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 Kinetics of Distribution of the Fat-Soluble Inert Gas Cyclopropane in the Body

A kinetic analysis is made of the experimentally measured time course of respiratory uptake of the highly fat-soluble, inert gas cyclopropane by normal human subjects. The analysis is based on the well-known perfusion-limited model in which a number of body compartments are arranged in parallel with the lungs via the circulating blood. Three distinct body compartments are derived from the data. These are tentatively identified as: (a) adipose tissue (b) fat-poor tissue of low perfusion such as resting muscle, skin, and connective tissue (c) fat-poor tissue of high perfusion such as brain, heart, gut, liver, and kidney. Blood flow rates to the several compartments are also derived from the data. The rates to compartments (a) and (b) are each approximately 10 per cent of the estimated total cardiac output. The derived perfusion (blood flow rate/compartment weight) of the three compartments are in the range, respectively, (a) 2 to 4, (b) 1 to 2.5, (c) 25 to 75 ml/min/100 gm. Uncertainties arising from the experimental data and from simplifications of the model (neglect of lung fill-up phase of uptake and gross diffusion of cyclopropane from one tissue into another) are discussed. The present type of uptake experiment is significant for the problems of total body fat determination, of gross body composition in relation to weight change, of gross shunting of blood flow from one compartment to another, of anesthesia by fat-soluble substances, and of decompression sickness.     

Heterogeneity of human adipose blood flow

Background

The long time pharmacokinetics of highly lipid soluble compounds is dominated by blood-adipose tissue exchange and depends on the magnitude and heterogeneity of adipose blood flow. Because the adipose tissue is an infinite sink at short times (hours), the kinetics must be followed for days in order to determine if the adipose perfusion is heterogeneous. The purpose of this paper is to quantitate human adipose blood flow heterogeneity and determine its importance for human pharmacokinetics.

Methods

The heterogeneity was determined using a physiologically based pharmacokinetic model (PBPK) to describe the 6 day volatile anesthetic data previously published by Yasuda et. al. The analysis uses the freely available software PKQuest and incorporates perfusion-ventilation mismatch and time dependent parameters that varied from the anesthetized to the ambulatory period. This heterogeneous adipose perfusion PBPK model was then tested by applying it to the previously published cannabidiol data of Ohlsson et. al. and the cannabinol data of Johansson et. al.

Results

The volatile anesthetic kinetics at early times have only a weak dependence on adipose blood flow while at long times the pharmacokinetics are dominated by the adipose flow and are independent of muscle blood flow. At least 2 adipose compartments with different perfusion rates (0.074 and 0.014 l/kg/min) were needed to describe the anesthetic data. This heterogeneous adipose PBPK model also provided a good fit to the cannabinol data.

Conclusion

Human adipose blood flow is markedly heterogeneous, varying by at least 5 fold. This heterogeneity significantly influences the long time pharmacokinetics of the volatile anesthetics and tetrahydrocannabinol. In contrast, using this same PBPK model it can be shown that the long time pharmacokinetics of the persistent lipophilic compounds (dioxins, PCBs) do not depend on adipose blood flow. The ability of the same PBPK model to describe both the anesthetic and cannabinol kinetics provides direct qualitative evidence that their kinetics are flow limited and that there is no significant adipose tissue diffusion limitation.     

Model of gas transport during high-frequency ventilation

We analyze gas exchange during high-frequency ventilation (HFV) by a stochastic model that divides the dead space into N compartments in series where each compartment has a volume equal to tidal volume (V). We then divide each of these compartments into alpha subcompartments in series, where each subcompartment receives a well-mixed concentration from one compartment and passes a well-mixed concentration to another in the direction of flow. The number of subcompartments is chosen on the basis that 1/alpha = (sigma t/-t)2, where -t is mean transit time across a compartment of volume, and sigma t is standard deviation of transit times. If (sigma t/-t)D applies to the transit times of the entire dead space, the magnitude of gas exchange is proportional to (sigma t/-t)D, frequency, and V raised to some power greater than unity in the range where V is close to VD. When V is very small in relation to VD, gas exchange is proportional to (sigma t/-t)2D, frequency, and V raised to a power equal to either one or two depending on whether the flow is turbulent or streamline, respectively. (sigma t/-t)D can be determined by the relation between the concentration of alveolar gas at the air outlet and volume expired as in a Fowler measurement of the volume of the dead space.     

