1The Veterinary School, University of Bristol, Langford, Bristol BS18 7DU, UK. 2Department of Medical Physics and Bioengineering, Bristol General Hospital, Bristol BS1 6SY, UK. 3Department of Anaesthetics and Intensive Care Medicine, University of Wales College of Medicine, Cardiff CF14 4XN, UK 4Present address: 79 Sandford Road, Winscombe, North Somerset BS25 1JJ, UK 5Present address: 17 Shaldon Road, Horfield, Bristol BS7 9NN, UK*Corresponding author
A provisional analysis of loss of propofol from tissue samples was presented to the Anaesthetic Research Society Meeting, Dundee, July 1998 (Br J Anaesth 1998; 81: 6301).
Declaration of interest: The in vivo work for this study was carried out in the Wellcome Comparative Anaesthetic Laboratory, which was provided by the Wellcome Trust. Financial support was provided by the Perry Foundation and the propofol was generously supplied by Imperial Chemical Industries Limited (now Astra-Zeneca).
Accepted for publication: December 21, 2000
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Abstract |
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Br J Anaesth 2001; 86: 693703
Keywords: anaesthetics i.v., propofol; pharmacokinetics, propofol; solubility, partition coefficients; solubility, lipid; sheep
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Introduction |
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Materials and methods |
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Procedure
Caveat
This was an exploratory study so the procedure developed as the investigation progressed, as is evident from the summary in Table 1, where group P has been divided into subgroup Pa, in which arterial cannulation was performed before the propofol was started, and subgroup Pb, in which it was performed during the infusion.
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Euthanasia
In all groups, euthanasia was performed while the animal was still deeply anaesthetized: an intravenous injection of a saturated solution of potassium chloride at the appropriate time (Table 1) rapidly induced cardiac arrest. Within 40 min, the requisite tissue samples were removed, sealed in plastic bags and stored in a freezer at 20°C for subsequent analysis for propofol content.
Group T
A bolus of propofol 10 mg kg1 induced anaesthesia and ensured that the animals were deeply anaesthetized when, 27 min later, the potassium chloride was injected. The tissue samples were analysed on three to five occasions between 6 and 26 months post mortem.
Subgroup Pa
In order to obtain arterial samples throughout the infusion, cannulation was performed under an alternative form of anaesthesia before any propofol was administered. Induction was with thiopental in four animals, halothane in three and isoflurane in one; in each sheep, maintenance was with the same volatile agent, or with isoflurane in the sheep with thiopental induction. Once each animal was anaesthetized, its trachea was intubated with a cuffed tracheal tube which was connected to a circle-absorber breathing system, supplied with about 300 ml min1 of oxygen and incorporating an in-circle vaporizer. As soon as the cannulations were complete, a bolus of propofol 3 mg kg1 was administered, followed by an infusion of the agent at 1 ml min1 for 2 h. The in-circle vaporizer was used to add the same volatile agent as before the propofol, at concentrations required to ensure adequate anaesthesia, as judged clinically, throughout the procedure. Paired sampling of arterial and venous blood was scheduled for 1, 3, 5, 7, 10, 15, 20, 30, 45, 60, 75, 90, 105 and 120 min after the start of the propofol infusion. Euthanasia followed while the infusion continued. Tissue samples were analysed on two or three occasions between 1 and 330 days post mortem; blood samples were analysed once between 1 and 31 days.
Subgroup Pb
Here it was realized that it would be sufficient to obtain arterial samples during only the later part of the infusion; therefore the arterial cannulation was performed after inducing anaesthesia with a larger bolus of propofol 6 mg kg1 followed by the 2-h infusion. In the first two ewes, the rate of infusion was 1 ml min1, as in subgroup Pa; in the last four, the rate was 2 ml min1 to provide additional information on propofol kinetics. As soon as possible after commencing the infusion, the trachea of each animal was intubated and connected to the circle breathing system. In all six sheep, the propofol was supplemented with isoflurane, from the in-circle vaporizer, according to the criterion used for subgroup Pa. Venous sampling was as in subgroup Pa; in addition three to six paired arterial and venous samples were taken in the last 10 min before cardiac arrest was induced at 123152 min. Tissue samples were analysed once only, 9106 days post mortem; blood samples were analysed once at 350 days.
