Vol. 278, Issue 1, H137-H150, January 2000
Toluidine blue O and methylene blue as endothelial redox
probes in the intact lung
Said H.
Audi1,2,
Lars E.
Olson1,3,
Robert D.
Bongard3,
David L.
Roerig4,5,6,
Marie L.
Schulte3, and
Christopher A.
Dawson1,2,3,4,5,6
1 Department of Biomedical Engineering,
Marquette University, Milwaukee 53201-1881; Departments of
2 Pulmonary and Critical Care Medicine,
3 Physiology,
4 Anesthesiology, and
5 Pharmacology and Toxicology, Medical College of
Wisconsin, Milwaukee 53226; and 6 Zablocki
Veterans Affairs Medical Center, Milwaukee, Wisconsin 53295
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ABSTRACT |
There is increasing
evidence that the redox activities of the pulmonary endothelial surface
may have important implications for the function of both lungs and
blood. Because of the inherent complexity of intact organs, it can be
difficult to study these activities in situ. Given the availability of
appropriate indicator probes, the multiple-indicator dilution (MID)
method is one approach for dealing with some aspects of this
complexity. Therefore, the objectives of the present study were to
1) evaluate the potential utility of two thiazine redox
indicators, methylene blue (MB) and toluidine blue O (TBO), as MID
electron acceptor probes for in situ pulmonary endothelium and
2) develop a mathematical model of the pulmonary disposition of
these indicators as a tool for quantifying their reduction on passage
through the lungs. Experiments were carried out using isolated rabbit
lungs perfused with physiological salt solution with or without plasma
albumin over a range of flow rates. A large fraction of the injected
TBO disappeared from the perfusate on passage through the lungs. The
reduction of its oxidized, strongly polar, relatively hydrophilic blue
form to its colorless, highly lipophilic reduced form was revealed by
the presence of the reduced form in the venous effluent when plasma
albumin was included in the perfusate. MB was also lost from the
perfusate, but the fraction was considerably smaller than for TBO. A
distributed-in-space-and-time model was developed to estimate the
reduction rate parameter, which was ~29 and 1.0 ml/s for TBO and MB,
respectively, and almost flow rate independent for both indicators. The
results suggest the utility particularly of TBO as an electron acceptor
probe for MID studies of in situ pulmonary endothelium and of the model for quantitative evaluation of the data.
transplasma membrane electron transport; multiple-indicator
dilution; mathematical modeling
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INTRODUCTION |
THE PULMONARY ENDOTHELIUM is capable of reducing
certain blood-borne electron acceptors as they pass through the
pulmonary capillary bed. The mechanisms involved include transplasma
membrane electron transport systems that utilize intracellular electron donors to reduce extracellular acceptors (1, 10, 12, 34, 50). These
redox systems control the pulmonary disposition of certain redox active
drugs (10), and, by analogy with the functions of transplasma membrane
transport systems in other cell types, they may be mechanisms by which
the endothelial cells influence and/or sense the redox status of the
blood (15, 19, 22, 28, 32, 35-37, 46, 47, 51). Studying metabolic
processes such as these electron transport systems within an intact
functioning organ is complicated by the many factors that can influence
the disposition of probes for such processes within an organ (4, 7, 8,
23, 29), and probe disposition can be affected by factors other than
the targeted process. The bolus injection multiple-indicator dilution
(MID) method has been used for studies of other pulmonary endothelial
surface reactions (9, 16-18, 20, 21, 24, 30, 49). A principal
feature of this MID method is that it provides the temporal information
needed to identify separately the contributions of various factors that may influence the overall disposition of a probe for a particular metabolic process. Identification of useful probes is one step in the
development of an MID method for a specific cellular function. The
purpose of the present study was to evaluate two thiazine compounds,
methylene blue (MB) and toluidine blue O (TBO), as electron acceptor
probes for the pulmonary endothelium in intact lungs. Both were
previously shown to be electron acceptors for transplasma membrane
electron transport in bovine pulmonary arterial endothelial cells grown
in cell culture (12, 34, 40). A useful MID probe must fulfill several
criteria; some are specific to the particular study conditions, but
some are general. An important general criterion is that the probe must
be a good enough substrate that the rate of the reaction under study is
fast enough to have a significant impact on probe disposition within
the 0.5- to 2-s pulmonary capillary transit time but slow enough that
the reaction kinetics of interest, rather than only the rate of probe
delivery, dominates the probe disposition (4, 23). Therefore, the
determination of the kinetics of MB and TBO disposition on passage
through the pulmonary circulation was a central focus of the present
study. We addressed the problem of quantifying the kinetics of probe disposition on passage through the lungs by representing the
hypothesized processes involved in the form of a mathematical model.
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METHODS |
Isolated Lung Preparation
The isolated rabbit lung preparation used has been described previously
(3, 10). Each of 22 New Zealand White rabbits [2.51 ± 0.23 (SD)
kg body wt] was given chlorpromazine hydrochloride (25 mg/kg im)
followed by pentobarbital sodium (15-20 mg/kg iv). A carotid
artery catheter was inserted for heparinization (1,200 IU/kg) followed
by exsanguination. The chest was opened, and cannulas were placed
in the pulmonary artery, left atrium, and trachea. The cannulated
lungs were removed and suspended vertically from the trachea, with the
arterial and venous cannulas connected to a temperature-controlled
(37°C) recirculating perfusion system primed with a physiological
salt solution (PSS) containing (in mM) 4.7 KCl, 2.51 CaCl2,
1.19 MgSO4, 2.5 KH2PO4, 118 NaCl,
25 NaHCO3, and 5.5 glucose and, in most cases, either 5%
BSA (referred to as PSS-albumin) or 5% dextran (average mol
wt 74,200) (referred to as PSS-dextran). The perfusate was pumped
(Masterflex roller pump) into the pulmonary artery from a reservoir
into which the perfusate drained from the left atrium. The first 200 ml
to pass through the lungs were used to clear the lungs of residual
blood and were discarded before commencing recirculation. The
standard flow rate was 200 ml/min, with the flow rate adjusted
temporarily according to the experimental protocol as indicated in
Bolus Injections. Pulmonary venous pressure
was set equal to pleural pressure between adjustments required for a
particular experimental protocol. Pulmonary arterial and left atrial
pressures, measured relative to the level of the left atrium,
were monitored continuously. The lungs were ventilated with a gas
mixture of ~17% O2-5% CO2-balance
N2 at a frequency of 11 breaths/min, with
end-inspiratory and end-expiratory pressures of ~6 and 1 Torr,
respectively, maintained with water overflow valves. The resulting
perfusate PO2,
PCO2, and pH were 123 ± 4.6 (SD)
Torr, 36.2 ± 2.9 Torr, and 7.40 ± 0.05, respectively.
To measure the venous effluent indicator concentration versus time
curves, the venous effluent could be diverted into the sample tubes of
a Gilson-Escargot fraction collector modified to sample at 
6.67
samples/s. For experiments in which TBO was studied in
PSS-albumin-perfused lungs, the venous effluent tubing passed through a
previously described photodetector (40), measuring optical absorbance
at wavelengths of 490 and 590 nm, before flowing into the fraction
collector tubes. Each fraction collector tube contained 20 µl of 0.8 mM potassium ferricyanide solution so that complete oxidation of any
reduced MB (MBH) or TBO (TBOH) in the effluent would occur before the
absorbance was measured. Thus total MB, MBH + oxidized MB
(MB+), total TBO, or TBOH + oxidized TBO (TBO+)
concentration in the venous effluent was measured in the fraction collector tubes. The photodetector measured TBO+ rapidly
enough after leaving the lung that autoxidation of any TBOH present was
small. FITC-dextran, which was also measured by the photodetector, was
included in the bolus for the purpose of determining the transport
function between the two sampling sites as indicated in Bolus
Injections.
