Vol. 274, Issue 3, R686-R693, March 1998
Circadian rhythms in diving behavior and ventilatory response
to asphyxia in canvasback ducks
Melanie
Woodin and
Richard
Stephenson
Department of Zoology, University of Toronto, Toronto, Ontario,
Canada M5S 3G5
 |
ABSTRACT |
Underwater feeding behavior was measured in
10 captive canvasback ducks (Aythya
valisineria) for 12 days under a 12:12-h light-dark photoperiod. Feeding activity exhibited a daily rhythm, with 76% of
dives occurring at night. In separate experiments on six of these
ducks, a circadian rhythm was observed in the duration of voluntary
dives. Dives at night (14.7 ± 0.7 s) were significantly longer
than those during the day (10.7 ± 0.7 s). These day-night differences in diving behavior were accompanied by day-night
differences in respiratory responses to progressive asphyxia. In the
same six ducks, ventilation increased exponentially as a function of inspired CO2 concentration during
rebreathing in a closed-circuit barometric plethysmograph. The
exponential rate constant for inspired ventilation was significantly
smaller at night (0.23 ± 0.02) than during the day (0.26 ± 0.01). We suggest that intermittent apneic exercise is facilitated by
reduced respiratory chemosensitivity and that the respiratory and
behavioral control systems are synchronized by the circadian timing
system in diving ducks.
plethysmography; hypoxic hypercapnia; respiratory chemosensitivity; avian respiration
 |
INTRODUCTION |
MANY SPECIES of birds and mammals forage underwater.
Diving behavior, which often exhibits a distinct daily rhythmicity (4, 14, 21, 24, 33, 34), typically consists of bouts of aerobic dives (31,
35). These dives tend to be short compared with maximal breath-hold
times, and they are separated by similarly brief intervals at the water
surface (24, 31).
Current models of the physiological regulation of dive patterns
are either explicitly based on, or implicitly incorporate, aspects of
the "aerobic dive limit" concept (22). Although not discounting
the potential for short-term modification of dive patterns through
anaerobic mechanisms (9), the aerobic dive limit hypothesis predicts
that, during routine aerobic diving behavior, dive times are directly
or indirectly determined by the quantity of
O2 stored in the lungs, blood, and
muscle and the rate at which the
O2 is consumed (22). If
O2 or a correlated variable serves
as a signal to terminate a dive (i.e., to resume lung ventilation),
then the respiratory sensitivity to hypoxemia or a correlated variable
is an integral component of this model. It has been suggested that
diving species have a relatively low respiratory responsiveness to
asphyxia (6), although supporting evidence is scarce. It is assumed
that this adaptation would enable diving species to utilize a greater
fraction of their O2 store and
therefore to remain submerged for longer.
In this study, it was hypothesized that the circadian organization of
avian diving behavior may reflect an underlying circadian oscillation
in respiratory chemosensitivity. Day-night differences in respiratory
responses to hypoxia and hypercapnia have been demonstrated in rodents
(26, 27, 30) and humans (28), but no information is available for birds
or diving species. To test this hypothesis, the circadian rhythm in
diving behavior was monitored in captive canvasback ducks, and the
ventilatory response to progressive asphyxia was measured at times
corresponding to maximal and minimal dive activities.
 |
METHODS |
Ten adult canvasback ducks (Aythya
valisineria; 7 females, 3 males; body mass range
900-1,200 g) were housed in an indoor diving tank under a 12:12-h
light-dark photoperiod (lights on at 6:30 AM EST). The ducks were
trained to dive for food that was delivered to the floor of the tank by
a semiautomatic feeder. This feeder, which was based on the design used
by Bevan et al. (2), provided the ducks with unlimited access to food.
The ducks were trained to activate a submerged paddle switch to deliver 1.5-2 g of food pellets. Ducks used this self-feeding system for several weeks and were observed to maintain normal body weight before
recordings were initiated.
Animal preparation.
