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BioMed Central Page 1 of 29 (page number not for citation purposes) BMC Clinical Pharmacology Research article Open Access The pharmacokinetics of the interstitial ...



BMC Clinical Pharmacology 2003 3 http www biomedcentral com 1472 6904 3 3
reviews of the structure and function of the interstitial Measurement of steady state volume of distribution Vss
space 2 3 To ensure that a consistent calculation of Vss was used all
the values of Vss were recalculated by applying PKQuest
An accurate pharmacokinetic description of the interstitial 8 to the published venous concentration data In this
space is essential for the development of a physiologically calculation deconvolution of the intravenous input is
based pharmacokinetic model PBPK for extracellular used to find the 2 or 3 exponential unit dose bolus
solutes Although PBPK models have been used exten response function r t
sively to describe human pharmacokinetics nearly all of
these studies have involved solutes that have intracellular P
distributions and thus do not require detailed modeling 1 r t Bi e t Ti
of the interstitial space One exception is the recent appli i 1
cation of PKQuest to the extracellular solutes inulin and The expression for Vss is then found from the area under
the beta lactam antibiotics 4 PKQuest is a new PBPK the curve AUC and mean residence time MRT for this
program that has been applied to the human pharmacok r t for unit dose
inetics of a large number of solutes 4 8 Although the
agreement between the PKQuest PBPK model predictions P P
and the experimental data for these extracellular solutes 2 Vss MRT AUC Bi Ti2 Bi T 2
was satisfactory subsequent application of PKQuest to i 1 i 1
other extracellular solutes demonstrated that there was a Measurement of equilibrium volume of distribution Veq
small but systematic error in the PKQuest predictions The direct approach to the determination of Veq is to give
This error is the stimulus for this more in depth analysis a constant IV infusion for a period long enough to estab
of interstitial pharmacokinetics lish a steady state plasma concentration Ceq For solutes
in which the systemic clearance results only from renal
Probably the most detailed application of a PBPK model clearance the peripheral tissue and central concentra
to an extracellular solute is the study of Tsuji et al 9 of tions must be in equilibrium at this steady state and Veq is
the pharmacokinetics of cefazolin in the rat In this inves defined by
tigation nearly every PBPK parameter required by the
model was directly measured including organ blood 3 Veq Atot Ceq
flows and weights renal and hepatic clearance and the
time dependence of cefazolin concentration in the differ where Atot is the total amount of solute present For the
ent organs Tsuji et al 9 estimated interstitial volumes special case where there is no metabolism and renal clear
from measurements of the steady state inulin tissue con ance in the only excretion route Atot can be determined by
centrations The interstitial volumes in the original quantitative urine collection after stopping the infusion If
PKQuest PBPK model were based on these inulin volumes the clearance is from just the central compartment e g
of Tsuji et al 9 scaled to give the correct total volume in renal excretion Veq also referred to as Vdrug is equal to Vss
humans As will be shown below inulin is not a good sol 10
ute to use to measure interstitial volume and this probably
contributed to the error in the earlier PKQuest PBPK The value of Veq can also be estimated for subjects in renal
predictions failure that have a very low rate of renal clearance As
shown in Appendix I for the case where the clearance is
Methods very small compared to the rate of exchange between com
All the experimental data were obtained from earlier pub partments Veq is approximately equal to Vdext using the
lications In most cases the published data represented notation of Wagner 11
the average of the experimental measurements in a
number of subjects and it was assumed that it represented 4 Veq Vdext D B
one average subject In a few cases indicated by a N 1
in Table data for a single subject were published and where B is the coefficient of the slow terminal exponen
