© 1995 American Heart Association, Inc.
Articles |
Tracer Oxygen Distribution Is Barrier-Limited in the Cerebral Microcirculation
From the McGill University Medical Clinic in the Montreal General Hospital and the Departments of Medicine, Physiology, and Mechanical Engineering, McGill University, and the André Viallet Research Center of the Hôpital St-Luc, Montreal, Quebec, Canada.
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Abstract The kinetics of tracer oxygen distribution in the brain microcirculation of the awake dog were investigated with the multiple indicator dilution technique. A bolus containing 51Cr-labeled red blood cells, previously totally desaturated and then resaturated with [18O]2 (oxygen), 125I-albumin, 22Na, and [3H]water, was injected into the carotid artery, and serial anaerobic blood samples were collected from the sagittal sinus over the next 30 seconds. The outflow recovery curves were analyzed with a distributed-in-space two-barrier model for water and a one-barrier model for oxygen. The analysis provided an estimate of flow per gram brain weight as well as estimates for the tracer water and oxygen rate constants for blood-to-brain exchange and tracer oxygen parenchymal sequestration. Flow to tissue was found to vary between different animals, in concert with parallel changes in oxygen consumption. The 18O2 outflow curves showed an early peak, coincident with and more than half the magnitude of its vascular reference curve (labeled red blood cells), whereas the [3H]water curve increased abruptly to a low-in-magnitude curve at low flow values and to a small early peak at high flow values. Analysis indicates that the transfers of both 18O2 and [3H]water indicators from blood to brain are barrier-limited, with the former highly so because of the large red blood cell capacity for oxygen, and that the proportion of the tracer oxygen returning to the circulation from tissue is a small fraction of the total tracer emerging at the outflow.
Key Words: cerebral blood flow • blood-brain barrier • tracer oxygen • labeled water
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Introduction |
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Brain capillaries are much less permeable than those of any other organ to passively permeating materials, and there is considerable evidence that the endothelial lining of brain capillaries acts as a tight barrier for many substrates as well.1 2 A growing number of studies have addressed the blood-brain barrier characteristics,3 and it is now well documented that most hydrophilic molecules and ions pass through this particular membrane extremely slowly. The permeabilities to small solutes have been found to be
1/100 those found for the capillary
membrane in muscle tissue,4 and the general viewpoint that
has evolved is that the blood-brain barrier resides at the level of
the capillary endothelium. The brain capillary
interendothelial cell functions are sealed tightly
by an almost impermeable circumferential tight junctions, which
massively diminish the transendothelial
intercellular passage of plasma constituents,5 and the
brain capillary endothelial cells exhibit a much
reduced density of intracellular vesicles compared with heart and
muscle.6 The structure contrasts starkly with the liver,
where sieve plates provide for free tracer movement between
microvascular lumen and interstitial space.7
Physiologically, the capillary bed of the brain
might be considered, in some senses, equivalent to a continuous lipid
membrane, more permeable to lipophilic than hydrophilic substances.
Thus, on simultaneous injection of a hydrophilic (glycerol)
and a lipophilic (propanol) substance of similar size, the permeability
of brain capillaries to the more lipophilic substance is found to be
much larger than that for the hydrophilic substance.8
Hydrophilic substrates that gain access to the brain at high rates
ordinarily pass through the endothelial cells by
means of special transport systems (which are usually of a facilitated
nature).9 10 On the other hand, hydrophilic substances for
which there is no facilitated transport behave passively, with smaller
molecular weight materials tending to behave like tracer water
molecules.11 12
The question that arises is whether there is a similar resistance to
the passage of tracer oxygen. If there is, one would expect, at the
tissue level, that consumption of oxygen beyond the barrier would
result in tissue oxygen tensions substantially lower than in the
adjacent microvasculature.13 Observed tissue values are
substantially below venous PO2 values, but it
is not clear how low they are. Average brain tissue
PO2 values, directly measured with
polarographic PO2 electrodes, which are large,
and average cell, venous, and arteriolar tensions are 20
mm Hg.14 Values derived from tissue spectrophotometry, on
the other hand, indicate that brain tissue PO2
values may be considerably lower than this. In isolated mitochondria,
cytochrome aa3 is completely oxidized above
PO2 values of 1.0 mm Hg.15
Reflectance spectrophotometry reveals a significant amount of reduced
cytochrome aa3 in the brain of the anesthetized
animal,16 suggesting that very low
PO2 values may be present in tissue.
Neither value is explainable with the classical Krogh17
model, which envisages no resistance to the passage of oxygen from
blood capillary to tissue; tissue values substantially lower than
venous would be explained if there were a microvascular resistance to
the transfer of oxygen.
