Inhalation anesthesia using physiologically based pharmacokinetic models.

Drug Metabolism Reviews

ISSN: 0360-2532 (Print) 1097-9883 (Online) Journal homepage: http://www.tandfonline.com/loi/idmr20

Inhalation Anesthesia Using Physiologically Based Pharmacokinetic Models Vera Fiserova-Bergerova To cite this article: Vera Fiserova-Bergerova (1992) Inhalation Anesthesia Using Physiologically Based Pharmacokinetic Models, Drug Metabolism Reviews, 24:4, 531-557, DOI: 10.3109/03602539208996304 To link to this article: http://dx.doi.org/10.3109/03602539208996304

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DRUG METABOLISM REVIEWS, 24(4), 531-557 (1992)

INHALATION ANESTHESIA USING PHYSI0LOG ICA LLY BASED PHAR MACOKl NETlC MODELS* VERA FISEROVA-BERGEROVA, Ph. D. Department of Anesthesiology University of Miami School of Medicine Miami. Florida 33101

I.

11.

INTRODUCTION.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532 A. Physiologically Based Modeling . . . . . . . . . . . . . . . . . . . 532 B. Experimental Studies. . . . . . . . . . . . . . . . . . . . . . . . . . . 533 METHODS AND THEORETICAL CONSIDERATION . . . . . A. Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Definition of Fat Groups . . . . . . . . . . . . . . . . . . . . . . . . C. Metabolic Clearance . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Calculation of Parameters. . . . . . . . . . . . . . . . . . . . . . . .

534 534 536 537 537 538

111.

SIMULATION RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . 538 A. Validation of the Model; Comparison of Simulation with Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538 B. Factors Affecting Uptake and Elimination . . . . . . . . . . . . 545

IV.

CONSIDERATIONS IN SELECTING THE SIMULATION MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

548

*This paper was refereed by Lorenz Rhomberg, Ph.D.. Office of Research and Development, Environmental Protection Agency, Washington, DC 20460. tSend correspondence to: Vera Fiserova-Bergerova (Thomas), Ph. D.,Department of Anesthesiology, University of Miami School of Medicine, PO Box 016370,Miami, FL 33101.

53 I Copyright 8 1992 by Marcel Dekker, Inc

FISEROVA-BERG EROVA

532

A. Kinetics of Metabolism: Linear or Nonlinear Model. . . . . . 548 B. Number of Compartments and Exponential Functions . . . . 550 V.

CONCLUSIONS.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

551


Appendix: Calculation of Parameters. . . . . . . . . . . . . . . . . . . 55 I References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554

1. INTRODUCTION

A. Physiologically Based Modeling A pharmacokinetic model describing pulmonary uptake of inhalation anesthetic agents was the first physiologically based model predicting uptake of inhalation agents and providing insight on their motion within the body [I-41. The concept of the model is simple. The uptake is dictated by three parameters: tissue volume, tissue perfusion rate, and solubility of the anesthetic agent in biological matrices. The solubility is defined by the appropriate blood-gas and tissue-gas partition coefficients at body temperature. Based on the perfusion rate and solubility, the tissues are pooled in 3 groups known as vessel-rich group (VRG), muscle group (MG), and fat group (FG) [I]. Later on, when the importance of metabolism was recognized, the liver was treated separately as an excretory organ, with a rate constant influenced by the metabolic clearance 14-61. During clinical anesthesia, the inspired concentration of the anesthetic agent is manipulated so that the concentrations of the vapor in alveolar air and arterial blood are constant, and thus the uptake of the anesthetic agent by each tissue is independent of the uptake by other tissues. The rising of the concentration of the anesthetic agent in each tissue is described by an exponential function in which the exponent is a rate constant, defined by the perfusion rate multiplied by the blood-tissue distribution coefficient and divided by tissue volume. This model, however, does not apply if concentrations in alveolar air and arterial blood change. Such situations arise when the agent is inhaled at a constant or fluctuating inspired concentration, and during the wash-out period [5-71. In such circumstances, the uptake and wash-out in each tissue are affected by uptake and wash-out in other tissues, and the rate constants become hybrid constants reflecting the redistribution of the agent among tissues. The hybrid rate constants can be predicted from the same parame-


PHARMACOKINETICS FOR ANESTHESIA

533

ters as the rate constants already described for administration of anesthesia at constant alveolar concentration. However, the calculation of hybrid constants from these parameters is complex and can be accomplished by the mathematical procedure called Laplace transform [5, 6, 81. Models using such hybrid constants are used in inhalation toxicology [9-161 and have been employed to evaluate the occupational exposure of operating room personnel to anesthetic agents and to evaluate the recovery time of ambulatory patients to street fitness [7].

