Effect of Global Ventilation to Perfusion Ratio, for Normal Lungs, on Desflurane and Sevoflurane Elimination Kinetics

Details of experimental methods and experimental results are presented in the companion experimental paper.³⁹  In brief, seven juvenile, 2.5-month-old piglets (weight, mean ± SD 25 ± 2 kg) with normal lungs were anesthetized with intravenous anesthetics. Subanesthetic levels of sevoflurane and desflurane were administered simultaneously with an open circuit technique for 45 min. Arterial and mixed venous blood samples were collected at predetermined times during the 45 min washin and during 45 min of washout. Sevoflurane and desflurane partial pressures in the blood samples were measured with a mass spectrometer–based method.^40,41  Uptake and elimination measurements were carried out for three different conditions³⁹  of alveolar minute ventilation (V_A) and cardiac output value (Q): normal V_A/Q (0.91); low V_A/Q (0.32); and high V_A/Q (1.73). Minute ventilation was varied between these three conditions by adjustment of respiratory rate. Cardiac output was increased with dobutamine infusion and decreased by inflation of a right atrial balloon.

We start our simplified mathematical modeling approach by considering the kinetics of anesthetic elimination from body tissues. A single well-mixed compartment, as depicted in figure 1A, has a uniform anesthetic partial pressure and is being supplied with fresh, anesthetic-free blood flowing in at rate Q, and flowing out also at rate Q, where the outflowing blood is equilibrated to the gas partial pressure of the compartment. The differential equation describing the washout of anesthetic gas from this single well-mixed compartment is

where P(t) is the gas partial pressure in the compartment and in exiting blood at time t; Vol_cmpt is the volume of the compartment (up to this point considered to be occupied only by the flowing fluid, i.e., blood), Q is the liquid fluid flow (units of volume/time), and λ_bg is the Ostwald solubility of the gas in blood (units of ml gas · ml blood^-1 · atm^-1) that links gas partial pressure (units of pressure) to gas content of the fluid (units of volume of gas/volume of liquid). When gas partial pressure is expressed in atmospheres, the Ostwald blood gas solubility is numerically equal to the blood/gas partition coefficient (dimensionless). For constant blood flow Q, the kinetics of gas washout, starting from an initial gas partial pressure of P_i at time zero, are well known⁴ :

The decay in gas partial pressure P(t) from any starting pressure P_i is a monoexponential function of time t, with time constant τ_cmpt given by

The numerator of this time constant represents the total gas content in the compartment at time t, and the denominator represents how quickly this compartment is being flushed out by fresh blood flow.

The well-mixed compartment of interest here is filled not only with blood, but rather a small volume of blood (V_bld) supplying a much larger volume of tissue (V_tiss), as depicted in figure 1B. The gas content of the compartment is then (total content) = P(t) · (Vol_bld · λ_bg + Vol_tiss · λ_tg), where λ_tg is the Ostwald solubility coefficient for gas dissolved in tissue.^5,23,42  Equation 2 still applies, but the monoexponential time constant becomes

Blood volume in many body tissues is a small fraction of tissue volume, and most anesthetics, including desflurane and sevoflurane, partition preferentially from blood into tissue (i.e., λ_tg > λ_bg). Therefore, λ_tg · Vol_tiss >> λ_bg · Vol_bld, and as an approximation, the first term in the numerator can be neglected. Also, for a well-mixed tissue compartment, compartment gas partial pressure P(t) equals exiting venous blood partial pressure P_v(t). The mass balance for the tissue compartment then becomes a slight modification of equation 1:

The solution for washout from starting gas partial pressure P_i is a monoexponential decay (i.e., equation 2 still applies) with time constant

This approximation emphasizes that the important parameter for body tissue elimination kinetics is not the gas solubility in blood that describes how the gas partitions between a blood phase and gas phase, but rather the tissue/blood partition coefficient λ_tg/λ_bg that describes how gas partitions between tissue and blood.^{1,4,7,8,15,17,18,21,28} 

In the interest of arriving at simplified approximate equations that directly show the importance of parameter groups, we start by treating the entire body as one well-mixed compartment, a composite of the traditional vessel-rich, or visceral, group; the muscle group; and the fat group. In figure 1C, the blood flowing out of our compartment exits at mixed venous gas partial pressure, and the blood flow to the whole-body compartment is the entire cardiac output. Mixed venous blood is recycled back to the compartment through a gas exchanger (the lung) capable of clearing all the anesthetic gas in one pass. It is obvious that equation 2 still applies, and the time constant compared to figure 1B has not changed.

