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First published online May 5, 2005
Journal of Experimental Biology 208, 1971-1991 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01583
Physiological control of diving behaviour in the Weddell seal Leptonychotes weddelli: a model based on cardiorespiratory control theory
Department of Zoology, University of Toronto, Toronto, Ontario, Canada M5S 3G5
e-mail: rstephsn{at}zoo.utoronto.ca
Accepted 10 March 2005
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Key words: diving, Weddell seal, cardiorespiratory control, model, behaviour
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).
Several attempts have been made to understand the adaptive advantages that
are realized by engaging in bouts of short dives vs other possible
strategies, such as maximizing time underwater in each dive
(Castellini et al., 1988;
Fedak and Thompson, 1993;
Kooyman et al., 1980). For
example, following the pioneering study by Dunstone and O'Connor
(1979), several investigators
have exploited the basic principles of optimal foraging theory
(Houston and Carbone, 1992;
Kramer, 1988) to show that on
average the diving tactics used by various species may improve the efficacy or
efficiency of foraging, at least in terms of time and/or energy budgets.
Despite their heuristic value, the validity of optimal diving models is
currently open to debate because there remains considerable uncertainty about
the physiological mechanisms involved in the proximate control of diving
activities, which means that there is also uncertainty about the appropriate
constraints to include in the models.
The most obvious and important constraints arise from the fact that
submerged mammals cannot breathe and there is a limit to breath-hold duration.
This issue was addressed experimentally by Kooyman and others, and developed
into the 'aerobic dive limit' (ADL) concept (Kooyman et al.,
1983,
1980), defined as the maximum
length of time that an animal can dive without significant elevation of
post-dive plasma lactate concentrations. The ADL has also often been
calculated in terms of the estimated O2 storage capacity of the
animal and its rate of O2 consumption during dives
(Kooyman and Ponganis, 1998),
and a behaviour-based estimate of the ADL has also been attempted
(Burns, 1999) using the
correlation between post-dive surface interval and post-dive plasma lactate
concentration (Kooyman et al.,
1980). In most studies the majority of dives in the majority of
species are observed to be of durations less than the ADL, and it is now
widely accepted that routine foraging dives are a sustainable aerobic activity
- a conclusion that represents an important and enduring contribution of the
ADL hypothesis. The ADL concept (and models based upon it) assumes that oxygen
supply is a limiting factor, but there is no explicit model that explains what
actually triggers the initiation and termination of dives, especially those
shorter than the ADL. It seems likely that numerous physiological,
psychological and environmental factors govern the voluntary diving behaviours
of marine mammals. The goal of this study was to determine whether the
respiratory control system could, at least in principle, be an important
component of this complex behavioural control system.
The ADL concept was never intended to be a model for the physiological
regulation of diving behaviour, but in the absence of a better alternative it
has often been used, at least implicitly, in that context. As a consequence,
oxygen has been assigned a key role in most attempts to understand the
physiological mechanisms underlying diving behaviour
(Borg et al., 2004;
Burns, 1999;
Butler and Jones, 1997;
Castellini et al., 1988;
Fedak and Thompson, 1993;
Kooyman and Ponganis, 1998;
Kooyman et al., 1980).
However, from the perspective of respiratory control this ADL-based approach
is inadequate and should be elaborated, for several reasons. First of all, in
mammals the peripheral chemoreceptors (principally the carotid body
chemoreceptors) respond to partial pressure of oxygen in the arterial blood
rather than O2 content and there is a non-linear relation between
partial pressure and content (i.e. the sigmoid blood oxygen dissociation
curve). The aortic bodies may detect O2 content of arterial blood
(Lahiri et al., 1983), but
there is no evidence that they have an important role in respiratory control
in diving species (Daly et al.,
1977; Jones and Purves,
1970). Secondly, the partial pressures of carbon dioxide in the
arterial blood and brain tissue play a dominant role in the regulation of
breathing in mammals (Phillipson et al.,
1981). It can be argued that depletion of O2 and
accumulation of CO2 are coupled during breath-hold dives, so that
elevation of the partial pressure of CO2 may indirectly indicate
depletion of the O2 store. However, this neglects the fact that
partial pressures of O2 and CO2 both stimulate
respiration, and these stimuli interact non-additively. A potential role for
CO2 in the regulation of dive and surface times has been suggested
before (Boutilier et al., 1993,
2001;
Butler and Stephenson, 1988;
Halsey et al., 2003;
Parkos and Wahrenbrock, 1987;
Pasche, 1976b;
Stephenson et al., 1986;
Wilson et al., 2003), but
there has not yet been a serious attempt to include this variable in a formal
physiological model.