B. Experimental Studies Carpenter et al. [ 17-19] studied uptake and elimination of four anesthetic agents, administered as a mixture for 30 min or 2 h to patients (males and females) undergoing elective surgery. Contrary to the routine administration, subanesthetic concentrations of isoflurane, enflurane, halothane, and methoxyflurane were administered at constant inspired concentrations with concentration of each agent equal to about one-third of the concentration providing anesthesia (EC,,). Statistical analysis of the pulmonary washout data suggests that the exhalation curve consists of five exponential decays. The authors speculated that one decay, with a half-life of about 6 h, can be attributed to diffusion of the anesthetic agent into the fat immediately adjacent to highly perfused tissues. Later on, similar studies were performed in the same laboratory with sevoflurane (201 and desflurane 1211, and a five-compartmental mammillary model was proposed based on hybrid analysis of the five decays observed on the pulmonary elimination curves. However, tissue volumes and perfusion rates derived by the mammillary model grossly deviate from physiological values. For example, the calculated volume of muscle and skin of 9-7 L is grossly underestimated compared to 34 L usually cited for an adult [I-3, 221, as is the total volume of tissues in which the anesthetic agent is distributed (calculated values account for only 34-57% of body mass). Also, the calculated cardiac output of 4 L/min (range 3.3-5.6) is smaller than expected to be in an anesthetized adult. In this paper, 5-compartmental and 6-compartmental physiologically based simulation models were used to simulate experiments by Carpenter et al. [17-19]. Simulation and experimental data on uptake and elimination of inhalation anesthetic agents were compared and the better-suited 6-compartmental model was used to investigate the effects of body fat, metabolism, and exposure duration on the uptake and elimination of isoflurane, enflurane, halothane, and methoxyflurane.

FISEROVA-B ERG EROVA

534

11. METHODS AND THEORETICAL CONSIDERATION


A. Simulation Model Physiologically based 5-compartmental and 6-compartmental models were used to describe alveolar concentrations and amounts of isoflurane, enflurane, halothane, and methoxyflurane retained and eliminated during and following anesthesia. The 6-compartmental model, including the parameters for a reference man, are shown in Fig. l . To compare experimental and simulation data, the volumes and perfusion rates of tissue groups were adjusted to the average body height and body weight of the two groups of patients studied by Carpenter et al.: A group, exposed for 30 min. mean body height and weight 171 c d 6 5 kg [18]; B group, exposed for 2 h. 170 c d 7 3 kg 1171, which means, that compared to the reference man, the A group is on the slimmer side and the B group on the heavier side (see Appendix). The physiological parameters of the two groups and partition coefficients used in the study are shown in Tables I and 2, respectively. The Laplace transform was used to find the solution of differential equations describing the model 15, 6, 81. The computation was performed on an IBM-XTcomputer using software prepared in our laboratory; to generate the graphic image, the output data files were imported into the Lotus spreadsheet.

TABLE 1 Volumes and Perfusion Rates Used in the 6-Compartmental Model to Simulate the Experimental Data“

Parameter unit’ Lung Liver Other VRG MG Inner adip. tissue Subcut. adip. tissue

BHIBW ( c d k g ) 17 1165”

BHIBW (cmlkg) 170173’

Volume (L)

Perfusion (L/min)

Volume (L)

Perfusion ( Llmin )

0.44 1.82 4.05 35.28 3.10 8.69

6.08“ 1.46 2.7 I 1.06 0.66 0.19

0.47 1.80 4.00 34.89 6.65 9.60

6.00 I .44 2.68 1 .os

0.65 0.18

“Values for a reference man (170/70) are shown in Fig. I . ’BH = body height; BW = body weight; other VRG = vessel-rich tissues (except liver and lungs); MG = muscles and dermis. ‘Cardiac output.

535



-

9.2

FGc"t

0.18

ME TA BO Ll S M

FIG. 1. Six-compartmental simulation model. Lung group includes functional residual capacity, lung tissue, and arterial blood; vessel-rich group (VRG) includes brain, gastrointestinal tract, glands, heart, kidneys, and spleen; MG group includes muscles and dermis; FG,,group denotes inner adipose tissue; FG,,, denotes subcutaneous adipose tissue. Volume of each tissue group for a reference man (70 kg, 170 cm) is indicated in the left corner of the rectangle (V in liters). Perfusion rates are indicated at the right, below the lines picturing the vasculature ( F in literdmin); V,,, is alveolar ventilation (in literdmin). The arrows indicate instantaneous equilibration of vapor pressure between tissue and blood.

536

FISEROVA-BERGEROVA

TABLE 2


Partition Coefficients Used for Simulation

lsoflurane Enflurane Halothane Methoxyflurane

Blood

Liver

VRG

Muscle

1.4 I .9 2.3 15

4. I 4.4 6.0 25

2.4 3.0 4.5

2.2 3.2 3.4 16

16

Fat 74 100

170 850

Nore: Values are compiled from data in Refs. 23 and 24.

B. Definition of Fat Groups The International Commission on Radiological Protection has compiled information on body fat [22]. According to their report, body fat includes two kinds of adipose tissues: ( I ) subcutaneous adipose tissue, which, for a reference man, accounts for about 60% of body fat (50% for male and 68% for female); and (2) the inner adipose tissue, which, for a reference man, accounts for about 35% of body fat. About 5% to 10% of the body fat is interstitial fat, which is a part of blood and lean tissues. There is only scattered information on the volumes and perfusion rates of these tissues, and the estimated values vary depending on the tested population [ 221. There is, however, a general agreement that gaining or losing weight is mainly manifested by the changing volume of inner adipose tissue [22]. In this simulation study, the volume of fat-free tissues was estimated from the total body water, calculated from the average body height and body weight of the patients. Body fat was determined as the difference between body weight and mass of fat-free tissues. Since the reported experimental data are mean values obtained from male and female patients, it was assumed that 60% of body fat of a reference man is subcutaneous adipose tissue, perfused at the rate of 0.02 L/min/kg. and that 35% of body fat is inner adipose tissue, which is perfused at the rate of about 0.12 L/min/kg. The literature 122) indicates that body weight affects the volume of inner adipose tissue much more than the volume of subcutaneous adipose tissue. In this study, the difference is a multiple of 3.5 (for details see Appendix). In the 5-compartmental model, the two adipose tissues were combined by adding their volumes as well as their perfusion rates. Volumes and perfusion rates of the two adipose tissues, estimated by equations described in the Appendix, are in the range of physiological values and were used in the model without any attempt to modify them in order to optimize the fit to experimental data.