Six of the ducks underwent surgery a minimum of 1 wk before
experiments. All procedures were performed under general anesthesia (halothane, 1-2.5% in a 50% air-50%
O2 mixture) using sterile materials. A temperature-sensitive radiotransmitter was implanted into
the abdomen through a midline incision and sutured to the muscle of the
abdominal wall. Care was taken to avoid damaging the abdominal plumage
so that the ducks could resume diving behavior within 1 day of
recovery. The ducks were then given a topical antibiotic (Cicatrin) and
a broad-spectrum antibiotic (Penlong XL, Rogar/STB, 0.3 ml/kg im). The
ducks were kept in postsurgical isolation for 2 h until full recovery
from anesthesia and then returned to the diving tank. The six animals
with radiotransmitters were used for measurement of circadian rhythms
in dive duration and for plethysmographic analysis of ventilatory
sensitivity to progressive asphyxia.
Diving behavior.
An indirect measure of the temporal organization of diving behavior of
the group of 10 ducks was obtained by recording activations of the
feeding device. The circadian rhythm was first measured during a 2-wk
control period during which the ducks were left undisturbed (with
the exception of an experimenter filling the food hopper once every
4 days and the cleaning the tank once per week). Measurements continued
during subsequent experiments to ensure that disturbance and handling
did not disrupt the diving rhythm.
To characterize the circadian diving rhythm in more detail, six of the
ducks were studied in pairs in a different diving tank. They continued
to use a semiautomatic feeder. This diving tank was visually isolated,
and the ducks were observed by videocamera. Body temperature
(Tb) and diving behavior were
monitored continuously for 1 mo using crystal-controlled
radiotransmitters (Mini-mitter, TM-DISC). Reception of the radio signal
was adjusted by manipulating loop antenna length and water conductivity
(addition of sea salt). In this way, the body temperature signal could
be recorded while the animal was at the water surface, but the radio
signal was attenuated when the animal was submerged. The radio dropout
intervals were used as a measure of dive duration. Therefore, during
diving bouts [i.e., 3 or more dives in series separated by short
intervals (<1 min) at surface],
Tb was recorded during
the intervals between successive dives.
Measurement of ventilation.
A closed-circuit plethysmography system was used to measure resting
lung ventilation in six animals (Fig. 1).
The system operates on the principle that air is warmed and humidified
during inspiration causing an expansion in volume, which in turn
results in an increase in pressure within the fixed-volume animal
chamber (15). The ventilatory pressure waveform was monitored using a
differential pressure transducer (model DP45-14, Validyne
Engineering), which measured the difference in pressure between the
animal chamber and an identical reference chamber. The ventilatory
pressure signal was calibrated using an animal ventilator (Columbus
Instruments). Tb was continuously
recorded using implantable radiotransmitters (Mini-mitter; TM-DISC or
VM-FH-DISC). The transmitters weighed ~4.9 g when fully encapsulated,
they had a response time constant of 77 s and a resolution of
0.1°C. Nasal temperature was also continuously recorded using a
thermocouple probe (Physitemp Instruments, EXT-6) taped to the bill at
the opening of the nares. Chamber temperature and humidity were
recorded periodically from a small thermometer and hygrometer located
in the animal chamber.

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Fig. 1.
Schematic diagram of closed-circuit plethysmograph. Dotted lines
represent electrical connections. Bold lines represent primary
recirculating airflow. Fine lines represent airflow for gas analysis
and O2 supply.
1, Three-way stopcock used to include
or exclude KOH solution (CO2
scrub) in primary air circulation; 2,
3-way stopcock used to enable CO2
analyzer to sample gas before or after KOH solution.
|
|
The animal chamber gas was recirculated at a rate of 5.8 l/min using a
diaphragm pump (Cole-Parmer Instrument).
O2 and
CO2 concentrations in dry gas were
continually monitored and recorded using electrochemical fuel cell and
infrared analyzers, respectively (models S-3A/1 and CD-3A, Ametek).
Small fans were placed in the chambers to keep the gases mixed.
The volume of gas in the animal chamber plus recirculating system (Vc)
with a duck in place was determined by gas dilution following the
injection of a known volume of pure
CO2
(VCO2)
directly into the experimental chamber
|
(1)
|
where
FCO2 is
the increase in fractional concentration of
CO2 following injection.
