AMER. ZOOL., 28:973-983 (1988)
Ventilation and Its Effect on "Infinite Pool" Exchangers1
MARTIN E. FEDER AND ALAN W. PINDER
Department of Anatomy and The Committee on Evolutionary Biology,
The University of Chicago, Chicago, Illinois 60637
SYNOPSIS. Unlike internal exchange surfaces, the skin contacts an "infinite pool" of air
or water with which exchange of gases, water, ions, and other solutes may occur. Even
though the "infinite pool" may be well mixed, an unstirred diffusion boundary layer is
always present about the skin and may constitute a significant resistance to exchange. The
thickness of the diffusion boundary layer (as approximated by the fluid dynamic boundary
layer) is related to the flow of the respiratory medium, viscosity and density of the medium,
and the morphology of the exchange surface. Oxygen microelectrode studies suggest that,
in most circumstances, the diffusion boundary layer in water is at least as thick as the
blood-respiratory medium distance in amphibian skin. Accordingly, the movement of
water about the skin {i.e., skin ventilation) should have pronounced effects on cutaneous
exchange, especially at low "free stream" velocities. Mounting physiological evidence
suggests that: (1) skin ventilation can augment cutaneous gas exchange; and (2) some
vertebrates actively ventilate their skins, especially in aquatic hypoxia. The ubiquity and
significance of diffusion boundary layers are central to a general understanding of cutaneous exchange and all surface-mediated exchange processes.
fluid always surround exchange surfaces in
Unlike internal lungs and gills, the out- gas or liquid, even if the fluid is well stirred
ermost surface of vertebrates is in direct (Barry and Diamond, 1984). Hence any
contact with the respiratory environment. factor affecting unstirred layers (e.g., "venAccordingly, cutaneous gas exchange is tilation" of the skin) may affect cutaneous
often assumed to occur between the skin exchange of diffusable substances. These
and a well-mixed "infinite pool" (Piiper and points, however, are not widely recogScheid, 1975, 1977) of air and water. nized. This paper examines the signifiIndeed, exchange with "infinite pools" is cance of unstirred layers for organisms
commonplace, involving numerous sub- exchanging diffusable substances with
stances in addition to respiratory gases "infinite pools," reviews the potential and
(water, ions, nutrients, wastes) and occur- actual means by which organisms can
ring in diverse contexts (avian eggshell, respond to limitations imposed by unstirred
plant leaves, water-sediment interface, and layers, and attempts to engender a more
so on). The exchange surface in such cases widespread appreciation of diffusion
often lacks a dedicated ventilatory pump. boundary layers. As Barry and Diamond
Even so, ventilation of the exchange sur- (1984, p. 767) observed in regard to the
face will be inconsequential if the "infinite effects of unstirred layers on membrane
pool" of gas or water is actually homoge- phenomena, "biologists have traversed or
begun a sequence of four reactions: unneous (Piiper and Scheid, 1977).
awareness, awareness but with hasty and
Even as Piiper and Scheid invoked "infi- vigorous denial of any possible quantitative
nite pools," they specifically acknowledged importance; grudging acceptance of
that stagnant layers and stratification within importance; and, finally, serious attempts
"infinite" pools potentially may limit gas to eliminate the effect or to measure or
exchange (1975, p. 219; 1977, p. 246). As correct for it." With this paper, we hope
has long been known, stagnant layers of to hasten arrival at the fourth stage.
INTRODUCTION
THE DIFFUSION BOUNDARY LAYER
1
From the Symposium on Cutaneous Exchange of
Gases and Ions presented at the Annual Meeting of
the American Society of Zoologists, 27—30 December
1986, at Nashville, Tennessee.
973
Around stationary objects immersed in
moving fluids (e.g., air or water) is a region
of fluid, termed the "fluid dynamic bound-
974
M. E. FEDER AND A. W. PINDER
zone in which fluid moves at
'free stream velocity' ( U )
Moving
fluid
5' thickness of boundary
In which fluid velocity
layer.
