AMER. ZOOL., 37:65-72 (1997)
Optimal Hematocrit: Theory, Regulation and Implications1
GEOFFREY F. BIRCHARD
Department of Biology, George Mason University,
Fairfax, Virginia 22030-4444
Two major principles have been applied
to the theoretical understanding of physiological systems: (1) maintenance of steady
states, and (2) the principle of minimum
work (Murray, 1926; LaBarbera, 1990). The
study of oxygen transport is among the oldest quantitative fields in physiology and
thus optimization models (models which incorporate principles one and two above)
have been applied many times to this system (Murray, 1926; LaBarbera, 1990). The
steady state maintained by the oxygen transport system is the partial pressure of oxygen at the mitochondria for aerobic production of ATP. The work involved (energy
used by the system), which theoretically
should be minimized within the limits of
maintaining the steady state, includes cardiac muscle contraction (for pressure generation) and the construction and maintenance of the vasculature and blood.
The Poiseuille-Hagen equation is a fundamental component of most models examining optimization in the cardiovascular
system (Murray, 1926; Crowell and Smith,
1967; LaBarbera, 1990):
where Q is laminar flow, AP is the pressure
difference, T| is blood viscosity, and r and /
are vessel radius and length, respectively.
As knowledge about the factors affecting
the flow properties of blood has grown,
studies of the influence of viscosity on
cardiovascular function have increased
(Usami, 1982; Withers et al., 1991; Gallaugher et al., 1995).
Blood is a complex suspension of formed
elements (blood cells) in a solution of proteins and electrolytes. The heterogenous nature of the blood affects its "tendency to
flow" or viscosity. The major factors affecting blood viscosity are hematocrit, protein
concentration (particularly fibrinogen), red
cell deformability, shear rate (an estimate of
the relative velocity of fluid movement),
and temperature (Snyder, 1971; Usami,
1982; Schmid-Schonbein, 1996). The influence of hematocrit has been of particular interest because of its dual but opposing effects on systemic oxygen transport (cardiac
output • oxygen carrying capacity). An increase in hematocrit results in a linear in' From the Symposium Control of Arterial Blood crease in oxygen carrying capacity of blood
Gases: Cardiovascular and Ventilatory Perspectives and an exponential increase in viscosity.
presented at the Annual Meeting of the Society for In- Combining the linear and exponential functegrative and Comparative Biology, 26—30 December
tions results in the relationship between
1995, at Washington, D.C.
65
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SYNOPSIS. Hematocrit is likely to be optimized because of its influences on
oxygen transport. However, optimal hematocrit must also change because
shear rates and blood vessel radii within circulations change temporally.
Blood vessel endothelia regulate shear stress on their walls by changing their
radius. Wall shear stress is dependent on shear rate and viscosity. Because
there is regulation of vessel radius by the endothelium it is hypothesized that
hematocrit may be regulated near optimal by changes in plasma volume. The
implication of such regulation is that changes in vascular volume (blood volume) would occur with alterations in red blood cell mass. Data are presented
which indicate that regulation of optimal hematocrit normally occurs through
changes in plasma volume. The regulation of optimal hematocrit has significant implications for processes that depend on oxygen transport (e.g., exercise) because of the effect of blood volume on cardiac output.
66
GEOFFREY F. BIRCHARD
10
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8 "
1.
7 "
x>
9
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a
IJ
6 "
*
5 "
o
4 "
3 "
2 "
/
\
/
/
/
/
Shear Rate
1 n
a
11.3 sec'
o
go see1
+
225 sec'
<
20
40
60
80
Hematocrit (%)
FIG. 1. The effect of shear on oxygen flow-hematocrit
curves in horses. Data are from Fedde and Wood
(1993).
oxygen transport and hematocrit being parabolic in shape (Murray et al., 1963; Erslev,
1966; Crowell and Smith, 1967; Snyder,
1971; Usami, 1982). Oxygen transport is
maximized at some particular hematocrit
and at lower and higher hematocrits oxygen
transport decreases due to reduced oxygen
carrying capacity and increased viscosity,
respectively. Crowell et al. (1959) coined
the term "optimal hematocrit" for the maximum for this function; the theoretical relationship between hematocrit and oxygen
transport was subsequently derived mathematically (Crowell and Smith, 1967). The
analysis by Crowell and Smith (1967) continues to be the basis of hypotheses on this
subject (Wells and Baldwin, 1990; Withers
et al, 1991; Gallaugher et al., 1995).