Experimental protocol.
At the start of each experiment, the animals were allowed to rest
quietly in the chamber until all variables had reached an apparent
steady state. During this period, which usually lasted ~30 min,
O2 was bled into the
plethysmograph at a flow rate sufficient to maintain the
O2 concentration between 20.98 and
21.02%. CO2 concentration was
kept at
0.05% by bubbling the gas through concentrated KOH solution.
A recording of CO2 production and
lung ventilation was made for 5 min; then the duck was exposed to
progressive asphyxia during a period of rebreathing. To accomplish
this, the O2 supply was turned
off, and the CO2 scrubbers were
temporarily bypassed. Lung ventilation, gas exchange, and temperature
were recorded continuously during the rebreathing period. The
experiment was terminated when CO2
concentration reached 6%. Each duck was used three times at 9 AM and
three times at 9 PM, and at least 60 h separated consecutive
experiments.
Analysis of plethysmography data.
Tidal volume (VT, ml
BTPS) was calculated as follows
(18)
|
(2)
|
where
|
(3)
|
and
|
(4)
|
where Pm is the observed ventilatory pressure deflection; Pcal is
the pressure deflection due to cyclic injection and withdrawal of a
known volume, Vcal; Ga represents the ratio of tidal volume at
respiratory air sac conditions to the small increase in volume that
occurs when the tidal gas expands from its volume at chamber conditions; Gn is analogous to Ga but represents the volume change from
air sac to nasal temperature, Tn
(K); tI is the
inspiratory time (s); ttot is the total breath
time (s); PB is the barometric pressure (mmHg);
PcH2O is the
water vapor pressure of gas in the animal chamber (mmHg);
PnH2O is the
saturated water vapor pressure of gas at
Tn (mmHg);
PaH2O is the
saturated water vapor pressure of gas in the respiratory air sacs
(mmHg); Tb is abdominal air sac
temperature (K); and Tc is the
temperature (K) of gas in the animal chamber.
Respiratory frequency (fr) was
calculated as 60/ttot, using an average value of
ttot derived from 30 to 50 breaths. Respiratory CO2 production
(
CO2, ml/min
STPD) during steady-state conditions before the onset of asphyxia was calculated as follows
|
(5)
|
where
r is the recirculating gas flow rate (ml/min
STPD),
FCO2,o is
the fractional concentration of
CO2 leaving the animal chamber and
FCO2,i is
the fractional concentration of
CO2 entering the animal chamber.
O2 consumption
(
O2, ml/min
STPD) and
CO2 during rebreathing
asphyxia were determined as follows
|
(6)
|
|
(7)
|
where
FO2,1,
FO2,2,
FCO2,1, and
FCO2,2 are
fractional concentrations of O2
and CO2 at the start
(t1) and end
(t2) of the measurement interval, respectively. This calculation accounts for the
change in number of dry gas molecules in the plethysmograph due to a
respiratory exchange ratio (RER) <1.0 (see
APPENDIX for derivation).
Data sets were compared using paired-sample
t-tests as appropriate. Differences
are considered significant at the 95% confidence level
(P < 0.05).
 |
RESULTS |
Diving activity exhibited a daily rhythm (Fig.
2). In 10 undisturbed ducks, the underwater
feeder was activated a total of 8,273 times in 12 days. Seventy-six
percent of the dives occurred during darkness and 24% in the light.
The lights-on and lights-off transitions were followed by abrupt
increases in diving activity. The increase in diving activity at
lights-on was transient (1-2 h), whereas that at lights-off was
maintained for ~8 h (Fig. 2). Feeding dives were least frequently
performed between ~8 and 11 AM, and the greatest number occurred
between ~9 and 11 PM (Fig. 2). In six of the ducks, dive durations,
surface intervals, and Tb during a
diving bout and during nondiving intervals were analyzed over a 2-h
time bin in these two time periods (Table
1). Dive durations were 37% greater at
9-11 PM than at 9-11 AM (P = 0.01). There was no significant difference in surface intervals at
these two time intervals. Tb
during diving bouts and nondiving periods was significantly higher at
9-11 AM than at 9-11 PM (P = 0.03). In addition, Tb was
significantly higher during diving bouts than during nondiving periods
at 9-11 AM and 9-11 PM (P = 0.003).