Bolus Injections
To measure the disappearance of MB+, TBO+, or
TBOH from a bolus during passage through the lungs, the ventilation was
halted in end expiration and the venous outflow was diverted
into the fraction collector. A 0.9-ml bolus containing reference
indicators 125I-labeled human serum albumin (~0.09
µCi/ml) and/or FITC-dextran (1.5 mg/ml, average mol wt
2,000) and test indicators MB+, TBO+, or TBOH
(0.1-0.15 nmol/ml) was then introduced into the arterial inflow
tubing via an injection loop. Consecutive 2-ml samples were collected
at a rate and duration appropriate for the flow rate used. The first
sample was used as a background reference sample. Measured quantities
of the injectate solution were added to the next three samples. All of
these samples emerged in the venous effluent before the appearance of
the injected indicators, and they were used as standards for
determining the effluent concentrations of 125I, FITC,
MB+, or TBO+ as fractions of their injected
concentrations. A 1-ml aliquot of each collected sample was used to
determine 125I concentration by gamma scintillation
counting. The remainder was analyzed spectrophotometrically. The
photodetector output was calibrated with known concentrations of FITC,
TBO+, or MB+ in the perfusate solution. Eight
percent of the TBO signal at 590 nm was measured at 490 nm, with no
detectable FITC signal at 590 nm. The reference indicator recoveries
based on the standards were not significantly different from 100%. For
MB, the perfusate was PSS-dextran. For TBO, both PSS-dextran and
PSS-albumin were used.
To prepare the TBOH injectates, 3 ml of the respective perfusate
containing 160 µM TBO, 1.5 mg FITC-dextran and 200 µM NADH were
added to a test tube having two ports. The mixture was bubbled through
one of the ports for 10 min with 5.8% CO2 in
N2 to deoxygenate while maintaining the pH at 7.4. Diaphorase (0.2 U in 0.02 ml) was then added to the solution under
anoxic conditions. After the disappearance of blue color from the
solution, the ports were sealed and low-dead space syringes were filled
with the injectate directly from the sealed tube. The injection loop
was prefilled with 3 ml of deoxygenated perfusate just before the
addition of the 0.9-ml TBOH injectate.
At the end of each experiment, the lungs were removed and the pulmonary
arterial and left atrial cannulas were connected directly together.
Boluses containing the 125I-labeled albumin and
FITC-dextran were injected and fraction collector samples and
photodetector output were collected at each flow rate used in the
experiment. At least one such bolus also included the respective
thiazine compound. The data obtained from these samples were used to
measure the part of the bolus transit time and dispersion that was
caused by the injection, tubing, and sampling system and to affirm that
any separation between the thiazine test indicator
concentration curves and the reference indicator concentration
curves was caused only by passage through the lungs and not some
interaction with the perfusion system connected to the lungs.
To measure the indicator concentration versus time curves over a range
of flow rates, the first step was to raise the flow rate to the highest
level to be used in the experiment, with the left atrial pressure set
equal to atmospheric pressure at the level of the left atrium. The
resulting arterial pressure divided by 2 was the value at which the
average of the arterial left atrial pressure was set for each of the
lower flow rates by adjusting the height of the reservoir. This was
done so that the vascular volume was approximately the same at each
flow rate. The flow rate was then set at ~200, 400, 600, or 800 ml/min in TBO experiments or 50, 100, 200, or 300 ml/min in
MB experiments, and a bolus was injected and samples collected
as indicated above. Injections were then made at two or three of the
other designated flow rates in similar fashion.
To determine whether dextran in the perfusate might have any
influence on TBO or MB disposition in the lungs, after the
above-described protocol had been completed in one of the
lungs from the TBO and MB groups perfused with PSS-dextran,
the perfusate was changed to PSS with neither dextran nor albumin. Then
a TBO+ or MB+ bolus (also dextran free) was
injected at a flow rate of 800 or 300 ml/min,
respectively. Also, in one lung perfused with PSS-dextran the photodetector was included to confirm that effluent MBH and TBOH
concentrations were below detectable levels when there was no plasma
albumin in the perfusate.
Additional Measurements
The equilibrium binding of TBO+ and TBOH to BSA was
measured by ultrafiltration using the Amicon MPS-1 micropartition
system with a YM30 membrane at room temperature as previously described (3). The concentration of TBO+ or TBOH was 12 µM in
phosphate-buffered (pH 7.4) 0.9% NaCl solution containing 5% BSA.
TBOH was prepared by adding 0.5 µmol sodium hydrosulfite/ml of
TBO+ solution. TBOH was measured after reoxidation to
TBO+. The albumin-bound fractions were 59 and 79% for
TBO+ and TBOH, respectively.
The apparent octanol-to-water partition coefficient for TBOH and
TBO+ at room temperature was determined as previously
described (10) by using a concentration of 10.4 µM TBO+
or TBOH in 0.1 M phosphate buffer (pH 7.4). TBOH was prepared as
indicated in Bolus Injections for the ultrafiltration studies. The values of the partition coefficients were 0.95 and 10.3 for TBO+ and TBOH, respectively. The previously reported values
for MB+ and MBH were 0.22 and 16, respectively (10).
To determine the TBOH autoxidation rate, TBOH was prepared in a manner
similar to the TBOH injectate described above. TBO and NADH (final
concentration of 160 µM for both) were added to tubes containing 3 ml
Hanks' balanced salt solution and 10 mM HEPES at pH 7.4 with or
without 5% BSA or 5% dextran. Each solution was bubbled with
N2 for 10 min, and diaphorase (0.2 U) was added. The
resulting TBOH solution (0.1 ml) was added to a spectrophotometric cuvette containing 2 ml Hanks'-HEPES buffer with or without 5% BSA or
5% dextran at pH 7.4 and equilibrated with atmospheric PO2. Absorbance at 590 nm was
recorded at 5-s intervals for 3 min in a Beckman DU 7400 spectrophotometer at 37°C.
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RESULTS |
Experimental Results
The pressure, flow, and volume data reflecting the conditions under
which the injections were carried out are given in Tables 1 and 2. The
average pressures and vascular volumes were higher for the
TBO than the MB experiments because of the higher flow rate range
covered. The injections themselves had no detectable effect on
perfusion pressures, suggesting that any effects that these compounds
might have on vascular tone were below the level of detectability in
these studies.
Examples of graphs of indicator concentrations normalized to their
respective injected amounts versus time, for the various combinations
of PSS-dextran, PSS-albumin, MB+, TBO+, and
TBOH and at different flow rates, are shown in Figs.
