Introduction:
　Two major factors affect the solubility of volatile anesthetics in human blood during clinical anesthesia.  Hypothermia increases ^[1-3], but crystalloid hemodilution decreases ^[4,5] blood/gas partition coefficients (λ_B/G ) of volatile anesthetics.  Although the effects of hypothermia and crystalloid hemodilution on blood solubility of halothane, enflurane and isoflurane have been observed during cardiopulmonary bypass (CPB) by some researchers ^[5-8], no study has been performed to investigate the combined effect of these two factors carefully and systemically.  In addition, data on the two newest agents, sevoflurane and desflurane, are limited.  In order to provide such information for predicting blood solubility at different clinical conditions for all modern halogenated volatile anesthetics, we measured the λ_B/G of desflurane, sevoflurane, isoflurane, enflurane, and halothane under different temperature and crystalloid hemodilution conditions.
Methods：
　Approved by the Committee of Scientific Research in our hospital, informed consent was obtained from each of the twelve male health unmedicated volunteers (32±7 yr.).  230 ml of venous blood anticoagulated with 2500U heparin was obtained from each volunteer.  Blood was separated into its plasma and blood cell fractions by centrifugation (1500 rpm, 15 min.).  Blood sample of hematocrit 40% was prepared by removing a certain amount of aliquot of plasma or red blood cells from each blood sample based on its hematocrit before the separation.  By adding different amounts of normal saline into the hematocrit 40% blood sample obtained above, five additional blood samples with different hematocrit (36%, 32%, 28%, 24%, and 20%) were prepared.λ_B/G of anesthetics for each hematocrit blood sample were measured at six temperatures: 37℃, 33℃, 29℃, 25℃, 21℃, and 17℃.λ_B/G of desflurane, sevoflurane, and enflurane were simultaneously measured with a mixture of the three anesthetic vapors in air for blood sample from each of six volunteers.λ_B/G of isoflurane and halothane were simultaneously measured with a mixture of the two anesthetics in air for blood sample from each of the other six volunteers. 
　The λ_B/G of the five anesthetics were measured within 12 hr of blood collection by a GOW-MAC 580 gas chromatography (GOW-MAC Instrument- Co. Bethlehem, PA, USA), equipped with a 6-meter-long stainless steel column (0.32 cm in diameter) packed with chromosorb-P 60/80 Mesh maintained at 75℃.  A 10 ml/min nitrogen carrier stream flow was delivered through the column to a flame ionization detector supplied by hydrogen at 35 ml/min and by air at 300 ml/min.  Output from gas chromatography was collected by a integrator and peak areas were calculated automatically.  Primary and secondary (compressed gas tank) standards were used to calibrate the gas chromatography.  Primary standards were produced by injection of aliquot of each volatile anesthetic into a glass flask of known volume with glass syringe.  The primary standards (glass flask) were used to calibrate the secondary standards.  The secondary (tank) standards were injected at intervals to calibrate the gas chromatography during each study.  Peak areas were proportional to concentrations over the entire range of the concentrations tested, and the regression equation was used to convert peak area to agent concentration (R₂>0.9995).
　　We determine λ_B/G by using two-stage headspace equilibration method, which was described before ^[9].  20-ml gas-tight glass syringe calibrated precisely and capped with a three-way stopcock was sealed by coating the plunger with a thin layer silicone grease.  Approximately 7 ml of blood sample was drawn into a syringe and anesthetic gas mixture (0.6% desflurane, 0.4% sevoflurane, and 0.4% enflurane; or 0.7% isoflurane and 0.6% halothane) was added to 18-ml scale, and then the three-way stopcock was closed.  The syringe was shaken vigorously and immersed in a waterbath with a chosen test temperature.  Every 15 min for 2 hr, the syringe was shaken vigorously for 5-10 seconds.  After the third shaking, plunger of the syringe was withdrawn to the 20-ml scale with stopcock closed.  This created a slight negative pressure in the syringe.  The stopcock was then opened briefly to allow air entering the syringe and the pressure in the syringe to reach ambient pressure.  After this 2 hr period (the first equilibration), the concentration of anesthetics (C₁ ) in the gas phase of the syringe was analyzed by gas chromatography.  All gas and some blood in the syringe were expelled and exact 4 ml of blood (Vb) was remained in the syringe for the second equilibration.  Then vapor-free air was drawn to 18-ml scale.  The syringe was shaken vigorously and immersed in the waterbath with the same temperature as in the first equilibration.  A same procedure in the second equilibration is applied as in the first equilibration.  Blood/gas partition coefficient was calculated as:
λ_B/G  =  ( Vg/Vb) ×[C₂/(C₁-C₂)]
　Where C₁ and C₂ is the anesthetic concentration in the gas phase of the syringe at the end of the first and second equilibration periods, respectively; Vg is the gas volume in the syringe for the second equilibration; and Vb is the blood volume remained in the syringe for the second equilibration.
　Normal saline/gas partition coefficients (λ_S/G) of desflurane, sevoflurane, isoflurane, enflurane, and halothane at each of the six temperatures (37℃, 33℃, 29℃, 25℃, 21℃, and 17℃) were measured for six times by using the same method as blood.
　Means and standard deviations were obtained for λ_B/G in different temperatures and hematocrit values, λ_S/G in different temperatures.  We regressed log_eλ_B/G on hematocrit, log_el_B/G and log_eλ_S/G on temperature.  The slope of regression line of log_eλ_B/G and log_eλ_B/G on temperature was defined as temperature coefficient (percentage change in λ_B/G or λ_S/G per centigrade degree, %/℃) ^[10].  The slope of regression line of log_eλ_B/G on hematocrit was defined as hematocrit coefficient (percentage change in λ_B/G per percentage change in hematocrit, %/1%hematocrit).  The ratio of mean λ_S/G to mean λ_B/G in hematocrit 40% undiluted blood at the same temperature was defined as R_S/B.  We regressed hematocrit coefficient on R_S/B, and temperature coefficient on respective λ_B/G at 37℃.  Using multiple linear regression method, we analyzed the combined effect of hypothermia and crystalloid hemodilution on the logarithm of λ_B/G of the five anesthetics.  P<0.05 was accepted to indicate a statistical significance.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