Finally, and perhaps most importantly, the ADL concept neglects the dynamic
aspects of cardiorespiratory control. The chemoreflex control system is a
negative feedback loop with significant circulatory delay between the
effectors (internal and external gas exchange surfaces) and the sensory
receptors. A controller of this type may induce changes in respiratory drive
that are temporally out of phase with the changes in O2 store
(Cherniack and Longobardo,
1986; Khoo, 2000).
Furthermore, neural feedforward inputs add to the chemoreflex inputs to modify
respiratory drive (Shea,
1996). Hence to be fully explanatory, rather than merely
descriptive, the ADL concept must be expanded to include information about
changes in partial pressures of both O2 and CO2,
chemoreflex characteristics (thresholds and sensitivities of both central and
peripheral chemoreceptors), how they vary over time, and how they combine with
non-chemoreflex inputs to affect overall respiratory drive.
It is often assumed that asphyxia develops with time under water and the
diving animal remains submerged until a strong drive to breathe or some other
stimulus triggers it to return to the surface
(Castellini and Castellini,
2004; Davis et al.,
2004; Milsom,
2000). As a dive progresses, the gradually increasing respiratory
drive is assumed to be counteracted by inhibitory inputs arising perhaps from
sensory receptors in the upper respiratory tract or from central neural
origin. The present study was designed to evaluate an alternative hypothesis
(Woodin and Stephenson, 1998);
that apnoea is initiated and maintained during dives by disfacilitation of
breathing, not active inhibition, and that under routine conditions a diving
mammal is stimulated to return to the water surface by any positive value of
net respiratory drive. That is, it is postulated that the threshold level of
chemical respiratory drive that triggers an aquatic mammal to begin a dive and
to return to the water surface is equivalent to zero net chemoreflex drive.
The plausibility of this hypothesis was examined using a mathematical model of
the cardiorespiratory control system, with parameter values derived from the
literature for an average adult Weddell seal Leptonychotes weddelli.
This species was chosen because it is a marine mammal species for which there
is a reasonably complete set of parameter values available, it usually dives
for durations less than the ADL and was the species upon which Kooyman based
his original formulation of the ADL concept.
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), which in turn was based on models developed by Cherniack
and colleagues (Chonan et al.,
1988; Longobardo et al.,
2002,
1966), Khoo and colleagues
(Khoo et al., 1991,
1982) and Duffin and
colleagues (Duffin and Mahamed,
2003; Duffin et al.,
2000). The cited publications should be consulted for a detailed
description of the underlying concepts and assumptions. The specific version of the model used in the present study is shown schematically in Fig. 1. It consists of six body compartments (alveolar lung, myocardium, brain, locomotor muscle, postural muscle and viscera) interconnected by the blood circulation. The locomotor and postural muscle compartments were treated as a combined compartment (i.e. assigned identical parameter values) in the present study. Parameter values used in computer simulations of diving in Weddell seals are given in Table 1. In all equations, volumes were expressed in litres, mass in kg, time in min, and partial pressures in mmHg (1 mm Hg=0.133 kPa). Abbreviations are summarized in Tables 1 and 2.
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The underlying assumption in this analysis is that respiratory drives represent a stimulus causing the animal to `decide' to begin and end a dive.
Gas exchange
Mass balance equations were used to calculate exchange of gases between
blood and atmosphere in the lung, and blood and tissues in the other model
compartments. It was assumed that `arterial' (i.e. pulmonary capillary)
partial pressures of oxygen (PaO2 and carbon
dioxide (PaCO2) and the respective alveolar
partial pressures (PAO2 and
PACO2), were equivalent. It was also
assumed that the partial pressures of gases in venous blood leaving the brain,
heart, muscle and viscera compartments were equal to those in the respective
tissues. O2 was assumed to be obtained only from blood haemoglobin
(i.e. dissolved O2 was neglected) in all tissue compartments except
muscle, which also included myoglobin saturation and desaturation. Blood and
tissue CO2 capacitances were assumed to be equal, so that
CO2 was added to tissue and blood in equal proportion by mass in
all tissue compartments. Hence, the change in quantity of CO2 and
O2 in one iteration (dt=t-t0,
where t is the current iteration and t0 the
previous one) is the sum of changes due to blood flow and metabolism:
 | (1a) |
 | (1b) |
where 
CO2i, O2i are the changes in
quantities of CO2 and O2 in compartment `i',
CaCO2 (t-ti),
CaO2 (t-ti) are the
concentrations of CO2 and O2 in arterial blood entering
compartment `i' after the relevant circulation lag time
(t-ti), and
iCO2
(t),
iO2 (t)
represent aerobic metabolic rate of compartment `i' in the current iteration
(t), measured as rates of CO2 production and O2
consumption, respectively:
 | (2a) |
 | (2b) |
where Mi is the mass of compartment `i'. This assumes that mass is numerically equivalent to tissue water volume.