In figure 1D, we now consider a lung that does not clear all of the anesthetic in one pass. Partial clearance in the lung for the entire cardiac output can be divided conceptually into a partial lung blood flow that is not cleared at all and is recycled into the body compartment, and a partial lung blood flow that is cleared completely and is returned to the body tissue compartment as gas-free blood. It is obvious in figure 1D that the part of blood flow that is not cleared at all is simply recycled into the well-mixed compartment and has no role in elimination kinetics. It is also obvious that the effective blood flow washing out the well-mixed compartment is the fraction of cardiac output that is cleared in one pass. Consistent with traditional pharmacokinetic terminology, we denote the amount of blood flow that is completely cleared of anesthetic as “clearance,” with units of milliliters blood/min. The fraction of cardiac output that is cleared in one pass will then be called “fractional clearance” and denoted as FrClr (dimensionless). The whole-body elimination time constant becomes

If, for example, the lung fractional clearance (FrClr) was 20% or one fifth, the overall elimination time constant would be increased, by the incomplete lung clearance, fivefold compared to the intrinsic tissue time constant of equation 2C.

An illustration of the potential effect of incomplete lung clearance on the tissue washout time constant is shown in figure 2. Tissue parameter data for the plots in figure 2 were chosen to mimic the muscle tissue compartment for the population averages for the pigs of our experiments.³⁹  A muscle compartment volume of 13,960 ml was estimated based the “standard 30-kg dog” presented by Cowles et al.,²³  scaled to our average pig weight of 25 kg. Average cardiac output for our piglets, for the “normal” V_A/Q condition, was measured at 3,300 ml/min. The fraction of cardiac output to muscle in the Cowles 30-kg dog of 0.31 was applied to estimate muscle blood flow at 1,023 ml/min. The tissue/gas partition coefficient λ_tg for desflurane in pig muscle of 0.56, and the blood/gas partition coefficient for desflurane in pig blood of 0.40, were taken from Zhou and Liu.⁴³  For purposes of illustration, the single muscle compartment was connected in figure 2 to a lung with fractional clearance assumed to be constant throughout the elimination. Under these assumptions, the intrinsic muscle tissue time constant (equation 2c or equation 3 with FrClr = 1.0) is estimated as 19.1 min. The marked effect on the muscle washout kinetics of progressively decreasing lung clearance from 1.0 to 0.2 is readily apparent in figure 2.

We next consider behavior of the lung during anesthetic elimination, and we divide this consideration into early stages of elimination, and later stages. We consider a normal, homogeneous lung with a single, narrow mode in the V_A/Q distribution. A mass balance on the lung provides the key differential equation⁴ :

P_alv is alveolar anesthetic gas partial pressure (atm), P_b is barometric pressure, V_lungeff is effective lung volume, and P₀ is standard pressure (1 atm). Effective lung volume V_lungeff is the total gas capacity of the lung, given by V_lungeff = V_frc + V_tave + λ_bg · V_lungbld · P₀ + λ_lungtiss · V_lungtiss · P₀,^5,23,29  where V_frc is functional residual capacity (milliliters gas); V_tave is time averaged tidal volume in the alveolus (for example, one half tidal volume for a sinusoidal breathing pattern); V_lungbld is the lung blood volume; λ_lungtiss is the gas solubility in lung tissue; and V_lungtiss is the tissue volume of the lung. Equation 4 states that the time rate of change of the amount of gas in the lung is equal to the net delivery by blood into the alveolus (positive for elimination since P_mv > P_art) minus removal in the gas phase by tidal ventilation.