<99% U
high U (5» low U)
x: distance from leading edge
Solid
surface
FIG. 1. The fluid dynamic boundary layer. Fluid
velocity is zero at any solid-fluid interface and less
than the "free stream" velocity within the boundary
layer. Lengths of arrows correspond to fluid velocity.
ary layer," whose flow velocity is less than
the "free-stream velocity" of the
unimpeded fluid (Fig. 1). Fluid velocity is
zero at the object-fluid interface, and
increases gradually with distance from the
object (Vogel, 1983). Thus, flux of substances between the outer surface of an
organism and the "free stream" must
transit a layer of absolutely or relatively
stagnant fluid, which will retard bulk flow,
necessitate diffusion, and thereby resist
flux. Consequently, a gradient will exist
between a substance's concentration at the
surface-fluid interface and its concentration in the free stream of moving fluid; the
region in which the concentration differs
from the free-stream concentration is the
"diffusion boundary layer" (Vogel, 1983;
Jorgensen and Revsbech, 1985).
How significant is the resistance to flux
represented by the diffusion boundary
layer? One gauge of the diffusion boundary
layer's resistance is its thickness. Typically,
the thickness of the diffusion boundary
layer (5C) is less than the thickness of the
fluid dynamic boundary layer (<5), which may
therefore serve as an upper bound for estimates of 5C (Hitchman, 1978). The considerable understanding of fluid dynamic
boundary layers therefore allows us to
anticipate some characteristics of both
organisms and their environments that
should determine the resistance of the diffusion boundary layer and its likely consequences for cutaneous exchange (Vogel,
1983):
(1) Flow velocity (Fig. 2A, 2B): The
thickness of the fluid dynamic boundary
layer (5) is proportional to the square root
of the inverse of the free stream velocity
(Vogel, 1983; j0rgensen and Revsbech,
FIG. 2. Some physical factors that affect the thickness of the fluid dynamic boundary layer. A and B,
general relationship between thickness (b) and the free
stream velocity (U). C, S as a function of the distance
(x) from the leading edge of a flat plate in a fluid
moving at an arbitrary velocity (low U) and a fivefold
greater velocity.
1985). Any movement of the respiratory
medium relative to an organism's surface,
be it environmentally-induced currents,
locomotor movements of an organism,
or specific ventilatory behaviors, will decrease 8.
(2) Distance from leading edge (Fig. 2C):
At the leading edge of a flat plate in a
moving fluid, the transition from zero flow
(at the plate's surface) to the free-stream
velocity (U) is relatively abrupt; i.e., 8 is
small. As the distance from the leading edge
(x) increases, the transition from zero flow
to the free-stream velocity becomes more
gradual; i.e., 8 increases. The relationship
between x and 8 (operationally defined as
the region in which flow velocity is less than
99% of U) is given by the equation:
8 = 5[(X M )/(PU)]°- 5
(1)
where n is dynamic viscosity, and p is density. Thus the outer limit of the boundary
layer forms a parabola with respect to distance from the leading edge (Vogel, 1983).
(3) Turbulence. The foregoing relationships are for laminar flow. If flow is
turbulent, a laminar sub-layer will persist
but turbulence in outer portions of the
boundary layer will afford some mixing.
Boundary layer thickness will be less than
for laminar flow, as described by the following equation:
8 = 0.376[(xM)/(pU)f2
(2)
(4) Size. Because 8 is proportional to x° 5
(eq. 1), very small organisms should have
less thick boundary layers on the average
than large organisms. Similarly, small
appendages {e.g., legs, external gills) should
975
VENTILATION OF "INFINITE POOL" EXCHANGERS
O2 ( pmol liter" 1 )
O2 ()jmol liter )
0
1.5
1.0
•
50
100
150
SURFACE
ROUGH
200
QAJ
250
)
Flow velocity:
0
50
1.5
100
150
SMOOTH SURFACE
200
( B)
1.0
-
Flow velocity:
0.5
/
0.5
low^__^^--^
high
'
0.0
250
^
—
~
i W/////////////Amm 1
Z6WBEGGIAT0A
/
/////////////////////,
¥//////,
,,,,////////////,
FIG. 3. Representative profiles of oxygen concentrations within the diffusion boundary layer, as measured
with oxygen microelectrodes. A, above marine sediment covered with a mat of sulfur bacteria (Beggiatoa). B,
over a decomposing fragment of algae (Fucus) coated by bacteria. In both cases, oxygen concentrations were
measured at high and low free stream velocities. From Jargensen and Revsbech (1985); reprinted with
permission.
have less thick boundary layers on the average than an organism's trunk. However,
large bodies will more likely experience
turbulent flow than small bodies, resulting
in relatively thin boundary layers (Vogel,
1983). Thus organisms (or parts thereof)
of intermediate size are likely to encounter
the greatest difficulties with boundary layers.