It was assumed that tissue respiratory quotient
(RQ=CO2/O2)
was equal to 1.0 in the brain compartment, where the tissues metabolize mainly
glucose, and 0.85 in the other compartments.
In the lung compartment, change in quantities of CO2 and
O2 in one iteration is the sum of changes due to blood flow
(cardiac output 
) and alveolar
ventilation (A):
 | (3a) |
 | (3b) |
where CO2A, O2A are the changes in
quantities of CO2 and O2 in the alveoli, and
C
CO2
(t-tv),
CO2
(t-tv) are mixed venous concentrations of
CO2 and O2 entering the lung after venous lag time
(t-tv).
 | (4a) |
 | (4b) |
 | (5a) |
 | (5b) |
where PA is alveolar partial pressure,
FA is alveolar fractional concentration,
VA is average alveolar volume, PB is
barometric pressure and PH2O is saturated water
vapour pressure at 37°C (47 mmHg). Lung volume (VL)
could differ between surface respiration and apnoea onset. The respiratory
exchange ratio (RER) was calculated as:
 | (6) |
Blood circulation
Three main functional categories were quantified: blood flow, circulatory
transfer functions and blood gases.
Blood flow
Cardiac output () was calculated as
the sum of blood flows through each of the model tissue compartments (except
lung) and the arterio-venous shunt
(a-).
a-
was an adjustable parameter that could differ between dive and surface
intervals. It was assumed that changes in
were associated with relatively large
changes in heart rate (fH, beats min–1)
and relatively smaller changes in cardiac stroke volume
(VS, litres), and the following relations were used,
calculated from data in Davis and Kanatous
(1999):
 | (7a) |
 | (7b) |
Maximum cardiac output
(max) was varied in this
model by adjusting maximum heart rate.
Brain blood flow (B) was
assumed to be dependent on fractional oxygen saturation of arterial blood
(SaO2) and PaCO2
in blood entering the brain (Fortune et
al., 1992):
 | (8) |
where Brest,
PaCO2rest and
SaO2rest are parameters representing standard
`resting' values, and Gq is a factor representing the relative cerebral
vascular sensitivity to CO2
(Fortune et al., 1992).
Myocardial, skeletal muscle and viscera compartment blood flows were
subject to `local regulation', modeled as follows:
 | (9) |
where i is blood flow
through compartment `i',
iO2 is oxygen
consumption of compartment `i', CaO2
(t-ti) is oxygen content of the arterial blood entering
the compartment after the appropriate circulatory lag time
(t-ti) and
is a `target' blood
oxygen extraction coefficient:
 | (10) |
where CvO2(t) is oxygen concentration of compartmental venous blood. Thus, compartmental blood flow was assumed to be dependent on metabolic rate of the tissue and arterial blood oxygen delivery.
For the myocardium, the target blood oxygen extraction coefficient was
fixed at a value 
that yielded published coronary blood flow under resting conditions
(Zapol et al., 1979).
Myocardial metabolic rate was assumed to change in direct proportion to
cardiac output. This mechanism therefore ensured an adequate supply of oxygen
to the heart muscle whenever blood oxygen content and heart work varied.