Liver samples
In all but the first of the 14 ewes in group P, two samples of liver were taken. The early sample was taken as soon as possible after cardiac arrest and placed in the freezer within 1020 min of the arrest; the second, standard sample was taken to the freezer 1025 min later, along with the samples of the other tissues. This was done to provide information on possible loss by continuing metabolism of propofol in the liver before freezing.
Analysis of propofol in blood and tissue
Analysis of propofol in blood samples was as described previously2 with derivatizations4 of two 1-ml subsamples, each analysed in duplicate. For analysis of propofol in tissue, a subsample of each frozen tissue sample was taken by grating and the remainder returned to the freezer. The grated subsample was chopped, and further broken down with a pestle and mortar to facilitate homogenization. It was then weighed and potassium dihydrogen phosphate (0.1 M) was added to produce a 1:2 w/v suspension. This was homogenized in a liquidizer, with only short bursts of activity to avoid heating, which would have denatured the tissue. Each subsample was then treated in the same way as the blood samples, each derivatization using 1.5 ml of homogenate.
Data processing
Processing was commenced only when all the data had been collected; a detailed account is given in Appendix 1. Analysis of variance was used to determine the best way of summarizing the loss rates from tissue samples. The resulting rates were used to estimate the concentration in each tissue sample at day 0, i.e. the day of sampling. Concentrations in liver samples were additionally corrected for metabolic loss before freezing. Regression analysis was used to estimate the arterial concentration at the time of cardiac arrest in each sheepdirectly in subgroup Pa, but in subgroup Pb a mean arterialvenous difference was added to the fitted venous concentration. Partition coefficients were obtained by dividing each day-0 tissue concentration by the corresponding arterial concentration at cardiac arrest. P<0.05 was regarded as significant.
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Results |
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Tissue concentrations
Estimated concentrations at the time of cardiac arrest are listed in Table 3 for each tissue and for each method of administration. The estimates are in terms of geometric mean with asymmetrical confidence limits. Estimates for liver are after correcting for loss before freezing.
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Discussion |
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Another possibility is degradation of propofol. Some evidence can be adduced that the distribution of the propofol vehicle may match the pattern of loss in Table 2. An earlier paper3 noted that the vehicle is very similar to Intralipid: a major component of both is soya bean oil. For convenience, the vehicle will be referred to below as intralipid, with a lower-case i. The earlier paper3 reported plasma concentrations of triglyceride. Those concentrations arose from measurements in some of the present sheep and in other crossbred ewes subjected to similar boluses and infusions of propofol. The initial increases in plasma concentration shortly after the injection of a bolus of propofol were sufficient to account for all the injected intralipid. Therefore, the amount of intralipid in each tissue would depend only on the amount of plasma it contained. Again there is nothing exceptional about the spleen when it is contracted but, when maximally engorged it contains about 12 times as much plasma as any other tissue (Table 5), and five times as much at the degree of engorgement estimated for the present studies after a bolus of propofol (Table 5). This implies that, in group T, the spleen contained five times as much intralipid as any other tissue.
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This hypothesis is clearly speculative but, when these findings on loss rate were presented to the Anaesthetic Research Society,7 none of the alternative hypotheses elicited from the members was consistent with all the observations.
The loss rate from liver during storage at 20°C was no different from that for other non-spleen tissues. Therefore, there was no liver-specific metabolism once the samples were frozen.
Tissue distribution
There is no ready means of knowing whether the concentrations for the bolus-only method (Table 3) were before, at or after the postinjection peak, except that the huge perfusion of the lung will ensure that the measured concentration relates to well after its first-pass peak. However, the concentrations were generally greater for the well-perfused tissues than for muscle and the concentrations in the former were greater than the corresponding concentrations in the infusion experiments.
After a 2-h infusion, well-perfused tissues should all be nearly in equilibrium with the arterial concentration at the time of cardiac arrest. The highest concentration was then found in the heart and was about double that in any other tissue. The smallest concentration was found in the lungs, where extraction of propofol has been reported in sheep;8 but the concentration in liver, where metabolism is known to occur, was comparable to that in other tissues (Table 3). Perhaps there was an even greater loss from lung tissue before freezing. Support for extraction by the lungs is possibly indicated by the pooled standard deviation for lungs (Table 3) being even greater than that for liver, and three to four times greater than for any other tissue. Further evidence of extraction by the lung may be hidden in the anomalous behaviour of ewe 37 (see below).