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Fig. 2.
Total number of feeding dives performed per hour by 10 ducks over 12 days. Lights came on at 6:30 AM and went out at 6:30 PM as indicated by
horizontal bar.
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Table 1.
Dive pattern and body temperature in undisturbed ducks during periods
of minimal (9-11 AM) and maximal (9-11 PM) daily diving
intensity
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|
Respiratory variables measured during steady-state air breathing are
presented in Table 2. None of the variables
differed significantly between 9 AM and 9 PM. Respiratory variables
measured during progressive asphyxia are presented in Table
3. There were no significant differences in
metabolic rate (
O2,
CO2, RER), breathing pattern
(fr,
tI/ttot),
or Tb between 9 AM and 9 PM in the
asphyxic state. There were, however, significant differences in
Tb between steady-state air
breathing and asphyxia (P = 0.0002) at
9 PM but not at 9 AM. Tb decreased
progressively during asphyxia to minima of 40.6 ± 0.2 and 40.8 ± 0.2°C at 9 PM and 9 AM, respectively.
During progressive asphyxia, inspired ventilation
(
I)
increased exponentially with both increasing
CO2 concentration (Fig. 3) and decreasing
O2 concentration. The ventilatory
response was analyzed as a function of
CO2 concentration, and an analysis
of the response as a function of
O2 concentration yields the same qualitative result because RER was invariant in each experiment.

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Fig. 3.
Day and night ventilatory responses to progressive asphyxia in a
representative animal. , 9 AM data; , 9 PM data.
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|
VT,
I,
VT/tI,
and
I/
CO2
were analyzed as a function of inspired
CO2 concentration (%) using an
exponential model of the following type:
y = a · eb[CO2], where y is a respiratory variable. The
coefficient a represents the magnitude
of y under air-breathing conditions,
and the exponent b is interpreted as a
measure of the sensitivity of y to
progressive hypercapnic hypoxia. The exponent
b was derived by least-squares linear
regression of lny against
CO2 concentration
([CO2]). The resulting
r2 values were
slightly, but consistently, higher than for linear regressions of the
untransformed data. Furthermore, examination of plots of residuals vs.
predicted values showed that untransformed data were heteroscedastic
and exhibited a curved relationship to the regression. These
undesirable characteristics were corrected by logarithmic
transformation, indicating that the exponential model provided a better
description of the data than a linear model. There were significant
day-night differences (P < 0.05) in
the value of the exponential rate constant
b, i.e., in the slopes of
lnVT/[CO2],
ln
I/[CO2],
ln(
I/
CO2)/[CO2],
and
ln(VT/tI)/[CO2] (see Table 3).
A least-squares regression of fr
against [CO2] yielded
a nonsignificant regression coefficient
(P = 0.527), indicating that fr did not change during
progressive asphyxia. Therefore an average value was calculated over
the entire rebreathing period and is presented in Table 3.
There were no statistically significant differences in
Tn between 9 AM and 9 PM in air or
during asphyxia. In addition, Tn did not differ significantly between air and asphyxia at either time of
day. The ducks often began to breathe through the open mouth when
inspired CO2 rose to ~6%. When
this occurred, Tn increased instantaneously by ~4°C, and experiments were terminated.
 |
DISCUSSION |
This study, which to our knowledge represents the first continuous
long-term recording of duck diving patterns, has confirmed that ducks
exhibit a circadian rhythm in diving behavior. Dives were more frequent
and of longer duration at night. Furthermore, the plethysmographic data
support the hypothesis that the ventilatory response to asphyxia is
lower at night, when the ducks are diving the most, than in the
morning, when they dive the least.