1-5. With PSS-dextran perfusion, only the oxidized forms were detected in
the venous effluent. The presence of TBOH in the effluent after TBO+ injections when the lungs were perfused with
PSS-albumin is reflected by the fact that the total TBO (TBOH + TBO+) concentrations were higher than the concentrations of
TBO+ alone (Fig. 3). The fractions of MB+ and
TBO+ that disappeared from the PSS-dextran and PSS-albumin
perfusates on passage through the lungs are summarized as extractions
in Fig. 6. The TBO+ extractions
were higher than the MB+ extractions even though the flow
rate range was also higher for TBO+. The extraction of
TBO+ from PSS-albumin was lower than from PSS-dextran,
reflecting the effects of the TBO+-BSA binding. When the
lungs were perfused with PSS with neither albumin nor dextran, the
effluent TBO+ and MB+ were indistinguishable
from those when the lungs were perfused with PSS-dextran, indicating
that the dextran had no detectable effect on TBO+ or
MB+ extraction. When TBOH rather than TBO+ was
injected with PSS-albumin as the perfusate, the effluent TBOH
concentration curves tended to be displaced to the right in comparison
to the reference indicator or to the TBO+ curves after
TBO+ injection (Fig. 4). This difference reflects the
tissue distribution of the TBOH (see DISCUSSION). When TBOH
was injected with PSS-dextran as the perfusate, the TBOH almost
completely disappeared from the perfusate (Fig. 5).
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Fig. 1.
Concentration (normalized to amount of injected indicator) vs. time
curves for oxidized methylene blue (MB+) and reference
indicator (CR) obtained at 4 flow rates in 1 lung perfused
with albumin-free perfusate [physiological salt solution
(PSS)-dextran]. Solid lines are model fits to data.
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Fig. 2.
Concentration (normalized to amount of injected indicator) vs. time
curves for oxidized toluidine blue O (TBO+) and reference
indicator (CR) obtained at 3 flow rates in 1 lung perfused
with albumin-free perfusate (PSS-dextran). Solid lines are model fits
to data.
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Fig. 3.
Concentration (normalized to amount of injected indicator) vs. time
curves for TBO+, total TBO [reduced TBO (TBOH) + TBO+], and reference indicator (CR)
obtained at 3 flow rates in 1 lung perfused with albumin-containing
perfusate (PSS-albumin). Solid lines are model fits to data.
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Fig. 4.
Concentration (normalized to amount of injected indicator) vs. time
curves for TBOH and reference indicator (CR) obtained at 3 flow rates in 1 lung perfused with albumin-containing perfusate
(PSS-albumin). Solid lines are model fits to data.
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Fig. 5.
Concentration (normalized to amount of injected indicator) vs. time
curves for TBOH and reference indicator (CR) obtained at 3 flow rates in 1 lung perfused with albumin-free perfusate
(PSS-dextran). Solid lines are model fits to data.
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Fig. 6.
Average extraction (±SE) of MB+ from PSS-dextran
(n = 6-8) and of TBO+ from PSS-dextran
(n = 8) or PSS-albumin (n = 4) vs. flow rate.
Extraction = 1  ([MB+] or
[TBO+])/ CR(t), where
concentrations were obtained at time of maximum of CR(t).
Dashed lines are isopleths for constant values of F × ln(1 extraction) indicated.
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Further evaluation of these results was carried out by expressing the
hypothesized interactions between these thiazine compounds and the lung
tissue in the following model.
Model
The thiazine dyes are assumed to participate in the following
associations and reactions within the perfusate and tissue.
Stoichiometric equations.
where B+ is the oxidized thiazine test indicator; BH is
the reduced thiazine test indicator; A represents the sites of
sequestration of BH within the tissue; E is thiazine reductase; DH is
the electron donor; D+ is the oxidized form of DH; P is
plasma protein; Z represents the nonspecific B+ tissue
binding sites; BHA is BH bound to A; BHP is BH bound to plasma protein;
B+P is B+ bound to plasma protein;
B+Z is B+ associated nonspecifically with
tissue; k1 and k
1 are plasma protein association and dissociation rate constants,
respectively, for B+; k2 and
k2 are plasma protein association and
dissociation rate constants, respectively, for BH;
ko is the autoxidation rate constant
(k7[O2]1/2[H+])
for BH within the perfusate; kr1 and
kr2 are the thiazine reductase association rate
constants k5[DH] and
k6[DH], for B+ and B+P,
respectively; k3 and k3
are the nonspecific tissue association and dissociation rate constants,
respectively, for B+; and k4 is the
tissue sequestration rate constant for BH.
Species balance equations.
A single capillary element of the kinetic model is composed of a
capillary volume (Qc) and a surrounding tissue volume
(Qt). The spatial and temporal variations in the
concentrations of the vascular reference indicator and B+
and BH are described by the following species balance equations based
on the above stoichiometric equations and the following assumptions.
1) The reference indicator, having perfusate concentration [R], was convected through the pulmonary vascular bed
without interacting with the tissue. 2) When the plasma protein
(P) was present in the perfusate, the equilibration between P and
B+ or BH was rapid relative to the capillary transit time
(
c). 3) The
endothelial cell reduction of B+ mediated by E was
irreversible. 4) The association of B+ with Z was
rapid relative to c.
5) The equilibration of BH between Qc and
Qt with tissue to perfusate partition coefficient 
was
rapid relative to c.
6) The PO2 and
[DH] were constant under the study conditions.
SINGLE CAPILLARY ELEMENT.
![<FR><NU>∂[R]</NU><DE>∂<IT>t</IT></DE></FR> + <IT>W</IT> <FR><NU>∂[R]</NU><DE>∂<IT>x</IT></DE></FR> = 0](/content/vol278/issue1/fulltext/H137/img002.gif)
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(1)
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![− <FR><NU>E<IT>k</IT><SUB>rl</SUB>[B<SUP>+</SUP>]</NU><DE>Q<SUB>c</SUB></DE></FR> + <IT>k</IT><SUB>o</SUB>[BH] + <FR><NU>(<IT>k</IT><SUB>−3</SUB>B<SUP>+</SUP>Z − <IT>k</IT><SUB>3</SUB>[B<SUP>+</SUP>]Z)</NU><DE>Q<SUB>c</SUB></DE></FR>](/content/vol278/issue1/fulltext/H137/img004.gif)
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(2)
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![+ <IT>k</IT><SUB>1</SUB>[B<SUP>+</SUP>][P] − <FR><NU>E<IT>k</IT><SUB>r2</SUB>[B<SUP>+</SUP>P]</NU><DE>Q<SUB>c</SUB></DE></FR> + <IT>k</IT><SUB>o</SUB>[BHP]](/content/vol278/issue1/fulltext/H137/img006.gif)
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(3)
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![<FR><NU>∂B<SUP>+</SUP>Z</NU><DE>∂<IT>t</IT></DE></FR> = − <IT>k</IT><SUB>−3</SUB> B<SUP>+</SUP>Z + <IT>k</IT><SUB>3</SUB> [B<SUP>+</SUP>] Z](/content/vol278/issue1/fulltext/H137/img007.gif)
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(4)
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![+ <FR><NU>E<IT>k</IT><SUB>rl</SUB>[B<SUP>+</SUP>]</NU><DE>(Q<SUB>c</SUB> + &lgr;Q<SUB>t</SUB>)</DE></FR> − <FR><NU>&lgr;Q<SUB>t</SUB></NU><DE>(Q<SUB>c</SUB> + &lgr;Q<SUB>t</SUB>)</DE></FR> (<IT>k</IT><SUB>4</SUB>[A][BH])](/content/vol278/issue1/fulltext/H137/img010.gif)
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(5)
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![+ <IT>k</IT><SUB>2</SUB>[BH][P] − <IT>k</IT><SUB>o</SUB> [BHP] + <FR><NU>E<IT>k</IT><SUB>r2</SUB>[B<SUP>+</SUP>P]</NU><DE>Q<SUB>c</SUB></DE></FR>](/content/vol278/issue1/fulltext/H137/img012.gif)
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(6)
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E = [E]Qc, Z = [Z]Qc, and B+Z = [B+Z]Qc, where [E],
[Z], and [B+Z] are the moles of
thiazine reductase and free and bound nonspecific tissue binding sites
per milliliter of capillary volume, respectively. [R](x,t),
[B+](x,t),
[BH](x,t),
[BHP](x,t), and
[B+P](x,t) are the respective
vascular concentrations at distance x from the capillary inlet
(x = 0) and time t. W is the average linear
flow velocity within Qc.