Partition coefficients
Raw tissue/blood coefficients
The partition coefficients in Table 4 arise from dividing all the fitted day-0 tissue concentrations (converted to µg ml1) for each sheep by the corresponding estimated arterial concentration at the time of cardiac arrest. The differences between tissues therefore follow the same pattern as the tissue concentrations in Table 3. The systematic differences between the two infusion rates are related to the triglycerides from the propofol vehicle, which accumulate in blood during the infusionsmore so at 2 ml min1 leading to smaller partition coefficients. Therefore, the coefficients in Table 4 are relevant only to the particular circumstances of those infusions.
Tissue/water and tissue/normal-blood coefficients
A set of more generally applicable tissue/water coefficients was derived as follows. From data previously reported1 3 or obtained from published work,911 it was found possible to derive a general equation (Appendix 2, equation 12) for the blood/water partition coefficient as a function of the triglyceride concentration in plasma and of packed-cell fraction. This was then quantified for the present study in equations 16 and 17, to give the blood/water coefficient as a function of time for each sheep. Tissue/water coefficients could then be derived by multiplying each tissue/blood coefficient by the blood/water coefficient for the end of the corresponding infusion. Unlike in Table 4, differences between the mean tissue/water partition coefficients for the two infusion rates were not significant, so overall geometric means and confidence limits were calculated. These are displayed in Table 6, together with a set of tissue/normal-blood partition coefficients. These were obtained by dividing each tissue/water coefficient by the blood/water coefficient for normal sheep blood (35.0; Appendix 2, equation 13).
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Possible systematic errors
Both sets of coefficients (Tables 4 and 6) are susceptible to systematic errors arising from incomplete equilibration between tissue and blood. A cup-and-bucket simulation method was devised for correcting for this (details are available from the authors). It was applied to each individual coefficient, and a geometric mean was calculated for each tissue. For the well-perfused tissues, the incompleteness was no more than 1% except for liver (4% because of one very large tissue/blood coefficient). Therefore, these coefficients would be little influenced by errors in the assumed perfusions (Table 3). Muscles showed about 20% incompleteness, but this value is somewhat uncertain because the results were then critically dependent on the perfusion assumed. Therefore, the coefficients given for muscle should be regarded simply as lower limits. In addition, the coefficients for liver and lungs will always be low because in vivo metabolism and extraction8 respectively prevent these tissues ever reaching equilibrium with blood.
There are three further sources of uncertainty in the partition coefficients. First, volatile anaesthetics can affect the binding of drugs to proteins, but for halothane and isoflurane the effect is small (016%) at 1 minimum alveolar concentration (MAC)1315 and probably smaller at the <1 MAC needed in our study to supplement the propofol infusion. Secondly, non-linearity of binding of propofol has been reported, but only for low concentrations (1%) of human serum albumin and haemoglobin and not for human plasma.16 In the present study, despite the nearly twofold differences in mean tissue concentrations between the two infusion rates (Table 3) the corresponding differences in mean tissue/water coefficients were not significant and no more than 14% for the non-metabolizing, well-perfused tissues (brain, heart, kidney, spleen). This suggests little non-linearity in the present circumstances. Finally, we estimate that uncertainties in some of the parameters used in Appendix 2, taken from earlier work,1 might change the tissue/water coefficients by ±20% and the tissue/normal blood coefficients by ±10%.
Other sources of partition coefficients
Ludbrook and colleagues17 give a plot of calculated brain concentrations of propofol in sheep against measured sagittal-sinus concentration during and after a 45-min infusion of 1 ml min1 of propofol. The slope of the plot corresponds to a brain/blood partition coefficient of about 3.5. This is comparable to our estimates of 3.2 (Table 6) for before any propofol and 2.4 for the end of a 2-h infusion of 1 ml min1 (Table 4). Brain/blood concentration ratios of 3.5 and 2.9 have been found18 for propofol in the rat after 15- and 30-min infusions respectively. Perhaps this decrease with duration of the infusion reflects increasing lipid accumulation in the blood.