used in the calculations The program UN SCAN IT Silk tial term of the bolus response function eq 1 and D is
Scientific Corporation was used to read the data from the the bolus dose The value of B was determined using the
published figures Most of the figures shown in this paper deconvolution feature in PKQuest to find the 2 exponen
are direct copies in jpeg format of standard PKQuest tial response function
PBPK model for extracellular solutes
A new PBPK model was developed that was consistent
with the experimental data in Tables 1 2 3 4 5 Table 6
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Table 1 Steady state Volume of Distribution relative to body weight VSS and total body water VSSW for selected solutes
Solute Reference Fraction Bound VSS liters Kg VSSW liters liter Comments
2 expon 3 expon
Mannitol 58 0 28 48 N 7 28 years 70 9 Kg 178 cm
EDTA 0 265 45
Mannitol 57 0 33 33 56 N 1 71 6 Kg 172 cm
amoxicillin 62 17 23 262 275 44 N 9 66 4 Kg
61 267 253 45 N 9 74 7 Kg 180 cm
morphine 6 glucuronide 59 0 1 247 245 42 N 20 74 2 Kg
42 30 40 50 N 10 71 Kg
morphine 3 glucuronide 60 275 273 47 N 3 Dose Kg
inulin 37 0 133 131 22 N 1 87 3 Kg 173 cm
39 0 131 136 23 N 1 77 1 Kg 186 cm
40 0 20 277 34 N 27 Non linear
Table 2 Equilibrium Volume of Distribution in Humans relative to body weight VEQ for selected solutes
Solute Reference Fast time constant Slow time constant VEQ liters Kg Comments
minutes minutes
Amoxicillin 46 9 8 909 0 26 N 4 53 Kg 45 years Renal failure
Clearance 10 ml min 1 73 m2
Morphine 6 glucuronide 47 23 2083 0 24 N 6 73 7 Kg 48 7 years Renal
Failure Ave clearance 10 ml min
Inulin 44 NA NA 0 15 N 3 Constant infusion Normal
Males ages 21 29
Sucrose 45 NA NA 0 159 N 3 Constant infusion
Inulin NA NA 0 162
Table 3 Steady state volume of distribution VSS and interstitial volume VI relative to body weight for lactam antibiotics as a
function of degree of protein binding
Solute Reference Fraction Bound VSS liters Kg VI liters Kg
amoxicillin 62 17 23 26 22
piperacillin 30 48 23 19
cefatrizine 31 62 194 155
ceforanide 32 82 161 12
dicloxacilllin 63 97 091 053
amoxicillin 29 17 23 33 29
flucloxacillin 93 15 11
summarizes the new set of PBPK parameters for the different organs The column labeled ecf fract is the frac
standardhuman with a total weight of 70 Kg and a 20 tion of the extravascular organ water that is extracellular
fat content The parameters are scaled for different body i e interstitial The adipose ecf fract is 1 because it is
weight and fat content 7 The major difference between assumed that all adipose tissue water is extracellular and
this parameter set and that used previously 7 is the dis the cells are pure lipid The brain ecf fract is zero because
tribution of the extracellular water ecf water among the the blood brain barrier will prevent the distribution into
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the interstitial space of any of the test solutes used in Table cardiac output of 5 62 L min is close to the value of 5 82
1 The term solid refers to the non fat organ solids It is L min in normal young men reported by Grimby et al
assumed that the entire animal s fat is in the single lipid 24
organ and that this organ is 80 fat This is a major over
simplification since adipose blood flow may show large The volume of distribution in the different organs for sol
variations in different adipose tissues 12 and two differ utes that bind to albumin is characterized by the parame
ent fat compartments have been used in some PBPK ter KAi the ratio of the albumin concentration in the EDTA
models 13 An attempt has been made to minimize the interstitial space to the plasma albumin concentration for
number of adjustable parameters and a single fat com organ i see Appendix II and III The PBPK values of KAi
partment has provided satisfactory fits to the solutes pre for the different organs are listed in Table 6 In the analysis
viously investigated with PKQuest including the highly of the pharmacokinetics of the protein bound lactam
fat soluble volatile anesthetics 5 Portal refers to the antibiotics an average value of KA see eq 10 for the
organs drained by the portal vein stomach small and entire human is estimated This corresponds to the organ