Computer simulation of O2 transport and utilization mechanisms at the onset of exercise.

During transitions in work rate, O2 uptake (VO2) kinetics at the working tissue level might be rate limited by O2 transport and/or by O2 utilization. A computer model with parallel working and non-working tissue compartments, connected to an ideal lung by a variable-sized venous blood volume, was developed to study this. The time constant for working tissue O2 demand (tau T) was set by a first-order linear metabolic response. The model attempted to replicate the VO2 response at the alveolar level of a single subject performing step transitions on a cycle ergometer from 25 to 105 W [total lag time (equivalent to 63% increase above baseline) = 40.2 s]. Measured cardiac output kinetics (total lag time = 44.1 s) were used as a model parameter. Blood flow to the nonworking tissue (QNW) was kept constant at 4.5 or 5.0 l/min. A critical PO2 of 20 Torr was set, and the Bohr effect on the O2-hemoglobin dissociation curve was included. The "best" simulation had tau T = 36 s, QNW = 4.5 l/min, and venous blood volume = 2 liters and was not O2 transport limited. The approximation to the real data was good in all but the phase 1 response, where the model underpredicted the measured response. However, when QNW was increased to 5.0 l/min, the model was O2 transport limited; yet the predicted VO2 response at the alveolar level was not notably different from the subject's data.(ABSTRACT TRUNCATED AT 250 WORDS)     

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 new class of biophysical models for predicting the probability of decompression sickness in scuba diving.

Interconnected compartmental models have been used for decades in physiology and medicine to account for the observed multi-exponential washout kinetics of a variety of solutes (including inert gases) both from single tissues and from the body as a whole. They are used here as the basis for a new class of biophysical probabilistic decompression models. These models are characterized by a relatively well-perfused, risk-bearing, central compartment and one or two non-risk-bearing, relatively poorly perfused, peripheral compartment(s). The peripheral compartments affect risk indirectly by diffusive exchange of dissolved inert gas with the central compartment. On the basis of the accuracy of their respective predictions beyond the calibration regime, the three-compartment interconnected models were found to be significantly better than the two-compartment interconnected models. The former, on the basis of a number of criteria, was also better than a two-compartment parallel model used for comparative purposes. In these latter comparisons, the models all had the same number of fitted parameters (four), were based on linear kinetics, had the same risk function, and were calibrated against the same dataset. The interconnected models predict that inert gas washout during decompression is relatively fast, initially, but slows rapidly with time compared with the more uniform washout rate predicted by an independent parallel compartment model. If empirically verified, this may have important implications for diving practice.     

Reduction of lung perfusion increases VA/Q heterogeneity

This study addresses the hypothesis that decreases in lung perfusion rate independently worsen gas exchange efficiency in an isolated left lower lobe in zone 2 conditions. In seven anesthetized dogs, the left lower lobe was isolated, leaving the bronchus and bronchial vasculature intact. Blood was taken from the femoral arteries and reinfused at a controlled rate into the pulmonary artery of the left lower lobe. The flow rate was varied between 100 and 400 ml/min. The multiple inert gas elimination technique was used to quantitate the matching of ventilation to perfusion. Reduction in lobe blood flow resulted in a significant increase in perfusion-related indexes of alveolar ventilation-perfusion heterogeneity, such as the log standard deviation of the perfusion distribution, the retention component of the arterial-alveolar difference area, and the retention dispersion index. The increased heterogeneity suggests a worsening of the intraregional matching between the ventilation and the perfusion when perfusion is less than normal.     

Kinetic measurements of gas exchange in the intact pulmonary microcirculation.

The kinetics of gas exchange are monitored in an isolated perfused lung preparation contained within a plethysmograph. The lungs are perfused with buffer, and there is no gas exchange until a 2.0-ml bolus of reactant is injected into the perfusion system. Subsequent gas exchange produces a pressure transient that is related to the corresponding volume of exchanged gas. The observed rate of volume change is the result of two separate processes: 1) the rate of gas exchange during transit through the capillary bed and 2) the distribution of vascular transit times between the point of injection and the capillary bed. The latter is assessed by a control injection containing a dissolved inert gas that is liberated in the alveoli as the bolus enters the capillary bed. Analysis of the experimental curves permits the separation of these two processes. A model of exchange kinetics indicates that this method has the capability of measuring kinetic events occurring during gas exchange in the microcirculation under physiological conditions.     