Two assumptions are commonly made to simplify equation 4. The first is that alveolar gas and arterial blood, for any homogenous lung unit, are equilibrated to the same gas partial pressure.^{4,5,10,11,23,29,42,44,45}  The second, applicable to later stages of elimination, is the pseudo steady-state assumption that the term in brackets (net delivery to the alveolus by blood) is approximately equal to the term in parentheses (net loss in expired gas).^44,45  Therefore, as P_mv, and P_art (= P_alv), are all changing slowly together, the net result is that dP_alv/dt becomes small enough to be neglected, and therefore the left term in brackets is approximately equal to the right term in parentheses. Equation 4 under these assumptions simplifies to the retention equation^44,45 :

The retention equation is the underlying basis for the multiple inert gas elimination technique that has been used successfully hundreds of times in describing lung gas exchange.³⁷  During these later stages of elimination, the retention (defined as P_art/P_mv, the ratio of arterial to mixed venous anesthetic partial pressure) is predicted to become constant as both P_art and P_mv continue to change together. We refer in this manuscript to these later stages of elimination as the “retention equation plateau.”

In equations 4 and 5, λ_bg is the Ostwald solubility coefficient, and the standard barometric pressure P₀ of 1.0 atm appears in these equations to maintain dimensional consistency. If instead we use the numerically equal value of the blood/gas partition coefficient (dimensionless) for λ_bg, equation 5 takes the slightly simpler form:

Fractional clearance of anesthetic gas from pulmonary blood is defined as the fraction of gas removed from mixed venous blood and can be expressed as

It is clear that if retention is constant in the latter stages of elimination, fractional clearance FrClr will also be constant. Fractional clearance can also be expressed by substituting the expression in the retention equation for P_art/P_mv, and rearranging:

This equation for fractional clearance has been presented previously.^1,2,34,46  Retention and fractional clearance curves for a desflurane blood/gas partition coefficient in pig blood of 0.40⁴³  are shown in figure 3, with three points on each curve corresponding to our experimental values of V_A/Q . Figure 3 also shows the retention and fractional clearance curves, and the corresponding three points, for sevoflurane with a blood/gas partition coefficient in pig blood of 0.48.⁴³ 

Constant fractional clearance in the later stages of elimination, where “later” is yet to be defined, will directly affect the terminal time constant (often called the “beta” constant in pharmacokinetics) for elimination for a single whole-body compartment interacting with the lungs, as discussed above. Substituting the expression for fractional clearance in equation 8 into equation 3, we obtain the late stage terminal time constant:

This simple connection between lung gas exchange and whole-body washout time constant shows that during later stages of elimination, lung gas exchange efficiency, even for normal lungs with a narrow unimodal V_A/Q distribution, directly affects the whole-body elimination time constant, because incomplete clearance directly reduces the effective blood flow that is washing out the body compartment. In the rightmost version of equation 9, the term in left parentheses is recognized as the intrinsic tissue time constant from equation 2C. The term in right parentheses is the impact of the lung in slowing whole body washout, and this impact of the lung is determined by (1) the overall lung V_A/Q ratio and (2) the blood/gas partition coefficient. Equation 9 can also be rearranged to more directly show the individual roles of cardiac output Q and alveolar minute ventilation V_alv:

Equation 10 tells us that the direct effect of increased cardiac output in speeding the tissue compartment washout (the Q in equation 2C) always dominates over the indirect effect of increased cardiac output in decreasing clearance and slowing the late-stage whole-body washout (the Q in equation 8), and therefore the net effect of an increase in cardiac output is to speed late-stage elimination. This result, however, is restricted to the assumption of a single body compartment where a change in cardiac output cannot be accompanied by a change in the organ level distribution of blood flow.^2,11,28  Equation 10 also helps to clarify the concepts of perfusion-limited elimination and ventilation-limited elimination.^4,21,44,47  For a gas that has a solubility coefficient much greater than 1, or when V_A is much less than Q, the second term in parentheses will dominate, changes in cardiac output will have little effect, changes in ventilation will have a large effect, and the late-stage elimination is ventilation-limited. For a gas that has a solubility coefficient much less than 1, or when Q is much smaller than V_A, the 1/ Q term in parentheses will dominate, changes in ventilation will have little effect, changes in cardiac output will have a large effect, and the late-stage elimination is perfusion-limited.