Many analyses of optimal hematocrit
have been based solely on measurements of
viscosity, hemoglobin concentration, and/or
hematocrit {e.g., Erslev, 1966; Wells and
Baldwin, 1990). Optimal hematocrit occurs
at the maximum in the relationship between
oxygen flow (oxygen carrying capacity/
viscosity) or (hematocrit/viscosity) and he-
Downloaded from http://icb.oxfordjournals.org/ at Pennsylvania State University on February 26, 2014
CD
matocrit (Fig. 1). This type of analysis generally assumes or ignores three factors: (1)
shear rate within the circulations are equal
(interspecific comparisons) or do not
change with treatment (intraspecific comparisons); (2) the geometry of the circulation, which affects vascular resistance is the
same in different species or is unchanged by
treatment; and (3) the optimal hematocrit is
equal throughout the circulation. This review examines some of these assumptions
in light of existing data and our current understanding of vascular regulation. A revised view of optimal hematocrit as a "regulated variable" is proposed and some of the
implications for exercise physiology are
briefly discussed.
Blood viscosity decreases exponentially
with increasing shear rate. Shear rate within
circulations depends primarily on flow rate.
Therefore, a single oxygen transport-hematocrit curve (optimal hematocrit) cannot
exist for a circulatory system because flow
(cardiac output) does not remain constant
within circulatory systems. A family of
oxygen transport-hematocrit curves exists
where optimal hematocrit increases with increasing shear rate (Fig. 1). This relationship between optimal hematocrit and shear
rate is significant because cardiac output increases with increasing metabolic rate.
Thus, it is consistent with the theory of optimal function theory that hematocrit increases with elevations of temperature in
ectotherms or during exercise in all animals
{e.g., Persson, 1967; Snyder, 1971; Frangioni and Borgioli, 1994; Gallaugher et al.,
1995). Under these circumstances a rise in
the shear rate likely compensates for any increase in viscosity due to hematocrit. In
fact, the infusion of additional red blood
cells by splenic contraction during exercise
can be regarded as a strategy to increase
oxygen carrying capacity and perhaps increase hematocrit towards a new optimal hematocrit. With regard to exercise it should be
noted that at high shear rates blood viscosity
is minimally affected by hematocrit
(Schmid-Schonbein, 1996). Because blood
viscosity is not highly dependent on hematocrit at high cardiac outputs it may not be possible to define an optimal hematocrit at high
work rates {e.g., Gallaugher et al., 1995).
OPTIMAL HEMATOCRIT
REGULATION OF OPTIMAL HEMATOCRIT
According to the general hypothesis of
optimized cardiovascular function, animals
should function near an optimal hematocrit
that is consistent with their vascular geometry and the shear rates found within their
circulations. Because the architecture and
physiology of vertebrate circulatory systems are similar, it is expected that hematocrit and optimal hematocrit should also be
similar across species (particularly at the
class level). Because hematocrit and optimal hematocrit are similar it is hypothesized
that mechanisms exist which regulate hematocrit near the optimal hematocrit.
If hematocrit is regulated near the optimal hematocrit (directly or indirectly) then
the Poiseuille-Hagen equation and the studies discussed above indicate that blood volume would change in response to changes
in viscosity. A blood volume response
requires some mechanistic link between viscosity and blood volume. The vascular endothelium, with its ability to regulate the
tension of the surrounding smooth muscle,
provides such a linkage. Rodbard (1975)
initially suggested that blood vessels regulate the hydrodynamic drag (wall shear
stress) that their endothelia experience. Wall
shear stress in a tube is equal to 4r\Q/Trr3.