(5) Shape and roughness. Shape has
important implications for boundary layer
thickness, as organisms (or parts thereof)
that are not flat will depart from the relationships outlined above. Semi-empirical
equations predicting 8 are available for various shapes of organisms (Nobel, 1974;
Vogel, 1983). All else equal, rough surfaces will tend to have less thick boundary
layers than smooth surfaces because
roughness promotes turbulence (Vogel,
1983).
(6) The real world. Vogel (1983) cautions about the uncritical application of
these formulae and principles to natural
systems. Real leaves, for example, develop
thinner boundary layers than ideal flat
plates, and the boundary layers about leaves
are even thinner in natural wind than in
artificial air streams in the laboratory
(Vogel, 1983). Importantly, relationships
describing fluid dynamic boundary layers
may not hold for diffusion boundary layers.
For example, the ratio fi:p (viscosity: density; see eqs. 1 and 2) is greater for air than
for water (Vogel, 1983), suggesting that
boundary layers should pose a greater
resistance to gas exchange in air than in
water, all else equal. However, because of
the greater diffusivity and solubility of respiratory gases in air than in water and the
greater velocity of air than of water in most
natural situations (Nobel, 1974), diffusion
boundary layers are a greater problem for
gas exchange in water than in air.
With the recent development of gas
microelectrodes with extraordinarily fine
spatial resolution (Revsbech, 1983), we are
gaining confidence that some effects envisioned above are actually manifested in
natural situations. With oxygen microelectrodes, for example, Jorgensen and Revsbech (1985) have characterized the diffusion boundary layer in water adjacent to
representative sediments (Fig. 3). Even in
rapidly flowing water, 5C typically was
between 200 and 1,000 fan, which is larger
976
M. E. FEDER AND A. W. PINDER
total "
""skin
"skin
A- Ko 2 skln
A- Ko 2 dbl
'skin
Free
stream
>—•
APO2dbl
Blood
Skiny
Boundary layer
i•
AP02skin
Distance
FIG. 4. Schematic summary of variables in the determination of the relative resistance of the diffusion
boundary layer to O 2 exchange. Oxygen diffuses from
the free stream (at a high Po2) to the blood (at a low
Po2) in cutaneous capillaries. Between the "free
stream" and the blood are two layers that retard
exchange of oxygen: the skin itself and the diffusion
boundary layer. Thus, the total resistance to cutaneous exchange is the sum of the individual resistances of the skin itself (RIkin) and of the diffusion
boundary layer (Rdb,). Each individual resistance is
equivalent to the reciprocal of its corresponding diffusive conductance, which is the product of the diffusion coefficient (Ko2), surface area (A), and inverse
thickness (l/t l t i n or \/5c). Each individual resistance
is also proportional to the gradient in oxygen partial
pressure (APo2) across the corresponding layer. See
text for details.
than the blood-respiratory medium distance in the skin of many amphibians (Czopek, 1965). In rapidly flowing water, 5C was
less than in slowly moving water, but 5C was
greater above a rough natural surface (filamentous bacterial colony) than a smooth
one (decaying algal fragment) (Jorgensen
and Revsbech, 1985).
ESTIMATING RESISTANCE OF THE
DIFFUSION BOUNDARY LAYER
Appreciation of a boundary layer's effect
on cutaneous exchange requires knowledge of its resistance to diffusion relative
to other resistances to exchange, either for
a whole organism or a relevant portion of
an organism. Although 8C (and, secondar-
ily, 5) are convenient approximations of
boundary layer resistance, many other factors also contribute to resistance. The following section outlines a more comprehensive procedure for determining the
resistance of the diffusion boundary layer
to O2 uptake, either absolutely or relative
to the total resistance to cutaneous exchange. This procedure draws heavily
upon similar models for O 2 uptake of
microelectrodes (Hitchman, 1978) and
water loss of plant leaves and vertebrate
skin (Nobel, 1974; Spotila and Berman,
1976). Although presented in terms of
oxygen uptake from water, the procedure
can be generalized to other solutes and solvents.