We would expect studies with tracer oxygen in the cerebral circulation to provide the needed information concerning the nature of the process underlying the transfer of oxygen from blood to tissue in the brain. Therefore, we have carried out a set of tracer oxygen indicator dilution studies to characterize the behavior of oxygen in the cerebral circulation. From the preceding description of capillary exchange in the brain, we would expect multiple indicator dilution data from the brain to more or less resemble that from the heart13 ; there should be evidence of a permeability limitation to tracer oxygen movement from blood to the tissue, and relatively little of the unmetabolized tracer oxygen would be expected to return to the blood from the extravascular space, in view of the low tissue PO2 levels. Therefore, it is curious that Grieb et al18 have recently suggested that tracer oxygen is distributed into the brain in a flow-limited fashion. In the present study, we examine tracer oxygen transport kinetics in the brain in detail by using a model analysis to derive parameters for the kinetics for tracer oxygen distribution and sequestration from the multiple indicator dilution data. As part of the reference set, we have included tracer water in our study; analysis of its outflow pattern provides an estimate of flow per unit tissue water space.19
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Surgical Procedure and Animal Preparation
Five mongrel dogs weighing between 21 and 33 kg underwent the experimental protocol. All dogs were fed a Purina dog chow diet ad libitum. The operative procedure was similar to that described by Crone,20 with the modifications described by Huet et al.21 The dogs were anesthetized with intravenous
-chloralose (80 mg/kg) in a 40%
polyethylene glycol 400 solution. One carotid artery was dissected
free, and a No. 16G polytetrafluoroethylene
(Teflon) catheter (Cathlon IV, Jelco) with a Luer-Lok obturator (No.
16G, Longdwel, Becton-Dickinson) was introduced into the carotid lumen
through a thyroid artery. The catheter was fixed to the skin before
suturing the wound. After abrasion of the external sagittal crest near
the interparietal process of the occipital bone, a 2-cm trepan hole was
drilled in the skull down to the cranial dura above the dorsal sagittal
sinus. A No. 16G Teflon catheter with a Luer-Lok obturator was then
introduced into the sinus by direct puncture in a posterior
inferior oblique direction toward the confluens sinuum. The
catheter was fixed in place with dental acrylic cement (Yates and
Bird), and the trepan hole was closed with this. The skin was then
sutured over the cement. The dogs were fully alert and in normal
condition the day after the surgery. However, no experiments were
carried out before a minimum of 3 days after surgery. Both catheters
were flushed daily with 3 mL of normal saline containing 0.3 mL of 1000
U/mL heparin to ensure patency of the catheters.
Animals were fasted for 6 hours before the experiment. As well, each
animal was brought to the laboratory for at least 1 hour before the
experiment in order to minimize the effects of anxiety. The animal was
clothed with a four-point restraining leather-tailored jacket
for the short duration of the experiment. An indicator dilution
experiment was then carried out in this nonsedated conscious animal,
with injection into the carotid and collection of outflow samples from
the sagittal sinus.21 The data necessarily come from the
cerebrum. Thirty timed anaerobic samples were collected
from the sagittal sinus over 30 seconds by use of the
multiple-syringe mercury-trough fraction collector devised by
Enns et al22 ; the apparatus allowed the
collection of 30 samples. An outflow pump was used to overcome the
pressure head of the mercury in the anaerobic collection
bath. An overflow tube was attached to the outflow tube in order to
keep the outflow pressure atmospheric, thereby avoiding retrograde flow
of blood from muscle tissue to the sagittal sinus.23
Before connecting the sagittal sinus catheter to the outflow pump and
anaerobic fraction collector, we checked that a minimum of
30 mL of sagittal sinus blood could be withdrawn per minute to conduct
our sample analysis. There was a limitation on the frequency of
the sampling; in view of the fact that a minimum of 0.3 mL of blood was
needed from each sample for mass spectrometry, it was not feasible to
obtain more than one sample per second.
Choosing the Appropriate Reference for the Oxygen
The labeled red blood cell curve was chosen as the ideal
vascular reference for the oxygen, given the fact that almost all of
the oxygen in the vascular space is bound to the hemoglobin (>98% of
the tracer oxygen in the blood is associated with the hemoglobin in the
red blood cells). Because little tracer is in the plasma, the effect of
this minor moiety is neglected.
Radioisotope Preparation and Assay and Saturation of Red Blood
Cells With 18O2
Approximately 6 mL of the animal's blood was prepared to
contain red blood cells, previously labeled with 25 µCi of sodium
[51Cr]chromate (Merck Frosst), 60 µCi
22NaCl (Amersham Canada), 50 µCi of
125I-labeled human albumin (Merck Frosst), and 200
µCi of [3H]water (NEN, Dupont Canada). The mixture
containing the radioactive tracers was deoxygenated in
a tonometer (Instrumentation Laboratory 237 [Fisher Scientific]) with
95% N2/5% CO2 and then
reoxygenated with 99% 18O2
(MSD Isotopes).
Each anaerobic sample contained 0.4 mL of blood. From
this, 0.1 mL was diluted with 1.5 mL of saline, pipetted into a
counting tube, and assayed for radioactivity in a Nuclear Chicago gamma
ray spectrometer set for the photopeaks characteristic of
125I and 51Cr. A volume of 0.2 mL of 25%
trichloroacetic acid was then added to lyse the red blood cells and
precipitate the red blood cell and plasma proteins, and after
centrifugation, 0.4 mL of the supernatant fluid was
pipetted into a scintillation vial containing 7 mL of scintillation
fluid for assay of the 22Na and 3H activities.
The samples were then counted in a Beckman LS-250B scintillation
counter. Crossover standards (consisting of each of the radioactive
tracers alone added to blood) and standards from the injection mixture
were treated identically. From the activity of the crossover standards
in their primary counting channel and their spillover into the
various other channels, the activity in the outflow samples due to each
tracer in its primary channel was determined.