Kinetic modeling of hyperpolarized 13C label exchange between pyruvate and lactate in tumor cells

Measurements of the kinetics of hyperpolarized (13)C label exchange between [1-(13)C]pyruvate and lactate in suspensions of intact and lysed murine lymphoma cells, and in cells in which lactate dehydrogenase expression had been modulated by inhibition of the PI3K pathway, were used to determine quantitatively the role of enzyme activity and membrane transport in controlling isotope flux. Both steps were shown to share in the control of isotope flux in these cells. The kinetics of label exchange were well described by a kinetic model that employed rate constants for the lactate dehydrogenase reaction that had been determined previously from steady state kinetic studies. The enzyme showed pyruvate inhibition in steady state kinetic measurements, which the kinetic model predicted should also be observed in the isotope exchange measurements. However, no such pyruvate inhibition was observed in either intact cells or cell lysates and this could be explained by the much higher enzyme concentrations present in the isotope exchange experiments. The kinetic analysis presented here shows how lactate dehydrogenase activity can be determined from the isotope exchange measurements. The kinetic model should be useful for modeling the exchange reaction in vivo, particularly as this technique progresses to the clinic.     

Programming xenon diffusion in maltose-binding protein

Protein interiors contain void space that can bind small gas molecules. Determination of gas pathways and kinetics in proteins has been an intriguing and challenging task. Here, we combined computational methods and the hyperpolarized xenon-129 chemical exchange saturation transfer (hyper-CEST) NMR technique to investigate xenon (Xe) exchange kinetics in maltose-binding protein (MBP). A salt bridge ～9 Å from the Xe-binding site formed upon maltose binding and slowed the Xe exchange rate, leading to a hyper-CEST ¹²⁹Xe signal from maltose-bound MBP. Xe dissociation occurred faster than dissociation of the salt bridge, as shown by ¹³C NMR spectroscopy and variable-B₁ hyper-CEST experiments. “Xe flooding” molecular dynamics simulations identified a surface hydrophobic site, V23, that has good Xe binding affinity. Mutations at this site confirmed its role as a secondary exchange pathway in modulating Xe diffusion. This shows the possibility for site-specifically controlling xenon protein-solvent exchange. Analysis of the available MBP structures suggests a biological role of MBP’s large hydrophobic cavity to accommodate structural changes associated with ligand binding and protein-protein interactions.     

Effects of hepatic blood flow on hepatic ethanol kinetics measured in cats and predicted from the parallel tube model

In cats anesthetized with pentobarbital, a long-circuit technique was used to measure hepatic blood flow while portal flow was varied from 0 to 300% of normal in random steps. Arterial, portal, and hepatic venous blood samples were analyzed for ethanol concentrations during continuous infusion of ethanol (20 mumol/(min.kg body weight) into the reservoir. Measured values for logarithmic mean sinusoidal ethanol concentration, hepatic venous ethanol concentration, hepatic ethanol uptake, and ethanol extraction were compared with the values predicted by the parallel tube model for hepatic uptake of substrates using Vmax and Km determined in each cat at the start of the experiment. Measured and predicted values were very similar at all blood flows above 65% control, but statistical regression analysis indicated a small but highly significant deviation of the measured values from the predicted values. At low flows, measured values of logarithmic mean sinusoidal and hepatic venous concentrations markedly exceeded the predicted values in most cats. The results indicate that the parallel tube model, which assumes all sinusoids are identical and equally perfused, provides a useful approximation for the effects of hepatic blood flow on hepatic ethanol kinetics except at low flows. However, there appears to be a significant degree of sinusoidal heterogeneity that results in a better fit to the distributed model. Our previously reported data for hepatic galactose uptake followed a similar pattern when reanalyzed in this more rigorous way.     