The diffusion boundary layer can be
modeled as a fluid layer in which convection is absent, with an abrupt transition to
the free-stream concentration at its outer
edge (Fig. 4). Thus, the total resistance to
diffusion between the cutaneous respiratory capillaries and an infinite pool (Rtotai)
will be the sum of two resistances in series
(Fig. 4): (1) that of the skin between the
exchange capillaries and the respiratory
medium (Rskin), and (2) that of the diffusion
boundary layer between the skin's surface
and the free stream (Rdb,). The relative
resistance of the diffusion boundary layer
is expressed by Rrel, which is defined as
Rdbl/Rlolal. Rre, may thus vary from 0, when
the resistance of the diffusion boundary
layer is not significant, to 1, when the entire
resistance to gas exchange is within the
boundary layer.
Procedures for evaluating resistance
Rtotai. Rskin. Raw. and Rre, can be evaluated
in several ways:
(1) Each resistance can be calculated
from the physical characteristics of skin and
the boundary layer, and their respective
thicknesses. Each resistance (R) is the
reciprocal of its corresponding diffusing
capacity (Do2), where:
R = t/(Ko 2 A) = (1/DOg),
(3)
Ko2 is Krogh's diffusion coefficient, A is
the surface area, and t is the thickness of
the resistance component. Rre, is then given
b) the following equation:
977
VENTILATION OF "INFINITE POOL" EXCHANGERS
8C / K o 2
[(tstin/Ko2skin) + (6C/Ko2dbl)]
1001
(4)
801
Values for Ko2 and some measurements of
skin thickness are available in the literature. Even if 5C can be measured, however,
calculation of Rrcl for a large organism is
likely to be difficult because of the complex
variation in 8C around the organism's surface.
(2) Each resistance can be approximated
by its corresponding gradient in oxygen
partial pressure. In steady state conditions,
gas flux across the boundary layer and
across the skin are each identical to the
total gas flux (Mo2). In each case, gas flux
can be described by Fick's equation:
R = APo 2 /Mo 2 = (1/Do 2 )
(5)
where APo2 is the oxygen partial pressure
gradient across the boundary layer and skin,
either individually or in combination. Thus,
because gas flux across each layer is identical, the resistance of each layer (i.e., 1/
Do2) will be directly proportional to the
partial pressure gradient across it. Solving
for Rrd yields:
Rrel = APo2 dbl /APo 2 [otal
= 1 -(APo 2skin /APo 2total )
(6)
(cf. Piiper and Scheid, 1975). Calculation
of Rrel with this equation requires the
determination of Po 2 at three locations: in
blood flowing to the skin, at the skin-water
interface, and in the free stream. As with
the first method, calculation of Rre| for a
large organism is likely to be difficult
because of the complex variation in Po2
around the organism's surface.
(3) Because R[otal = RsWn + Rdbl, each of
these resistances can be calculated either
if the other two resistances are known or
if one other resistance can be eliminated
experimentally. Both procedures have been
used to determine Rdb|. For example, Spotila and Berman (1976) and Spotila et al.
(1981) measured Rdbi for water loss by making agar replicates of organisms (amphibians, reptiles, and eggs), in which Rskin for
water loss is abolished. Under such conditions, Rdbl is equal to R[otai, which was calculated from empirical determinations of
water loss and eq. 5. Rskin was then calcu-
60 1
40-
L
R
total
V
R
dbl
20"
"skin
0
1
2
Flow velocity
3
4
FIG. 5. Expected relationship between the resistance
of the diffusion boundary layer (R^,) and flow velocity
(U). The figure assumes that Rdb, is always at least
50% of Rtola,. Asflowvelocity increases, Rdb| decreases.
Organismal responses affecting Rdb, (e.g., skin ventilation) can have marked effects at low U but much
lesser effects at high U. Conversely, organismal
responses affecting R,kCn (e.g., capillary recruitment)
will have negligible consequences at low U but assume
increasing importance at high U.
lated in a second step by comparing the
water loss of an organism to that of its agar
replicate. For respiratory gases, Rdb, of a
whole organism could be eliminated (or at
least minimized) by exposing the organism
to a very rapid flow of the respiratory
medium. By measuring Rto[al at both high
and low flow rates, Rdbl could be calculated
for the lower flow; i.e., any increase in the
total resistance at lower flow would be
attributed to a boundary layer.