The details of the manner in which the characteristics of the radiation and the chemical treatment of the samples provide for the resolution of the activities due to each of the four radioisotopes are as follows: 51Cr and 125I, as well as 22Na, are gamma emitters; thus, there is a contribution from 22Na, but none from 3H, during the assay of the gamma radiation. The low-energy 125I gamma radiation does not contribute to the radiation observed in the region of the 51Cr photopeak, and the contribution of the 51Cr activity to the 125I photopeak was, on average, 0.16 of the activity recorded in the 51Cr photopeak region. The protein precipitation brings down virtually all of the 125I activity and almost all of the 51Cr activity. The 22Na and 3H activities contained in the supernatant were assayed in the liquid scintillation counter; the crossover standards provide the key to correction of 51Cr and 125I activities for the 22Na contributions. The amounts of activities used for injections were approximately as follows: 51Cr-labeled red cells, 5 µCi; 125I-labeled albumin, 10 µCi; [22Na]sodium chloride, 13 µCi; and 3H-enriched water, 42 µCi.
Of the remaining blood in each sample, 0.3 mL was injected anaerobically into individual helium-filled sealed chromatographic vials, which contained crystalline potassium ferricyanide and trichloroacetic acid, to induce the release of the oxygen bound to the hemoglobin into the overlying gas phase in the vial.13 A 28-gauge helium-filled needle, connected through a switching valve to a direct interface quadrupole Hewlett-Packard 5970 series gas mass spectrometer, was introduced through the cork of the chromatographic vial. When the valve was turned, the head-space gas phase was aspirated into the high vacuum of the mass spectrometer. The gas samples were analyzed for their relative contents of the following masses: 32, 34, and 36 for oxygen isotopes; 40 for argon; and 44 for carbon dioxide. The system was set up in such a way that the inlet system and mass spectrometer were flushed with helium after each measurement.
The 18O2 enrichment above background in each sample and in an aliquot of the injection mixture was determined in either of two ways. From ordinary definitions, the 18O2 enrichment was determined from the mass peak area ratio of mass 36 to the sum of (32+34+36), after subtracting from the 36 peak area the appropriate proportion of the mass-40 peak, which represents the mass-36 isotope of argon. Alternatively, the mass peak area ratio of mass 36, after subtraction of the content of the mass-36 isotope of argon, to that of a reference gas was determined; carbon dioxide (mass 44) was used as a reference gas because its concentration in the blood in each of the samples was the same. Either approach gives essentially the same result; the second is slightly less sensitive to air leaks, which occasionally contaminated the samples. When a detectable leak was present, the value obtained from the oxygen analysis was excluded from the data set.
Data Analysis
Outflow profiles for each radioactive tracer were normalized
with respect to the amount injected; ie, they were expressed as a
fraction of the total activity injected per milliliter of the collected
venous blood. In this format, they are displayed as the outflow
fractional recovery of each indicator per second versus time. To obtain
an analogous expression for the oxygen data, a different approach had
to be used. Before each run, samples of the arterial and
sagittal venous blood and of the injection mixture were
analyzed for their oxygen contents. These data were used to
convert the 18O2 enrichment in each outflow
sample to a fractional recovery per milliliter as follows: The relative
18O2 content in each sagittal sinus venous
sample (the product of its 18O2 enrichment
and O2 content) was divided by the amount of
18O2 injected (the product of the injectate
enrichment with the oxygen content of the injection mixture and the
injection volume). That is,
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Oxygen consumption is equal to the product of blood flow and the difference in the oxygen contents of inflowing and outflowing blood. Flow values for the brain in these experiments cannot be obtained from the outflow curves because not all the injected tracer is delivered to the brain. Hence, flow is derived in an alternative fashion. This is detailed below.
Modeling the Distribution and Sequestration Processes
In exploring the kind of modeling that might provide a
description of the data set, we carried out in sequence an
analysis of the kinetics underlying the distribution of tracer
water in the cerebral circulation and then an analysis of the
processes underlying tissue entry and sequestration for tracer oxygen.
From the analysis of the tracer water curves, estimates of the
permeability–surface area products for tracer water and of
flow values per gram have been derived, and from the tracer oxygen
curves, estimates of the permeability–surface area products
and of the sequestration rate constants for tracer oxygen have been
obtained. The tracer water outflow modeling used was developed in a
manner essentially identical to the approach previously devised for the
evaluation of the distribution of tracer water from blood to tissue in
the working heart.24 In the brain, the permeability of
capillaries to low-molecular-weight interstitial
space labels is so small that their outflow curves in an indicator
dilution experiment ordinarily deviate so little from that of a plasma
albumin vascular reference that it is not possible to use the
data to estimate either their permeability–surface area
product for exchange or their extravascular space of distribution.
Thus, it is not possible to use such probes to partition the
extravascular space into interstitial and parenchymal
components. Therefore, we have used instead a single exchanging
reference substance, labeled water, which enters both compartments, and
have used the analysis of the labeled water data to gain
insight into the barriers at both capillary and parenchymal cell
surfaces in the brain. These results are then used in the
analysis of the simultaneously obtained tracer
oxygen data.
To provide an appropriate background for our analysis, we also
needed to consider the effect of red blood cell and plasma separation
on the manner in which putative vascular references for labeled water
and labeled oxygen would be expected to behave. In the lung, where
little time separation has been found between the outflow profiles for
labeled red blood cells and labeled albumin, we have previously
created an expected vascular reference outflow profile for labeled
water by adding labeled red blood cell and albumin profiles,
scaled in proportion to the manner in which the labeled water was
partitioned between the two phases in the injection
bolus.25 In the present study, on the other hand,
where there is a more well-defined time separation between the
outflow profiles for labeled red blood cells and labeled
albumin (Fig 1
), we have developed an approach based on bolus
flow (the central streaming of red blood cells in a
capillary26 ) to account for this.
