency oscillation in cats

Eight anesthetized tracheostomized cats were placed in an 8.2-liter airtight chamber with the trachea connected to the exterior. Thirty-two combinations of high-frequency oscillations (HFO) (0.5-30 Hz; 25-100 ml) were delivered for 10 min each in random order into the chamber. Arterial blood gas tensions during oscillation were compared with control measurements made after 10 min of spontaneous breathing without oscillation when the mean arterial PCO2 (PaCO2) was 30.1 Torr. Ventilation due to spontaneous breathing (Vs) and oscillation (Vo) were derived from the chamber pressure trace and a pneumotachograph, respectively. As the oscillation frequency increased, oscillated tidal volume (Vo) decreased from a mean of 39 (0.5 Hz) to 3.3 ml (30 Hz) when 100 ml was delivered to the chamber. From 6-25 Hz, apnea occurred with Vo less than estimated respiratory dead space (VD); the minimum effective Vo/VD ratio was 0.37 +/- 0.05. Although Vo was maximal at 10 Hz at each oscillation volume, the lowest PaCO2 occurred at 2-6 Hz, and arterial PO2 rose as expected during hypocapnia. Above 10 Hz, PaCO2 was determined by Vo and was independent of frequency, whereas at lower frequencies, PaCO2 was related to Vo; below 6 Hz, PaCO2 varied inversely with the calculated alveolar ventilation. As oscillations became more effective, both PaCO2 and Vs fell progressively and were highly correlated; apnea occurred when PaCO2 was reduced by a mean of 4.5 Torr. Mean chamber pressure remained near zero up to 15 Hz, indicating functional residual capacity did not change. We conclude that externally applied HFO can readily maintain gas exchange in vivo, with Vo less than VD at frequencies over 2 Hz.     

Transit time dispersion in pulmonary and systemic circulation: effects of cardiac output and solute diffusivity

We present an in vivo method for analyzing the distribution kinetics of physiological markers into their respective distribution volumes utilizing information provided by the relative dispersion of transit times. Arterial concentration-time curves of markers of the vascular space [indocyanine green (ICG)], extracellular fluid (inulin), and total body water (antipyrine) measured in awake dogs under control conditions and during phenylephrine or isoproterenol infusion were analyzed by a recirculatory model to estimate the relative dispersions of transit times across the systemic and pulmonary circulation. The transit time dispersion in the systemic circulation was used to calculate the whole body distribution clearance, and an interpretation is given in terms of a lumped organ model of blood-tissue exchange. As predicted by theory, this relative dispersion increased linearly with cardiac output, with a slope that was inversely related to solute diffusivity. The relative dispersion of the flow-limited indicator antipyrine exceeded that of ICG (as a measure of intravascular mixing) only slightly and was consistent with a diffusional equilibration time in the extravascular space of approximately 10 min, except during phenylephrine infusion, which led to an anomalously high relative dispersion. A change in cardiac output did not alter the heterogeneity of capillary transit times of ICG. The results support the view that the relative dispersions of transit times in the systemic and pulmonary circulation estimated from solute disposition data in vivo are useful measures of whole body distribution kinetics of indicators and endogenous substances. This is the first model that explains the effect of flow and capillary permeability on whole body distribution of solutes without assuming well-mixed compartments.     

The influence of gas exchange on lung gas concentrations during air breathing

A model study is made of the contribution that continuing respiratory gas exchange makes to the alveolar plateau slope for O₂ during air breathing. Calculations in the model of the O₂ concentration appearing at the mouth during expiration, are performed for single breaths of air at constant flow rates 18 litres/min and 120 litres/min. At 18 litres/min the breathing period is 5 sec, the initial lung volume is 2300 ml, and the O₂ uptake rate is 300 ml STPD/min; whereas at 120 litres/min these parameters are 4 sec, 1200 ml, and 1800 ml STPD/min respectively. In each case the initial lung O₂ tension is taken to be 98 mm Hg. It is found that at 18 litres/min, the O₂ concentration difference on the alveolar plateau over the last second of expiration is 0.4 mm Hg when gas exchange is omitted and 1.2 mm Hg when gas exchange is included in the model. At 120 litres/min, this difference is zero and 5.0 mm Hg respectively. The gas exchange component predicted from a corresponding well-mixed compartment model is the same at 18 litres/min (0.8 mm Hg) but is 6.0 mm Hg at 120 litres/min.     