The anomalous ewe 37
In this sheep the arterial concentration increased unusually rapidly (Fig. 1, top). This was not associated with an unusually steep increase in plasma triglyceride concentration (ewe 37 was one of those in which triglyceride concentrations were measured).3 In addition, for every tissue in ewe 37, the propofol concentration was greater than in any other sheep: as much as eight times greater than the next largest for lung. On the other hand, each partition coefficient for ewe 37 was within, or almost within, the corresponding range of values for other sheep infused at 1 ml min1, except for lung, where the coefficient for ewe 37 was three times the next largest, reaching a value of 0.95. This approaches the mean coefficients in Table 4 for many other tissues. This pattern of results suggests that extraction by the lungs was much less in ewe 37 than in the other sheep. It is consistent with the finding that extraction by the lungs was very variable between sheep.8
Possible mechanisms of extraction by the lungs
It seems very unlikely that this extraction is a result of elimination of propofol vapour in the expired gas because of the high boiling point of propofol (242.3°C) (J. B. Glen, personal communication). The alternative of some enzymatic transformation of propofol to a substance not detected by our analysis method, with a near absence of the necessary enzyme in ewe 37, seems more plausible. The non-linear nature of the extraction process19 also points to an enzyme, not evaporation. The presence of an enzyme in the lungs would be logical if it converted the propofol to a more volatile form (perhaps propane or propene, boiling points 42 and 47°C respectively), which would then be excreted in the expired gas. Although extrahepatic extraction has been reported in humans,20 21 the only evidence of the lungs being involved is of 1020% extraction in two of eight patients.22 This may be an indication that enzymatic processes are less transferable between species than are partition coefficients.
Implications for target-controlled infusions of propofol
Target-controlled infusion anaesthesia aims to provide and maintain a preset blood concentration of propofol. Therefore, as the blood/water coefficient increases with increasing triglyceride concentration during an infusion, the concentration in the water phase of blood will decrease progressively; and it is this concentration with which the site of action of propofol equilibrates.
The more recently introduced 2%, and 6%,23 preparations of propofol should lead to less accumulation of triglyceride in blood and hence to smaller blood/water and larger tissue/blood partition coefficients. This will facilitate uptake from blood to tissue, so that a given mg kg1 min1 infusion regimen should give smaller blood concentrations than intended but greater tissue concentrations.
In conclusion, this study provides a set of tissue/blood and tissue/water partition coefficients for propofol for some of the major organsan essential ingredient of the physiological modelling of pharmacokinetics. The study also shows that the physiological modelling of any agent requiring a lipid carrier will be more complex than for other agents. In parallel with this, empirical models may need to be fitted to new observational data obtained when using each new formulation. The study demonstrates that, logically, target-controlled infusion should aim for a constant concentration not in whole blood but in the aqueous phase of blood.
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Appendix 1 |
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A second, similar analysis used only log concentration but incorporated all samples with two or more measurements. The resulting individual slopes had large standard errors, about equal to each slope, and so required averaging. A first analysis of variance of the slopes, weighted inversely to the squares of the standard errors of the individual slopes, showed that this needed to be done separately for bolus and infusion data. In a similar weighted analysis of the bolus-only data, there was a significant difference of slope between spleen and the other tissues (P<0.0001), but no significant difference between the other tissues (P=0.7) nor between sheep (P=0.3). The splenic tissue showed a non-significant increase in propofol content during storage (P=0.3). In the infusion data, there was no significant difference between any of the tissues (P=0.8) nor between sheep (P=0.8). The loss rates are summarized in Table 2.
Estimated log concentration in each tissue sample at day 0
For each sample, the log concentration at day 0 was taken to be the intercept of a line fitted to the log measured concentrations for that sample. For non-spleen bolus tissues, the common, fitted slope was used, but for all the other samples zero slope was used. The fitting process was done separately for each tissue sample.
Correction of liver concentrations for loss before freezing
Loss rates from liver samples before freezing, obtained from measurements on the early and standard samples, were equally consistent between sheep whether expressed in terms of log concentration or actual concentration. For consistency with loss at 20°C, a mean loss rate of log concentration was calculated and assumed to apply to each liver sample during the time from cardiac arrest to the freezing of that sample. This led to a set of liver concentrations corrected to the time of cardiac arrest.