All animals responded to progressive asphyxia with a nonlinear increase
in ventilation and no change in
fr. This corroborates other
studies in birds in which hypercapnic hypoxia produced a nonlinear
ventilatory response (12), with the increase in ventilation due mainly
to a rise in VT with small
changes in fr (7, 12). Inhalation
of CO2 is known to evoke an
increase in ventilation in unanesthetized birds (20, 32), although the
effect on breathing pattern can be quite variable due, at least in
part, to the inhibitory effect of
CO2 on the intrapulmonary
chemoreceptors (25). In general, the avian hypercapnic ventilatory
response consists of an increase in
VT with small increases or
decreases in fr (1, 8, 20, 32). In
addition, birds have been shown to respond to a decrease in ambient
O2 with an increase in
ventilation, produced by increases in both
VT and
fr (3, 5, 7, 8, 12, 19, 20).
Comparisons of the ventilatory response to hypoxia, hypercapnia, and
hypoxic hypercapnia indicate that effects of CO2 and
O2 are additive in birds (20),
although the data presented by Colby et al. (12) suggest that there may
be a multiplicative interaction in adult bank swallows.
In the present study, it was found that simultaneous progressive
hypoxia and progressive hypercapnia (asphyxia) evoked a greater ventilatory response in the day than at night. This difference in
I, which was
entirely due to a difference in
VT, was manifest as a difference
in the exponential rate constant b.
Recent studies in humans (28) and rats (26, 27, 30) have provided
evidence for the existence of a circadian rhythm in mammalian
respiratory chemosensitivity, but the mechanisms of interaction of the
circadian timing system and the respiratory control system are unknown
at present. In rodents, it appears that the interaction could be mediated indirectly via circadian modulation of metabolic rate (26, 27,
30), but this was not the case in ducks. The exponential rate constant
describing the relationship between
I/
CO2
and inspired CO2 concentration
differed between 9 AM and 9 PM (Table 3). Thus the metabolism-specific
ventilatory response to hypoxic hypercapnia was greater during the day
than during the night.
The question as to whether diving mammals and birds have a reduced
respiratory sensitivity to CO2 is
unresolved. Seals appear to have a lower sensitivity to
CO2 than humans (13, 29), but it
is not established whether diving birds are less sensitive than
nondiving birds (1, 7). It has been suggested that a chemoreceptor
system with low sensitivity to CO2
would allow a diving animal to remain submerged for extended periods of
time (6, 13) because the drive to resurface would develop more slowly.
In support of this idea, we observed a circadian difference in dive
durations in the ducks in the present study, with longer dives
occurring at night when respiratory sensitivity was low. Previous
studies that did not convincingly demonstrate a lower chemosensitivity
in aquatic birds (1, 5, 7, 25) may have been confounded by
inappropriate timing of the tests. It is likely that experiments were
done during the day when the respiratory system was most sensitive to
chemical stimuli.
The correlation between high chemosensitivity and reduced dive times
raises the question as to whether the respiratory chemosensory system
plays a direct role in the control of dive times. If so, what kind of
role is it? The aerobic dive limit concept is descriptive but not
explanatory. That is, natural dive times of freely diving animals often
fall within the predicted limit, but this does not tell us anything
about whether O2 or any other
correlated variables actually act to signal the animal to resurface to
breathe. A threshold mechanism based on
O2 content would implicate the
respiratory chemosensory system, but such a scheme is likely to be too
simplistic given what is known about the numerous mechanisms involved
in respiratory control (11, 16).
We suggest an alternative hypothesis: that routine diving patterns are
determined by the temporal characteristics of a sustained instability
in the respiratory control system. The chemosensory system can be
viewed as a damped feedback control loop with delay and variable
feedforward drive (11, 16). Many diving vertebrates precede a series of
dives with a short period of hyperventilation (6). This destabilizing
maneuver is immediately followed by a step increase in metabolic rate
and, through the reduction in cardiac output, a simultaneous
lengthening of circulation time. Submersion of the head in water may
also cause a step decrease in the central drive to breathe. The
synchronized oscillations in metabolic rate
(
O2,
CO2, and metabolic acid
production), circulation delay, and perhaps central feedforward drive
could conceivably give rise to periodic oscillations in respiratory output (11). This respiratory instability model predicts that the
behavior of freely diving animals would become entrained to the natural
frequency of oscillations in respiratory drive. The natural frequency
of such oscillations is predicted to vary with such factors as the size
of the O2 and
CO2 stores, the buffering capacity
of the body fluids, the intensity of the diving bradycardia, and the
metabolic power input during underwater locomotion. In a feedback
control system, for any given set of the above conditions, the
amplitude and frequency of the oscillations would also be dependent on
the gain (sensitivity) of the chemosensory system (11). Specifically, a
reduction in the gain would tend to cause an increase in the period of
the oscillation (i.e., increased dive times).