Simulation of pulmonary O2 uptake during exercise transients in humans

Computer simulation of blood flow and O2 consumption (QO2) of leg muscles and of blood flow through other vascular compartments was made to estimate the potential effects of circulatory adjustments to moderate leg exercise on pulmonary O2 uptake (VO2) kinetics in humans. The model revealed a biphasic rise in pulmonary VO2 after the onset of constant-load exercise. The length of the first phase represented a circulatory transit time from the contracting muscles to the lung. The duration and magnitude of rise in VO2 during phase 1 were determined solely by the rate of rise in venous return and by the venous volume separating the muscle from the lung gas exchange sites. The second phase of VO2 represented increased muscle metabolism (QO2) of exercise. With the use of a single-exponential model for muscle QO2 and physiological estimates of other model parameters, phase 2 VO2 could be well described as a first-order exponential whose time constant was within 2 s of that for muscle QO2. The use of unphysiological estimates for certain parameters led to responses for VO2 during phase 2 that were qualitatively different from QO2. It is concluded that 1) the normal response of VO2 in humans to step increases in muscle work contains two components or phases, the first determined by cardiovascular phenomena and the second primarily reflecting muscle metabolism and 2) the kinetics of VO2 during phase 2 can be used to estimate the kinetics of muscle QO2. The simulation results are consistent with previously published profiles of VO2 kinetics for square-wave transients.     

Effects of cardiac oscillations and lung volume on acinar gas mixing during apnea

We evaluated the importance of cardiogenic gas mixing in the acini of 13 dogs during 2 min of apnea. 133Xe (1-2 mCi in 4 ml of saline) was injected into an alveolar region through an occluded pulmonary artery branch, and washout was measured by gamma scintillation scanning during continued occlusion or with blood flow reinstated. The monoexponential rate constant for Xe washout (XeW) was -0.4 +/- 0.08 (SE) min-1 at functional residual capacity (FRC) with no blood flow in the injected region. It decreased by more than half at lung volumes 500 ml above and 392 ml below FRC. With intact pulmonary blood flow, XeW was -1.0 +/- 0.08 (SE) min-1 at FRC, and it increased with decreasing lung volume. However, if calculated Xe uptake by the blood was subtracted from the XeW measured with blood flow intact, resulting values at FRC and at FRC + 500 ml were not different from XeW with no blood flow. Reasonable calculation of Xe blood uptake at 392 ml below FRC was not possible because airway closure, increased shunt, and other factors affect XeW. After death, no significant XeW could be measured, which suggests that XeW caused by molecular diffusion was small. We conclude that 1) the effect of heart motion on the lung parenchyma increases acinar gas mixing during apnea, 2) this effect diminishes above or below FRC, and 3) there is probably no direct effect of pulmonary vascular pulsatility on acinar gas mixing.     

Ventilation-perfusion inhomogeneity increases gas uptake: theoretical modeling of gas exchange.

Ventilation-perfusion (VA/Q) inhomogeneity was modeled to measure its effect on gas exchange in the presence of inspired mixtures of two soluble gases using a two-compartment computer model. Theoretical studies involving a mixture of hypothetical gases with equal solubility in blood showed that the effect of increasing inhomogeneity of distributions of either ventilation or blood flow is to paradoxically increase uptake of the gas with the lowest overall uptake in relation to its inspired concentration. This phenomenon is explained by the concentrating effects that uptake of soluble gases exert on each other in low VA/Q compartments. Repeating this analysis for inspired mixtures of 30% O(2) and 70% nitrous oxide (N(2)O) confirmed that, during "steady-state" N(2)O anesthesia, uptake of N(2)O is predicted to paradoxically increase in the presence of worsening VA/Q inhomogeneity.     

The variance of the distribution of traversal times in a capillary bed

A random walk model of capillary tracer transit times is developed that treats simulataneously: plug flow in the capillary, radial and axial diffusion in the capillary cylinder and tissue annulus, and endothelial barriers to solute transport. The mean transit time is simply the volume of distribution divided by blood flow. Variance of transit times has additive terms for radial, axial, and barrier influences that are reduceable to variances of simpler models of capillary exchange. The dependence of variance on the solute diffusion coefficient is not monotonic, but has a minimum near 0·5 × 10?6 cm²/s for reasonable parameters and no barrier, Small molecules like inert gases are expected to have larger variances with higher diffusion coefficients, while larger molecules and barrier limited solutes will have the reverse dependence. Available literature data indicates that capillary heterogeneity will have a major influence on whole-body variance of transit times.     

Hyperpolarized 129Xe MR Imaging of Alveolar Gas Uptake in Humans

Background

One of the central physiological functions of the lungs is to transfer inhaled gases from the alveoli to pulmonary capillary blood. However, current measures of alveolar gas uptake provide only global information and thus lack the sensitivity and specificity needed to account for regional variations in gas exchange.