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Theoretical Modeling
The theoretical modeling needed for the analysis of the
outflow dilution curves is developed in an Appendix (available with
reprints but not otherwise part of the presentation).
Equations are developed for the single capillary and for the whole
organ. At the level of the whole organ, expressions are developed for
the outflow profiles for labeled red blood cells, albumin,
water, and oxygen. The modeling is time dependent and is distributed in
space. In sequence, the processes underlying labeled red blood
cell/labeled albumin separation, labeled water exchange, and
labeled oxygen uptake are modeled.
It is appropriate to compare the present modeling with a recently
proposed differing approach. In the present modeling, tracer
leaving the capillary is expected to return at the place along the
capillary at which it entered the tissue.27 The
tortuousity of the brain capillary system,28 on the other
hand, led Sawada et al29 to address the question of
whether the brain tissue around each capillary can be considered
equivalent to a single well-stirred compartment, exhibiting a
uniform longitudinal concentration rather than developing the otherwise
expected concentration gradients. In the well-stirred model, the
concentration of the test tracer in the extravascular space must be the
same along the whole length of the capillary at any given time (this is
achieved by imposing an infinite longitudinal diffusion coefficient in
tissue). In the classic model, on the other hand, there is an
expectation that the steady state concentration of a consumed substance
will decrease as a function of the distance along the capillary in both
capillary and tissue, as described by Goresky and
colleagues.30 31 Sawada et al did not find it possible
experimentally to distinguish between the two possibilities by use of
model analysis of indicator dilution data acquired in the
brain. However, since flow has a relatively high capillary velocity,
0.15 cm/s,32 compared with oxygen diffusion, 0.0002
cm/s,33 the possibility of an equivalent to
well-stirred extravascular space even for this appears unlikely.
Moreover, if the brain tissue compartment were to behave as a
well-stirred compartment, we would expect that part of the tracer
oxygen would appear at the outflow early in time compared with the red
blood cells (this will be expected in the lungs, for instance). The
indicator dilution data from the brain do not show an early outflow
appearance of labeled oxygen compared with the labeled red blood cells,
indicating that such bypass is unlikely. In their study, Sawada et al
used both modeling approaches to estimate the rate constants for
cerebral capillary transfer of iodoantipyrine (a highly diffusible
substance). No significant difference was observed in the estimates of
the parameters whose determination was desired. In
consideration of all of this, we have implicitly assumed in the
present modeling that the underlying steady state oxygen
concentration in the vascular space and the tissue is a function of the
distance along the capillary, that axial diffusion in the capillary as
well as in the tissue relative to the flow can be neglected, and that
the possibility that there is a barrier-limited transfer of tracer
oxygen between capillary and tissue should be included in the modeling.
If there is no evidence for a limitation, the rate constant for the
tracer oxygen transfer from blood to tissue in the model fitting will
be expected to increase without limit, as was found in the
liver.23
Since heterogeneity of perfusion is expected,34 an analysis was used in which transit times in both capillaries and large vessels are assumed to be heterogeneous. A barrier-limited single-capillary model (one in which some of the tracer comes to the outflow without leaving the capillary; tissue concentration does not equilibrate with blood concentration at each point along the capillary27 ) is integrated into this description to build a whole-organ model, which was used in a fashion previously described.13 14 19 The model assumes that since large vessel flow supplies capillaries, capillary transit times are linearly related to their corresponding large-vessel transit times.19
Several general principles need review before proceeding further with the modeling. Flow values have generally been calculated from indicator dilution data by use of the area under the dilution curve for a reference substance, one which is not lost from the circulation during transit through the organ. The principle underlying this calculation is that of conservation of tracer. All of the tracer injected must be known to enter the organ, and the outflow curve must be representative of the outflow from the whole. In the present instance, the anatomy of the vasculature will lead to the distribution of some of the tracer into the external carotid territory, much of which is extracranial. Therefore, an alternative approach to the estimation of flow values is needed. The one that will be used here is that previously developed by Rose and Goresky19 for the analysis of multiple indicator dilution studies in the heart with labeled sucrose and labeled albumin, where the injection was carried out in a fashion that potentially allowed some of the indicator to escape into the aorta from the coronary ostium. Ziegler and Goresky35 had previously shown that the labeled sucrose–accessible interstitial space in the heart is relatively invariant over the normal flow range. Rose and Goresky devised a way to determine, with their modeling analysis of tracer exchange, a separable parameter related to flow, flow per unit interstitial space. With the relative invariance of the interstitial space, the parameter could then be interpreted directly to reflect flow per gram of tissue. In the present set of experiments, the tissue space that is accessible is the brain water space. The related parameter that is relatively invariant is the brain water content (ie, the brain water space per gram of tissue). From our analysis of tracer water indicator dilution data, we have therefore developed from the fitted parameters derived from the labeled water curve an intermediate estimate of the flow per unit water space and, from this, an estimate of flow per gram brain tissue. This provides a new way of estimating blood flow to the brain from this kind of experimental data.