Some species of diving animals (e.g., whales, seals, penguins) may not
show a circadian rhythm in respiratory chemosensitivity, because most
of their activity budget involves diving, at least during foraging
trips, which can last several weeks at a time (23, 24). Furthermore, it
is likely that the control of dive times in ectothermic divers (e.g.,
turtles, sea snakes, crocodilians, amphibians, and air-breathing
fishes) is more complicated than the proposed respiratory instability
model would imply. The dependence of metabolism on such factors as
water temperature and O2 tension, the increased capacity for anaerobic metabolism, the capacity for
cardiac shunting and cutaneous gas exchange, and the interdependence of
respiration and buoyancy all suggest that the simple model suggested
above may not represent a complete or adequate description of the
respiratory control process in diving ectotherms. Nevertheless, daily
rhythms in dive depths and duration have been recorded in some species
(e.g., leatherback sea turtle; Ref. 17), and it would be interesting to
know whether this behavior is correlated with changes in respiratory
chemosensitivity.
Further research is required to determine whether observed daily diving
rhythms represent endogenous circadian rhythms or whether they
represent a direct effect ("masking") of rhythmic stimuli, such
as the light-dark cycle or food availability. For example, many diving
birds and mammals exhibit a daily pattern in both the time of day that
they dive and in the depth and/or duration of those dives (4,
14, 21, 23, 24, 33, 34). However, this daily pattern is often
correlated with daily changes in the abundance and distribution of
their prey and may not represent an endogenous circadian rhythm. This
confounding variable is not likely to apply to canvasback ducks,
however, because they forage for benthic invertebrates which do not
show a daily rhythm in abundance. Preliminary observations in three
ducks found that the day-night differences in dive durations were
retained after several days in constant darkness (36).
In conclusion, this study has shown that canvasback ducks exhibit
significant day-night differences in their respiratory responses to
progressive asphyxia, which are correlated with circadian rhythms in
diving behavior. Ducks dive most often, and for longer, at night when
respiratory sensitivity to combined hypoxia and hypercapnia is lower.
Further work is required to determine whether these observations bear
any direct causal relationship and, if so, which mechanisms mediate
these effects. The data suggest that diving performance may be
facilitated by reduced respiratory sensitivity to progressive asphyxia
and, furthermore, that the circadian timing system may serve to
synchronize the behavioral and respiratory control systems in birds.
Perspectives
This study has confirmed and extended recent studies in rodents and
humans (26-28, 30) suggesting that the respiratory control system
may experience modulation by the circadian timing system. An important
additional feature of the present study is that, by linking of the
day-night differences in respiratory chemosensitivity to the voluntary
diving behavior of the animals, it suggests an adaptive role for
circadian modulation of respiratory control. If reduced
chemosensitivity enables air-breathing animals to remain submerged for
longer, this may increase the underwater foraging efficiency of the
animals (9). The present study also raises the possibility that
chemosensory characteristics favoring diving activities may not be
optimal for the performance of other, nondiving behaviors. Ducks engage
in numerous nondiving activities during the day. Some of these
behaviors, such as swimming and flight, involve intense aerobic
exercise (35), and there are data from human exercise studies to
suggest that performance could be compromised by low respiratory
chemosensitivity (10). Thus there may be a significant advantage to
temporal separation of diving activities (apneic exercise) requiring
low chemosensitivity and nondiving exercise requiring increased
chemosensitivity. The present data suggest that both behavioral and
respiratory rhythms are indeed synchronized in this way in ducks.