large intestine pancreas and spleen Bone refers to the weighted sum
inert solid component of bone that has no volume of dis
tribution or blood flow The blood flow and water com
ponent of the skeleton is distributed among the rest of the 5 K A ecfi K iA ecfi
organs i i
The organ weights in Table 6 are close to the values in the where ecfi is the interstitial volume of organ i The PBPK
Report on the Task Group on Reference Man 12 The organ weighted values are listed in the last column of
skin is the sum of the weight of the dermis and epider Table 6 and correspond to an average value of KA of 4 94
mis The organ other represents primarily the loose con 17 45 0 28 This is identical to the value that was esti
nective tissue and the organ tendon represents the mated using the lactam antibiotics see fig 15
denser connective tissue components The total body
water is 41 84 liters in agreement with the results of As described previously 4 capillary permeability limited
Chumlea et al 14 It is assumed in Table 6 that the solutes are characterized by the organ parameter fclear i
blood volume includes the intra organ blood volume the fraction of solute that equilibrates with the tissue in
so that the organ parameters refer to the extravascular one pass through the capillary The fclear of organ i is
composition related to the capillary permeability surface area product
PSi by the relation
Although the blood flows to the different organs in Table
6 are in general agreement with the proposed reference 6 fclear i 1 exp fPPSi Fi
values of Williams and Leggett 15 they have been fine
tuned in order to optimize the PBPK model predictions where fP is the fraction free in the plasma and Fi is the
for selected solutes The resting muscle blood flow was organ plasma volume flow liters min Kg 7 The
adjusted to a value of 2 25 ml min 100 g 0 0225 L Kg parameter fclear ranges from 0 impermeable capillary to
min to fit the D2O data of Schloerb et al 16 as 1 flow limited In PKQuest the default procedure is to
described previously 6 This value for muscle blood flow input just one parameter the fclear muscle and the per
is similar to the recent measurements in man of resting meability of all the other organs are then automatically
muscle blood flow of 2 3 17 and 3 12 ml min 100 gm determined using the default values of PSi PSmuscle pro
Ruotsalainen 239 using 15O H2O PET scans and of grammed into PKQuest This accounts for the other phys
2 5 ml min 100 gm 18 using plethysmographic meas iological factors that determine fclear organ plasma flow
urements of calf blood flow This value is somewhat and plasma protein binding The following set of default
higher then 133Xe measurements which vary from 1 4 to PS values are assumed liver kidney and portal organs are
1 9 ml min 100 gm 19 Similarly the adipose blood flow limited heart and lung have a PS 50 times that of
flow in Table 6 was adjusted 5 to a value of 4 4 ml min skeletal muscle brain has a PS 0 for solutes that have
100 gm to fit the enflurane data of Munson et al 20 fclear muscle 1 due to the blood brain barrier and the
This value is close to the recent human 15O H2O meas rest of the organs have a PS equal to that of muscle 25
urements of subcutaneous abdominal 4 8 ml min 100 As can be seen from eq 6 solutes that have a high
gm visceral 5 9 and perirenal 4 9 fat blood flow 21 intrinsic capillary permeability PS can have a functional
The tendon e g connective tissue blood flow is poorly capillary permeability limitation fclear 1 if there is a
characterized and has a large variation The value of 1 ml high degree of plasma protein binding i e fP is small
100 gm min is representative of direct measurements of This dependence of fclear on protein binding is applied
tendon blood flow using microspheres 22 23 The total
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Table 4 Interstitial volume VI fraction of total extravascular water
Species Solute Reference Organ VI Comments
Rat EDTA 35 64 65 sk mus 081 091 Renal ligature sampled 30 minutes after
skin 55 73
intestine 28 32
66 sk mus 12 Renal ligature samples from live rat
67 1 sk mus 075 Constant infusion Measured time course of
tissue uptake
intestine 15 25 Muscle stomach and intestine equilibrated in