537


C. Metabolic Clearance Metabolism of halothane and methoxyflurane is a capacity-limited process 1251, which can be inhibited in the presence of other anesthetic agents [26-281. To describe capacity-limited metabolism, metabolic clearance is defined as a function of the concentration of the agent at metabolic sites [29]. Since functions describing the dependence of metabolic clearance on concentrations of the administered mixture cannot be defined, owing to lack of human data, a simplified linear model using different clearance values for anesthesia and postanesthesia periods was tested. Clearance for the anesthesia period was determined from the pulmonary uptake rate at the end of anesthesia, after subtracting the tissue uptake rate. Pulmonary uptake rate was determined as a difference between inspired and alveolar concentration multiplied by alveolar ventilation, using experimental data by Carpenter et al. [17, 181. The tissue uptake rate was estimated by simulation of exposure to the inspired concentration, assuming no metabolism. To minimize the error induced by the inaccuracy in the estimate of tissue uptake, the clearance was calculated using values obtained for the end of exposure when the tissue uptake is relatively small and metabolism uses up most of the pulmonary uptake. Halothane clearance after anesthesia was made equal to hepatic blood flow. Methoxyflurane clearance for the postanesthesia period was found by fitting the simulation to experimental data. Extrahepatic metabolism of methoxyflurane was postulated since no reasonable fit to experimental data was obtained if metabolic clearance was equal to or below hepatic blood flow. To account for extrahepatic metabolism, liver was included in the VRG compartment so that the metabolic clearance could be raised up to 75% of cardiac output (which is that fraction of cardiac output which perfuses liver and other vessel-rich tissues). In the process of finding the clearance values, all physiological parameters were maintained the same as in the simulation of isoflurane and enflurane.

D. Experimental Data Since Carpenter et al. [ 17, 181 presented the concentrations in exhaled air in a graphic form, the experimental points were digitalized using superimposition with an appropriate semilogarithmic paper. Other data (time constants, area under the curves, fractions exhaled) were taken from tables published by the same authors. The time constants were converted to halflives by multiplying by the natural logarithm of 2 (In 2)

538

FISEROVA-BERGEROVA


E. Calculation of Parameters The half-lives were calculated by dividing In 2 by the exponent (rate constant), obtained for each compartment using Laplace transform. The areusunder-the-decays (AUC) were calculated as the definite integral of the exponential function, that is, by dividing the y intercept of each decay by its rate constant. The y intercepts were calculated by residual analysis of the simulated exhalation curves, using 2 points obtained in the time period when the contribution of the particular decay was predominant (shown on the bottom line of Fig. 2 ) .

111. SIMULATION RESULTS

A. Validation of the Model; Comparison of Simulation with Experimental Data Four parameters were used to verify the model: ( I ) elimination half-life, (2) alveolar concentration during and following exposure, (3) fraction of the retained amount which was exhaled after exposure, (4) areas-under-decay of the exhalation curves (AUC). The results from the simulations, using the 5 and 6-compartmental models were compared with experimental data obtained from studies in volunteers exposed to a mixture of four anesthetic agents for 30 min [18] or for 2 h [17]. In the simulation study, the volumes and perfusion rates of tissues were adjusted to body weight and body height of the experimental groups (Table I ) . Clearance values as shown in Table 3 were used.

1. Elimination Half-Life The experimental data and simulation results are compared in Fig. 3 (the shortest half-lives are not shown inasmuch as they were shorter than 2 min in both the experimental and simulation studies). The differences in halflives between groups A and B are induced by differences in body build. No striking differences were observed between simulation and experimental values obtained for both groups. From 32 pairs of values, the simulation results were within the range of the experimental values (mean -+ 2 SE) in 18 instances (56%), and outside the range of experimental values (mean -+ 3 SE) in only 8 instances (25%). The differences between experimental

539



ISOFLURANE

ENFLURANE

HALOTHANE

n

40

30 20 10 0

96 50 40

30 20 10

0 5 -15

mln

1 - 2 hrs

6 - 2 4 hrs

2 6 s hrs

FIG. 2. Percentage of total exhaled amount recovered under the major decays: comparison of experimental and simulation results. The values are given for 0.5-h and 2-h exposures obtained by using a 6-compartmental model (plain bars) and in an experimental study (shaded bars; Table 4 in Ref. 18). The time intervals shown under the exposure durations indicate the approximate time during which the contribution of the decay is predominant. The input data for simulation are adjusted to the mean body build of the experimental groups (see Appendix).