Results
　λ_B/Gs in hematocrit 40% non-crystalloid hemodilution blood were 0.55±0.02 for desflurane, 0.68±0.03 for sevoflurane, 1.38±0.05 for isoflurane, 1.98±0.12 for enflurane, and 2.59±0.12 for halothane.  In all conditions, λ_B/G and λ_S/G were in the order of desflurane < sevoflurane < isoflurane < enflurane < halothane (Table 1).
　As temperature decreased, log_eλ_B/G and log_eλ_S/G of the five anesthetics at all hematocrit increased linearly (R₂=0.87-0.98, P<0.05, Table 1).  The slopes of regression line were lie between -0.0433 and -0.0262.  This slope was defined as temperature coefficient ^[10], and represented that λ_B/G or λ_S/G increased 4.33% to 2.62% per 1 ℃ decreased in temperature.  The temperature coefficient increased linearly as the log_e λ_B/G at 37℃ increased (R₂=0.86, Figure 1).  When the results of all agents and all hematocrit values were pooled, the temperature coefficient of λ_B/G are -3.61% (95% CL -3.41%, -3.80%).
　During saline hemodilution, as hematocrit decreased, log_eλ_B/G of the five anesthetics at six temperatures decreased linearly (R₂=0.94-1.00, P<0.05).  The slopes of regression lines were lie between 0.0059 and 0.0230.  This slope was defined as hematocrit coefficient, and represented that λ_B/G decreased 0.59% to 2.30% per 1 % decreased in hematocrit (Table 2).  λ_S/G were significant lower (P<0.05) than λ_B/G in undiluted blood samples for five anesthetics at all temperatures tested, i.e. R_S/B < 1.00 (Table 2).  As R_S/B increased, the hematocrit coefficient decreased linearly (R₂=0.96, Figure 2).
　The combined effect of hypothermia and crystalloid hemodilution on λ_B/Gs of the five anesthetics were expressed as following five multiple linear regression equations:
　 Desflurane: log_eλ_B/G = - 0.0302*T + 0.0094*HCT＋0.119 R₂=0.973
 　Sevoflurane: log_eλ_B/G = - 0.0295*T + 0.0092*HCT＋0.306 R₂=0.961
 　Isoflurane: log_eλ_B/G = - 0.0382*T + 0.0154*HCT＋1.120 R₂=0.997
 　Enflurane: log_eλ_B/G = - 0.0408*T + 0.0198*HCT＋1.408 R₂=0.982
　 Halothane: log_eλ_B/G = - 0.0417*T + 0.0218*HCT＋1.649 R₂=0.994
Where T is temperature (℃) and HCT is hematocrit (%).
Discussion
　At all temperature and hematocrit tested, λ_B/G and λ_S/G of the five anesthetics are in the order of desflurane < sevoflurane < isoflurane < enflurane < halothane.  As anticipated, both λ_S/G and λ_B/G of volatile anesthetics increased as temperature decreased (Table 1), a finding consistent with previous studies ^[1-3].  Table 1 also gives the slope of regression line between logarithm of solubility and temperature, which is defined as temperature coefficient ^[10].  Taking all agents and all hemodilution conditions tested in this study into account, linear correlation was found between temperature coefficient and its logarithm of λ_B/G at 37℃ (Figure 1).  This agrees with the comprehensive review made by Allott’s et al ^[10].  However, when data of all agents and all hemodilution conditions are pooled, the temperature coefficient is -3.61% (95% CL -3.41%, -3.80%).  This is lower than value reported by Lockwood et al (-5.4%) ^[2].  In their study, they found a simple linear relation between blood solubility and temperature, and calculated the temperature coefficient as slope of regression line divided λ_B/G at 37℃.
　Hematocrit was selected to indicate the degree of crystalloid hemodilution in this study.  Decrease in hematocrit represented the dilution of whole blood including blood cells and serum constituents influencing the blood solubility of volatile anesthetics ^[11].  For a given temperature, the change of λ_B/G caused by crystalloid hemodilution depends on the ratio between λ_S/G and λ_B/G in hematocrit 40% undiluted blood (R_S/B).  For all the five anesthetics at all the temperatures tested in this study, the λ_S/Gs were lower than λ_B/Gs in undiluted blood (Table 1), i.e., R_S/B < 1.0 (Table 2).  Therefore, as hematocrit decreased by adding saline to blood, the log_eλ_B/G decreased for all the anesthetics in a linear fashion (Table 1 and Table 2).  Different effect of crystalloid hemodilution on blood solubility for different anesthetics was noted in this study.  Table 2 shows that anesthetics with a relatively low λ_B/G, such as desflurane and sevoflurane, have a higher R_S/B, and are less changed by crystalloid hemodilution.  Conversely, anesthetics with relatively high λ_B/G, such as halothane, has a lower R_S/B and is more changed by crystalloid hemodilution.  As R_S/B increased, hematocrit coefficient decreased in a linear fashion (Figure 2), indicating that one can predict hematocrit coefficient of a volatile anesthetic by knowing its λ_B/G and λ_S/G.