40 minutes
stomach 23
adipose 49
50 skin 61 Renal ligature divided skin into dermis and
sub cutaneous samples
subcutis 51
68 1 sk mus 15 Constant infusion Volume increased with
time for skin and colon Range indicates
volume at 60 to 120 minutes
skin 44 63
sm intestine 29
colon 3 41
adipose 1 0
Sulfate 69 1 skin 65 Nephrectomized
Mannitol skin 66
Sulfate 70 1 2 muscle 12 Nephrectomized
Inulin 9 sk mus 12 Constant infusion
intestine 12
71 1 sk mus 1 Constant infusion Tissue uptake
corresponds to capillary PS 0 6 ml min 100
Rabbit EDTA 72 sk mus 077 Renal ligature
EDTA 73 1 2 sk mus 10 Renal ligature Measured time course of
tissue uptake
Sucrose sk mus 11 Equilibrated in 30 minutes
Inulin sk mus 1
74 sk mus 09 Renal ligature Determined time constant T
heart 28 T 1 min
intestine 2 T 1 5 min
ear 5 T 12 min
Cat EDTA 75 sk mus 13 Renal ligature
Dog EDTA 76 sk mus 16 Renal ligature
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Table 4 Interstitial volume VI fraction of total extravascular water Continued
Sulfate 70 1 2 muscle 20 Constant infusion Equilibration time 30
Sucrose 49 1 sk mus 23 Constant infusion Cannulated prepopliteal
lymphatic and measured lymph sucrose
Thiosulfate 51 2 muscle 13 Renal ligature Equilibration time 180 min
skin 77 Equilibration time 180 min
tendon 75 Equilibration time 360 min
Inulin muscle 1 Equilibration time 180 min
skin 48 Equilibration time 180 min
tendon 26 Equilibration time 360 min
Man Inulin1 2 77 sk mus 08 11 Bolus plus constant infusion Tissue biopsy
after 20 120 minutes
1Assumed total organ water ml 100 gm of skeletal muscle 75 heart 78 skin 60 subcutaneous tendon ear 60 stomach 75 intestine 73
adipose 18 3 liver 70 lung 79 35 78 2Assumed plasma volume ml 100 gm of skeletal muscle 0 4 heart muscle 2 0 skin 0 6 64 78
Table 5 Interstitial albumin volume as fraction of interstitial EDTA volume VIA VIE the interstitial albumin concentration relative to
plasma albumin CI CP and the product KA VIA VIE CI CP
Species Reference Organ CI CP VIA VIE KA Comments
Rat 64 sk mus 0 8 0 73 0 58 Constant infusion of I125 rat
serum albumin Wick tissue
skin 0 69 0 6 0 4
tendon 0 61 0 45 0 27
50 skin dermis 0 72 0 44 0 32
skin subcut 0 72 0 57 0 41
Rabbit 79 sk mus 0 76 0 53 0 4 Lymph albumin
skin 0 49 0 47 0 23
Table 6 Spreadsheat description of PBPK parameters for the 70 Kg 20 fat standardhuman
Organ Weight Lipid Solid Solid ecf water water Kg ecf flow L Kg flow L min Ka Ka ecf
Kg Fraction Fraction Kg Fraction L water L
Blood 5 5 0 0 18 0 99 0 595 4 51 0 82 2 68345
liver 1 8 0 0 3 0 54 0 23 1 26 0 7 0 2898 0 25 0 45 0 5 0 1449
portal 1 5 0 0 22 0 33 0 3 1 17 0 78 0 351 0 75 1 125 0 35 0 1228
muscle 26 0 0 22 5 72 0 15 20 28 0 78 3 042 0 0225 0 585 0 5 1 521
kidney 0 31 0 0 2 0 062 0 165 0 248 0 8 0 04092 4 1 24 0 35 0 0143
brain 1 4 0 0 2 0 28 0 1 12 0 8 0 0 56 0 784 0 1 0
heart 0 33 0 0 2 0 066 0 25 0 264 0 8 0 066 0 8 0 264 0 5 0 033
lung 0 536 0 0 2 0 107 0 2 0 428 0 8 0 08576 10 482 5 6184 0 35 0 03
skin 2 6 0 0 3 0 78 0 6 1 82 0 7 1 092 0 1 0 26 0 25 0 273
tendon 3 0 0 15 0 45 1 2 55 0 85 2 55 0 01 0 03 0 25 0 6375
other 5 524 0 0 15 0 828 0 8 4 695 0 85 3 75632 0 02 0 1104 0 25 0 9390
bone 4 0 1 4 0 5 0 0 0 0 0 0
adipose 17 5 0 8 0 0 1 3 5 0 2 3 5 0 044 0 77 0 35 1 225
Total 70 0 2 14 15 41 84 17 4572 5 6184 4 9406
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below in the application of PKQuest to a series of centrations in antecubital venous blood which differs
lactam antibiotics with varying protein binding from the arterial concentration due to the exchange with
the tissues drained by the antecubital vein A new feature
All the PBPK calculations use PKQuest 7 A small modi has been added to PKQuest that allows one to directly cor
fication of the earlier version of the software is required to rect for this effect in the PBPK model fitting The tissue
account for the new situation where the interstitial vol flow distribution supplying the antecubital vein was
ume of distribution of protein is less than that of EDTA established by applying PKQuest to the experimental data
see Appendix III Four parameters characterize the inter for a number of solutes for which simultaneous arterial
stitial volume of distribution for each organ i 1 ecf i and antecubital vein concentrations are available Levitt