Blood concentrations
The measured concentrations were first corrected for an exponentially declining loss in storage of 0.7% per day compound.2
In the infusion experiments, the tissues would be at or approaching equilibrium with the arterial concentration at the time of cardiac arrest. In subgroup Pa (Fig. 1, top), the arterial concentration at cardiac arrest was estimated for each sheep by fitting a straight line to all the measurements (from 15 min onwards to avoid transients after the initial bolus) (Fig. 1, bottom) and extrapolating the line by a few minutes to the time of cardiac arrest (Table 1). In subgroup Pb, the venous concentration at cardiac arrest was similarly estimated for each sheep, and then corrected to an estimated arterial concentration by using the arteriovenous pairs of measurements in the last 12 min of each infusion.
An analysis of variance of the arterialvenous differences in subgroup Pb showed that there were no significant differences between the means for the two infusion rates used in that subgroup, but that there were significant differences between sheep. Therefore, for each sheep, the fitted venous concentration at cardiac arrest was corrected by the addition of the mean arterialvenous difference for that sheep.
Partition coefficients
The above processing provided, for each infusion sheep, the estimated concentration in each tissue at the time of sampling, and the estimated concentration in arterial blood at the time of cardiac arrest. Therefore, partition coefficients were obtained by dividing each tissue concentration by the corresponding arterial concentration. Each tissue concentration was first converted from µg g1 to µg ml1 by multiplying by the corresponding tissue density (Table 4).
Summarizing tissue concentrations and partition coefficients
Analysis of variance of tissue concentrations and of partition coefficients (in terms of either actual or log values) showed clear differences between tissues (P<0.0001) for each method of administration. Examination of the residuals showed that, after allowing for different standard deviations in different tissues, the distribution of the residuals was consistent with normality for log concentration and log partition coefficient (P>0.2) but not for actual concentration or partition coefficient (P<<0.001). Within each tissue, variances of log concentration and of log partition coefficient were sufficiently consistent to justify pooling the standard deviations of the log values between methods of administration, except that a separate, larger standard deviation was needed for muscle in the bolus group. Means and confidence limits were then calculated in terms of log values (using the pooled standard deviation) and converted to geometric means with asymmetrical limits (Table 3).
Statistical analyses
These were done with the statistical package GLIM.24 25 The Shapiro-Francia W' test26 was used to test the normality of distributions. All logarithms were to the base 10.
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Appendix 2 |
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C0=0.222.
Subsequently the measured concentration could be well represented by an instantaneous step increase followed by a linear increase with time. For the 1 and 2 ml min1 infusion rates the step increases were respectively
Cbol1=1.151
Cbol2=1.918.
The slope of the linear trend, in mmol litre1 h1, could be represented by
dC/dt=0.26+0.0151xx
where x is the infusion rate in mg kg1 h1.
Diprivan 1% contains 100 mg triglyceride (soya-bean oil)11 per ml. Therefore, an infusion of 1 ml min1 Diprivan contains 100x60/M mg kg1 h1 triglyceride, where M is body mass in kg. Therefore, in terms of mmol litre1 min1,
dC/dt=0.004 33+1.51xI·/M
where I· is the infusion rate of propofol in ml min1.
Therefore, the total concentration of triglyceride at any time, in mmol litre1, is given by
C=C0+Cbol+(0.004 33+1.51xI·/M) xt(1)
where t is time in minutes.
In fact, the step increase in the 1 ml min1 sheep was much the same as in the 2 ml min1 sheep (1.92 mmol litre1), but the concentration then decreased rapidly to join the line defined by equation 1. On the other hand, the step increase to be expected from the bolus of 3 mg kg1 used in most of the present 1 ml min1 sheep can be expected to produce a step increase of a little less than 1.15 mmol litre1, followed by a drift up to the line of equation 1. That the equation is indeed reasonably applicable to all the present sheep is shown by the fact that the tissue/water partition coefficients (Table 6), which depend on equation 1, have much the same pooled standard deviation between sheep as the raw tissue/blood coefficients (Table 4).
To convert to fractional concentration (litre litre1) of triglyceride in plasma, ftr, multiply by 0.861 (mean millimolar mass, g mmol1) and divide by 877 (mean density, g litre1):10
ftr=0.000 982x{C0+Cbol+(0.004 33+1.51xI·/M) xt}. (2)
Estimation of the triglyceride/water partition coefficient, tr/w, for propofol
Let vx, mx, x be the volume, mass and density respectively of component x in 1 ml of Diprivan, where x can be p=propofol, tr=triglyceride or a=aqueous phase. Also let mp,x and Cp,x be the mass and mass/volume concentration respectively of propofol in phase x. Then
mp,a=Cp,axva
where
va=1vtrvp.