Early in elimination, in contrast to the later stages of elimination, P_alv is changing rapidly, and the retention equation cannot be applied to predict P_art/P_mv. Some insight into the early stages of elimination can be gained, however, by considering the limiting case of an anesthetic gas with a solubility in blood approaching zero. For sparingly soluble gases, the term describing net delivery in blood in equation 4 approaches zero, and equation 4 reduces to

For a gas that is sparingly soluble in tissue (λ_tg ≈ 0) as well as in blood (λ_bg ≈ 0), effective lung volume becomes V_frc + V_tave, and the differential equation describing washout becomes

The solution is a monoexponential decay in alveolar partial pressure from starting pressure P_i:

For our piglets, functional residual capacity is estimated as 669 ml by scaling the data of Ludwigs et al.⁴⁸  to our pig weight of 25 kg and linearly interpolating to our set positive end-expiratory pressure of 5 cm H₂O. An average tidal volume for our experiments, globally for all conditions, estimates tidal volume as 268 ml, giving functional residual capacity + ½ tidal volume as 803 ml. For the three different minute ventilation settings in our experiments, the three time courses predicted for alveolar washout for a hypothetical, very low solubility gas are graphed in figure 4. Of note, all of the functional residual capacity time constants, even for low minute ventilation, are small, with this part of washout completing in about 1 min or less.

For more soluble gases, the approach from P_art/P_mv = 1 to the retention equation plateau is not easily predicted with simplified models, because the kinetic behavior is governed by the behavior of the lung kinetics interacting with the tissue kinetics. It can be appreciated qualitatively that the approach to the retention equation plateau will be slower than predicted by τ_frc because gas exiting the alveolus in arterial blood speeds the decay, but gas entering from mixed venous blood slows the decay, and P_mv during elimination will be larger than P_art. More quantitative descriptions would require simultaneous solution of both differential equations for lung and body tissue (equations 1A and 4), either numerically^{5,10,11,13,21,23,29,42}  or analytically.^4,28  Alternatively, the early stages of anesthetic washout can be described with experimental data. In the current study, the experimental data for P_art and P_mv from our companion experimental study³⁹  are analyzed by calculating the retention at each time point and plotting retention versus time.

Data for P_art and P_mv were taken from our companion experimental study.³⁹  For each individual animal, and each of the three V_A/Q conditions, arterial (P_art) and mixed venous (P_mv) mass spectrometer signals were scaled to that individual’s arterial signal at the end of the 45-min anesthetic (sevoflurane and desflurane) administration. For each V_A/Q condition and each subject, the scaled P_art was divided by scaled P_mv to calculate the retention for that individual, V_A/Q condition, and time. Then, for each V_A/Q condition, P_art/P_mv was averaged for each time over the seven animals, 99% CIs were determined using the Student’s t distribution, and values were plotted as means and CIs versus time (fig. 5 for desflurane and fig. 6 for sevoflurane). Scaled desflurane mixed venous partial pressure means and 99% CIs were plotted as spline-smoothed curves on a semi-log plot (fig. 7). Desflurane elimination kinetics in mixed venous blood from 20 to 45 min were compared to two theoretical monoexponential washout kinetics, the intrinsic time constant for the muscle compartment, and the fractional clearance–corrected time constant (fig. 7). A similar analysis for sevoflurane was performed, with a similar plot in figure 8. The rationale for focusing on the muscle compartment, when we restrict our attention to the time period from 20 to 45 min, is presented in the appendix. The intrinsic muscle compartment time constants (equation 2C, or equation 3 with FrClr = 1) were calculated from the following: measured cardiac output times the fractional flow to muscle for the Cowles “standard 30-kg dog”²³ ; muscle tissue volume from the Cowles 30-kg dog, scaled to our pig weight of 25 kg; pig tissue/gas partition coefficients for desflurane (0.56) and sevoflurane (1.17) in muscle from Zhou and Liu.⁴³ ; and pig blood/gas partition coefficients of 0.40 for desflurane and 0.48 for sevoflurane from Zhou and Liu.⁴³  Fractional clearance for the clearance-corrected muscle time constant (equation 3) was calculated (equation 8) from measured cardiac output and alveolar minute ventilation, and λ_bg from Zhou and Liu.⁴³ 