the interstitial volume of EDTA as the fraction of the total in preparation This analysis indicated that antecubital
organ water 2 mecf a multiplicative constant that vein blood represents approximately 10 muscle 20
scales all the values of ecf i 3 frecf i interstitial vol skin 5 other 5 adipose and the rest 60 A V
ume of the solute relative to that of EDTA and 4 for sol anastomoses In PKQuest specifying arm as the sample
utes that are protein bound cProt i which is the site outputs the antecubital vein concentration and uses
PKQuest parameter corresponding to KAi Standard values this concentration to optimize the PBPK parameters using
of ecf Table 6 frecf 1 and cProt KAi Table 6 are pre the PKQuest minimization routines 7 This allows one
programmed in PKQuest The only parameter that needs to use antecubital vein blood samples when adjusting
to be input by the user is mecf Setting mecf 1 indicates PBPK parameters for an arbitrary uncharacterized solute
that the solute distributes in the standard ecf space The
default value of mecf is 1 indicating that the solutes dis Figure 1 shows the results of this analysis for two of the
tributes in all the tissue interstitial and intracellular extracellular solutes DTPA and inulin that were investi
space The complete PBPK pharmacokinetics of each sol gated to determine the organ composition of antecubital
ute is characterized by a short Maple worksheet that lists blood The squares show the experimental measurements
the parameters that differ from the default standardhu of the 99Tcm DTPA left column and inulin right col
man parameters The complete worksheets for the 11 sol umn sampled simultaneously from the artery black
utes are included in the additional file and antecubital vein red after a bolus venous input The
PKQuest worksheets doc For all of the solutes investi lines show the PBPK model fits for the arterial black and
gated in this paper the kidney is the major excretion path antecubital vein red concentrations The difference
way The renal clearance is described two different ways in between the arterial and antecubital vein concentrations
these worksheets If the clearance is close to the free become negligible after the first 5 to 10 minutes because
plasma glomerular clearance than the parameter rclr the antecubital vein blood is supplied primarily by high
glomerular filtration rate is used For solutes that are blood flow skin and A V anastomoses in the hand 26
cleared both by glomerular filtration and tubular secre For the solutes investigated in this paper the differences
tion the single parameter Tclr kidney is used the rate of between arterial and antecubital vein concentration are
renal clearance of the free unbound plasma solute very small e g see fig 2 and this correction is of minor
importance It is fortunate that this is the case Otherwise
PKQuest is used to find the values of the adjustable one could not use antecubital vein data for PBPK mode
parameters that provide the best fit to the experimental ling Unless otherwise stated all the PBPK model data
data by minimizing the error function shown in the figures in this paper correspond to antecu
bital vein blood
modeli datai
7 Error Function Chiou 27 has emphasized that the measurement of the
i datai noise
steady state volume of distribution Vss using eq 2 is
The parameter noise adds a weighting factor that dependent on the sampling site and has shown that the
reduces the contribution of the low concentration data value of Vss determined using antecubital vein blood will
points The default value for noise is 10 of the average be greater than the true value of Vss using arterial blood
concentration Optionally PKQuest allows the choice of This effect can be quantitated for the extracellular solutes
a mean square error term and an arbitrary noise can be investigated in this paper using the experimental or PBPK
input model data shown in figure 1 Using this data the value
of Vss for the antecubital sampling site is from 4 PBPK
Correction for antecubital vein sampling model to 10 experimental data greater than the true
Ideally one would like to be able to sample arterial blood arterial Vss The values of Vss reported below are for the