To provide the background for this kind of approach, we need knowledge of the water content of the brain. For gray matter, the water content is 0.80 mL/g36 ; for white matter, 0.66 mL/g36 ; and for the dog brain as a whole, 0.75 mL/g.37 The last is, of course, the value we used. The interstitial water content, the sucrose-accessible space,38 is 0.18 mL/g for gray matter36 and 0.15 mL/g for white matter36 ; the weighted average, 0.17 mL/g, was used. In fitting the modeling to the present experiments, we used this knowledge to partition the tissue water space into two parts, interstitial water space and cell water space, with known relative volumes. At the modeling level, this has the effect of reducing by one the number of parameters to be determined.
The modeling analysis was first used to gain insight into the
behavior of labeled water in the brain under the present
experimental circumstances. Fits to the labeled water curve were
derived by use of a putative vascular water reference between the
labeled red blood cell and labeled albumin curves, with its
precise position dictated by the proportional water contents and
transit times of red blood cells and plasma. The modeling used was one
in which capillary and large-vessel heterogeneity
could vary from the extreme in which capillary transit times are
uniform (heterogeneity index b=0) to that in which
large-vessel transit times are uniform
(heterogeneity index b=1).19
Least-mean-squares analysis provided estimates of three
parameters (Par1,
Par2, and Par3) for labeled water:
Par1, which represents
k1
ref (the product of k1
[the capillary permeability–surface area product for tracer
water exchange per milliliter interstitial space water]
and ref [the b-weighted ratio of
interstitial space water to capillary water]);
Par2, which represents k2 (the
capillary permeability–surface area product for tracer water
per milliliter interstitial space water); and
Par3, which represents k3 (the
parenchymal cell permeability–surface area product per
milliliter interstitial space water). From these
parameters, values for flow, capillary
permeability–surface area product for tracer water, and
parenchymal cell permeability–surface area product for tracer
water were obtained. Least-mean-squares fitting to the tracer
oxygen data then provided optimized estimates of three
parameters describing tracer oxygen transport to tissue:
Par1, which represents
k1ref, the product of k1
(the capillary permeability–surface area product for tracer
oxygen exchange per unit tissue oxygen extravascular space, with the
dimensions milliliters per second per milliliter) and
ref (the b-weighted ratio of the tissue oxygen to
the capillary oxygen space [the product is then the ratio of the
capillary permeability–surface area product for tracer oxygen
to the capillary oxygen space]); Par2, which
represents k2 (the capillary
permeability–surface area product for tracer oxygen reentry
per unit tissue oxygen extravascular space); and
Par3, which represents kseq (the
rate constant for tracer oxygen sequestration). From these
parameters, estimates of values for the capillary
permeability–surface area product for tracer oxygen and for
the mass of extravascular oxygen, which would have been present if
the sequestering process was suspended, were obtained.
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Table 1
provides values for body weight and
estimated brain weights for the different animals; the latter were
extrapolated from previously published data.21 37 The
table also provides values for oxygen extraction, for the hemoglobin
content of the sagittal sinus blood, and for the systemic blood
hematocrit.
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Outflow Profiles
Fig 1
illustrates the tracer outflow profiles from
two example experiments. The illustration shows outflow dilution
patterns from, on the left, an animal with a low estimated flow per
unit tissue and, on the right, another with a higher estimated flow per
unit tissue. Flow was estimated from the tracer water data, as
previously outlined. Outflow profiles are shown in semilogarithmic
format and in rectilinear format. The two kinds of
representation convey differing kinds of visual information.
The semilogarithmic plot is adapted to portraying curve shapes,
especially at the lower levels of fractional recovery per milliliter,
which are amplified in this kind of plot, whereas the rectilinear plot
particularly provides direct visual information concerning relative
areas under the curves (ie, recoveries) in each data set.
The reference labeled red blood cell, albumin, and water transport functions are found to exhibit similar patterns in each panel. The labeled red blood cell curve peaks first and then exhibits an approximately exponential decay with time. Labeled albumin and sodium curves were found to be essentially identical; hence, the labeled sodium curve is not displayed in the figures in order to make these clearer. Compared with the labeled red blood cell curve, the labeled albumin curve shows somewhat less steep upslopes, a slightly lower and later peak, and a less steep downslope. The shapes of the labeled red blood cell and albumin curves differ in the two experiments: the time of appearance of the tracers at the outflow is shorter in the higher flow experiment, the curves rise to higher peaks and are more compact, and the mean transit times of the curves are shorter. The forms of the labeled water curves also differ in the two experiments illustrated. In the left panel (that with the lower flow), the labeled water curve exhibits a rapid rise to a low-in-magnitude peak that is slightly delayed with respect to the vascular references and then decreases slowly. In the right panel (the higher flow example), the labeled water curve rises to a low-in-magnitude early peak, coincident in time with the vascular reference peaks and somewhat higher than the later part of the curve on the semilogarithmic plot, which then slowly declines. The labeled oxygen curves, on the other hand, both show quite high peaks, more or less coincident in time with those of the labeled red blood cell curves. Smooth curves have been fitted to each of the data sets. There is a tendency in each panel for the data to show an oscillation around the fitted curve with a period corresponding to the respiratory rate in these sitting animals.
A one-barrier model was found not to fit the labeled water curves;
it differed in systematic fashion. The results of fitting a
two-barrier model to the outflow labeled water curves are shown in
Fig 2 for the experiments previously illustrated in Fig 1. To provide insight into the effects of the two barriers, the fit to
the whole curve is illustrated along with the three components of the
fit. These are as follows: (1) a component coming through to the
outflow without leaving the vasculature (the throughput component), (2)
tracer entering the interstitial space and returning to the
outflow without entering the parenchymal cells (the
interstitial returning component), and (3) tracer entering
the parenchymal cells and returning later in time (the cellular
returning component). The throughput and interstitial
returning components form the predominant proportion of the early part
of the labeled water curve.