This relationship shows that blood vessels
should respond to changes in flow or viscosity by adjusting their radius and thereby
returning shear stress on their walls toward
"normal" levels. Rodbard (1975) hypothesized that the vascular endothelium varied
the secretion of a substance, first called endothelial derived relaxing factor and now
known to be nitric oxide, which causes vasodilation and/or vascular remodeling in response to increases in wall shear stress (see
Bevan et al., 1995).
Both shear rate and viscosity are linked
to blood volume because alterations in shear
stress on walls of blood vessels result in
changes in vessel radius. To change blood
volume through increases or decreases in
plasma volume, either fluid shifts between
compartments or variation in water retention must occur. A change in intravascular
protein concentration could be one mechanism to change blood volume, particularly
for acute changes (Convertino, 1991). Proteins could be transferred to or from the interstitial fluid, or the liver could alter turnover of plasma proteins. The change in the
concentration of vascular proteins would result in changes in plasma volume through
shifts of interstitial water into/or out of the
circulatory system. Chronically, the possible responses include resetting of baroreceptors or vasodilation and/or remodeling
induced by endothelially generated nitric
oxide. Both mechanisms could result in a
perceived change in vascular fullness (perceived by the low pressure baroreceptors) of
the circulation. A change in activity of low
pressure baroreceptors would alter renal sodium and water retention and thus plasma
volume and blood volume (Schrier, 1990;
Convertino, 1991).
The experimental evidence for regulation
of optimal hematocrit includes results from
studies of isolated vessels and intact organisms. Increases in shear stress on walls of
vessels caused by alterations in flow or viscosity effect vasodilation in vitro and vascular remodeling in vivo (Khayutin, 1990;
Bevan et al., 1995). Evidence in whole animals comes from transfusion studies. Following infusion of packed red blood cells
hematocrit decreases over time and blood
volume expands through a plasma volume
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Crowell and Smith (1967) explicitly
stated, and it follows from any analysis
based on the Poiseuille-Hagen equation,
that optimal hematocrit increases as vessel
radius increases. Further, because radius is
raised to the fourth power, optimal hematocrit is sensitive to small changes in
this variable. The implication of general
changes in vessel radii are that changes in
vascular volume and the blood volume also
occur (because the volume of a cylinder =
irr 2 /). Castle and Jandl (1966) pointed out
that the optimal hematocrit increases with
an increased blood volume. Hypervolemia
has two effects: (1) increased central venous
pressure, venous return, stroke volume and
higher cardiac output, and (2) decreased
vascular resistance (through vasodilation)
(Murray et al., 1963; Convertino, 1991).
The effects of hypervolemia on the cardiovascular system result in conditions which
support a greater optimal hematocrit.
67
68
GEOFFREY F. BIRCHARD
100
60 80 CD
Voli
50 -
^
as
a>
60 "
1
a
40 -
40 "
30 -
20 "
10
—I—
—i—
—i—
20
30
40
20
—i—
50
60
70
RBCM (ml/kg)
80
20
22
24
26
28
RBCM (ml/kg)
FIG. 2. A. Rat blood volume (D), plasma volume (A) and hematocrit (V) as a function of red blood cell mass.
Data are from Birchard, 1985; Birchard and Tenney, 1991 and Ou et al., 1985. Blood volume was manipulated
by either exposure to hypobaric hypoxia (equivalent to sea level, 2287, 3200, and 5490 m) or treatment with
sodium cyanate (to increase hemoglobin-oxygen affinity). B. Data from A showing only the normal range. The
regression equations are: Blood volume = 8.96 + 1.77(red blood cell mass), r2 = .63, P < .001. Plasma volume = 10.71 + .67(red blood cell mass), r2 = .29, P < .001. Hematocrit = 37.41 + .40(red blood cell mass),
r2 = .15, P < .02.
increase (e.g., Erslev, 1966; Thorling and
Erslev, 1968; Schumaker et al., 1985; Valeri
et al., 1986). The expansion of the blood
volume (and dilution of the red blood cell
mass) are usually correlated with an improvement in cardiovascular function and
tissue oxygen delivery (Thorling and Erslev,
1968; Schumaker et al., 1985). Finally, the
observed positive correlation between blood
hemoglobin concentration and blood volume (Snyder, 1983) and hemoglobin oxygen affinity and blood volume (Birchard
and Tenney, 1991) are consistent with this
hypothesis.