for the calculations of steady state volume of distribution antecubital vein data A small correction will be applied
and for PBPK model fitting However all of the data used when these results are used to estimate the true extracellu
in this paper was obtained by measuring the plasma con lar volumes
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DTPA Inulin
Arterial 1 black
andexperimental
antecubital vein
squares of Cousinsofet 99Tc
concentrations al m 56
DTPA right column and inulin left column after a bolus
Arterial black and antecubital vein red concentrations of 99Tcm DTPA right column and inulin left column after a bolus
injection using the experimental data squares of Cousins et al 56 The solid lines indicate the PBPK model predictions for
the arterial black and antecubital vein red concentrations The top row shows a plot of the absolute concentration and the
bottom row is a semi log plot of the same data The PBPK parameters for DTPA were identical to those used for EDTA see
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Figure 2 of PBPK model predictions and experimental data for mannitol plotted using linear left or semi log right
Comparison
Comparison of PBPK model predictions and experimental data for mannitol plotted using linear left or semi log right The
predictions for the experimental data of Laker et al 57 top and Elia et al 58 bottom are shown using the parameters in
Table 6 Both the model arterial black and antecubital vein red concentration curves are shown
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Results resulting presumably from varying concentrations of
Experimental measurements of whole animal and collagen and hyaluronan in the different tissues The sixth
individual organ volumes of distribution for extracellular column is the product of these two ratios
Table 1 summarizes the experimental measurements in K iA CI CP VIA VIE CI VIA VIE CP
humans of the steady state volume of distribution Vss for 9
mannitol EDTA amoxicillin morphine 3 glucuronide Albumin concentration in EDTA space CP
morphine 6 glucuronide and inulin The volume of distri This product for organ i which will be referred to as KAi is
bution is expressed in terms of total body weight Vss lit the relevant parameter determining the pharmacokinetics
ers Kg and total body water Vssw liters liters The latter of albumin bound solutes such as the lactam antibiot
calculation was based on an assumption of a value of 41 ics see Appendix II
liters of water for the standard 70 Kg man with 20 body
fat 14 The total body water was adjusted for body fat PBPK model for extracellular solutes
estimates if information was available Table 2 lists the The PKQuest PBPK model 7 was applied to the extracel
values of the equilibrium volume of distribution Veq for lular solutes using the new set of parameters Table 6 A
amoxicillin morphine 6 glucuronide sucrose and inulin comparison of the model predictions with the experimen
see Methods Table 3 lists the Vss and the interstitial vol tal data is shown in figs 2 3 4 5 for mannitol EDTA mor
ume VI for a series of lactam antibiotics with varying phine 6 glucuronide and morphine 3 glucuronide
amounts of plasma protein binding VI was estimated by solutes with low or negligible protein binding Since one
subtracting a plasma water volume of 2 68 liters 70 Kg of the purposes of this analysis is to find a single unique
from Vss The human serum protein binding values used PBPK model applicable to all extracellular solutes the
in Tables 1 2 3 were from the following references amox identical set of PBPK parameters has been used in all these
icillin 28 29 piperacillin 30 cefatrizine 31 cefora figures The only parameter that was varied for each solute
nide 32 dicloxacillin 33 flucloxacillin 29 33 is the renal clearance determined using the optimization
morphine 3 glucuronide and morphine 6 glucoronide feature in PKQuest see Methods Figure 2 shows the
34 Table 4 lists the interstitial volume as a fraction of PBPK model predictions for both the arterial and antecu
total extravascular organ water for selected solutes in rats bital vein concentration see Methods It can be seen that
rabbits cats dogs and man the difference is small In all other figures only the