Under the assumption of rapid equilibration between the free and plasma
protein-bound B+ and
BH
and
![[B<SUP>+</SUP>P] = <FR><NU>[B<SUP>+</SUP>][P]</NU><DE><IT>K</IT><SUB>1</SUB></DE></FR>](/content/vol278/issue1/fulltext/H137/img014.gif)
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(7)
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where
K1 = k1/k1 and
K2 = k2/k2 are the plasma
protein equilibrium dissociation constants for B+ and BH, respectively.
Under the assumption of rapid equilibration between B+ and
Z
and
![B<SUP>+</SUP>Z = <FR><NU>[B<SUP>+</SUP>]</NU><DE>Q<SUB>f</SUB></DE></FR>](/content/vol278/issue1/fulltext/H137/img016.gif)
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(8)
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where
Qf = k3/Zk3
has units of volume and acts as a virtual volume of distribution for
B+.
Adding Eqs. 2-4 and 5-6 and substituting
Eqs. 7 and 8 results in
![= − <FR><NU>[<A><AC>B</AC><AC>˜</AC></A><SUP>+</SUP>] <IT>K</IT><SUB>red</SUB></NU><DE>Q<SUB>c</SUB> + Q<SUB>F</SUB></DE></FR> + <FR><NU>Q<SUB>c</SUB> [<A><AC>BH</AC><AC>∼</AC></A>] <IT>k</IT><SUB>o</SUB></NU><DE>Q<SUB>c</SUB> + Q<SUB>F</SUB></DE></FR>](/content/vol278/issue1/fulltext/H137/img018.gif)
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(9)
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![= <FR><NU>[<A><AC>B</AC><AC>˜</AC></A><SUP>+</SUP>] <IT>K</IT><SUB>red</SUB></NU><DE>Q<SUB>c</SUB> + Q<SUB>T</SUB></DE></FR> − <FR><NU>Q<SUB>c</SUB> [<A><AC>BH</AC><AC>∼</AC></A>] <IT>k</IT><SUB>o</SUB></NU><DE>Q<SUB>c</SUB> + Q<SUB>T</SUB></DE></FR> − <FR><NU>[<A><AC>BH</AC><AC>∼</AC></A>] <IT>K</IT><SUB>seq</SUB></NU><DE>Q<SUB>c</SUB> + Q<SUB>T</SUB></DE></FR>](/content/vol278/issue1/fulltext/H137/img020.gif)
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(10)
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where ![[<A><AC>BH</AC><AC>∼</AC></A>]](/content/vol278/issue1/fulltext/H137/img021.gif)
= [BH]
2,
[
+] = [B+]1, 1 = 1 + [P]/K1, and 2 = 1 + [P]/K2. The model parameters are
QF = Qf/1 (ml), which is
the measure of the magnitude of the rapidly equilibrating nonspecific
interactions of B+ with the tissue; QT = Qt/2 (ml), which is the measure of the magnitude of the rapidly equilibrating partitioning of the BH between
tissue and perfusate; Kred = (Ekr1 + Ekr2
[P]/K1)/1 (ml/s), which
is the measure of the B+ reduction rate;
Kseq = [A]k4QT (ml/s), which is
the measure of the BH sequestration rate within the tissue; and
ko (s1), which is the rate of
autoxidation of BH within the perfusate.
Whole organ.
To construct an organ model from the single capillary element model,
the distribution of pulmonary capillary transit times [hc(t)] needs to be taken into account
(4, 29). Previously, we (5) estimated that for normal rabbit lungs in
this perfusion system, the pulmonary capillary mean transit time
(c) was ~44% of
the total vascular mean transit time
( ), the relative
dispersion of hc(t) (RDc = 
c/c)
was ~0.9, and the skewness coefficient of hc(t)
(m3c/3c) was ~2, where m3c and
3c are the third central moment and
standard deviation of hc(t), respectively. For the
present analysis, we used these values to approximate hc(t) using a shifted random walk function, which
is a probability density function whose functional values are
determined by these three moments as previously described (2).
The organ reference indicator outflow concentration vs. time curve
[CR(t) = (q/F)hc(t)*hn(t), where
* is the convolution operator, q is the mass of the injected
indicator, F is the total flow through the organ, and
hn(t) is the noncapillary (arteries, veins,
connecting tubing and the injection system) transit time
distribution] was obtained. The hn(t) was
also represented by a shifted random walk function whose parameters
were specified by iteratively convolving a trial
hn(t) with hc(t)
until the optimal least-squares fit to CR(t)
was obtained (2).
To estimate model parameters from the data from each injection,
Eqs. 9 and 10 were solved numerically for the
appropriate boundary conditions (given in Estimation of Model
Parameters for Specific Experiments) using the finite-difference
method at each iteration of a Levenberg-Marquardt optimization routine
(4, 31). The solution is for a single capillary element with
Cin(t) as the capillary input concentration curve.
The model solution for a single capillary having the maximum capillary
transit time also provides the output for all capillary transit times
between the minimum and maximum capillary transit times (4). To provide the whole organ output for vascular reference indicator
[CR(t)], and test indicator
[C(t)], the outputs for all transit times are summed, each weighted according to hc(t) (4).
Autoxidation of BH in arteries, veins, and connecting tubing.