FISEROVA-BERGEROVA

540

TABLE 3


Metabolic Clearance (L/min) Used in Simulations

Isof I urane En f I urane Halothane Methoxyflurane

During anesthesia

After anesthesia

0.0014 0.026 0.17 O.ooOo7

0.0014 0.026 1.47 4.00

and simulated results were larger for extensively metabolized agents (halothane and methoxyflurane) than for poorly metabolized agents (isoflurane, enflurane).

2. Alveolar Concentration Experimental data and simulated results for exposures of patient groups A and B are compared in Figs. 4-6. During exposure, the main differences between simulation and experimental data appear during the first 10 min of exposure to halothane and methoxyflurane (Fig. 4). Nonlinear metabolism could contribute to the differences, as is explained later. The 6-compartmental model shows somewhat higher values than the 5-compartmental model, but the difference, never exceeding 2 I % of the mean values, is barely noticeable (Fig. 4). After the exposure, the alveolar concentrations declined as shown in Figs. 5 and 6. During the first postexposure hours, the experimental data fit both the 5- and 6-compartmental models (Fig. 5 ) . but later on, the 5compartmental model became unacceptable (Fig. 6).

3. Fraction Exhaled Fractions of pulmonary uptake exhaled following 30-min and 2-h exposures are shown in Fig. 7. There is a good agreement between simulation and experimental data. In the experimental studies, no significant difference was observed between data obtained in the 30-min exposure study and in the 2-h exposure study 1181. The differences observed in the simulation studies are also negligible. Similar results (not shown) were obtained using the 5-compartmental model.

IS0

..

EN F


MOF

HAL

mini

.. ..

..

c.

50 40

30 20 10

"1

.. n

I

10

cc

0

'

..

.

A

B

A

B

A

B

A

B

FIG. 3. The half-lives of the four major decays of exhalation curves: comparison of experimental and simulation results. On the ordinates are elimination half-lives in minutes or hours for studies A (BHIBW, 171 c d 6 5 kg, 30-min exposure) and B (170 cm/73 kg, 2-h exposure). Half-lives calculated by Laplace transform using a 6-compartmental model are shown as plain bars, experimental values as shaded bars [taken from Table 1 in Ref. 18 (A) and Ref. 17 (B)].The differences in half-lives between groups A and B are introduced by differences in the body build. Exposure duration had no effect on half-lives. *The simulation value exceeds mean 5 2 SEM of experimental values. **The simulation value exceeds mean ? 3 SEM of experimental values.

542

FISEROVA-BERGEROVA 1

IS0

IS0

. &*

ENF

HAL


u-

ENF

:-

HAL

(La 0.5

0.

MOF

MOF

0

10

20

30

MINUTES

0

20

40

80

80

100

120

MINUTES

FIG. 4. The rising of alveolar concentration during 30-min and 2-h exposures to a mixture of four anesthetic agents: comparison of experimental and simulation results. On the ordinate is the ratio of alveolar concentration at the time indicated on the abscissa (FA)and inspired concentration ( F , ) . Symbols denote experimental values obtained from Fig. I in Ref. 18 (left) and Fig. 1 in Ref. 17 (right); A isoflurane. ISO; A enflurane, ENF; o halothane, HAL; 0 methoxyflurane, MOF. Lines are obtained by simulation models, taking into consideration the differences in body build of patients entering the 30-min and 2-h exposure studies (see Appendix); 6compartmental model (solid line) and 5-compartmental model (broken line). 4. Areas Under Major Decays The areas recovered under the four major decays in the experimental and simulation studies are compared in Fig. 2. Areas under the exponentials with half-lives shorter than 2 min are not shown. They account for less than 1.5% of the total areas in both experimental and simulated studies.

5. Conclusions The agreement between the uptake and elimination data obtained with poorly metabolized isoflurane and enflurane in experimental studies by Carpenter et al. [17-191 and in our simulation study (Figs. 4-7) supports


543


0

.1

0

U* \

U*

.01

.OO'

I

I

2

I

I

I

4

HOURS

FIG. 5. Pulmonary elimination of isoflurane and halothane during the first 5-h following 30-min or 2-h administration: comparison of experimental and simulation results. On the ordinate is the ratio of alveolar concentrations at the time indicated on the abscissa ( F A )and at the disconnection of the delivery of the agents (FAO).Symbols denote experimental values obtained from Fig. 3 in Ref. 18. Lines are obtained by simulation using a 6-compartmental (heavy lines) or 5-compartmental model (thin lines; shown for 2-h exposures only). --- A isoflurane; -o halot hane .

the concept of two adipose tissue groups as well as the algorithm for calculation of volumes and perfusion rates shown in the Appendix. The agreements between measured and calculated half-lives (Fig. 3) and areas under the decays (Fig. 2) are also reasonably good considering the confounding factors in statistical analysis of muhiexponential functions 1301 and the uncertainties in the estimation of volumes and perfusion rates of the tissues.