antecubital vein concentration is shown
The solutes listed in Table 4 have a rapid possibly flow
limited exchange between the blood and interstitial space All of the solutes shown in figs 2 3 4 5 have been
so that the interstitial space equilibrates with the blood In assumed to be flow limited This is clearly not the case for
contrast albumin has a very slow rate of tissue plasma inulin which is the prototypical capillary permeability
exchange with a time constant of about 100 hours in the limited solute In addition the interstitial volume of dis
rat 35 Because of this low permeability the steady state tribution of inulin VI is clearly significantly smaller than
interstitial albumin concentration in a given tissue CI is that of EDTA Table 1 In PKQuest the parameter mecf
less than the plasma concentration and is determined by scales the interstitial volume of all non blood organs by
the balance between the rate of trans capillary exchange the same amount Thus for inulin there are 3 adjustable
and the rate of removal by lymph flow 36 The standard parameters 1 the renal clearance rclr 2 the intersti
procedure used to measure this concentration CI is to sam tial volume relative to that for EDTA mecf and 3 the
ple the lymph draining that tissue or to use the wick capillary permeability for muscle fclear muscle
method to sample the free tissue albumin The interstitial which sets the permeability for all the other organs see
albumin volume of distribution VIA for that tissue is then Methods The parameter fclear indicates the fraction of
defined by the solute that equilibrates with the tissue in one pass
through the capillary The flow limited case corresponds
8 VIA Total Extravascular Albumin CI to an fclear equal to 1 Figure 8 shows the PBPK model
results for four different sets of experimental inulin data
The fourth column in Table 5 lists the steady state albu The values of mecf 0 42 and fclear muscle 0 409
min tissue plasma concentration ratios CI CP and the corresponding to PSmuscle 0 61 ml min 100 g see eq
fifth column lists the corresponding ratio VIA VIE where 6 were first determined by optimizing the fit to the data
VIE is the interstitial volume of EDTA for skeletal muscle of Odeh et al 37 top row fig 6 A good fit average
skin and tendon VIA is less than VIE because the interstitial error less than 2 was obtained with the 3 adjustable
matrix behaves like a size exclusion gel restricting the parameters To test the validity of this result 3 other sets
albumin volume of distribution 3 This excluded vol of experimental data were fitted using these identical val
ume is larger in skin and tendon then in skeletal muscle ues of mecf and fclear muscle and only adjusting the
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Comparison
or 3semi log
of antecubital
right PBPK model predictions line and experimental data squares for EDTA 58 plotted using linear
Comparison of antecubital PBPK model predictions line and experimental data squares for EDTA 58 plotted using linear
left or semi log right
renal clearance The result of this procedure are shown in antibiotics listed in Table 3 amoxicillin piperacillin
figure 6 for the experimental data of Orlando et al 38 cefatrizine ceforanide flucloxacillin and dicloxacillin
second row Ladegaard Pedersen et al 39 third row The influence of the protein albumin binding on the
and Prescott et al 40 bottom row The agreement pharmacokinetics of these solutes is characterized by the
between the PBPK model and the experimental data is default PKQuest values for KAi in the different organs
quite good except for the long time data of Prescott et al Table 6 see Appendix II and III and the experimental
40 This discrepancy is expected since the inulin clear values for the fraction bound in plasma fp Table 1 The
ance in the experiments of Prescott et al was non linear effect of including a capillary permeability limitation was
decreasing by about 50 at low concentrations long investigated for these solutes because as discussed above
times It is not clear why the data in the other three exper see eq 6 one would predict that solutes with a high
iments in fig 6 do not show this marked non linearity amount of protein binding should be capillary permeabil