Figure 5 shows the time course of calculated P_art/P_mv (retention) during desflurane elimination, as means (over the seven animals at each time point) and 99% CIs. In all three V_A/Q conditions, the values reached the retention equation plateau within 5 min. The ratio of scaled P_art to scaled P_mv is initially greater than 1 in all cases, reflecting the fact that not all body tissues were completely equilibrated at the end of a 45 min administration. The experimental values of retention on this retention equation plateau are compared graphically to the values calculated from the retention equation (applied to the average values of V_A/Q of 0.91, 0.32, and 1.73), with the central section of the graph of figure 3 reproduced and aligned to the right of the data plot in figure 5.

Figure 6 shows the corresponding analysis for the sevoflurane data. There is a similar trend for retentions to reach a plateau after the first 2 to 5 min, especially notable in the time period from 2 to 10 min. Later time periods in figure 6 are difficult to interpret; the noise in the sevoflurane data becomes large as the signals approach zero late in washout. As a consequence of the mass spectrometer setup and the chosen inspired concentrations of sevoflurane and desflurane, the signal to noise ratio for the sevoflurane data analysis was on the order of 20 to 50 times smaller than the corresponding desflurane signal to noise ratios. The result is the large error bars, compared to desflurane, in the sevoflurane retention plots late in washout, where two very small quantities are divided as they both approach zero. The very small signal for sevoflurane in late stages of washout also makes the calculation of the ratio of two small numbers susceptible to systematic, nonrandom measurement errors—for example, any small amount of drift in the mass spectrometer baseline.

Figure 7 presents the measured P_mv values for desflurane during elimination, connected by a spline-smoothed curve on a semi-log plot (means with 99% CIs). Also plotted are the monoexponential washouts (linear on a semi-log plot) from the 20-min time point that are predicted for the muscle compartment alone. The more rapid washout (steeper slope of a straight line on the semi-log plot; dot-dash line) is predicted by the intrinsic time constant of the muscle compartment (intrinsic tissue compartment time constant, methods), i.e., the washout that is predicted for complete lung fractional clearance. The slower linear, monoexponential washout (solid line) is predicted by the intrinsic muscle time constant corrected for the fractional clearance by the lung (late-stage effective time constant; see Materials and Methods, equation 9). Figure 8 presents the corresponding analysis for sevoflurane.

Our study develops a simplified mathematical model of inhaled anesthetic elimination that explicitly shows the dependence of elimination on overall lung V_A/Q, in contrast to both of the two most prominent previous approaches to mathematical modeling of elimination. One prominent approach to previous mathematical modeling of elimination has used numerical (or, in early studies, analog electrical) solutions to the system of differential equations that arise from compartmental modeling.^{2,5,9–13,21–24,27–29,34,42,49,50}  Each compartment included in the model (for example, lungs/central, visceral, muscle, and fat compartments in a four-compartment model)^2,23,42  is represented by a differential equation, and the resulting uptake and elimination curves can be compared to the experiment. Because this approach includes a differential equation for the lungs, equivalent or identical to equation 4, the effect of overall lung V_A/Q is implicitly included. The numerical solutions, however, do not provide any equations that explicitly show the functional form of the dependence of kinetics on V_A/Q .

Another prominent approach to mathematical modeling of washout data is the empiric fitting of kinetic data for P_art (or for P_et) to sums of multiple exponential terms of the form

Terms are empirically added to the model according to whether or not they improve the fit of the multiexponential curve to the data points. Carpenter et al. used five terms fit to prolonged (several days) washout data for multiple anesthetics.^15,16  Because the recovered rate constants k_i were substantially separated in magnitude, it was assumed as an approximation that each coefficient A_i and rate constant k_i corresponds to a distinct tissue group, resulting in the five-compartment model^15–18  for anesthetic elimination: lungs/central compartment, vessel-rich group, muscle group, fat group, and the “fourth compartment,” attributed to intertissue diffusion.^1,15–18  Earlier work interpreted uptake kinetics in a similar way for a four-compartment model.⁷ 