This final procedure for assessing Rdb, by
manipulating the velocity of the respiratory medium rests upon several simplifying
assumptions:
(a) Cutaneous oxygen exchange is
entirely diffusion limited. Experimental
evidence suggests that in fact cutaneous
oxygen exchange is >80% diffusion limited (Gatz et al., 1975; Piiper et al, 1976;
Moalli et al., 1980; Burggren and Moalli,
1984; Pinder, 1987), but not wholly so.
(b) The boundary layer and the skin are
a uniform thickness over the entire surface
of the animal. In fact, both will vary. The
skin on the abdomen of a frog, for example, is about twice as thick as skin on the
hind limb (Czopek, 1965; Burggren and
Mwalukoma, 1983). As outlined above, 8C
978
M. E. FEDER AND A. W. PINDER
arterial
40
30
of
20
blood
10
cutaneous
blood
venous blood
illary recruitment may therefore obscure
or exaggerate apparent changes in Rdb, due
to experimental variation in water flow.
Concurrent measurements of functional
surface area during determinations of Rdbl
may resolve this difficulty.
CONSEQUENCES OF BOUNDARY
LAYER RESISTANCE
Because of the relationships between 5C
and
flow velocity (eqs. 1 and 2), some con100
sequences of boundary layer resistance may
be anticipated (Fig. 5):
80
(1) Variation in Rdb, should be most crit60
ical to oxygen uptake when Rskin is relasaturation
tively small and should be inconsequential
of
40
blood
to relatively impermeable skin. At large
Rrei. Rdbi w 'll be most critical to oxygen
20
uptake at low ventilation velocities (Fig. 5),
at which the boundary layer is relatively
5
U
S
U
S
U
thick. The boundary layer may become
S = stirred
limiting to Mo2 at very low flow velocities
U = unstirred
(U).
FIG. 6. Effect of experimental ventilation of the skin
(2) As long as Rrel is large, body moveon blood oxygenation in exclusively skin-breathing
bullfrogs (Rana catesbeiana) immobilized with curare ments that are rapid relative to typical
and submerged in normoxic water at 5°C. Arterial ambient flows may be effective in regulatblood (solid lines) flows to the skin, where it gains
oxygen. Thus, the difference between its oxygen con- ing gas exchange.
(3) The relative effectiveness of organtent and that of cutaneous venous blood (broken lines)
represents cutaneous oxygen uptake. Note that the ismal responses regulating Rdbl (e.g., body
arterio-venous difference is greater when the respimovements) and Rskin (e.g., capillary
rometer was stirred (S) than when unstirred (U). Closed
and open circles represent data from two individuals. recruitment) will depend upon the scaling
of both Rre, and Rdb, with the ventilation
velocity of the external medium. For example, if U exceeds 3 on the arbitrary scale
should fluctuate according to the variables of Figure 5, cutaneous capillary recruitin eqs. 1 and 2. The procedure should give ment could appreciably affect R[otal and
reasonable average values for whole ani- potentially regulate gas exchange, but
mals, but not for specific portions of ani- changing U by body movements will affect
Rtota, relatively little. If, on the other hand,
mals.
(c) Variation in Po 2 between the arterial U is between 0 and 1, changing cutaneous
and venous ends of the cutaneous capillar- capillary recruitment will make very little
ies can be ignored. Because skin is predom- difference to Rlotal but body movements will
inantly diffusion limited, this difference in cause large changes in Rtota|. If Rskin is much
Po 2 is small relative to the Po 2 gradient greater than Rdb,, then variation in Rdbl will
across the skin (Piiper, 1982; Pinder, 1987), be inconsequential except at very low U.
A major challenge for understanding
and so can be ignored in a first approxicutaneous exchange is to replace the arbimation.
(d) Rskin is constant. Capillary recruit- trary units of Figure 5 with determinations
ment affects the "functional surface area" of actual resistances and flows. Complete
of skin-breathing vertebrates (Feder and determinations of Rrel are as yet unavailBurggren, 1985), however, and may vary able for cutaneous gas exchange of whole
with water flow velocity (Burggren and organisms in water; however, demonstraFeder, 1986). Changes in Rskin due to cap- tions that U affects exchange rates are both
0
979
VENTILATION OF "INFINITE POOL" EXCHANGERS
flow in
cutaneous
vein
0
flow in
systemic
artery
to skin
0
flow in
cutaneous
artery
blood 2 0
pressure
(mmHg)
stop
aeration 8 stirring
start
start
aeration
stirring
.
i
r
FIG. 7. Effect of skin ventilation on blood flow to and from the skin. Both the systemic and the cutaneous
arteries supply the skin. Some (but not all) return from both supplies is via the cutaneous vein. Blood flow in
all vessels decreases markedly when ventilation is stopped and increases quickly when ventilation is restored.