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The results of the fitting to the labeled-oxygen curves are shown
in Fig 3. Once again, the fit to the oxygen tracer curve
is illustrated along with the components of the fit. The major
component is, in each case, the throughput component (the oxygen tracer
that passed along the capillaries without leaving them). The minor
component is the returning component of the labeled oxygen curve, which
is predicted from the modeling to have returned to the vasculature from
tissue, having escaped sequestration. It is the smaller and later part
of the outflow response. It is also of interest to predict the forms
the labeled oxygen curve and the returning component would have had if
sequestration had not occurred, ie, if kseq had been zero.
These are generated by setting, within the fitted solution,
kseq equal to zero. The reconstructions make it evident
that the predominant part of each of the labeled oxygen curves is the
part that has traversed the circulation without leaving the
vasculature. It is also evident that the greater proportion of the
tracer leaving the circulation has been consumed by the sequestration
process and that only a smaller proportion of this escapes consumption
to return to the circulation.
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The mean transit times for labeled red blood cells, albumin,
and tracer oxygen and the lumped parameters derived from
the least-squares fitting to the labeled albumin, labeled
water, and tracer oxygen outflow curves are presented in Table 2. The mean transit times for the labeled oxygen are
only slightly different from those for the labeled red blood cells, as
expected from the illustrated representative
experiments. It is this observation that led us to select a
one-barrier model for oxygen disposition in the cerebral
circulation; it was inferred that the data would not support a more
complex analysis. The lumped parameters arising
from the fit to the labeled water curves
(k1ref, k2, and
k3) and the differently defined parameters
derived from the labeled oxygen curves
(k1ref, k2, and
kseq) are tabulated. The parameter
Par1 (or k1ref) contains, for
labeled water, the permeability–surface area product for
labeled water per milliliter vascular water space. For labeled oxygen,
the value for Par1, the analogous
parameter, which is related to the total vascular oxygen
content, was only 0.10 of that for labeled water. The relative
magnitude of the two parameters accounts for the relatively
low escape rate of tracer oxygen from the circulation. The ratio of the
two, which describes the relative ratio of the two escape rates from
the cerebral capillary, does not correspond with the ratio of the
permeability–surface area products because of the greatly
differing intravascular spaces of distribution, when these are
expressed in terms of the plasma concentrations for the two tracers
(the vascular spaces of distribution then differ by a factor of >100).
For labeled water, there is a substantial variation in the values for
Par3, the parameter related to the
parenchymal cell permeability–surface area product. The
illustrative experiments show that for the low-flow experiments,
the data are truncated before the component corresponding to tracer
returning from the parenchymal cells has reached substantial magnitude
(the experiments were designed to give better resolution for the tracer
oxygen curves, earlier in time; the number of sample wells in the
anaerobic collector was limited), and it is likely that for
these experiments the Par3 estimates are less accurate and
are perhaps too low.
|
In Table 3, the values for flow and other physical
parameters are given. Since the brain water content is
expected to be normal and unchanging under the circumstances of the
experiment, the value has been used to normalize the physical
parameters to the more usually used parameter,
brain weight. The calculated values for flow varied from 0.008 to 0.016
mL · s-1 · g-1 (the extremes are the
two experiments illustrated). The concomitant variation in the
capillary permeability–surface area product per gram brain (in
milliliters per second per gram) for tracer water in these animals is
shown in Fig 4. The spread of values in this disparate
group of animals is large. The parenchymal cell
permeability–surface area product for tracer water is smaller
than that for the capillaries. With the large surface area of the
neurons and glia, this can be construed to indicate that the
permeability of the glial and neuronal cells to tracer water is likely
much lower than that for the capillaries. When the binding of tracer
oxygen to the hemoglobin in red blood cells is taken into account (the
red blood cell capacity or red blood cell pool effect), it is predicted
that this will greatly diminish the proportional rate of loss of tracer
oxygen from the microvasculature. With the expanded space available to
the tracer oxygen in the red blood cells, the fractional loss across
the capillary walls will be much lower than otherwise would have been
expected. When appropriate adjustment is made for this, the capillary
permeability–surface area for oxygen is larger rather than smaller
than that for labeled water. The permeability–surface area
product for tracer oxygen in the brain capillaries appears to be,
on average, about two orders of magnitude larger than that for tracer
water (despite its much lower capillary escape rate). The
apparent extravascular space of distribution available for tracer
oxygen, estimated by setting the sequestration rate constant in the
final solution to zero, is of the order of 6 mL/g, approximately eight
times the brain water space. The extravascular tracer oxygen clearance
is substantial, as expected.
|
|
Fig 5 shows the concomitant variation in oxygen
consumption with flow. The data suggest that those animals with higher
flow also have a higher oxygen consumption. The variation is not
susceptible to more detailed analysis, since the experiments
were not designed to create change in oxygen consumption or flow.