　During surgery, especially in cardioplumonary bypass (CPB), both hypothermia and crystalloid hemodilution affect the blood solubility of volatile anesthetics ^[5-8].  As we discussed above, anesthetics are more soluble in blood at lower temperature.  Conversely, crystalloid hemodilution exerts an opposite effect on anesthetic blood solubility because all the modern halogenated volatile anesthetics are less soluble in saline than in blood.  These two major factors counteract each other completely in some clinical situations.  For example, Nussmeier et al. reported that the blood/gas partition coefficient of isoflurane with hypothermia (23℃) and hemodilution (hematocrit of 23%) was similar to that in undiluted blood at normal body temperature ^[5].  Feingold found that during CPB, increased blood solubility due to hypothermia was initially antagonized by crystalloid hemodilution ^[7].  Despite hypothermia and crystalloid hemodilution affect λ_B/G in an opposite direction and the two factors often simultaneously occur during clinical anesthesia, change in one factor is not parallel to the change in another during entire anesthesia and surgery course in the most clinical settings ^{[5-8, 12]}.  This non-parallel change in temperature and hematocrit may result in a significant change in blood solubility.  Table 1 shows the whole picture of changes in solubility of volatile anesthetic possibly encountered clinically.  The values of λ_B/G located in upper-right column (17℃ and hematocrit 40%) are from 2.3 times (for desflurane) to 3.5 times (for halothane) greater than the values located in the column of 37℃ and hematocrit 20% for the same agent.  λ_B/G determination is time consume and requires some special equipment.  It is not convenient to measure several samples at different temperatures even in research laboratory either.  So, it is not practical to directly monitor dynamic changes in λ_B/G of an anesthetic during clinical anesthesia for guiding inhaled anesthetic administration.  However, the two major factors affecting blood solubility, body temperature and hematocrit, could be measured easily and quickly in operating room.  Therefore, knowledge of combined effects of hypothermia and crystalloid hemodilution on blood solubility is necessary for making theoretical predictions for various purposes under different clinical conditions.  By using the multiple linear regression method, we found the regression equations for predicting the combined effect of hypothermia and crystalloid hemodilution on blood solubilities of the five anesthetics.  The main purposes of this study was to find equations to predict λ_B/G of volatile anesthetics at different cross points of various temperatures and crystalloid hemodilution that may occur in clinical anesthesia.  In order to test this, we collected λ_B/G values (measured λ_B/G) reported in literatures with different temperatures and hematocrit values (crystalloid hemodilution, if any) ^{[1, 3-8, 13]}, and calculated λ_B/G values (predicted λ_B/G) by using one of the five regression equations (shown in Results) based on the volatile anesthetic, temperature and hematocrit tested at the determination of corresponding measured λ_B/G in literatures.  Bland and Altman’s “limits of agreement” analysis ^[14] were performed between predicted λ_B/G against corresponding measured λ_B/G (Figure 3).  The mean difference between measured to predicted λ_B/G is -0.0307 on the log scale, and the limits of agreement (equal to mean±2*SD of the differences, which will include about 95% of the data points) are 0.1528 and -0.3617 (Figure 3).  These limits tell us that for about 95% of data points, the predicted λ_B/G calculated by multiple regression equations may differ from the measured value by 30% below to 17% above (Figure 3).  This analysis indicates that within the range of temperature and hematocrit encountered clinically, the multiple linear regression equations obtained from this study are adequate to predict λ_B/G for modern, halogenated volatile anesthetics.  The equations could be used to predict blood solubility at various temperatures and crystalloid hemodilution conditions in order to explain concomitant changes in pharmacokinetics of volatile anesthetics.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