Also
Cp,tr=(mpmp,a)/vtr
={mpCp,ax(1vtrvp)}/vtr.
Therefore the triglyceride/water partition coefficient for propofol is given by
tr/w=Cp,tr/Cp,a={mp/Cp,a(1vtrvp)}/vtr
where, using published values for mp, mtr,11 Cp,a,9 and tr,10 and assuming 1 g ml1 for the density of propofol (it has very little influence on the outcome),
mp=10 mg
Cp,a=0.018 57 mg ml1
vtr=mtr/tr=0.1 g/0.877 g ml1
vp=mp/p=0.01 g/1 g ml1.
Therefore
tr/w=4715.(3)
Derivation of the blood/water partition coefficient of propofol, b/w, as a function of the partition coefficients and fractional concentrations of the components of blood
Let Cn=mass/volume concentration of propofol in n, fm,n=volume fraction of m in n (in plasma where n is omitted), and m/n=volume/volume partition coefficient of propofol between m and n, where m and n can be b=blood, c=(red) cell, pl=plasma, pr=protein, tr=triglyceride, w=water and npl=non-protein liquid (water plus triglyceride). Then
which reduces to
pl/w=fprx(
pr/w1)+ftrx(
tr/w1)+1.(4)
Also
b/w=
pl/wx(1fc,b)+
c/wxfc,b.
Therefore
b/w={fprx(
pr/w1)+ftrx(
tr/w1)+1}x (1fc,b)+
c/wxfc,b.(5)
Quantification of the equation for the blood/water partition coefficient
In similar crossbred ewes, measurements on samples of normal blood, spiked with 5 µg propofol ml1,1 gave fpr=0.0427 (76.4 g protein per litre of plasma ÷ 1.79 g protein per ml protein), pr/npl=283 and
c/pl=1.42. From these data, other terms in equation 5 can be derived as follows:
pr/w=
pr/nplx
npl/w(6)
and
c/w=
c/pl x
pl/w(7)
where
which reduces to
The concentration of triglyceride in plasma from normal sheep has been estimated above: C0=0.222 mmol litre1=0.191 g litre1; however, in the spiked blood,1 the 5 µg ml1 of propofol would be accompanied by 50 µg ml1 (= 0.050 g litre1) of triglyceride.11 Therefore, for the spiked blood, the concentration would be 0.191+0.050= 0.241 g litre1; and, in litre litre1
ftr=0.000 275.(9)
Then, using equations 9 and 3 in equation 8 gives
and, from equation 6,
pr/w=283x2.35=666.(10)
Therefore, in the spiked blood, using equations 10, 9 and 3 in equation 4,
pl/w=0.0427x665+0.000 275x4714+1=30.69.
Then equation 7 leads to the generally applicable cell/water partition coefficient,
c/w=1.42x30.69=43.58.(11)
Substituting equations 10, 3 and 11 in equation 5 gives
b/w=(0.0427x665+ftrx4714+1)x(1fc,b)+43.58xfc,b
=(29.40+4714x ftr)x(1 fc,b)+43.58xfc,b.(12)
For normal (unspiked) sheep blood, equation 2 reduces to
ftr=0.000 982xC0=0.000 218
and5
fc,b=0.35
whence equation 12 becomes
b/w=30.42x(10.35)+43.58x0.35=35.03.(13)
During the infusions, the pattern of measurements of packed-cell fraction (fc,b) in all the present sheep can be adequately represented by a very rapid drop from normal values to a constant:
fc,b=0.26.(14)
Substituting equation 14 in equation 12 gives
b/w=(29.40x0.74+43.58x0.26)+4714x0.74xftr
=33.09+3488xftr.(15)
Finally, substituting equation 2 in equation 15 gives b/w as a function of time for each sheep in the 1 and 2 ml min1 infusion groups respectively:
b/w1=37.79+(0.0148+5.17/M)xt(16)
b/w2=40.42+(0.0148+10.35/M)xt.(17)
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References |
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