Because BH autoxidation can occur outside the capillary region within
the conducting arteries and veins and the tubing connecting the lungs
to the injection and sampling sites, this autoxidation was also
addressed in the model. In this part of the system, Eqs. 9 and 10 reduce to
![<FR><NU>∂[<A><AC>BH</AC><AC>∼</AC></A>]</NU><DE>∂<IT>t</IT></DE></FR> + <IT>W</IT> <FR><NU>∂[<A><AC>BH</AC><AC>∼</AC></A>]</NU><DE>∂<IT>x</IT></DE></FR> = − <IT>k</IT><SUB>o</SUB> [<A><AC>BH</AC><AC>∼</AC></A>]](/content/vol278/issue1/fulltext/H137/img023.gif)
|
(11)
|
![<FR><NU>∂[<A><AC>B</AC><AC>˜</AC></A><SUP>+</SUP>]</NU><DE>∂<IT>t</IT></DE></FR> + <IT>W</IT> <FR><NU>∂[<A><AC>B</AC><AC>˜</AC></A><SUP>+</SUP>]</NU><DE>∂<IT>x</IT></DE></FR> = <IT>k</IT><SUB>o</SUB> [<A><AC>BH</AC><AC>∼</AC></A>]](/content/vol278/issue1/fulltext/H137/img024.gif)
|
(12)
|
which
can be analytically solved for
](/content/vol278/issue1/fulltext/H137/img025.gif)
and
[+](
,t), where x = is the inlet to either the capillaries or to the photodetector
![[<A><AC>BH</AC><AC>∼</AC></A>] (&xgr;,<IT>t</IT>) = [<A><AC>BH</AC><AC>∼</AC></A>]<SUB>i</SUB>(0,<IT>t</IT> − <OVL><IT>t</IT></OVL><SUB>o</SUB>)<IT>e</IT><SUP>−<OVL><IT>t</IT></OVL><SUB>o</SUB><IT>k</IT><SUB>o</SUB></SUP> for <IT>t</IT> > <OVL><IT>t</IT></OVL><SUB>o</SUB>](/content/vol278/issue1/fulltext/H137/img026.gif)
|
(13a)
|
![+ [<A><AC>BH</AC><AC>∼</AC></A>]<SUB>i</SUB>(0,<IT>t</IT> − <OVL><IT>t</IT></OVL><SUB>o</SUB>) (1 − <IT>e</IT><SUP>−<OVL><IT>t</IT></OVL><SUB>o</SUB><IT>k</IT><SUB>o</SUB></SUP>) for <IT>t</IT> > <OVL><IT>t</IT></OVL><SUB>o</SUB>](/content/vol278/issue1/fulltext/H137/img028.gif)
|
(13b)
|
where
[+]i(0,t) and
![[<A><AC>BH</AC><AC>∼</AC></A>]<SUB>i</SUB>(0,<IT>t</IT>)](/content/vol278/issue1/fulltext/H137/img029.gif)
are
[](x,t) and
](x,t), respectively, at either the injection site or the capillary outlet, and
o is the mean transit
time either between the injection site and the capillary inlet or
between the capillary outlet and the sampling site. The values of
ko for TBOH were 2.73 × 102 and 2.45 × 102
s1 in PSS-albumin and PSS-dextran, respectively,
estimated from the data in Fig. 7 as
indicated in the APPENDIX.
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Fig. 7.
TBO+ vs. time in 5% dextran and 5% albumin solutions when
respective deoxygenated TBOH solutions were rapidly equilibrated with
atmospheric oxygen.
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|
Estimation of Model Parameters for Specific Experiments
TBO+ injections in lungs
perfused with PSS-albumin.
In the lungs perfused with PSS-albumin, the outflow concentrations of
TBO+ and total TBO (TBOH + TBO+) were measured at different sampling sites as
described in METHODS. The first step in the model
interpretation of these data was to reconstruct the TBO+
curve measured by the photodetector as it would have appeared had it
been measured at the fraction collector sampling site where the total
TBO was measured. This was carried out as follows. The photodetector
concentration curves acquired at 25 Hz for TBO+ and FITC
were converted to discretely sampled curves with the same
sampling time interval as the sample collector time interval using a
infinite impulse response filter and decimator. The transfer function
from the photodetector sampling site to the fraction collector was
obtained by numerically deconvolving (13) the photodetector FITC tubing
curve and the 125I fraction collector tubing curve. The
resulting transfer function was then convolved with the discretized
photodetector TBO+ curve to estimate the TBO+
curve at the sample collector site.
For a given bolus injection, the model was fit to the measured total
TBO and the reconstructed TBO+ data as follows.
Equations 9 and 10 were first solved with the initial (t = 0) conditions
[+](x,0) = [
(x,0) = 0 and boundary conditions ](0,t) = 0 and [+](0,t) = Cin(t)q/F. The solution of Eqs. 9 and 10 under these conditions provides the concentrations of
TBO+ and total TBO at the capillary outlet. To account for
any autoxidation of TBOH that might occur between capillary outlet and
photodetector sampling site, the capillary outlet was
subjected to Eq. 13, a and b, for
o, where in
this case,
[+]i(0,t) and
are
the concentration versus time curves for
[+] and
[![<A><AC>BH</AC><AC>∼</AC></A>],](/content/vol278/issue1/fulltext/H137/img032.gif)
respectively, at the
capillary outlet, and
o is the mean transit
time between the capillary outlet and the photodetector. For these data, the identifiable model parameters are QF,
QT, Kred, and Kseq,
with ko fixed at the value estimated from the data
in Fig. 7.
TBO+ and
MB+ injections in lungs
perfused with PSS-dextran.
For TBO+ and MB+ injections in lungs perfused
with PSS-dextran, because [P] = 0, 1 = 1, QF = Qf, and Kred = Ekr1 and Eqs. 9 and 10 simplify
to
![<FR><NU>∂[B<SUP>+</SUP>]</NU><DE>∂<IT>t</IT></DE></FR> + <IT>W</IT> <FENCE><FR><NU>Q<SUB>c</SUB></NU><DE>Q<SUB>c</SUB> + Q<SUB>F</SUB></DE></FR></FENCE> <FR><NU>∂[B<SUP>+</SUP>]</NU><DE>∂<IT>x</IT></DE></FR> = − <FR><NU>[B<SUP>+</SUP>] <IT>K</IT><SUB>red</SUB></NU><DE>Q<SUB>c</SUB> + Q<SUB>F</SUB></DE></FR>](/content/vol278/issue1/fulltext/H137/img033.gif)
|
(14)
|
The model fit to the TBO+ or MB+ data from each
injection was obtained by solving Eq. 14 with the initial
condition [B+](x,0) = 0 and boundary
condition [B+](0,t) = Cin(t)q/F. For these data, the
identifiable model parameters are QF and
Kred.
TBOH injections in lungs perfused with PSS-albumin or PSS-dextran.
For the TBOH injection data, the model was fit to the total TBO
data from each injection by solving Eqs. 9 and 10 with the initial conditions
[+](x,0) = (x,0) = 0 and boundary
conditions
and
The above boundary conditions account for the autoxidation of
the TBOH during transit time
o upstream from the capillary inlet. For the PSS-albumin data, the identifiable model parameters are QT and Kseq, with
QF and Kred fixed to the mean values estimated from the TBO+ injections
given in Table 3. For the PSS-dextran data,
the identifiable model parameter is QT, with QF
and Kred fixed to the mean values estimated from
the TBO+ injections given in Table
4 and Kseq fixed to the
value given in Table 5.
Model Results
Examples of the model fits to the data are included in Figs. 1-5,
and Tables 3-6 summarize the model
parameter values. Examples of the sensitivity functions
iS(t) (6) obtained for the optimized parameters
are given in Figs. 8 and
9 for TBO+ and total TBO
after TBO+ injections into the PSS-albumin perfusate and
for TBOH after TBOH injections into the PSS-albumin perfusate,
respectively. For the ith model parameter,
i, Si(t) = 
C(t)/i, where C(t) is the calculated
test indicator effluent concentration. Si(t) was
approximated by the change in C(t) resulting from a 1% change in
i divided by the change in
i (6). When Si(t) is
multiplied by the value of the parameter estimate,
i, the relative amplitude of this function for
each respective parameter provides an indication of the relative
contribution of the parameter to the model fit to the data at a given
time. Comparison of the respective shapes of their respective
iSi(t) reveals the degree to
which any pair of parameters is correlated. Interpretation with respect
to the individual parameters is discussed below.
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Fig. 8.
Sensitivity functions [S(t)] for 4 parameters,
Kred, QF, QT, and
Kseq, from model fit to TBO+ and total
TBO (TBOH + TBO+) concentration data obtained after
injection of TBO+ into a lung perfused with PSS-albumin.