Experimental conditions were as in Figure 6.
numerous and diverse. Rates of oxygen
consumption increase with flow speed in
aquatic anemones and coral; the increase
in respiration can be related directly to the
decrease in boundary layer thickness (Patterson, 1985; Patterson, Sebens, and Olson,
unpublished manuscript). As reviewed by
Patterson et al. (unpublished) and Vogel
(1983), current speed may affect nutrient
uptake and gas exchange (both photosynthetic and respiratory) in aquatic plants and
algae (<?.g., Whitford, 1964; Westlake, 1967;
Wheeler, 1980; Gerard, 1982). Vogel
(1983) ascribes the reduced gill size of insect
larvae that live in torrential currents in part
to reduced boundary layers. Boundary layers may pose a significant barrier to nutrient
uptake in the gut, and have pervasive effects
on active transport and passive diffusion
within both plants and animals (Barry and
Diamond, 1984). In animals with very
permeable skins {e.g., most amphibians and
some reptiles), Rre, is large and hence the
air velocity has a very large effect on rates
of water loss (Spotila and Berman, 1976;
Foley and Spotila, 1978). In avian eggs, by
contrast, Rskin is so much greater than Rdb,
that air velocity should never affect water
vapor loss (Tracy and Sotherland, 1979;
Spotila «/ al, 1981).
We have recently begun to explore the
implications of diffusion boundary layers
for cutaneous gas exchange in amphibians.
As stated above, 5C in water (even in stirred
water) is likely to exceed the blood-respiratory medium distance in amphibian skin.
Our experiments suggest that boundary
layer resistance is almost always significant
for these animals due to low resistance of
their permeable skins. Burggren and Feder
(1986) physically immobilized frogs (Rana
catesbeiana) and measured oxygen uptake
partitioning between lungs and skin while
either stirring the water in the respirometer or leaving it still. Cutaneous oxygen
uptake decreased 30% when the water was
980
M. E. FEDER AND A. W. PINDER
Flow in
cutaneous
vein
Flow in
systemic
artery
to skin
o
Flow in
cutaneous
artery
o
30
Blood
pressure
(mmHg)
t rr
r
TTTT T
t
movements
stop
stirring
start
stirring
FIG. 8. Blood flow to the skin increases during spontaneous movement (indicated by arrows) in lightly
curarized bullfrogs submerged in unstirred water. Experimental conditions were otherwise as in Figures 6
and 7.
not stirred. Because cutaneous capillary
recruitment also increased 30% in unstirred water, the change in cutaneous
oxygen uptake probably under-represents
boundary layer resistance to O 2 flux.
Although this experiment shows that flow
of the respiratory medium does affect cutaneous oxygen uptake, the importance of
this effect to the animals was minor because
most oxygen uptake was through the lungs.
Ventilation of the skin must be more critical to exclusively skin-breathing amphibians in water, as suggested by experiments
in which the Po 2 of blood flowing to and
returning from the skin (Fig. 6) and blood
flow to the skin (Fig. 7) were measured in
bullfrogs immobilized by curare and submerged in normoxic water at 5°C. When
the chamber in which the frogs were submerged was not stirred, blood flow to the
skin, systemic arterial Po 2 , cutaneous venous Po 2 , and the A-V Po 2 difference all
decreased dramatically. Because both the
flow and the amount of O 2 gained by the
blood passing through the skin were
reduced, these data imply that the absence
of ventilation increased Rdb, and reduced
Mo 2 .
PHYSIOLOGICAL AND BEHAVIORAL
RESPONSES TO BOUNDARY
LAYER RESISTANCE
Submerged vertebrates are not always
immobile, however, and may have the
option of ventilating their outer surface to
disperse boundary layers of oxygendepleted water. In an experiment similar
to the one above (Pinder, unpublished) but
in which frogs were not totally immobilized
by curare, body movements were apparently adequate to compensate for the lack
of stirring in the chamber (Fig. 8). After
stirring was stopped, heart rate and cutaneous blood flow started to decline as
before, but after a few minutes increased
again as the frog started moving slightly.