Regulation of optimal hematocrit also implies that blood volume in intact animals
consistently responds to increases in viscosity. Increases in viscosity normally occur
through increases in hematocrit as a result
of a greater red blood cell mass. Control of
red blood cell mass appears to be independent of mechanisms regulating plasma vol-
ume (Schrier, 1990; Jelkmann, 1992). If optimal hematocrit is regulated, the increases
in red blood cell mass (which raise hematocrit and thus viscosity) should also be correlated with increases in both plasma volume and blood volume (which reduce hematocrit) and vice versa. However, such a
response necessarily will occur only over
the range of blood volumes which can be
accommodated without changing arterial
pressure, because changes in arterial pressure would activate other regulatory systems. Below the point where increases in
vascular tone can maintain blood pressure
(anemia), plasma volume should increase.
Above the point where decreased vascular
tone allows accommodation of increased
volume without increased pressure (polycythemia), further increases in red blood cell
mass should result in compensatory decreases in plasma volume to some minimum. This hypothesis for maintenance of
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a
a.
^?
Hem
a
69
OPTIMAL HEMATOCRTT
140
cri
BV
120
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CO
E
CD
100
X
80
PV
(ml;
en
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60
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-*-'A
A
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c
m
A
40
T3
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o
20
| Cold Blooded |
10
20
30
|Hot Bloodedj
40
50
60
RBCM (ml/kg)
FIG. 3. Horse blood volume (•), plasma volume (A) and hematocrit (O) data as a function of red blood cell
mass. Regression equations were calculated for all data (N = 70). For clarity only data which could be classified as either standardbred and draught (open) or thoroughbred (solid) horses are shown. Regression equations
for blood volume = 28.13 + 1.82 (red blood cell mass), r2 = .84, P < .001; plasma volume = 28.52 + .81
(red blood cell mass), r2 = .50, P < .001; hematocrit = 27.06 + .39 (red blood cell mass), r2 = .58, P < .001.
Data are from Courtice, 1943; Julian et al., 1956; Collery and Keating, 1958; Obara and Nakijima, 1961; Dalton
and Fisher, 1963; Marcilese et al., 1964.
optimal hematocrit was tested by analyzing
data for blood volume, plasma volume, red
blood cell mass, and hematocrit from previous experimental work and from the literature.
Data for rat blood show a complex relationship between blood volume, plasma
volume, hematocrit, and red blood cell mass
(Fig. 2A). A similar pattern has been observed in dogs and humans (Birchard, unpublished). The pattern is consistent with
the restrictions of the proposed model;
above the normal range a decrease in
plasma volume with increasing red blood
cell mass was found. The data below the
normal range are too few to evaluate the response adequately. If the data from the "normal" range (typical hematocrit and red
blood cell mass) are examined, both plasma
volume and blood volume increase significantly with red blood cell mass (Fig. 2B).
However, the magnitude of the slope for hematocrit is less than that for plasma and
blood volume. The same relationships have
been found in the horse (Fig. 3), dog, cat,
dairy cow, and human (Birchard. unpublished). These data are consistent with a system which functionally regulates optimal
hematocrit over the typical range of red
blood cell mass. Further, the observed relationships make it clear that no species specific optimal hematocrit exists.