Reference indicator concentration curves
[CR(t)] are also provided for timing
perspective. See text for definition of model parameters.
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Fig. 9.
Sensitivity functions [S(t)] for the 2 parameters
QT and Kseq from model fit to TBOH
concentration data obtained after injection of TBOH into a lung
perfused with PSS-albumin.
|
|
| |
DISCUSSION |
Both TBO+ and MB+ were extracted from the
PSS-dextran perfusate on passage through the lungs. However, the
TBO+ extractions were considerably greater than those of
MB+. The TBO+ extractions were >70% even at
flow rates above those reported for the normal resting pulmonary flow
rate for rabbits in this size range (276-540 ml/min; Ref. 38).
This is in contrast to MB+, for which the extraction was
only ~15% at only 300 ml/min. The role of reduction in the
extraction of MB+ during its passage through the lungs was
demonstrated previously (10). The fact that TBO+ was also
reduced during passage through the lungs was revealed only when albumin
was present in the perfusate. This is because the highly lipophilic
TBOH has such a high solubility in the lung tissue that, with no
protein in the perfusate, the effluent contained little trace of any
TBOH that might have been formed. The presence of TBOH in the effluent
when the lungs were perfused with the albumin-containing perfusate
resulted from its affinity for the albumin, which offset its affinity
for the tissue. The present study does not identify the location of the
TBO+ reduction. However, a previous study, with a
TBO-containing polymer that could not enter the cells, established the
ability of endothelial cells to reduce TBO+ on the cell
surface (12). Therefore, it appears likely that this surface reduction
accounts for at least part of the disappearance of the relatively
hydrophilic TBO+ within the lungs.
Another key observation was that the extractions of both
MB+ and TBO+ were inversely proportional to
flow rate to the extent that variations in the reduction rate
parameter, Kred, with flow rate were small over the
fairly wide range of flow rates studied. The implication of this
observation is that the reduction rate, rather than the rate of
convective supply of the indicators, dominates the extraction. One
might visualize the reduction reaction as a barrier that must be
traversed for TBO or MB to enter the tissue. In the terminology commonly used in the indicator dilution field, their extractions tend
toward "barrier-limited" rather than "flow-limited" (23) behavior. The isopleths in Fig. 6 are for the most parsimonious nested
version of the model developed herein, commonly referred to as the
Crone-Renkin model (7), for which the solution for Kred is Kred = F × ln(1 extraction). For this model,
barrier-limited extraction as a function of flow rate produces curves
parallel to these isopleths. Thus the extent to which the
TBO+ and MB+ extraction data parallel these
isopleths may be thought of as a preliminary indication of the extent
to which the extractions correspond to barrier- or reaction-limited
behavior. The alternative of flow-limited behavior would produce
horizontal lines in Fig. 6. As discussed below, the inclusion of
additional detail in the model can explain most of the deviation from
the Crone-Renkin model prediction observable in Fig. 6.
The model developed herein to interpret the test indicator probe
disposition represents a simplistic view of the overall processing of
the indicators by the lung. Steps have been left out of the stoichiometric equations that could be added if warranted by
experimental manipulations of the relevant variables in future studies.
The attempt was to accommodate aspects of the tissue disposition of TBO
and MB predicted by previous studies under the present range of
experimental conditions. Even so, the model is fairly complex, having
several parameters that were either input, i.e., obtained from sources
separate from the data from an individual bolus, or estimated by
fitting the model to the bolus data. The fitted parameters include
terms that are not separately identifiable without a more complex set
of experimental conditions. Furthermore, all of the model parameters do
not contribute equally to the fits to the data from each type of
experiment performed or from the same type of experiment but at
different flow rates. In fact, the effects of some phenomena
represented in the model are not detectable in all experimental
conditions. To help put this in perspective, the sensitivity functions
for the model fits to the TBO+ and total TBO data from the
PSS-albumin experiments are shown in Fig. 8. The sensitivity functions
reveal the extent, and the time epoch, to which the optimized model
parameters make their contributions to the fit of the model to the data
(2, 6). Thus the dominant role of Kred in the fits
to the TBO+ data, especially near the peak of the reference
indicator curve can be seen in Fig. 8. QF has most of its
influence at early and late times with respect to the reference
indicator passage and little influence near the peak of the reference
indicator. The very different shapes of the sensitivity functions for
these two parameters also imply their relatively independent
contributions to the model fit. This is expressed quantitatively for
the examples in Fig. 8 by the fact that the correlations (3, 26)
between QF and Kred were <0.34 at all
flow rates studied. The physical counterpart of QF is not
certain. It may include a volume into which at least some
TBO+ diffuses before its reduction, possibly inside the
cell. However, a compound that binds to plasma protein may likewise
have an affinity for molecules on the cell surface, presumably
including plasma albumin itself associated with the endothelial surface
or glycocalyx (2, 43, 44).
The contribution of QT to the fit to the TBO+
data is small and barely detectable on the same scale as S(t) for
Kred and QF at the high end of the
range of flow rates studied. On the other hand, when the model is fit
to the total TBO data, the contribution of QT is
substantial and the impact of Kseq, which does not
contribute to the TBO+ fit, is evident.
Kred, QF, and QT are the
dominant parameters in the PSS-albumin experiment. The sensitivity
functions for the MB+ and TBO+ experiments in
the PSS-dextran-perfused lungs are not shown because they are
qualitatively similar to those for TBO+ in PSS-albumin
sensitivity functions, but without QT. Thus, for the
PSS-dextran experiments, wherein the returning flux of TBOH is
insignificant, Kred and QF are the
controlling parameters.
The sensitivity functions for the TBOH injected into PSS-albumin reveal
the importance of QT and Kseq (Fig. 9).
TBOH is a lipophilic amine compound, and except for the small effects
due to autoxidation, the model for its tissue disposition is the same as the general model developed for lipophilic amines in a previous study (3). The reasons for variations in the model parameters QF, QT, and Kseq for the
MB+, TBO+, and TBOH injections with flow rate
have been discussed previously (2, 3). In essence, the phenomenon
occurs because two or more reversible processes having different
dissociation rate constants, which are not sufficiently different for
the processes to be distinguishable in the data obtained at a given
flow rate, become lumped into one process in an MID model. When the
flow rate is changed the relative contribution of each process to the
data also changes, and the lumped parameter(s) representing these
processes will be flow rate dependent. One conclusion with regard to
the present study is that the reversible processes represented by
QF and QT include distributed dissociation rate
constants not explicitly represented in the model or evident in the
data from a single flow rate (3). Likewise, the term sequestration
applied to Kseq means that the dissociation rates are long
relative to the capillary transit time, not that the processes are
necessarily irreversible.
The overall tissue disposition of TBO and MB apparently involves the
reduction, and nonspecific binding of the oxidized forms, and the
partitioning of the reduced forms between tissue and perfusate volumes
as represented in the model. However, it has also been demonstrated in
endothelial cells in culture that TBOH can be reoxidized and
sequestered within the cells (33). The sequestration apparently occurs
because the oxidized forms of the thiazines are strongly polar,
cationic (14), relatively hydrophilic compounds and thus relatively
membrane impermeant. Thus the oxidized forms cannot so readily escape
their intracellular site(s) of oxidation, and partitioning in
accordance with membrane potentials of the sequestering intracellular
organelle(s) may play a role as well (27). This sequestration
contributes relatively little to the disposition of the TBO within the
time frame of the bolus transient in normal lungs, as evidenced by the
small value of Kseq (<3 ml/s) in comparison to
Kred (>17 ml/s). However, preliminary results suggest that the sequestration rate may be increased in the lungs of
rats adapted to hyperoxia, to the extent that it can have a substantial
influence even during the bolus transient (39). Thus
Kseq may take on greater significance in conditions
in which intracellular reactions that reoxidize the reduced thiazine
compounds may be affected.