By providing a temporal organization to both behavior and physiology,
the circadian timing system may serve to optimize overall locomotor
performance and thereby enhance the evolutionary fitness of semiaquatic
diving species.
 |
APPENDIX |
Calculation of
O2 and
CO2 in a Closed-Circuit
Plethysmograph
Rates of O2 consumption
(
O2, ml/min
STPD) and
CO2 production
(
CO2, ml/min
STPD) of an animal in a closed
chamber can be calculated from a knowledge of the volume of dry gas
present in the chamber (Vc, ml STPD)
and the instantaneous rates of change of the fractional concentrations
of O2
(FO2) and
CO2
(FCO2),
respectively, in the dry gas. Thus
|
(A1a)
|
|
(A1b)
|
where
subscripts 1 and 2 refer to quantities measured at the time at which
the chamber is closed
(t1) and at a
later time (t2). The
interval between
t1 and
t2 must be short
enough to avoid violating the assumption of linearity that is implicit
in this analysis.
Equations A1a and A1b only apply when the volume of gas
within the chamber is constant over the measurement interval
(t2-t1). This condition would be met if the respiratory exchange ratio (RER =
CO2/
O2)
is equal to 1.0, or if an inert gas
(N2) were added or removed at
the appropriate rate under conditions in which RER is <1.0 or RER is
>1.0, respectively. Under most circumstances, RER is <1.0, in which
case the total number of gas molecules in the chamber will decrease
over time, leading to a progressive overestimation of both
FO2 and
FCO2.
Hence, the rate of decrease of
FO2 (and
therefore
O2)
will be underestimated and the rate of increase of
FCO2 (and
therefore
CO2) will be
overestimated by an amount that is dependent on the prevailing RER.
In the current experiments, the animal chamber was a fixed volume, so
that the consequent change in the number of gas molecules resulted in a
progressive decrease in pressure. However, the recirculation tubing had
a significant compliance, so that the change in pressure could not be
used to calculate the change in the number of dry gas molecules (using
ideal gas law), nor could it be used reliably as a feedback signal for
compensating infusions of N2.
Therefore the following analysis was derived. For convenience, the
quantities of gas are expressed as isobaric volumes (i.e., volumes that
would be measured in a chamber of infinite compliance).
All equations refer to dry gas. The volume of gas (Vc) at the instant
that the chamber is closed
(t1) is known.
The dry gas contains only O2,
CO2 and inert gas (mainly
N2) so that at any time
|
(A2a)
|
and
|
(A2b)
|
The
volume of inert gas
(VN2) is
assumed to remain constant over time and is given
by
|
(A3a)
|
Rearranging
and substituting Eq. A2b yields
|
(A3b)
|
and
|
(A3c)
|
At
any time, the volumes of O2
(VO2) and
CO2
(VCO2)
are given by
|
(A3d)
|
|
(A3e)
|
and
the rates of consumption of O2 and
production of CO2 are
|
(A4a)
|
|
(A4b)
|
For situations in which RER is not equal to 1, the total volume of
gas is different at
t1 and
t2; therefore
Eqs. A4a and A4b can
be reexpressed by substituting Eqs.
A3d and A3e
|
(A5a)
|
|
(A5b)
|
Substituting Eq. A3c to replace the
unknown Vc2
|
(A6a)
|
|
(A6b)
|
Substitute Eq. A3b to replace
VN2
|
(A7a)
|
|
(A7b)
|
 |
ACKNOWLEDGEMENTS |
We thank Dr. C. Bluhm and the Delta Waterfowl and
Wetlands Research Station, Manitoba, for providing the canvasback
ducks.
 |
FOOTNOTES |
This work was supported by the Natural Sciences and Engineering
Research Council of Canada.
Address for reprint requests: R. Stephenson, Dept. of Zoology,
University of Toronto, 25 Harbord St., Toronto, ON, Canada M5S 3G5.
Received 12 May 1997; accepted in final form 30 October 1997.
 |
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