Conditions which increase or decrease
the rate of oxygen consumption (and presumably cardiac output and thus wall shear
stress) are also correlated with appropriate
changes in blood volume. Cold acclimation
in endotherms results in an increase in
blood volume (e.g., Brown et al., 1954;
Everett and Matson, 1961), and changes in
the rate of oxygen consumption (due to altered thyroid function) in humans are correlated with blood volume (Gibson and Harris, 1939). Further, blood volume increases
significantly with training and decreases
with detraining or bed rest (Coyle et al.,
1986; Convertino, 1991; Saltin and Strange,
1992; Fortney et al., 1994). These responses
are all consistent with the regulation of optimal hematocrit in response to some integrated level of wall shear stress throughout
the vascular system.
IMPLICATIONS
The effects of shear rate and blood volume on optimal hematocrit indicate that re-
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—
QL
°
70
GEOFFREY F. BIRCHARD
5
0.01
100
1000
Body Mass (kg)
Log Total Hemoglobin Index
FIG. 4. A. Allometric plot of Vo 2max as a function of body mass in mammals. Data from Lechner (1978);
Coyle et al. (1986); Birchard and Tenney (1991); Jones and Longworth (1992). Closed symbols, dashed line
indicate the data and the allometric relationship for which blood volume data are available. B. Allometric plot of
Vo 2max as a function of weight specific blood volume • hematocrit; Vo2mnx = .0001 (blood volume • hematocrit)''29,
r2 = .47, P < .003.
alistic comparisons within and between species are difficult, if not impossible, when
oxygen transport has not been actually determined. The continued debate over the importance of hemoglobin concentration and
blood volume as factors determining exercise performance is particularly relevant
(e.g., Gledhill, 1992; Saltin and Strange,
1992; Jones, 1994).
A relationship between oxygen transport
and the rate of maximal oxygen consumption (Vo 2max ) and/or endurance has been
proposed (Convertino, 1991; Saltin and
Strange, 1992). The factors which show a
high correlation with oxygen transport and
performance are blood volume and hemoglobin concentration (Convertino, 1991;
Gledhill, 1992). This is best illustrated by
examining data from horses. A distinct difference exists in the ranges of blood volume
and hematocrit for "cold blooded" (standardbred and draught) and "hot blooded"
(thoroughbred) horses (Fig. 3). More specifically, Persson (1967) found a strong cor-
relation between total hemoglobin (hemoglobin concentration • blood volume) and
Vo 2max in this species. However, these
analyses indicate that care must be taken
when examining studies where these factors
have been manipulated. Hemoglobin concentration and blood volume are not necessarily independent variables. The amount
of training experienced by the subject,
the magnitude of the red blood cell mass
increase, and the time after hematocrit/hemoglobin manipulation varies considerably
between studies (Gledhill, 1992). For example, if the blood doping protocol pushes
the circulation out of the normal blood
volume-hematocrit range for a particular
red blood cell mass, the effects observed on
Vo 2max and cardiovascular function may be
different (i.e., untrained vs. highly trained
subjects). Finally, with regard to studies of
the effects of erythrocyte infusion, it should
be noted that the assumption of proportionality between Vo 2max and oxygen transport
at the organismic level is unrealistic. Dur-
Downloaded from http://icb.oxfordjournals.org/ at Pennsylvania State University on February 26, 2014
0.001
71
OPTIMAL HEMATOCRIT
their enhanced oxygen transport capacity
and greater Vo 2max .
ACKNOWLEDGMENTS
I thank S. M. Tenney and J. Leiter for
helpful discussions during the development
of some of the ideas presented here. B. L.
Osborn, G. C. Packard and two anonymous
reviewers made helpful comments on earlier versions of this manuscript. Finally
many thanks to C. L. Reiber and T. Wang
for providing the stimulus and opportunity
to present these ideas.
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ing exercise the cardiovascular system
serves other important functions, notably
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proposed a genetically based difference in
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shear stress on walls of vessels and the relationship between wall shear stress and
vessel resistance (which decrease as 1/r3
and 1/r4, respectively), it follows that animals with greater blood volumes should
have appreciably greater flow capacities at
any pressure and thus be able to sustain
greater rates of aerobic metabolism. The
differences in vascular regulation observed
by Shen et al. (1995) may indicate that increased vascular production of nitric oxide
in elite physical performers is related to
72
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