Methods and Principal Findings

Here we exploit the solubility, high magnetic resonance (MR) signal intensity, and large chemical shift of hyperpolarized (HP) ¹²⁹Xe to probe the regional uptake of alveolar gases by directly imaging HP ¹²⁹Xe dissolved in the gas exchange tissues and pulmonary capillary blood of human subjects. The resulting single breath-hold, three-dimensional MR images are optimized using millisecond repetition times and high flip angle radio-frequency pulses, because the dissolved HP ¹²⁹Xe magnetization is rapidly replenished by diffusive exchange with alveolar ¹²⁹Xe. The dissolved HP ¹²⁹Xe MR images display significant, directional heterogeneity, with increased signal intensity observed from the gravity-dependent portions of the lungs.

Conclusions

The features observed in dissolved-phase ¹²⁹Xe MR images are consistent with gravity-dependent lung deformation, which produces increased ventilation, reduced alveolar size (i.e., higher surface-to-volume ratios), higher tissue densities, and increased perfusion in the dependent portions of the lungs. Thus, these results suggest that dissolved HP ¹²⁹Xe imaging reports on pulmonary function at a fundamental level.     

Myocardial O2 consumption in porcine left ventricle is heterogeneously distributed in parallel to heterogeneous O2 delivery

Myocardial blood flow is unevenly distributed, but the cause of this heterogeneity is unknown. Heterogeneous blood flow may reflect heterogeneity of oxygen demand. The aim of the present study was to assess the relation between oxygen consumption and blood flow in small tissue regions in porcine left ventricle. In seven male, anesthetized, open-chest pigs, local oxygen consumption was quantitated by computational model analysis of the incorporation of 13C in glutamate via the tricarboxylic acid cycle during timed infusion of [13C]acetate into the left anterior descending coronary artery. Blood flow was measured with radioactive microspheres before and during acetate infusion. High-resolution nuclear magnetic resonance 13C spectra were obtained from extracts of tissue samples (159 mg mean dry wt) taken at the end of the acetate infusion. Mean regional myocardial blood flow was stable [5.0 +/- 1.6 (SD) and 5.0 +/- 1.4 ml.min(-1).g dry wt(-1) before and after 30 min of acetate infusion, respectively]. Mean left ventricular oxygen consumption measured with the NMR method was 18.6 +/- 7.7 micromol.min(-1).g dry wt(-1) and correlated well (r = 0.85, P = 0.02, n = 7) with oxygen consumption calculated from blood flow, hemoglobin, and blood gas measurements (mean 22.8 +/- 4.7 micromol.min(-1).g dry wt(-1)). Local blood flow and oxygen consumption were significantly correlated (r = 0.63 for pooled normalized data, P < 0.0001, n = 60). We calculate that, in the heart at normal workload, the variance of left ventricular oxygen delivery at submilliliter resolution is explained for 43% by heterogeneity in oxygen demand.     

Inert gas clearance from tissue by co-currently and counter-currently arranged microvessels

To elucidate the clearance of dissolved inert gas from tissues, we have developed numerical models of gas transport in a cylindrical block of tissue supplied by one or two capillaries. With two capillaries, attention is given to the effects of co-current and counter-current flow on tissue gas clearance. Clearance by counter-current flow is compared with clearance by a single capillary or by two co-currently arranged capillaries. Effects of the blood velocity, solubility, and diffusivity of the gas in the tissue are investigated using parameters with physiological values. It is found that under the conditions investigated, almost identical clearances are achieved by a single capillary as by a co-current pair when the total flow per tissue volume in each unit is the same (i.e., flow velocity in the single capillary is twice that in each co-current vessel). For both co-current and counter-current arrangements, approximate linear relations exist between the tissue gas clearance rate and tissue blood perfusion rate. However, the counter-current arrangement of capillaries results in less-efficient clearance of the inert gas from tissues. Furthermore, this difference in efficiency increases at higher blood flow rates. At a given blood flow, the simple conduction-capacitance model, which has been used to estimate tissue blood perfusion rate from inert gas clearance, underestimates gas clearance rates predicted by the numerical models for single vessel or for two vessels with co-current flow. This difference is accounted for in discussion, which also considers the choice of parameters and possible effects of microvascular architecture on the interpretation of tissue inert gas clearance.     

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.