2

nouns


Ol

O l

.oool-

.0001~

1 0

2

0

4

DAYS

IY)

4

2

DAYS

30 MINUTES

*OF

nr1 ENF

t

0

150

a

4 DAIS

FIG. 6. Pulmonary elimination of anesthetic agents following 2-h and 30-min exposures to a mixture of four anesthetic agents: comparison of experimental and simulation results. On the ordinate is the ratio of alveolar concentrations at the time indicated on the abscissa ( F A ) and at the disconnection of the delivery of the agents (FA0). Symbols denote experimental values obtained from Figs. 2 and 3 in the Ref. 17 (upper graphs), and Fig. 2 in Ref. 18 (lower graphs). Lines are obtained by a 6-compartmental simulation model (left side) and by a 5-compartmental model (right side). - _ - - - A isoflurane, ISO; - . - A enflurane, ENF; -o halot hane , HAL; . . . . . 0 methoxyflurane, MOF. The figure shows that the 6compartmental model describes the experimental data better than the 5compartmental model.

PHARMACOKINETICS FOR ANESTHESIA 100.

IS0

ENF

EAE

E AE

545 HAL

M OF

90.

w


Y

22 8

80. 70-

6050-

Q

2 z 8K

h

40-

302010L

FIG. 7. Fraction of pulmonary uptake exhaled after 30-min and 2-h administration of a mixture of four anesthetic agents: comparison of experimental and simulation results. Es are mean values obtained in experimental studies A and B (Table 3 in Ref. 18); As and Bs are results of simulation of both experimental studies obtained using a 6-compartmental model and parameters shown in Tables 1-3. ISO, isoflurane; ENF, enflurane; HAL, halothane; MOF, methoxyflurane. B. Factors Affecting Uptake and Elimination 1. Effects of Body Weight and Exposure Duration

The two experimental studies by Carpenter et al. [17, 181 differ in two parameters: exposure duration and body fat of the patients. To determine the contribution of body fat and exposure duration to the differences in expired concentrations observed in the two Carpenter studies, the 6compartmental model was used to simulate situations in which the two groups of patients with different body builds underwent exposure for 30 min and for 2 h (Fig. 8). The simulation shows that the elimination half-lives are affected only by body build, but not by exposure duration. On the other hand, concentrations of anesthetic agents in body fluids and exhaled air are mainly affected by exposure duration and are affected to a lesser extent by body fat. The longer the exposure and the larger the body fat volume, the higher the concentration becomes.

546

FISEROVA-BERGEROVA

O1


HALOTHANE

i

1

DAYS

4

0

'

7-

DAYS

FIG. 8. Effect of exposure duration and body fat on pulmonary elimination of halothane and isoflurane: simulation study. The 6-compartmental model was used to simulate 2-h and 30-min exposures of patients with different body builds: -170 c d 7 3 kg, - - - - - 171 c d 6 5 kg. On the ordinate is the ratio of alveolar concentrations at the time indicated on the abscissa ( F A )and at the disconnection of anesthetic agent delivery (FAo). The effect of body build is most apparent on the 1st and 2nd postanesthesia days. The duration of external exposure affects the positioning of the curve on the postanesthesia days. The effects of both exposure duration and body fat are most apparent on the postanesthesia days when the wash-out from the fat depot dictates the pulmonary wash-out rate. The effects of both exposure duration and body fat on exhalation of isoflurane and halothane are shown in Fig. 8. The same pattern, not shown in Fig. 8, was observed for enflurane and methoxyflurane. Experimental data and simulation also show that exposure duration had a profound effect on the amount retained in the body (Fig. 9) but not on the fraction exhaled (Fig. 7). Body fat had a relatively small effect on both uptake and fraction exhaled.

2. Effects of Adipose Tissues: One or Two Compartments The simulation revealed that separate treatment of subcutaneous and inner adipose tissues had no apparent effect on concentrations of anesthetic agents in alveolar air during administration of anesthesia (Fig. 4) or during the first 24 h thereafter (Fig. 5). Afterward, the need for treating the two

PHARMACOKINETICS FOR ANESTHESIA 450

547

I

mg

4 00


350

300 250

200

150

100

50

0.5 I

so

2

0.5

2 ENF

0.5 2 HAL

0.5 MOF

IRS

FIG. 9. Effect of body build and exposure duration on the amount absorbed: simulation study. The 6-compartmental model, using parameters shown in Tables 1-3, was used to simulate 0.5-h and 2-h inhalation exposures to I mg/L of isoflurane (ISO). enflurane (ENF), halothane (HAL), and methoxyflurane (MOF). The body height and body weight of the subjects were 171 c d 6 5 kg (plain bars) and 170 c d 7 3 kg (shaded bars). On the ordinate is the amount of the absorbed agent in milligrams. The effect of body build was relatively small compared to the effect of exposure duration. types of adipose tissues separately is apparent (Fig. 6). The inner adipose tissue plays a predominant role on the second postanesthesia day, as shown in Fig. 8, where the simulations for subjects with different body weight (and consequently different volumes of inner adipose tissue) are compared. Two days after the end of external exposure (inhalation), the wash-out of the anesthetic agents from subcutaneous adipose tissue is the rate-limiting step in pulmonary wash-out. Simulation revealed that the differences

FISEROVA-BERGEROVA


548

between the effects of the two adipose tissues on the shape of the exhalation curve may become indistinct when the patient resumes normal activity and distribution of cardiac output changes. Carpenter et al. [17-191 speculated that the decay with the half-life of about 6 h is a result of diffusion between well-petfused organs and adjacent adipose tissue. This possibility cannot be excluded and it is possible that the transportation rate to the inner adipose tissues is a product of both petfusion and diffusion.