General aspects of the sensitivity to the input parameters controlling
bolus dispersion and capillary transit times have been discussed at
length previously (4, 29). The main reason for the larger values of
Kred obtained from the present model, reported in
Tables 3, 4, and 6, in comparison to the Crone-Renkin model predictions, which can be read in Fig. 6, is the effect of capillary perfusion heterogeneity not included in the Crone-Renkin model. One of
the important reasons for parameterizing the data using the particular
modeling approach described herein is the potential for preventing a
change in perfusion heterogeneity from being aliased by a change in
tissue parameters (4). In the present study, the capillary transport
function was assumed to be typical of the normal rabbit lung (5).
However, in future studies of abnormal conditions, in which that
assumption would not necessarily hold, inclusion of a flow-limited
indicator such as labeled water in the bolus would provide the
necessary information to account for a change in perfusion
heterogeneity as discussed previously (4, 42).
Another input parameter was the TBOH autoxidation rate
(ko), which was included to evaluate the assumption
that the TBO+ data measured on-line can represent the
TBO+ exiting the lung capillaries without contamination by
autoxidation of effluent TBOH. The autoxidation turned out to be a
minimal contributor to the on-line signal as can been seen in Fig.
10, in which a model simulation of the
effluent TBO+, the effluent TBOH, and the TBO+
resulting from autoxidation of effluent TBOH is shown for the lowest
flow rate in the range studied (i.e., the flow rate providing the
longest time for autoxidation to occur).
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Fig. 10.
Simulated effluent concentration vs. time curves after injection of
TBO+ in a lung perfused with PSS-albumin. Curves are for
TBO+ that passed through lungs without being reduced, TBOH
generated by reduction of TBO+, and TBO+
resulting from autoxidation within perfusate of TBOH formed in lungs.
|
|
As indicated above, it was the presence of the albumin in the perfusate
that revealed the reduction of TBO+. Because even without
albumin binding the MB+ extraction was low, we did not
pursue the consequences of including albumin in the perfusate for MB
uptake. On the other hand, TBO uptake was high enough to provide an
adequate window for examining the influence of albumin binding. As
expected from the fact that TBO+ associates with plasma
albumin, the presence of albumin decreased the rate of TBO+
disappearance from the perfusate. However, the decrease was not as
great as predicted from the TBO+-BSA binding measured by
ultrafiltration, under the assumption that only the free TBO
participates in the uptake process. Under the assumption that the
BSA-bound TBO+ is not reducible and using the average
values of Kred from the PSS-albumin and PSS-dextran
experiments, the predicted albumin binding would be only 39%, instead
of the 59% obtained by ultrafiltration. This difference between the
two is a common observation for the extraction of protein-bound
substrates in the liver (45, 48) and other organs (25, 41). Several
explanations have been proposed, including the possibility that
albumin-bound ligand or substrate can interact directly with the cell
surface process. Thus, for the TBO interaction with the pulmonary
endothelium, it is conceivable that binding to BSA slows but does not
prevent TBO reduction. This would be consistent with the observation
that TBO covalently bound to an acrylamide polymer is reduced on the surface of pulmonary arterial endothelial cells in culture (12). It
would also be consistent with the notion that endogenous electron acceptors such as the quinonoid forms of antioxidants such as tocopherylquinone and ubiquinone associated with plasma proteins such
as low-density lipoproteins might be reducible without dissociating (11).
A similar analysis can be carried out on the data from the TBOH
injections, from which albumin binding can be predicted by comparing
the QT obtained in the PSS-dextran (average value 483 ml)
and PSS-albumin experiments (Table 5; Ref. 3). The TBOH-BSA binding
predicted on this basis is ~91%, which is higher than the 79%
obtained by ultrafiltration, but the prediction is fairly sensitive to
accuracy in the TBOH concentration data from the PSS-dextran
experiment, in which the signal is quite small (Fig. 5).
This study was carried out in anticipation of the use of these thiazine
compounds to determine the effects of various interventions directed at
determining the influence of physiological and/or pathophysiological
stresses on these redox functions of the pulmonary endothelium within
intact lungs. The results suggest that both MB and TBO have potential
utility in this regard. However, the low Kred for
MB suggests that MB would be useful mainly for detecting substantial
increases in Kred, because any decrease would be
barely detectable at normal flow rates. TBO may be more versatile
because of the higher extraction. For studies in isolated lungs, the
presence of albumin in the perfusate would be required to evaluate the role of the sequestration process in the overall disposition of TBO+. The use of TBOH itself as test indicator might also
be useful in this regard. The model should provide a tool for
quantitative comparisons in such experiments, and it can also be used
to provide a sense of the robustness of the quantification under a
given set of experimental conditions.
| |
APPENDIX |
Estimation of TBOH Autoxidation Rate From Test Tube Experiments
For autoxidation of BH (and for BHP in PSS-albumin) within the
perfusate solutions in the test tube, the temporal variation in the
concentrations of the oxidized (B+) and reduced (BH) forms
is described by the following
![<FR><NU>d[BH]</NU><DE>d<IT>t</IT></DE></FR> = [BHP]<IT>k</IT><SUB>−2</SUB> − <IT>k</IT><SUB>2</SUB>[BH][P] − <IT>k</IT><SUB>o</SUB>[BH]](/content/vol278/issue1/fulltext/H137/img036.gif)
|
(A1)
|
![<FR><NU>d[BHP]</NU><DE>d<IT>t</IT></DE></FR> = − [BHP]<IT>k</IT><SUB>−2</SUB> + <IT>k</IT><SUB>2</SUB>[BH][P] − <IT>k</IT><SUB>o</SUB>[BHP]](/content/vol278/issue1/fulltext/H137/img037.gif)
|
(A2)
|
![<FR><NU>d[B<SUP>+</SUP>]</NU><DE>d<IT>t</IT></DE></FR> = [B<SUP>+</SUP>P]<IT>k</IT><SUB>−1</SUB> − <IT>k</IT><SUB>1</SUB>[B<SUP>+</SUP>][P] + <IT>k</IT><SUB>o</SUB>[BH]](/content/vol278/issue1/fulltext/H137/img038.gif)
|
(A3)
|
![<FR><NU>d[B<SUP>+</SUP>P]</NU><DE>d<IT>t</IT></DE></FR> = − [B<SUP>+</SUP>P]<IT>k</IT><SUB>−1</SUB> + <IT>k</IT><SUB>1</SUB>[B<SUP>+</SUP>][P] + <IT>k</IT><SUB>o</SUB>[BHP]](/content/vol278/issue1/fulltext/H137/img039.gif)
|
(A4)
|
Under
the assumption that when albumin is present the equilibration is rapid
between the free and albumin-bound species, Eqs. A1-A4
reduce to
![<FR><NU>d[<A><AC>BH</AC><AC>∼</AC></A>]</NU><DE>d<IT>t</IT></DE></FR> = −<IT>k</IT><SUB>o</SUB>[<A><AC>BH</AC><AC>∼</AC></A>]](/content/vol278/issue1/fulltext/H137/img040.gif)
|
(A5)
|
![<FR><NU>d[<A><AC>B</AC><AC>˜</AC></A><SUP>+</SUP>]</NU><DE>d<IT>t</IT></DE></FR> = <IT>k</IT><SUB>o</SUB>[<A><AC>BH</AC><AC>∼</AC></A>]](/content/vol278/issue1/fulltext/H137/img041.gif)
|
(A6)
|
For
the initial conditions (t = 0) in the test tube experiments
](/content/vol278/issue1/fulltext/H137/img042.gif)
= ![[<A><AC>BH</AC><AC>∼</AC></A><SUB>0</SUB>]](/content/vol278/issue1/fulltext/H137/img043.gif)
and
[](0) = ![[<A><AC>B</AC><AC>˜</AC></A><SUP>+</SUP><SUB>0</SUB>],](/content/vol278/issue1/fulltext/H137/img044.gif)
the solution for
[+](t) is
 = [<A><AC>B</AC><AC>˜</AC></A><SUP>+</SUP><SUB>0</SUB>] + [<A><AC>BH</AC><AC>∼</AC></A><SUB>0</SUB>] (1 − <IT>e</IT><SUP>−<IT>k</IT><SUB>o</SUB><IT>t</IT></SUP>)](/content/vol278/issue1/fulltext/H137/img045.gif)
|
(A7)
|
To
estimate a value for ko, Eq. A7 was fit to
the test tube [+](t)
autoxidation data shown in Fig. 7.