The movements were not large, and consisted of occasional extension of the hind
981
VENTILATION OF "INFINITE POOL" EXCHANGERS
.03
stirred respirometer
Cutaneous
.02
unstirred respirometer
(nmolg'min1) .01
0
.04
.08
Total M o ,
.12
(nmolg"1 min1)
FIG. 9. Incidental effect of locomotor movements on cutaneous oxygen uptake in frogs (Rana pipiens) spontaneously active at 25°C. Frogs were breathing both air and water. In unstirred water, more active frogs (i.e.,
those with elevated total rates of oxygen consumption [Mo,]) had a greater cutaneous oxygen uptake than
less active frogs. In stirred water, cutaneous oxygen uptake was constant.
limbs to push against the wall of the chamber.
Body movements for the apparent purpose of ventilating the skin occur under
more natural conditions. The hellbender
(Cryptobranchus alleganiensis), a large aquatic
salamander that breathes almost exclusively through its skin, rocks or sways from
side to side (Guimond and Hutchison, 1973;
Boutilier et al., 1980; Boutilier and Toews,
1981). These movements appear more frequent during hypoxia and hypercapnia and
after exercise (Boutilier et al., 1980; Boutilier and Toews, 1981). Similarly, the Lake
Titicaca frog (Tebnatobius culeus), which can
rely almost entirely on the skin for gas
exchange, starts "bobbing" if it is submerged in hypoxic water. These frogs stand
on the bottom with legs extended to expose
maximum surface area, and push off from
the bottom with their hind legs several
times a minute, usually becoming suspended in the water and slowly settling back
down (Hutchison et al., 1976). Overwintering frogs {Rana pipiens), which remain
submerged in cold water, move about
spontaneously (Emery et al., 1972). Because
these movements are not associated with
feeding, social interaction, predation, or
any other obvious function, skin ventilation is a possible explanation.
Cutaneous gas exchange may also be
facilitated as an incidental side effect of
locomotion (Pinder and Burggren, 1986).
For frogs (R. pipiens) in unstirred water,
cutaneous O2 uptake from water increased
in proportion to the amount of spontaneous activity (Fig. 9), and hence the frequency of skin ventilation. By contrast,
cutaneous O2 uptake was constant regardless of the amount of activity when frogs
were in stirred water, in which the skin
was ventilated continually.
CONCLUSION
We have only begun to skim the surface
in understanding diffusion boundary layers and their significance to cutaneous
exchange. Our state of knowledge is partially due to the unavailability, until
recently, of instrumentation capable of
mapping diffusion boundary layers about
complex organisms in natural situations.
The development of suitable microelectrodes (Revsbech, 1983; J0rgensen and
Revsbech, 1985) will surely contribute to
the dissipation of our ignorance. More
importantly, our state of knowledge stems
from a tendency of biologists to ignore diffusion boundary layers and their possible
significance (Barry and Diamond, 1984).
The physical processes underlying boundary layer formation have long been understood, and empirical indications that
boundary layers are significant for cutaneous exchange have long been available
in the literature. These facts notwithstanding, diffusion boundary layers are still con-
982
M. E. FEDER AND A. W. PINDER
sidered "just a nuisance to the experimentalist" with only occasional physiological
significance (Barry and Diamond, 1984, p.
857). Our major conclusions therefore bear
repetition: Diffusion boundary layers are a
ubiquitous feature of exchange between the
outer surface of multi-cellular organisms
and their environment, as well as of
exchange across membranes within organisms (Barry and Diamond, 1984). Particularly in water, ventilation of the surface
of organisms is likely to affect the resistance of diffusion boundary layers, even
though organisms may exist in "infinite
pools." If we are to achieve a general
understanding of gas exchange, we must
understand these phenomena.
ACKNOWLEDGMENTS
We thank Juan Markin for his continuing assistance in research and writing, Jeffrey Graham and Clifford Hui for their
painstaking review of the manuscript, and
Michael LaBarbera for numerous explanations of fluid mechanics. Our work has
been supported by a grant from the
National Science Foundation (DCB8416121).
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