3. Effects of Metabolism To study the effect of metabolism on exhalation of halothane and methoxyflurane, the simulations with a 6-compartmental model were repeated using arbitrarily selected values for metabolic clearance between zero (suppressed metabolism) and 4 (perfusion rate of all well-perfused tissues). Metabolism persistently shortened the half-lives of all decays and reduced the amount exhaled. Simulation also revealed that, if metabolism is suppressed during anesthesia, the pulmonary elimination would be prolonged, but the exposure duration would have little or no effect on the recovery of the anesthetic agents in the exhaled air (when C1 = 0 the recovery is 100%).On the other hand, if metabolism during anesthesia was extensive, the recovery in exhaled air decreased with exposure duration. For example, if the metabolic clearances during and following exposure were 1.47 L/min for halothane and 4 L/min for methoxyflurane, the recovery of the retained amount in exhaled air after 30-min and 2-h exposures to halothane was 55% and 46%, respectively; and to methoxyflurane, 15% and 12%, respectively. On the other hand, if metabolism was suppressed during anesthesia, the recovery in exhaled air was 65% for halothane and 22% for methoxyflurane, regardless of the duration of delivery of the agents. Thus, the finding in Carpenter’s studies that recovery of halothane and methoxyflurane in exhaled air was unaffected by exposure duration indicates that the metabolism during anesthesia was largely suppressed.

IV. CONSIDERATIONS IN SELECTING THE SIMULATION MODEL

A. Kinetics of Metabolism: Linear and Nonlinear Model The linear kinetic models can be applied only if all parameters affecting the rate constants (and consequently the half-lives) do not change. These



549

parameters are volumes and perfusion rates of tissues, partition coefficients, and metabolic clearance. These conditions for linear kinetics were met for poorly metabolized isoflurane and enflurane (C1 < 0.03 L/min). On the other hand, the comparison of simulation and experimental data of extensively metabolized halothane and methoxyflurane indicates that metabolism during anesthesia was much slower than after anesthesia. As a result of slow metabolism, the half-lives during anesthesia administration are longer than elimination halflives during postanesthesia. as was shown in both experimental and simulation studies. Suppression of metabolism of halothane and methoxyflurane during anesthesia raises a question about the validity of linear models for description of anesthesia. It has been shown that excretion of nonvolatile drugs administered in large doses cannot be described by exponential functions [31]. On the other hand, experimental data as well as the simulation by nonlinear models 17, 291 indicate that exhalation curves of volatile agents after anesthesia can be described by a sum of exponentials. The explanation of the controversy may lie in the efficacy of pulmonary clearance: When the inhalation of the agent ends, the agent present in liver is readily depleted by the metabolism and the supply of the agent is rapidly reduced due to extensive pulmonary excretion. Thus the availability of the anesthetic agent in the liver is instantly reduced to the range of apparent first-order kinetics. Therefore the linear model can be used to describe the exhalation of anesthetic agents following inhalation anesthesia. The application of linear models to describe uptake, distribution, and elimination of inhalation agents during anesthesia is more difficult to justify. In the absence of suitable human data for construction of a nonlinear model, we attempted to apply the linear model, making the following assumptions and simplifications. Metabolism of the anesthetic agents takes place in well-perfused tissues. Pharmacokinetic processes initiated in these tissues are characterized by a very short half-life (less than 5 min). For practical purposes it can therefore be assumed that an apparent steady state between the supply rate of the anesthetic agent to the metabolic site and metabolic rate is established within 10 min after the start of anesthesia. At the same time, the rising of the concentration of the agent in arterial blood becomes so slow that metabolic rate and metabolic clearance appear to be constant. This means that the conditions for the application of a linear model are met. However, due to the saturation of the metabolizing enzyme system, the metabolic clearance during anesthesia is smaller than following anesthesia. Figure 4 shows that a linear model with a properly reduced metabolic clearance for the anesthesia period is applicable for description of pulmonary uptake and excretion with the exception of the


550

FISEROVA-BERGEROVA

first 10 min of anesthesia administration. These 10 min coincide with a period which clinical anesthesiologists call “induction.” Induction is characterized by the rapid rise of the inhaled agent in blood, brain, and other well-perfused tissues, which cause changes in some respiratory and cardiovascular functions. Since there is a little control over these changes, the description of the induction period remains questionable. We concluded that, in the absence of data supporting the nonlinear function in the model, a linear model using different metabolic clearances for anesthesia and postanesthesia periods can be used to describe uptake, distribution, and elimination of inhalation anesthetic agents after the induction period. It remains to be seen if a simplification such as this is acceptable for the description of metabolites excretion.