|
|
Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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The shapes of the labeled water and labeled oxygen curves and their changes with flow and the results of their analyses indicate that these tracers are functionally barrier-limited in their distribution from the brain capillaries to the brain parenchyma. The labeled water curves exhibit an early low-in-magnitude upslope, which, in the higher flow instances, changes to a low and early peak, coincident in time with those of the vascular references. Similar shapes11 39 40 41 and flow-induced shape changes11 39 have previously been observed in brain tracer water curves in rats, monkeys, and humans. The labeled oxygen curves, on the other hand, show intermediate-sized peaks in all experiments, coincident in time with those of the labeled red blood cell curve and almost of the same shape, on the semilogarithmic representations. The early part of the labeled water curve, especially where an early peak is present, consists of a vascular throughput of label and material that has entered the interstitium and returned to the vasculature without entering the parenchymal cells. The more substantial early peak of the labeled oxygen curve consists of tracer that has a transit time similar to that of labeled red blood cells, indicating that little of the tracer emerging from the system has left the vascular space. The downslopes of the oxygen curves are close to those of the labeled red blood cells, indicating that the return of tracer oxygen from the extravascular space to the vascular space is small, whereas for tracer water, the downslope was flat and prolonged, corresponding to the expectation that all of the label leaving the microvasculature will return later in time. For labeled oxygen, one can infer that the larger proportion of the outflowing oxygen tracer has come through the microcirculation without leaving the capillaries.
The sodium label behavior confirmed the suitability of the experimental preparation in terms of the selectivity of the outflow sampling, ie, no significant amount of perfused muscle draining into the sagittal sinus. The simultaneity of the labeled sodium and labeled albumin curves assures us that blood aspirated from the sagittal sinus comes only from the cerebral circulation, since it has been reported that there is no dissociation between the albumin molecules and the sodium molecules in the cerebral circulation, in contrast to muscle.41
Suitability of the Model
The single-capillary modeling, for both the labeled water and
labeled oxygen curves, includes both the barrier-limited case and
the flow-limited extreme, in which the permeability will increase
without limit. At the multicapillary level, the
heterogeneity modeling includes the extremes in which
either the large-vessel or capillary transit times are constant.
The heterogeneity modeling is identical to that used by
Sawada et al,29 but the overall modeling differs in that
it has been assumed that oxygen concentrations in the tissue as well as
the vascular space are a function of the distance along the
capillary.
The modeling accounts for the shapes of both the tracer water and oxygen curves. It provides fits to the data that systematically follow the shapes of the outflow profiles. For the labeled water data, a single-barrier model was found not to generate curves corresponding to the shapes of the experimentally observed outflow profiles. A two-barrier heterogeneous flow model was found necessary to provide a systematically good fit to the tracer water data, as previously observed by Larson et al.42 For tracer oxygen, the decreased rate of loss from the capillary circulation in comparison with tracer water might initially appear anomalous. However, the capillary loss necessarily occurs from the plasma phase of blood, and since the proportion of oxygen tracer in the red blood cells is >100 times as large as that in the plasma, it will be as if the loss is occurring from a plasma flow >100 times as large as is actually present. Since bulk desaturation can be very rapid (50% in 50 ms43 ), red blood cell unbinding kinetics will not be expected to be limiting. Because of the large accessible red blood cell pool of tracer, the fractional loss of red blood cell and plasma tracer oxygen will be much diminished in relation to what otherwise would have been observed if the tracer were distributed only in the plasma. The calculated capillary permeability–surface area product for tracer oxygen is, in consequence, much increased in relation to the proportional passage of the tracer oxygen across the capillary walls.
The capillary permeability–surface area product estimates for
water and oxygen, given in Table 2, were recalculated by use of the
water content values for brain (0.75±0.02 mL/g37 ), so
that these could be expressed in terms of brain weight instead of per
milliliter water (Table 3). The average value for tracer water was
0.079±0.020 (mean±SD)
mL · s-1 · g-1. Anatomic estimates of
the capillary surface area in the brain are of the order of 150
cm2 · g-133 ; from this, the
average minimal permeability value for tracer water can be calculated
to be 5.3x10-4 cm · s-1, a value
of the same order as that for cardiac capillaries, estimated in similar
fashion (6x10-4
cm · s-113 ). Since the bulk of the
diffusional permeation of tracer water occurs through the
endothelial cells,44 this suggests that
the tracer water permeability of the brain capillary and cardiac
endothelial cells is of the same magnitude. The
permeability estimate from the two-barrier model is higher than
that previously estimated in monkeys (1.9x10-4
cm · s-139 ) and humans
(2.4x10-4 cm · s-140 ) with
a one-barrier single-capillary model. The increase in the value
with the two-barrier analysis is expected. With a
two-barrier analysis of a set of data, the permeabilities
of the two components are always higher than that found with an
equivalent single-barrier model. The labeled water
permeability–surface area product for the cellular components
appears low compared with that for the capillaries, since the surface
area for neurons and glia is likely 100 to 10 000 times that of the
capillaries. Ultrastructural observations indicate that the tracer
water likely passes across multiple membrane-bound spaces. The derived
labeled water single permeability–surface area product for
cells may be interpreted in similar fashion to the above, as an
equivalent description for a multiple-barrier process. Derivation
of appropriate values would demand modeling much closer to the actual
structure. Alternatively, water channels across
endothelial cell membranes may be more frequent in
endothelial cells than in neurons and glia. For tracer
oxygen, the calculated average capillary permeability–surface area
product was 1.17
mL · s-1 · g-1, and from this,
the minimal capillary permeability to tracer oxygen was
78x10-4 cm/s (the cardiac capillary permeability,
estimated similarly, would have been 115x10-4 cm/s). The
permeability of the capillary endothelium of the brain
to tracer oxygen is of the same order as that of the cardiac
capillaries. The values are somewhat lower than those for
endothelial cell monolayers,45 which
likely contain some discontinuities.
Extravascular Space Available to Tracer Oxygen
In this instance, the kinetic analysis indicates that
average extravascular space available to tracer oxygen, if
sequestration did not occur, would be, when expressed in terms of
equivalent milliliters of plasma, 6.3 mL/g. In the liver, the value
found for tracer oxygen with a similar approach was 2.5
mL/g,23 a value larger than that found for labeled xenon
by use of the multiple indicator approach in the liver, 1.8
mL/g.46 Oxygen is moderately lipid soluble (it partitions
into olive oil from water in the concentration ratio
5:147 ), and the lipid content of the normal brain
is substantially larger than that in the normal liver. Hence, the
larger value for the brain is expected. Although the larger
distribution space in brain is likely mainly a lipid solubilization
phenomenon, it is possible that some of the space represents an
enzymic space effect48 49 associated with the binding of
tracer oxygen to cytochromes aa3 and P450.
Nevertheless, the present brain experiments indicate that with consumption in this highly metabolically active tissue, local tissue oxygen tensions will be moderately decreased with respect to those in the blood.
Modeling Limitations and Future Potentials
The brain is more heterogeneous, in terms of blood
flow, metabolism, and capillary density,50 51 52 53
than most other organs in which blood tissue exchange has been
analyzed. Variation in local flows has been incorporated into
the modeling used in the present analysis, but at the
tissue level, single average parameters corresponding to
capillary density and levels of metabolism have been used.
The derived parameters corresponding to these should be
regarded as average approximations. An additional kind of
heterogeneity has been observed in cerebral capillary
flow. Confocal microscopy of rat brain cortex indicates that 10% to
20% of cerebral capillaries may not contain erythrocytes at any given
moment.54 55 Two disparate effects will be expected at the
level of the modeling. In the case of labeled water, since labeled
water and labeled albumin will enter red blood cell–free
capillaries, the value for the slip layer will be overestimated.
However, the effect of the change in this value will be small, since
the transit times of the red blood cells and albumin differ to
only a small extent (a difference in average transit times of 0.6
seconds). In the case of labeled oxygen, since the tracer content of
the red blood cells is >100 times that of the plasma, the tracer will
more or less completely follow the distribution of the red blood cells.
The capillaries supplied only with plasma will not be effective sources
of tracer oxygen for tissue and will be effectively excluded from the
calculations. Labeled red blood cells are thus the appropriate
reference for labeled oxygen.
The present analysis includes a capability for analysis of data that might potentially reflect capillary recruitment. The modeling provides for estimation of both capillary permeability–surface area products and of the heterogeneity parameter b. The latter can be separately estimated when there is an independent estimate of blood flow. Conventional analyses have suggested that when flow is increased in response to metabolism56 or hypercarbia,57 there is an increase in the capillary permeability–surface area product. On the other hand, with the heterogeneity approach used in the present analysis, Kuschinsky and Paulson54 have found that capillary permeability–surface area products remain essentially constant at different flow levels and that the heterogeneity of flow is diminished at higher levels of flow and increased at lower levels of flow. The heterogeneity change with flow appears to be the major change. The inference of change in the heterogeneity of flow with change in the level of flow, rather than change in capillary recruitment with flow, corresponds more closely to imaging observations.54
The modeling will ultimately best be applied with technology that provides local information attached to structural areas. If the system is stable, positron emission tomography with successive studies could provide the information base. All of the parameters derived from outflow curves could then be provided for each local area. The analysis and information would then be able to be attached to appropriate homogeneous areas of interest.
Inferences From the Present Study
Tracer oxygen outflow curves were invariably below and almost
parallel to labeled red blood cell curves, on the semilogarithmic
representation, suggesting that there is only a small
proportion of the tracer returning from brain tissue to plasma. Model
analysis of the data substantiated these impressions. It
indicated that fractional tracer oxygen transfer to brain across
cerebral capillaries occurred in a barrier-limited fashion, with
consumption of the major proportion of the tracer that has entered
tissue. The consumption within the tissue then results in the low
recorded oxygen tensions in the parenchyma. The analysis
demonstrates that the decreased escape is due to the large red blood
cell capacity for oxygen, ie, that the capillary permeability for
oxygen is quite high. The consequence of the decreased capillary
fractional escape is that it allows a greater proportion of the oxygen
to be carried to the more distal part of the capillary. It decreases
the proportion of the oxygen that would have left at the proximal end
and provides more oxygen for the tissue at the distal end of the
capillary. This is a desirable functional design. If there were no red
blood cell pool effect, a larger proportion of the oxygen would be lost
at the upstream end of the capillary and there would potentially be a
markedly reduced proportion available for the tissue at the distal end
of the capillary.
|
Acknowledgments |
|---|
This study was supported by grants from the Medical Research Council of Canada, the Quebec Heart Foundation, and the Fast Foundation. The authors wish to thank Eva Ibrahim, Kay Lumsden, and Bernard Rocheleau for their technical assistance and Mary Ann Adjemian for typing this manuscript.
|
Footnotes |
|---|
Reprint requests to Dr Carl A. Goresky, University Medical Clinic, Room C10.148, Montreal General Hospital, 1650 Cedar Ave, Montreal, Quebec H3G 1A4, Canada.
Received October 17, 1994; accepted July 19, 1995.
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