| |
ACKNOWLEDGEMENTS |
This study was supported by National Heart, Lung, and Blood
Institute Grant NH-24349, the Falk Trust, the Whitaker Foundation, and
the Department of Veterans Affairs.
| |
FOOTNOTES |
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Address for reprint requests and other correspondence: C. A. Dawson,
Research Service 151, Zablocki VA Med. Ctr., 5000 W. National Ave.,
Milwaukee, WI 53295-1000 (E-mail:
dawsonc{at}vms.csd.mu.edu).
Received 24 May 1999; accepted in final form 20 July 1999.
| |
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and
A. B. Fisher.
Endothelial NADPH oxidase as the source of oxidants in lungs exposed to ischemia or high K+.
Circ. Res.
83:
730-737,
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2.
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Am J Physiol Heart Circ Physiol 278(1):H137-H150
TOP
ABSTRACT
INTRODUCTION
![<FR><NU>∂[B<SUP>+</SUP>]</NU><DE>∂<IT>t</IT></DE></FR> + <IT>W</IT> <FR><NU>∂[B<SUP>+</SUP>]</NU><DE>∂<IT>x</IT></DE></FR> = [B<SUP>+</SUP>P]<IT>k</IT><SUB>−1</SUB> − <IT>k</IT><SUB>1</SUB>[B<SUP>+</SUP>][P]](/content/vol278/issue1/fulltext/H137/img003.gif)
![<FR><NU>∂[B<SUP>+</SUP>P]</NU><DE>∂<IT>t</IT></DE></FR> + <IT>W</IT> <FR><NU>∂[B<SUP>+</SUP>P]</NU><DE>∂<IT>x</IT></DE></FR> = −[B<SUP>+</SUP>P]<IT>k</IT><SUB>−1</SUB>](/content/vol278/issue1/fulltext/H137/img005.gif)
![<FR><NU>∂[BH]</NU><DE>∂<IT>t</IT></DE></FR> + <IT>W</IT> <FENCE><FR><NU>Q<SUB>c</SUB></NU><DE>Q<SUB>c</SUB> + &lgr;Q<SUB>t</SUB></DE></FR></FENCE> <FR><NU>∂[BH]</NU><DE>∂<IT>x</IT></DE></FR> = <FENCE><FR><NU>Q<SUB>c</SUB></NU><DE>Q<SUB>c</SUB> + &lgr;Q<SUB>t</SUB></DE></FR></FENCE>](/content/vol278/issue1/fulltext/H137/img008.gif)
![⋅ ([BHP]<IT>k</IT><SUB>−2</SUB> − <IT>k</IT><SUB>2</SUB>[BH][P]) − <FENCE><FR><NU>Q<SUB>c</SUB></NU><DE>Q<SUB>c</SUB> + &lgr;Q<SUB>t</SUB></DE></FR></FENCE> <IT>k</IT><SUB>o</SUB>[BH]](/content/vol278/issue1/fulltext/H137/img009.gif)
![<FR><NU>∂[BHP]</NU><DE>∂<IT>t</IT></DE></FR> + <IT>W</IT> <FR><NU>∂[BHP]</NU><DE>∂<IT>x</IT></DE></FR> = − [BHP]<IT>k</IT><SUB>−2</SUB>](/content/vol278/issue1/fulltext/H137/img011.gif)
![[BHP] = <FR><NU>[BH][P]</NU><DE><IT>K</IT><SUB>2</SUB></DE></FR>](/content/vol278/issue1/fulltext/H137/img013.gif)
![<IT>k</IT><SUB>−3</SUB> B<SUP>+</SUP>Z = <IT>k</IT><SUB>3</SUB> [B<SUP>+</SUP>]Z](/content/vol278/issue1/fulltext/H137/img015.gif)
![<FR><NU>∂[<A><AC>B</AC><AC>˜</AC></A><SUP>+</SUP>]</NU><DE>∂<IT>t</IT></DE></FR> + <IT>W</IT> <FENCE><FR><NU>Q<SUB>c</SUB></NU><DE>Q<SUB>c</SUB> + Q<SUB>F</SUB></DE></FR></FENCE> <FR><NU>∂[<A><AC>B</AC><AC>˜</AC></A><SUP>+</SUP>]</NU><DE>∂<IT>x</IT></DE></FR>](/content/vol278/issue1/fulltext/H137/img017.gif)
![<FR><NU>∂[<A><AC>BH</AC><AC>∼</AC></A>]</NU><DE>∂<IT>t</IT></DE></FR> + <IT>W</IT> <FENCE><FR><NU>Q<SUB>c</SUB></NU><DE>Q<SUB>c</SUB> + Q<SUB>T</SUB></DE></FR></FENCE> <FR><NU>∂[<A><AC>BH</AC><AC>∼</AC></A>]</NU><DE>∂<IT>x</IT></DE></FR>](/content/vol278/issue1/fulltext/H137/img019.gif)
 = [<A><AC>B</AC><AC>˜</AC></A><SUP>+</SUP>]<SUB>i</SUB>(0,<IT>t</IT> − <OVL><IT>t</IT></OVL><SUB>o</SUB>)](/content/vol278/issue1/fulltext/H137/img027.gif)
 = <FR><NU>C<SUB>in</SUB>(<IT>t</IT>) <IT>q</IT></NU><DE>F</DE></FR> <IT>e</IT><SUP>−<IT>k</IT><SUB>o</SUB><OVL><IT>t</IT></OVL><SUB>o</SUB></SUP>](/content/vol278/issue1/fulltext/H137/img034.gif)
 = <FR><NU>C<SUB>in</SUB>(<IT>t</IT>) <IT>q</IT></NU><DE>F</DE></FR> (1 − <IT>e</IT><SUP>−<IT>k</IT><SUB>o</SUB><OVL><IT>t</IT></OVL><SUB>o</SUB></SUP>)](/content/vol278/issue1/fulltext/H137/img035.gif)