ity limited All the other parameters were identical to
Figures 7 8 9 10 11 12 compare the PBPK model predic those used in figs 2 3 4 5 The addition of a capillary per
tions with experimental data for the six lactam meability limitation provides a significant improvement
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Comparison
for 4experimental
of PBPK linear
data of left
or semi log
predictions
and bottom
experimental
row data for morphine 6 glucuro
Comparison of PBPK linear left or semi log right plots of model predictions and experimental data for morphine 6 glucuro
nide for experimental data of Lotsch et al 59 top row and Penson et al 42 bottom row
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Comparison
for 5experimental
of PBPK linear
data of left
or semi log
right plots of model predictions and experimental data for morphine 3 glucuro
Comparison of PBPK linear left or semi log right plots of model predictions and experimental data for morphine 3 glucuro
nide for experimental data of Penson et al 60
in the fit between the PBPK model and the experimental This new PBPK parameter set Table 6 also provided
data for the two antibiotics with the highest degree of good fits not shown to the other solutes that have been
binding dicloxacillin 97 bound fig 12 and flucloxa previously investigated with PKQuest propranolol 7
cillin 93 bound fig 11 For ceforanide fig 10 D2O and ethanol 6 anesthetic gases and toluene 5
which is 82 bound there is a slight improvement in the The slightly modified Maple worksheets describing these
fit with the addition of a small permeability limitation solutes are available on the PKQuest web site http
The value of the PS product for these three permeability www pkquest com
limited solutes is 11 3 ml min 100 g fclear 0 25 for
dicloxacillin 7 0 ml min 100 g fclear 0 344 for flu Discussion
cloxacillin and 5 ml min 100 g fclear 0 52 for cefora Volume of distribution of selected extracellular solutes in
nide For the other antibiotics amoxicillin piperacillin humans
and cefatrizine with protein binding of 62 or less the Table 1 summarizes the experimental measurements in
addition of a capillary permeability limitation does not humans of the steady state volume of distribution Vss for
significantly improve the fit For these flow limited antibi mannitol EDTA amoxicillin morphine 3 glucuronide
otics amoxicillin piperacillin cefatrizine there is only 1 morphine 6 glucuronide and inulin In order to be
adjustable parameter the renal clearance For the capil included in this table solutes had to meet the following
lary permeability limited solutes ceforanide flucloxacil criteria 1 extracellular distribution 2 low level of
lin dicloxacillin there are two adjustable parameters the plasma protein binding 3 no evidence of any unusual
renal clearance and fclear muscle tissue binding or accumulation 4 major excretory path
way is renal 5 linear pharmacokinetics and 6 published
Page 13 of 29
page number not for citation purposes
BMC Clinical Pharmacology 2003 3 http www biomedcentral com 1472 6904 3 3
Comparison
6 of PBPK linear left or semi log right plots of model predictions and experimental data for inulin
Comparison of PBPK linear left or semi log right plots of model predictions and experimental data for inulin The parame
ters rclr mecf and fclear muscle were adjusted to give the optimal fit to the data of Odeh et al 37 top row These values
of mecf and fclear muscle were then used to fit the experimental data of Orlando et al 38 second row Ladegaard Peder
sen et al 39 third row and Prescott et al 40 bottom row varying only the renal clearance to obtain the best fit
Page 14 of 29
page number not for citation purposes
BMC Clinical Pharmacology 2003 3 http www biomedcentral com 1472 6904 3 3
Figure 7 of
Comparison
experimental data
of Sjovall
linear left
predictions
experimental data for amoxicilllin for
Comparison of PBPK linear left or semi log right plots of model predictions and experimental data for amoxicilllin for
experimental data of Sjovall et al 61 top row and Arancibia et al 62 bottom row The flow limited PBPK model is used
no capillary permeability limitation
Page 15 of 29
page number not for citation purposes


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