B. Number of Compartments and Exponential Functions The number of compartments in the physiologically based model and the number of exponential decays needed to describe pulmonary uptake and elimination may not necessarily be the same. Based on differences in perfusion rates of tissues, solubility of the agent, and ability of the organs to remove the agent from circulation, the 6-compartmental model is fully justified. On the wash-out curves, each compartment is depicted by an exponential function. However, only those exponentials are distinguishable which have a different starting point, and a rate constant ratio larger than 5 1301. Otherwise the number of apparent exponentials can be smaller than the number of compartments in the model. For example, the simulation shows that the half-lives for the lung group, liver, and other VRG are very short and so similar that these three exponential decays are undistinguishable from one another. Another example: Uptake by adipose tissues during the first hours of anesthesia plays a negligible role compared to uptake by the better-perfused tissues and therefore is not apparent during the relatively short anesthesia used in studies by Carpenter et al. [17, 181. On the other hand, the same authors observed to decays with long half-lives on the desaturation curve 24 h after anesthesia, when wash-out from inner and subcutaneous adipose tissues plays a predominant role at different periods of time. Simulation studies show that these two exponentials may overlap if the patient resumes normal activity and thus increases pulmonary ventilation and cardiac output, and alters distribution of cardiac output by raising perfusion of subcutaneous adipose tissue faster than perfusion of inner adipose tissue [32]. Under such circumstances both adipose tissues can be treated as one compartment.


55 I


V. CONCLUSIONS Carpenter et al. [17-19] have shown that, following inhalation anesthesia, the pulmonary elimination of the agent is better described by 5 exponentials than by the conventional 3 exponentials, speculating that two exponentials are related to uptake and elimination in adipose tissues. To test this hypothesis, experimental conditions from the studies by Carpenter et al. were simulated using physiologically based models in which inner and subcutaneous adipose tissues were treated as one compartment or as two compartments with different perfusion rates. After comparing the experimental data with simulation, it was concluded that the separate treatment of inner and subcutaneous adipose tissues improves the fit to experimental data, the improvement mainly being apparent on the first postoperative day. Experimental data on extensively metabolized halothane and methoxyflurane indicate nonlinear kinetics of metabolism during anesthesia (when metabolism is suppressed), but not after anesthesia, when the exponential functions describing exhalation curves indicate linear kinetics. The abrupt switch from nonlinear kinetics to linear kinetics at the interruption of anesthesia is attributed to the rapid drop in the concentration of the agents in alveolar air and arterial blood, which is due to the efficacy of the pulmonary wash-out. The comparison of simulation with experimental data also revealed that, in the absence of data needed to describe the nonlinearity in metabolism, the linear model, which uses a different metabolic clearance during anesthesia and postanesthesia periods, can be used to describe pulmonary uptake and exhalation of extensively metabolized agents. A model such as this describes the experimental data well and, contrary to the mammillary model, it is in accord with physiological parameters. Because of the similarity of the half-lives of some compartments, or because of the subdued effects of some compartments at a certain period of time, the number of decays distinguishable in experimental studies may be smaller than the number of compartments employed in the physiologically based simulation model. Duration of external exposure, body build, postanesthesia activity of the patient, and the presence of other drugs affect the shape of the elimination curve of the inhalation anesthesia agents.

APPENDIX: Calculation of Parameters The information used to calculate volumes and perfusion rates of tissue groups was compiled from Refs. 1-6, 12, 22, 30, and 32-34. The algorithm for calculation of volumes and perfusion rates used in the 6compartmental model is as follows:

552

FISEROVA-BERGEROVA

Body weight (BW in kilograms) and body height (BH i n centimeters) are given. The “ideal” body weight, BW*, of the person was calculated using body mass index BMI = 2 4 , and the following equation:


BMI

=

BW

*

104/BH2

(1)

This yields

BW* = 0.0024 * BH2

(2)

The parameters for “ideal” body weight are further indicated by an asterisk. Total body water (TBW in liters) was calculated for the given and “ideal” body weights, substituting BW or BW*, respectively, in Eq. (3).

TBW = 0.1757 BH

+ 0.331 BW

- 12.86

(3)

Similarly, given the “ideal” fat-free body masses (FFM in kilograms) and their volumes (BV in liters) were calculated using Eqs. (4) and (5). FFM = TBWlQ.72

(4)

BV

(5)

= FFMlI.1

The parameters for “ideal” body weight were used to calculate the volumes of lean tissue groups: Liver:

V,i,

Other vessel-rich tissues:

VVRG = 0.0789 BV*

Muscle and skin:

V,

= 0.0355 BV*

= 0.688 BV*

The body fat mass was calculated as the difference between body weight and fat-free body mass, so that the fat volume, FV. for the given and “ideal” body weights are:

FV

=

(BW - FFM)/0.92

FV* = (BW* - FFM*)/0.92 The body fat includes 2 kinds of adipose tissue: subcutaneous adipose tissue, which, in a reference man, accounts for about 60% of the body fat; and inner adipose tissue, which accounts for about 35% of the body fat 122,



553

331. The remaining 5% is interstitial fat, which is included in the volume of lean tissue groups. It has been shown that age and diet mainly affect the volume of inner adipose tissue and have little effect on the volume of the subcutaneous adipose tissue. Since quantitative data on distribution of increments of fat are not available, we arbitrarily chose 20% of the increment as being deposited in subcutaneous adipose tissue, 70% in inner adipose tissue, and 10% being interstitial fat. The volume of the two adipose tissues were estimated using the following equations: Volume of subcutaneous adipose tissue: VFcul = 0.6 FV* + 0.2 (FV - FV*) Volume of inner adipose tissue: VFin = 0.35 FV* + 0.7 (FV - FV*) Coefficients 0.6 and 0.35 are taken as an average for both sexes, and the effect of aging is not included because of lack of information. The perfusion rates ( F in liters/minute) of the tissue groups were calculated under the assumption that changes in body fat have no effect on perfusion rate of the organs.