Effect of increased inspired CO2 on respiratory dead space in ponies

The objective of the present study was to determine the effect of elevated inspired CO2 on respiratory dead space (VD) of 12 normal, 8 carotid body-denervated (CBD), 7 hilar nerve-denervated (HND), and 6 CBD+HND ponies. The Fowler technique was used to determine VD on a breath-by-breath basis while the ponies breathed room air and inspired CO2 at 3 and 6%. During room air breathing, tidal volume (VT) and VD were greater in HND ponies than in normal and CBD ponies (P less than 0.05), and VT was less and VD/VT was greater after CBD than before CBD. For all groups. VD, VT, and breathing frequency (f) increased and VD/VT decreased significantly (P less than 0.01) with increasing inspired CO2. During CO2 breathing, VT and VD were higher (P less than 0.05) in the HND ponies than in all other groups, the decrease (P less than 0.05) in VD/VT was greatest in the CBD+HND group, and f was lower in the HND and HND+CBD than in the normal and CBD ponies. In addition, when inspired CO2 was increased from 0 to 6%, the decrease in VD/VT was greater and the increase in arterial PCO2 was less (P less than 0.05) after CBD than before CBD. For 70% of the ponies in all groups, VD increased linearly with increases in VT; for most of the remainder, VD tended to plateau at higher values of VT.     

Kinetics of cell populations in the compartment of maturing, non-dividing neutrophils of rat bone marrow]

The kinetics of cell movement through the compartment of maturing, nondividing neutrophils of the Wistar rat bone marrow was studied by autoradiography using H3-thymidine. There were transit and reserved neutrophil populations in each cell compartment. The transit periods of the maturing nondividing cells, the mean time of cell renewal in the subcompartments of metamyelocytes, the band and the sementonuclear neutrophils were determined with consideration to the reserved cell population.     

How well mixed is inert gas in tissues?

The washout of inert gas from tissues typically follows multiexponential curves rather than monoexponential curves as would be expected from homogeneous, well-mixed compartment. This implies that the ratio for the square root of the variance of the distribution of transit times to the mean (relative dispersion) must be greater than 1. Among the possible explanations offered for multiexponential curves are heterogeneous capillary flow, uneven capillary spacing, and countercurrent exchange in small veins and arteries. By means of computer simulations of the random walk of gas molecules across capillary beds with parameters of skeletal muscle, we find that heterogeneity involving adjacent capillaries does not suffice to give a relative dispersion greater than one. Neither heterogeneous flow, nor variations in spacing, nor countercurrent exchange between capillaries can account for the multiexponential character of experimental tissue washout curves or the large relative dispersions that have been measured. Simple diffusion calculations are used to show that many gas molecules can wander up to several millimeters away from their entry point during an average transit through a tissue bed. Analytical calculations indicate that an inert gas molecule in an arterial vessel will usually make its first vascular exit from a vessel larger than 20 micron and will wander in and out of tissue and microvessels many times before finally returning to the central circulation. The final exit from tissue will nearly always be into a vessel larger than 20 micron. We propose the hypothesis that the multiexponential character of skeletal muscle tissue inert gas washout curves must be almost entirely due to heterogeneity between tissue regions separated by 3 mm or more, or to countercurrent exchanges in vessels larger than 20 micron diam.     

A mathematical model of alveolar gas exchange in partial liquid ventilation

In partial liquid ventilation (PLV), perfluorocarbon (PFC) acts as a diffusion barrier to gas transport in the alveolar space since the diffusivities of oxygen and carbon dioxide in this medium are four orders of magnitude lower than in air. Therefore convection in the PFC layer resulting from the oscillatory motions of the alveolar sac during ventilation can significantly affect gas transport. For example, a typical value of the Péclet number in air ventilation is Pe approximately 0.01, whereas in PLV it is Pe approximately 20. To study the importance of convection, a single terminal alveolar sac is modeled as an oscillating spherical shell with gas, PFC, tissue and capillary blood compartments. Differential equations describing mass conservation within each compartment are derived and solved to obtain time periodic partial pressures. Significant partial pressure gradients in the PFC layer and partial pressure differences between the capillary and gas compartments (P(C)-Pg) are found to exist. Because Pe> 1, temporal phase differences are found to exist between P(C)-Pg and the ventilatory cycle that cannot be adequately described by existing non-convective models of gas exchange in PLV The mass transfer rate is nearly constant throughout the breath when Pe>1, but when Pe<1 nearly 100% of the transport occurs during inspiration. A range of respiratory rates (RR), including those relevant to high frequency oscillation (HFO) +PLV, tidal volumes (V(T)) and perfusion rates are studied to determine the effect of heterogeneous distributions of ventilation and perfusion on gas exchange. The largest changes in P(C)O2 and P(C)CO2 occur at normal and low perfusion rates respectively as RR and V(T) are varied. At a given ventilation rate, a low RR-high V(T) combination results in higher P(C)O2, lower P(C)CO2 and lower (P(C)-Pg) than a high RR-low V(T) one.