The lungs/central compartment has the fastest kinetics compared to all the other compartments, and it has been assumed as an approximation^7,15–18  that after the early period of washin or washout, the role of the lungs in later stages of kinetics can be neglected. The expectation is then that the empirically recovered time constants for each compartment (the time constants τ_i = 1/k_i) should reasonably match the intrinsic tissue time constants^7,15–18  as calculated from the equation for “intrinsic tissue compartment time constant,” equation 2C in the Materials and Methods. Our study shows that this concept is incorrect. The lung overall V_A/Q ratio, and more specifically the dimensionless parameter group V_A/(λ_bgQ), continues to directly influence the terminal elimination constant for the entire elimination. During these later stages of elimination, it is true that the influence of V_frc/ V_A kinetics has decayed to a negligible role. The fractional clearance, however, takes on a constant value and plays a major role in modulating the intrinsic tissue time constants to determine the overall late-stage kinetics.

Figures 7 and 8 illustrate several features of late-stage desflurane and sevoflurane washout. First, although there is still some curvature in the time period from 20 to 45 min, the washout during this time is a close approximation to a monoexponential washout that would plot as a straight line on a semi-log plot. This is consistent with the anticipation that this period of washout can be approximately represented by a single muscle compartment connected to the lungs, as described in the appendix. Second, the clearance-corrected time constant for a monoexponential muscle compartment washout is generally a better predictor of the experimental data than the intrinsic time constant, supporting our point that incomplete lung clearance slows washout during the entire elimination. Third, the clearance-corrected time constant makes a very good prediction of the experimental washout kinetics. This fit of theory to experimental data is striking, considering that this match did not use any adjusted parameters for “best fit.” Finally, the correction for lung clearance makes little difference when lung fractional clearance approaches 1.0 (figs. 7C and 8C, high V_A/Q), i.e., when V_A/Q is high and/or solubility is small. When clearance is not close to 1.0, however, the uncorrected washout time constant substantially overestimates the speed of washout (figs. 7B and 8B, low V_A/Q). Of note, desflurane and sevoflurane are two of the least soluble inhaled anesthetics. These effects will be even more pronounced for higher solubility gases.

The dimensionless group V_A/(λ_bgQ), highlights two important factors in anesthetic elimination: the role of overall lung V_A/Q, and the role of the blood/gas partition coefficient. Even for normal lungs with efficient gas exchange for oxygen and carbon dioxide, and a narrow unimodal V_A/Q distribution, the overall lung V_A/Q ratio has a direct effect on anesthetic elimination kinetics. In general, higher V_A/Q ratios produce higher fractional clearance in the lung (fig. 3) and therefore less slowing of tissue washout kinetics (equation 9 for τ_late).

It has been taught intuitively for many years that lower blood gas solubility leads to faster overall uptake and elimination kinetics,^{1–3,6,9–11,13,24}  a fact completely consistent with experimental data,^{6,14–20,23,24}  mathematical models of kinetics solved numerically^{2,5,9–11,13,23,24,34}  or analytically,^4,28  and routine clinical experience. Surprisingly, however, it is hard to find in previous literature any equation that directly shows a connection between the overall terminal elimination time constant and blood gas solubility. Equation 9 for τ_late directly makes a connection between the beta elimination half-life in the later stages of elimination, and blood gas solubility.