FVRC = 0.67 V f R , F M , = 0 . 0 3 V,& FFin

=

0.12 V & ,

FFcul = 0.02 V$cul Where the coefficients are perfusion rates expressed in liters/minute/kilogram ( I ) . Since no information on perfusion rate of inner adipose tissue was found in the literature, it was calculated as a difference between cardiac output (Q in liters/minute). calculated from body surface (SA in square meters) and the sum of perfusion of the other tissues of a reference man (BW = 70 kg, BH = 170 cm). In an anesthetized man:

Q = 3.3 SA = 3.3 (0.0072

Bw.425 BH0.725)

and the coefficient for inner fat is,

*

(18)


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FISEROVA-BERGEROVA

The capaciry oftissues to retain the anesthetic agent is calculated by multiplying the volume of each tissue group by the appropriate tissue-gas partition coefficient at body temperature (Table 2). Since no information on the dependence of partition coefficients on interstitial fat is available, the same partition coefficients were used for both groups of patients. The capacity of the lung group (center compartment), C,,,,,, was estimated using the volume of lung tissue and arterial blood multiplied by the appropriate partition coefficients (A), and functional residual capacity. C,,,,,

=

(0.00907 Alung,/gas

+

0.0193 hblodgas+ 0.0552) BV*

(20)

The transportation rate of the agent through the tissue groups was calculated by multiplying the perfusion rates by the blood-gas partition coefficients. The transportation through the center compartment was defined by cardiac output multiplied by blood-gas partition coefficient, and by alveolar ventilation. The transportation through the liver was defined by hepatic blood flow and metabolic clearance, both multiplied by the blood-gas partition coefficient. To calculate the capacity of tissues and transportation rate of the agent at administered concentrations, the values are multiplied by the inspired concentration expressed in milligrams/liter. The calculated values are only estimates and may not be valid for children or obese or undernourished adults.

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the pharmacokinetics or metabolism of inhaled anesthetics in humans? Anesth. Analg., 66, 1-8 (1987). 1191 R. L. Carpenter, E. I. Eger 11, B. H. Johnson, J. D. Unadkat, and L. B. Sheiner, The extent of metabolism of inhaled anesthetics in humans, Anesthesiology, 65, 201-205 (1986). 1201 N. Yasuda, S. H. Lockhart, E. I. Eger 11, R. B. Weiskopf, J. Liu, M. Laster, S. Taheri, and N. A. Peterson, Comparison of kinetics of sevoflurane and isoflurane in humans, Anesth. Analg. , 72, 316-324 (1991). [21] N . Yasuda, S . H. Lockhart, E. I. Eger 11, R. B. Weiskopf, B. H. Johnson, B. A. Freire, and A. Fassoulaki, Kinetics of desflurane. isoflurane. and halothane in humans, Anesthesiology, 7 4 , 489-498 (1991). [ 221 International Commission on Radiological Protection, Report of the Task Group on Reference Man, ICRP Publ. 23, Pergamon Press, New York, 1975, pp. 43-45. [23] V. Fiserova-Bergerova, Gases and their solubility: A review of fundamentals, in Modeling of Inhalation Exposure to Vapors: Uptake, Disrribution, and Elimination (V. Fiserova-Bergerova, ed.), Vol. 1 , CRC Press, Boca Raton, FL, 1983, pp. 3-28. [24] N. Yasuda, A. G. Targ, and E. 1. Eger 11, Solubility of 1-653, sevoflurane, isoflurane, and halothane in human tissues, Anesth. Analg., 69. 370-373 (1989). [25] V. Fiserova-Bergerova and R. W. Kawiecki, Effects of exposure concentrations on distribution of halothane metabolites in the body, Drug Metab. Dispos., 12, 98-105 (1984). (261 V. Fiserova-Bergerova, Inhibitory effect of isoflurane upon oxidative metabolism of halothane, Anesth. Analg., 6 3 , 399-404 (1984). [27] V. Fiserova-Bergerova and D. F. Dolan, Transient inhibitory effect of isoflurane upon oxidative halothane metabolism. Anesth. Analg., 64, 1171-1177 (1985). [28] K. J. Fish and S. A. Rice, Halothane inhibits metabolism of enflurane in Fischer 344 rats, Anesthesiology, 59, 417-420 (1983). [ 29) V. Fiserova-Bergerova, Simulation model for concentration dependent metabolic clearance of halothane, Anesrhesiology, 59, A223 ( 1983). [30] V. Fiserova-Bergerova, Introduction to mathematical model, in Modeling of Inhalation Exposure to Vapors: Uptake, Distribution, and Elimination (V. Fiserova-Bergerova, ed.), Vol. I , CRC Press, Boca Raton, FL, 1983, pp. 51-70. (311 G. Levy, T. Tsuchiya, and L. €? Amsel, Limited capacity for salicyl phenolic glucuronide formation and its effect on the kinetics of salicylate elimination in man, Cfin. Pharmacol. Ther., 13, 258-268 (1972).



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