Table 1: λ_B/G and λ_S/G of five anesthetics at various temperatures and hematocrits.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

Values are given as the mean±SD, n=6

Des.= Desflurane, Sevo.=Sevoflurane, Iso.=Isoflurane, Enf.=Enflurane, Halo.= Halothane.

HCT= hematocrit.

NS= normal saline.

Slope = the slope of each regression line of log_el_B/G or log_el_S/G against temperature.

References:
1. Eger RR, Eger EI, II.  Effect of temperature and age on the solubility of enflurane, halothane, isoflurane, and methoxyflurane in human blood.  Anesth Analg 1985; 64: 640-2.
2. Lockwood GG, Sapsed-Byrne SM, Smith MA.  Effect of temperature on the solubility of desflurane, sevoflurane, enflurane and halothane in blood.  Br J of Anaesth 1997; 79: 517-20.
3. Laasberg LH, Hedley-Whyte J.  Halothane solubility in blood and solutions of plasma proteins: Effects of temperature, protein composition and hemoglobin concentration.  Anesthesiology 1970; 32: 351-6.
4. Nussmeier NA, Moskowitz GJ, Weiskopf RB, Cohen NH, Fisher DM, Eger EI.II.  In vitro anesthetic washin and washout via bubble oxygenators: Influence of anesthetic solubility and rates of carrier gas inflow and pump blood flow.  Anesth Analg 1988; 67: 982-7.
5. Nussmeier NA, Lambert ML, Moskowitz BA, Cohen NH, Weiskopf RB, Fisher DM, Eger EI.  Washin and washout of isoflurane administered via bubble oxygenators during hypothermia cardiopulmonary bypass.  Anesthesiology 1989; 71: 519-25.
6. Sada T, Maguire HT, Aldrete JA.  Halothane solubility in blood during cardiopulmonary bypass: The effect of haemodilution and hypothermia.  Can J Anaesth 1979 ; 26: 164-7.
7. Feingold A.  Crystalloid hemodilution, hypothermia, and halothane blood solubility during cardiopulmonary bypass.  Anesth Analg 1977; 56: 622-6.
8. Tarr TJ, Snowdon SL.  Blood/gas solubility coefficient and blood concentration of enflurane during normothermic and hypothermic cardiopulmonary bypass.  J Cardiothor Vasc Anesth 1991; 5: 111-5.
9. Yu RG, Zhou JX, Liu J.  Prediction of volatile anesthetic solubility in blood and priming fluids for extracorporeal circulation.  Br J Anaesth 2001; 86: 338-44.
10. Allott PR, Steward A, Flook V, Mapleson WW.  Variation with temperature of the solubilities of inhaled anesthetics in water, oil and biological media.  Br J Anaesth 1973; 45: 294-300.
11. Weathersby PK, Homer LD.  Solubility of inert gases in biological fluid and tissues: a review.  Undersea Biomed Res 1980; 7; 277-96.
12. Henderson JM, Nathan HJ, Lalande M, Winkler MH, Dube LM.  Washin and washout of isoflurane during cardiopulmonary bypass.  Can J Anaesth 1988; 35: 587-90.
13. Zhou JX, Liu J.  Dynamic change in blood solubility of desflurane, isoflurane, and halothane during open heart surgery.  Anesthesiology 2000; 93: A547.
14. Bland JM, Altman DG.  Statistical methods for assessing agreement between two methods of clinical measurement.  The Lancet 1986 (Vol 1); (Feb 8): 307-10.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />