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Department of Biomedical Engineering and Center for Computational Medicine and Biology, School of Medicine, The Johns Hopkins University, Baltimore, Maryland 21205
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
MATHEMATICAL MODEL
RESULTS
DISCUSSION
REFERENCES
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Administration of
hemoglobin-based oxygen carriers (HBOCs) frequently results in
vasoconstriction that is primarily attributed to the scavenging of
endothelium-derived nitric oxide (NO) by cell-free hemoglobin. The
ensuing pressor response could be caused by the high NO reactivity of
HBOC in the vascular lumen and/or the extravasation of hemoglobin
molecules. There is a need for quantitative understanding of the NO
interaction with HBOC in the blood vessels. We developed a detailed
mathematical model of NO diffusion and reaction in the presence of an
HBOC for an arteriolar-size vessel. The HBOC reactivity with NO and
degree of extravasation was studied in the range of 2-58 × 106 M
1 · s1 and
0-100%, respectively. The model predictions showed that the addition of HBOC reduced the smooth muscle (SM) NO concentration in the
activation range (12-28 nM) for soluble guanylate cyclase, a major
determinant of SM contraction. The SM NO concentration was
significantly reduced when the extravasation of HBOC molecules was
considered. The myoglobin present in the parenchymal cells scavenges
NO, which reduces the SM NO concentration.
mathematical model; microcirculation; extravasation; vasoconstriction; myoglobin
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
MATHEMATICAL MODEL
RESULTS
DISCUSSION
REFERENCES
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NITRIC OXIDE (NO) is involved in many important physiological and pathophysiological processes, including regulation of vascular smooth muscle tone, inhibition of platelet aggregation, and neurotransmission (25). One of the pathways of regulation of vascular smooth muscle tone is the release of NO from the endothelial cell. The released NO diffuses into the lumen where it reacts with hemoglobin (oxy and/or deoxy Hb, ~2.3 mM concentration in blood) inside the red blood cells (RBCs), and into the nearby smooth muscle cells. In the smooth muscle cells, NO stimulates its target hemoprotein soluble guanylate cyclase (sGC) that catalyzes the conversion of guanosine triphosphate to cGMP thus relaxing smooth muscle cells (13). This endothelium-dependent vasorelaxation coupled with the known reactivity of hemoglobin toward NO has created widespread interest in the scientific community. Physiologically, hemoglobin is contained in RBCs and the effective reaction rate of NO with RBCs is several orders of magnitude smaller than with free hemoglobin (12, 18). The difference in reactivity of RBCs has been attributed to a very low membrane permeability for NO (12) and extracellular diffusion limitation (18). In any case, the NO bioactivity is preserved in the blood under normal physiological conditions.
Cell-free hemoglobins are being developed as hemoglobin-based oxygen carriers (HBOCs) that can temporarily replace RBCs (42). Several of these HBOCs, including cross-linked hemoglobin (Xl-Hb), polyethylene glycol (PEG)-conjugated hemoglobin (PEG-Hb), and recombinant hemoglobin (rHb), are currently in developmental stages or clinical trials as oxygen-carrying therapeutics. These HBOCs have been demonstrated to provide oxygen delivery and maintain circulating volume (35, 41). However, the transfusion of many of these HBOCs causes hypertension in various species, including humans (8, 30, 31). This hypertension resulting from vasoconstriction is often attributed to the scavenging of NO by the hemoglobin or oxyhemoglobin of HBOC, which causes a decrease in the steady-state level of biologically active endothelium-derived NO in the blood and surrounding smooth muscle (15, 26). The HBOC could be in the vascular lumen and/or in the vascular wall due to the extravasation. Using recombinant hemoglobins of varying NO reactivity, Doherty et al. (5) showed that the magnitude of pressor response depends directly on the NO reactivity with hemoglobin. In addition, Rohlfs et al. (31) showed correlation between NO binding affinities and blood pressure response.
There is a need for the knowledge about NO diffusion distance and concentration in the blood vessel in the presence of an HBOC. However, direct measurements of NO concentration in the microcirculation with high spatial resolution are not available. The fragile and unsteady nature of the porphyrinic-based microsensors renders direct measurement of NO concentrations in vivo very difficult (19). Thus it remains to be determined to what extent the plasma-based HBOC or the extravasation of HBOC affects the NO concentration, sufficient to impair endothelial-dependent dilation in vivo.
Mathematical models based on fundamental principles of mass balance,
vessel geometry, and reaction kinetics can be used to predict NO
concentration distribution in vivo. Buerk (1) reviewed mathematical models of NO biotransport, including the effects of NO on
O2 transport and metabolism and hemoglobin scavenging of
NO. In brief, Lancaster (16) published one of the first
models of NO reaction-diffusion. His model used two endothelial cells 20 µm apart as point sources of NO production, and he concluded that
the NO could diffuse a relatively long distance of ~160 µm from its
source of production. Vaughn et al. (38) modeled the NO
production and consumption in a blood vessel and parenchymal tissue.
The model provides a general analysis of NO reaction and diffusion in
the lumen, endothelium, and abluminal (including both adventitia and
smooth muscle) regions. According to Vaughn et al.'s results, a
reaction rate constant of NO with hemoglobin of the order 15 s1 is required to obtain a NO concentration >250 nM at
the abluminal side that is necessary to activate 50% sGC
(34). However, there is disagreement on the amount of free
NO required to stimulate the sGC; recently, NO concentration in the
range of 5-100 nM has been reported for half-maximal activity of
sGC (4).
Butler et al. (2) published another model describing the diffusion of NO in the vasculature. Their model considered a cell-free layer in the lumen (a layer of plasma free of RBCs) and the reaction of NO with sGC. The results were presented for 80-1,500 µm radius vessels. The results indicated that the effect of the cell-free layer is significant in allowing a substantial amount of NO to diffuse outward to the smooth muscle cells in spite of effective scavenging by RBC hemoglobin.
The largest part of vascular resistance resides in the microcirculation, specifically in arterioles of 25-200 µm diameter. Thus there is a need for prediction of NO levels for small blood vessels of this size. In this study, we developed a mathematical model for an arteriolar size blood vessel to analyze the issue of free NO availability to the smooth muscle cell in the presence of various HBOCs. The analysis uses experimental values of the reaction kinetics of NO with HBOCs and extravasation to determine the NO availability.
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MATHEMATICAL MODEL |
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TOP
ABSTRACT
INTRODUCTION
MATHEMATICAL MODEL
RESULTS
DISCUSSION
REFERENCES
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Model geometry and governing equations.
An arteriolar blood vessel of intermediate size is modeled. The model
geometry shown in Fig. 1 includes
cell-free and cell-rich luminal regions, endothelial glycocalyx (G) and
its associated surface layer, endothelium (E), narrow interstitial
space (IS) between the endothelial and smooth muscle cells, smooth
muscle layer (SM) and parenchymal region. RBCs are considered in
homogeneous phase in the cell-rich luminal region. The endothelial
glycocalyx and its associated surface layer is a layer of
plasma-membrane-bound macromolecules of glycoproteins and
proteoglycans, and plasma proteins bound to these molecules
(29). The endothelium is modeled as a cylinder with NO
production concentrated on its surface in accordance with experimental
evidence (6), and the NO production is incorporated in the
boundary conditions. The NO released by endothelial cells diffuses to
the smooth muscle cells and activates guanylate cyclase or diffuses
into the lumen and reacts with hemoglobin. The hemoglobin may be in the
RBC or in the plasma, i.e., HBOC.
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(1) |
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(2) |
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(3) |
Boundary conditions.
The boundary conditions of continuity of flux and concentration are
applied at all of the interfaces and zero flux is imposed at the outer
edge of the parenchymal region. The continuity of concentration assumes
that the solubility of NO in all layers is the same. It is assumed that
the endothelial cell NO synthase (eNOS), which is responsible for the
NO production, is membrane bound (6). The eNOS is assumed
to be distributed uniformly on the membrane, thus releasing equal
amount of NO on both sides of endothelial cell region
(38). The release rates of eNOS are incorporated in the
boundary conditions at the glycocalyx-endothelium interface
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(4) |
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(5) |
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(6) |
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(7) |
Model parameters.
The parameters of the model and their variation range are provided in
the Table 1. The geometric parameters of
the model include the thickness of various regions. The endothelial
cell thickness is 0.5 µm, based on the electron microscopy studies of
Walmsley et al. (40). Pries et al. (29) have
reviewed the experimental evidence for the presence of the glycocalyx
and its associated surface layer and reported that its thickness can
vary between several tens of nanometers to 1 µm. A glycocalyx
thickness of 0.5 µm is assumed. The smooth muscle cell thickness is 6 µm based on the measurements by Haas and Duling (9). In
the calculations, we assume a single smooth muscle cell layer in the
vascular wall. The IS thickness is assumed to be 0.5 µm. The
cell-free layer thickness is a function of vessel diameter and
hematocrit (33). The potential use of HBOC is for a
clinical setting of low levels of systemic hematocrit. Therefore, as a
reference case, the blood hematocrit level in the cell-rich region was
assumed to be 22.5%, which corresponds to a systemic hematocrit of
~20% (33). The core hematocrit (cell-rich region
hematocrit) is slightly higher than the systemic hematocrit. The
calculations can be extended to lower hematocrits, down to zero, but
the systematic variation of hematocrit is not the main goal of this
study. For a 50-µm-diameter arteriolar vessel with 22.5% core
hematocrit, the total cell-free layer thickness is estimated to be 6.7 µm (33). We assumed that the glycocalyx is a part of the
total cell-free layer. Thus the actual cell-free region thickness
(total cell-free layer 
glycocalyx thickness) in our model is
6.2 µm for 22.5% core hematocrit. Because the tissue boundary
condition (Eq. 7) assumes zero flux of NO far away from the
vessel, we assumed the parenchymal region to extend to 2,000-µm
radius. However, the numerical value for this distance is not important
because we will show that the flux disappears at distances about 50 µm away from the wall.
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12
mol · cm2 · s1
(39), which is one of the highest reported. The diffusion
coefficient of NO is assumed constant in all regions and is taken as
3.3 × 105 cm2/s (20).
The rate constant (ki in Eq. 2) for
NO reaction with O2 is 9.6 × 106
M2 · s1 (17). The in
vivo tissue O2 concentration is ~27 µM (or 15.5 mmHg)
(28). Therefore, the overall rate constant
(ko in Eq. 3) of NO reaction with
O2 is 2.6 × 102
M1 · s1. The overall rate constant
ko, estimated for vascular smooth muscle sGC, is
5 × 104 M1 · s1
(39).
The ko for NO and hemoglobin is the product of
hemoglobin concentration with the reaction rate constant. Under normal
physiological conditions, all of the hemoglobin is inside RBC.
Therefore, the ko for NO reaction with
hemoglobin in the lumen can be approximated to NO consumption by RBC.
For cell-rich region, ko is assumed as 1,300 s1 at 22.5% hematocrit, which is similar to the reaction
rate of 1,280 s1 with RBC used by Vaughn et al.
(38). We also examined reaction rates of 770 and 250 s1, based on the experimentally measured values at very
low hematocrit (3, 18). The change in reaction rates had
minimal effect on the NO profiles and concentrations when HBOCs were present.
For the parenchymal tissue region, the capillaries and muscle fibers
were modeled as distributed homogeneous medium. The NO reaction rate
RNO was calculated with the capillary endothelial cell NO
production and NO consumption by the flowing RBCs and HBOC. For the set
of parameters, we chose hamster retractor muscle, for which extensive
experimental and theoretical studies of oxygen transport have been
carried out (37). On the basis of the endothelial NO
release rate of 5.3 × 1012
mol · cm2 · s1, a capillary
density of 1,435 per mm2 and a capillary radius of 1.8 µm, the capillary endothelial NO production rate is estimated at
8.6 × 107 M/s1. The capillary
consumption of NO is calculated by multiplying the fractional volume
occupied by capillaries (=0.0146) with the hemoglobin concentration and
the rate of reaction of NO with either RBC or HBOC. Because capillary
hematocrit is normally lower than systemic hematocrit
(14), 15% capillary hematocrit was chosen for a systemic
hematocrit of 20%. The 15% hematocrit yielded an overall consumption
rate of 5.2 s1 for parenchymal tissue region. Thus the
RNO for the parenchymal tissue region is
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(8) |
1,
the Damkohler number ranges from 65-390 for the reference case of
ko of 1,300 s1. This conclusion
was corroborated by direct numerical simulations, which considered the
convection term in the axial direction in the mass balance equation.
Numerical solution. The NO diffusion-reaction problem (Eqs. 1-8) was solved numerically with the use of FlexPDE software (PDESolutions; Antioch, CA). The complete domain was divided into seven subregions: cell-rich, cell-free, glycocalyx, endothelial, interstitial, smooth muscle, and parenchymal tissue. The solution had a relative accuracy of 0.001.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
MATHEMATICAL MODEL
RESULTS
DISCUSSION
REFERENCES
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Reference case.
The model was solved to calculate NO concentration in all regions of
the reference case of an arteriolar vessel of 25 µm radius with
22.5% hematocrit in the cell-rich region. Figure
2 shows the NO concentration in all
regions (only the region up to 50 µm in the parenchyma is shown). The
concentration of NO in most of the lumen is very small, except for the
cell-free region and the edge of the cell-rich region. The NO released
from the endothelial cells diffuses into the luminal cell-free region
before reaching the cell-rich region where it reacts extremely fast
with the hemoglobin present in the RBC. On the other side, after
diffusing through IS, the released NO reaches the smooth muscle cells
where its maximum concentration is 167 µM.
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Effect of HBOC presence in lumen.
Because many of the experimental and clinical studies with HBOCs were
performed with isovolemic exchange transfusion (31), we
investigated the effect of a 50% isovolemic exchange transfusion with
HBOC on the NO profile. We assumed HBOC solution concentration of 5 g/dl resulting in an in vivo blood concentration of 2.5 g/dl (i.e.,
2.5 g Hb/dl of blood), equivalent of 0.39 mM of hemoglobin tetramer. For the purpose of understanding the effect of reaction rate
of NO with hemoglobin on the NO profile, we have used three different
reaction rate constants of 2, 24, and 58 × 106
M1 · s1 (per heme basis, 1 Hb = 4 heme groups), which we denote as Hb1, Hb2, and Hb3, respectively.
These NO reaction rates are similar to the values for rHb4, rHb2, and
rHb1.1, respectively, reported by Doherty et al. (5). The
reaction rate for Hb3 is also similar to the wild-type human
hemoglobin. Figure 3 shows the NO profile for Hb1, Hb2, and Hb3. The NO concentrations have been reduced compared
with the reference case without cell-free hemoglobin. At the
endothelial side of smooth muscle region, the NO concentrations are
27.6, 13.7, and 11.9 nM, respectively, for Hb1, Hb2, and Hb3. Thus the
smooth muscle exposure to NO can be affected by changing the reaction
rate of NO with hemoglobin. The average NO concentrations in smooth
muscle in this and other cases are shown in Table
2.
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Effect of vessel size.
To understand the effect of geometric parameters on the availability of
NO to the smooth muscle cells, we considered additional arterioles with
radii 12.5 and 50 µm containing Hb3 at 50% isovolemic exchange. We
assumed the total cell-free layer thickness at 5.8 and 6.0 µm
(including glycocalyx thickness of 0.5 µm) for 12.5 and 50 µm
radius vessel, respectively (33). Other geometrical parameter values were as in the reference case. As shown in Fig. 4, the NO concentration in the smooth
muscle remains similar irrespective of the arteriolar diameter.
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Effect of parenchymal tissue region reaction rate.
In previous NO models, Butler et al. (2) assumed a
vascular smooth muscle region of infinite thickness and Vaughn et al. (38) combined adventitia and smooth muscle in one
abluminal region; capillary perfusion was not considered. In our
reference case, we included the NO production by the capillary
endothelium and the NO consumption by hemoglobin in the capillaries in
the parenchymal region. In addition, we investigated the effect of several other parenchymal-tissue reaction rates on the NO profile for
the 50% isovolemic exchange of Hb3. These reaction rates are from only
O2, only myoglobin, and myoglobin and NO production and
reaction from capillaries. For the only O2 case, we used
ko = 2.6 × 102
M1 · s1 and n = 2 (see Model parameters) and ignored the capillary production and reaction of NO in the parenchymal-tissue region. The myoglobin is
present in the cytoplasm of many skeletal and in cardiac muscle cells;
it plays an important role in O2 transport
(23), and its role in NO transport is being discussed
(7). Myoglobin concentration was assumed in the tissue at
0.38 mM as measured in the hamster retractor muscle (22),
and its reaction rate constant with NO is 4.3 × 107
M1 · s1 (11). Thus the
ko is 1.6 × 104
s1 and n = 1 in the parenchymal tissue
region for only myoglobin case. In the case of combined myoglobin and
capillaries in the parenchymal region, the overall reaction rate in
Eq. 8 is modified to
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(9) |
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Effect of HBOC extravasation.
Plasma-based hemoglobin can also affect the diffusion of NO to the
smooth muscle cells by the extravasation of hemoglobin into the IS
between endothelial cells and smooth muscle, where it could scavenge
the NO before the NO can reach smooth muscle cells. The extravasation
of cell-free hemoglobin has been observed experimentally
(21). To investigate this possibility, we varied the
amount of HBOC in the IS and show the resulting NO profiles in Fig.
6. In Fig. 6A, the NO profile
for the extravasation of varying amount of Hb1, which has the slowest
NO reaction rate, is shown. The NO concentration at the endothelial
side of smooth muscle region is 27.5, 26.3, 25.3, 18.8, and 14.2 nM,
respectively, for 1, 20, 39, 195, and 390 µM concentration of Hb1 in
the IS, which corresponds to 0.3, 5, 10, 50, and 100% extravasation.
As expected, the NO concentration decreases with increasing hemoglobin concentration in the IS. The NO concentration remains approximately one-half of the value in the absence of extravasation even at the
complete extravasation of the Hb1. For Hb2, the NO profile (Fig.
6B) is different from that for Hb1 because of the higher reaction rate of Hb2 with NO and the NO concentration at the
endothelial side of smooth muscle region is 13.4, 9.9, 7.8, 2.5, and
1.2 nM, respectively, for a 1, 20, 39, 195, and 390 µM concentration
of Hb2. The NO profile (Fig. 6C) and the NO concentration
are similar for Hb3 and Hb2. The NO concentration at the endothelial
side of smooth muscle region is 11.4, 6.4, 4.3, 0.9, and 0.3 nM,
respectively, for a 1, 20, 39, 195, and 390 µM concentration of Hb3.
Figure 6D shows the average NO concentration in the smooth
muscle for all three hemoglobins as a function of percent
extravasation. The average NO concentration was calculated as the
arithmetic average of smooth muscle NO concentration at the endothelial
and the parenchymal side. Importantly, the NO concentrations are in the
5-100 nM range required for the half-maximal activity of sGC.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
MATHEMATICAL MODEL
RESULTS
DISCUSSION
REFERENCES
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In this study, we have modeled the NO distribution for an arteriolar vessel to understand the effects of physicochemical properties related to NO binding to cell-free hemoglobin in the vascular lumen, in the IS between the endothelium and smooth muscle, and in the parenchyma on the NO concentration to which vascular smooth muscle is exposed.
Effective NO concentration for activating sGC in smooth muscle.
Figure 2 shows that the NO concentration in the smooth muscle cells is
~167 nM at a core hematocrit of 22.5%, which corresponds to a
systemic hematocrit of ~20%. Therefore, the NO concentration to
which smooth muscle cells would be exposed is smaller than the value of
250 nM required for activation of sGC reported by Stone and Marletta
(34). This high concentration of NO cannot be achieved
when the NO reaction rate of 1,300 s1 is used. Vaughn et
al. (38) have used 250 nM NO concentration to conclude
that the NO reaction rate should be 15 s1. Recently,
Condorelli and George (4) have reported a much lower NO
concentration range of 5-100 nM for the activation of sGC with a
half maximal activation concentration of 23 nM. Predictions of our
model are consistent with the range of 5-100 nM for the NO
concentration under in vivo physiological conditions.
NO scavenging by administration of HBOC. Although there are differences in physicochemical properties of various types of HBOCs and several mechanisms have been attributed to their vasoconstrictor activity, the reactivity of HBOCs with NO and extravasation of HBOCs are the main factors implicated for HBOC-induced vasoconstriction.
To examine the effect of NO scavenging, Doherty et al. (5) conducted experiments using rHb1.1, rHb2, and rHb4 of varying reactivity with NO, with rHb1.1 the most reactive and rHb4 the least reactive. The reactivity of these recombinant hemoglobins rHb1.1, rHb2, and rHb4 is similar to that for Hb3, Hb2, and Hb1, respectively, in our model. With the use of these recombinant hemoglobins in conscious rats, they found that the mean arterial pressure increases with higher reactivity with NO. With rHb4, the pressor response was similar to human serum albumin response with a very mild increase in mean arterial pressure. From our model predictions, the calculated NO concentration to which smooth muscle cells are exposed is between 12 and 28 nM (Fig. 3). However, this range of NO concentration is based on the assumption of no extravasation of HBOC into the abluminal side of endothelium. The relative capacity of different molecules to extravasate is dependent on molecular size of hemoglobin molecule (27), with large molecules extravasating at a slower rate than smaller molecules. The extravasation of cell-free hemoglobin has been studied by Matheson et al. (21). When extravasation of hemoglobin into IS is taken into account in our model, the NO concentration changes based on the concentration of HBOC in the IS between the endothelium and smooth muscle (see Fig. 6D). The smooth muscle cell's exposure to NO is significantly affected for Hb2 and Hb3. For these HBOCs, the NO concentration becomes lower than the physiological range of 5-100 nM reported for 50% activation of sGC (average 23 nM) at <50% extravasation (50% extravasation is equal to 195 µM of hemoglobin in the IS). However, the NO concentration is not reduced <14 nM for 100% extravasation of Hb1. Such high NO concentration in the smooth muscle region cannot be achieved for Hb2 and Hb3 even without extravasation. To further understand the effect of extravasation, we can consider the experimental study of Sakai et al. (32). They have used several cell-free hemoglobins to investigate the molecular dimension effects of HBOCs on vasoconstriction. Two of the studied HBOCs were XL-Hb and PEG-Hb with molecular diameters of 7 and 22 nm, respectively, and molecular mass of 66 and 189 kDa, respectively. The bolus infusion of 5 g/dl of XL-Hb caused an immediate hypertension in hamster. Infusion of PEG-Hb resulted in lesser vasoconstriction and hypertension. Measurements by the flash photolysis method showed that these modified hemoglobin molecules have similar hemoglobin-NO binding rates (~30 × 106 M1 · s1). Hence, the effect of
HBOCs on NO concentration in the lumen should be similar and the
vasoactivity cannot be explained solely on the basis of NO reactivity
in the lumen. Thus the extravasation to the IS has to be considered.
Because PEG-Hb is much larger than the XL-Hb, PEG-Hb would extravasate
to a lesser extent than XL-Hb. As seen for Hb2 (see Fig. 6B)
with similar NO reaction rate of 24 × 106
M1 · s1, a 50% extravasation could
reduce the exposure of smooth muscle cells to NO from a high of 14 nM
to 2 nM. Thus our model predictions are consistent with these
experimental results. The results of experimental study by Migita et
al. (24) of 50% isovolemic hemodilution in rat with
-Hb and PEG-Hb having NO binding rates of ~30 × 106 M1 · s1 are also in
qualitative agreement with the results of this model. The study showed
that the rats administered with -Hb (64 kDa molecular mass)
(10) had significant increase in mean arterial pressure
compared with no increase in PEG-Hb administered rats.
Kinetics of vascular wall and beyond. In our model, we have included various layers of vascular wall and a parenchymal region beyond the vascular wall. The addition of capillaries in parenchymal tissue region has significant effect on the NO profile (see Fig. 5); therefore, the simplifications of NO-binding kinetics in the regions of vascular wall and beyond should be carefully examined. With the use of a diffusion-reaction model for NO, Thomas et al. (36) estimated that the NO half-life in the extravascular tissue would substantially increase from 0.09 to >2 s when the parenchymal cells rate of consumption of NO was a function of both NO and O2 concentration compared with a function of only NO concentration. The half-life range of 0.09-2 s results in a diffusion distance of 24-115 µm before the NO concentration reduces to one-half of its value at source. However, in vivo, the capillary consumption and production of NO will determine the lifetime of NO in the extravascular region. Our model predicts that the NO concentration is reduced to much less than one-half of its value at source (endothelium) within 10-15 µm distance (see Fig. 5) for the Hb3. In vivo, this distance may be affected by the particular anatomic arrangements of the capillaries in the vicinity of the arteriole. In addition, the effect of myoglobin on the NO concentration should be significant for skeletal muscle and cardiac muscle tissue. Experiments with hearts of myoglobin-deficient mice have shown that these hearts had more pronounced vasodilatory response to the endogenously produced and exogeneously applied NO compared with the wild-type hearts with myoglobin at physiological concentration (7). These results suggest that in vivo myoglobin reaction could be significant in NO uptake.
In conclusion, the model described in this study can be used to interpret vasopressor activity in experimental studies with administration of HBOC. Predictions of the present NO diffusion-reaction model indicate that the HBOCs of wide range of NO reactivity and molecular size would influence the NO exposure of smooth muscle cell in the range where sGC is known to be activated. This would result in varied vasoconstriction response to each HBOC whether chemically or genetically modified. From our model results, we can conclude that the extravasation of smaller hemoglobin molecules having reaction rates similar to human wild-type hemoglobin scavenge the NO before it can reach smooth muscle cell. We also demonstrated that the presence of myoglobin can significantly affect NO concentration in the parenchymal and smooth muscle regions.| |
ACKNOWLEDGEMENTS |
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This work was supported in part by National Heart, Lung, and Blood Institute Grant HL-18292 and by a grant from the Eugene and Mary B. Meyer Center for Advanced Transfusion Practices and Blood Research at The Johns Hopkins University.
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FOOTNOTES |
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Address for reprint requests and other correspondence: M. Kavdia, Dept. of Biomedical Engineering, The Johns Hopkins School of Medicine, 720 Rutland Ave., 613 Traylor Bldg., Baltimore, MD 21205 (E-mail: kavdia{at}bme.jhu.edu).
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. Section 1734 solely to indicate this fact.
First published February 14, 2002;10.1152/ajpheart.00972.2001
Received 7 November 2001; accepted in final form 12 February 2002.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
MATHEMATICAL MODEL
RESULTS
DISCUSSION
REFERENCES
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