Our two companion studies, i.e., the current modeling study and the experimental study that provided the data for analysis, have several limitations. First, the current study was an exploratory post hoc analysis of a subset of a larger data set. This type of analysis is recognized as a way to generate hypotheses, but is not appropriate for testing of hypotheses. Second, we did not perform a complete factorial design with three levels each of cardiac output times three levels of ventilation. Rather, our experiments explored a limited subset of all nine possible conditions, with cardiac output and ventilation both changing between conditions. Third, cardiac output was varied in the desired directions, but there was no way to assess or influence the distribution of blood flow that could have accompanied these changes. Redistribution of blood flow between body compartments can impact elimination kinetics beyond the change in cardiac output alone. Both of the maneuvers to manipulate cardiac output (dobutamine to increase cardiac output; atrial obstruction to decrease cardiac output) could have changed distribution of flow as well as total flow. Additionally, both hypocarbia and hypercarbia can change the blood flow distribution. Fourth, an optimal condition for studying the kinetics of anesthetic elimination would be a starting point of complete equilibration of all of the body tissues to the same anesthetic partial pressure. Our 45-min administration obviously did not completely equilibrate all body tissues. Fifth, we did not directly measure the V_A/Q distributions in our piglets. Previous measurements of V_A/Q distributions in this model, however, have demonstrated normal distributions with a single narrow V_A/Q mode, minimal shunt, and minimal alveolar dead space.³⁶  Based on the close matching of V_A and Q for normal lungs, our mathematical model further makes the approximation that matching between V_A and Q is perfect, i.e., that the distribution is a single, idealized spike in both V_A and Q . Finally, in the interests of arriving at relatively simple equations for kinetic time constants, we recognize that many approximations were made that do not represent the full complexity of anesthetic kinetics. In particular, representation of the whole body with a single time constant does not address the known complexity of multiple tissues and multiple compartments.

The ratio of alveolar minute ventilation, V_A, to cardiac output, Q, influences the kinetics of inhaled anesthetic elimination throughout the entire elimination. After a brief and rapid decline in alveolar anesthetic partial pressure, the fractional clearance of anesthetic by the normal lung becomes constant, and incomplete clearance from the lung slows the anesthetic washout from tissues. The increase in the elimination time constant for body tissues is a function of the dimensionless group V_A/(λ_bg Q) that combines V_A, Q, and the blood/gas partition coefficient λ_bg. Slowing of tissue elimination by incomplete lung clearance becomes more pronounced at low V_A/Q ratios, and is predicted to become more pronounced as blood/gas solubility increases.

The work was supported by the Swedish Research Council (grant No. 2018-02438), Stockholm, Sweden, the Swedish Heart and Lung Fund, Stockholm, Sweden, and institutional sources of Uppsala University, Uppsala, Sweden, and the Otto-von-Guericke University Magdeburg, Magdeburg, Germany.

Dr. Baumgardner is president of Oscillogy LLC (Pittsburgh, Pennsylvania), the manufacturer of the multiple inert gas elimination technique by Micropore Membrane Inlet Mass Spectrometry system. The other authors declare no competing interests.

The functional residual capacity–dominated early time constant produces a very rapid early decrease in desflurane and sevoflurane elimination, decaying in less than 5 min as shown by the rapid approach to the retention equation plateau for all V_A/Q (figs. 5 and 6). The visceral group time constant can be estimated from Cowles et al.²³ and Mapleson's data⁵ on compartment volumes and fractional flows, combined with tissue partition coefficient data for the various central organs from Zhou and Liu.⁴³ We estimate, for desflurane, in our pigs the intrinsic visceral time constants for the normal, low, and high V_A/Q conditions, respectively, at 2.5, 1.3, and 3.7 min, and the clearance-corrected time constants at 3.5, 2.8, and 4.5 min. The corresponding estimates for sevoflurane for intrinsic visceral time constants are 3.8, 1.9, and 5.7 min, and the clearance-corrected time constants are estimated as 5.8, 4.8, and 7.3 min. Thus, after the first 20 min of elimination and approximately two to three effective visceral group time constants, the low arterial partial pressures (figs. 2 through 5 of the companion manuscript39) will be roughly matched in venous visceral blood with low venous partial pressures, and the visceral group will contribute little to the mixed venous washout kinetics. That leaves the muscle and fat groups (and possibly the intertissue diffusion group). Fat fractional flow, however, is about one tenth of the muscle fractional flow, limiting its contribution to mixed venous partial pressures. In addition, in our experiment, fat was very poorly equilibrated after 45 min, making it even less effective as a gas source for the mixed venous blood. It is therefore reasonable that the washout during 20 to 45 min is approximately monoexponential, since the washout is approximately described by a single muscle compartment.