For the skeletal muscle and viscera compartments, tissue metabolic rates
were set as adjustable parameter values during dives and surface intervals. In
addition to the `local regulation' of blood flow described above, these
compartments were also subject to `systemic regulation' of blood flow, modeled
by coupling target blood oxygen extraction coefficient
to net respiratory drive
(). The extent of this
cardiorespiratory coupling was independently adjustable for both dive and
surface intervals in each compartment, and the gain of the coupling mechanism
was normalized to standard resting lung ventilation
(rest):
if >
rest,
 | (11a) |
if <
rest,
 | (11b) |
where 
is
a standard resting blood oxygen extraction coefficient, and
and
are
user-defined limits for the target oxygen extraction coefficient in each
compartment. Within these limits, the `relative coupling gain'
(
) caused compartmental target blood
oxygen extraction coefficient
to vary in proportion to
the relative change in lung ventilation:
if >
rest,
 | (12a) |
if <
rest,
 | (12b) |
where max and
min are maximum lung
ventilation (a value determined in real animals by factors such as mechanical
limitations on lung ventilation) and minimum ventilation (apnoea),
respectively. In practice, the intensity of the `systemic' cardiovascular
response was adjusted by changing the degree of cardiorespiratory coupling
via the
and
values (Eqn
11). In this study, all tissues were assumed to remain within the ADL (i.e.
net anaerobic metabolism was excluded). Therefore in the viscera, which have
no appreciable O2 store,
never
exceeded 0.8 (Davis and Kanatous,
1999). In skeletal muscle, however, nearly zero blood flow
(m) could be achieved
during apnoea by setting
to a very
high value (a value of 10 was used in this study). To satisfy the ADL
constraint, if myoglobin oxygen saturation
(SmO2) decreased to a minimum value (0.01),
became 0.8 and muscle blood flow therefore became dependent on muscle
metabolic rate
(mO2) and
arterial blood oxygen content
[CaO2(t-ta)] for the
remainder of the dive (Eqn 9).
Elevations in compartmental blood flows during surface intervals were
constrained by maximum cardiac output and under limiting conditions, the
competing drives for blood flow in the different compartments were resolved by
imposing an arbitrary priority order:
B=h>m
>v. Thus, cerebral and
coronary oxygen delivery was always adequate, and skeletal muscle recovery was
given priority over viscera to facilitate myoglobin reoxygenation. When
present, the arterio-venous blood shunt
(n-v) functioned as a fixed
parameter and therefore assumed top priority, and because of this the maximum
shunt flow was never set so high as to limit cerebral and coronary blood
flows.
Circulatory transfer function
The arterial and venous transfer functions were each modeled as the sum of
two components, a circulatory lag time and a mixing function
(Lange et al., 1966).
Circulatory lag times were assumed to be proportional to cardiac output and
blood volume, and the latter was divided into arterial blood
(Vba) and venous blood (Vbv) in the
volume ratio 3:7. The arterial lag time represents the average time taken for
blood to flow from the lung to the muscles and viscera
[(t-ta)], and was calculated as:
 | (13a) |
It was assumed that circulatory lag time to the peripheral chemoreceptors
and brain (t-tc) was 70% of arterial lag time
(t-ta), and that the heart is half way between lung and
brain (i.e. circulatory lag time to the myocardium (t-th)
was 50% of chemoreceptor lag time (t-tc). Venous
circulatory lag time (t-tv) was calculated similarly:
 | (13b) |
The mixing function was modeled as a simple first order system with time
constant (
mix):
 | (14) |
where Vmix is the effective volume of the mixed subcompartments of the arterial (Vamix) and venous (Vvmix) systems (Fig. 1).
A step change in cardiac output cannot be modeled with a step change in
circulation lag (i.e. in the referenced row of the spreadsheet) because in a
real circulatory system a change in cardiac output is followed by a transition
period lasting the duration of the new `instantaneous steady-state'
circulatory lag time. During this transition period the `waveform' of blood
gases at any given point in the circulation appears compressed or expanded
when cardiac output increases or decreases, respectively. When cardiac output
changes continuously, as it does during a diving bout, the circulatory delay
is continuously in `transitional' mode. To account for this, the appropriate
lag time [expressed as the number of spreadsheet rows, R(t)]
was calculated for each iteration as follows:
 | (15) |
where R(t0) is the number of rows representing the actual circulation lag time in the previous iteration, R(t)* is the number of rows equal to the calculated instantaneous steady-state circulation lag time [of duration (t-ti*)] in the current iteration and dt is the duration of each iteration (min).
Blood gases
Contents and partial pressures of blood gases were related by oxygen and
carbon dioxide equilibrium curves. Bohr and Haldane effects were omitted.
Temperature of the blood and tissues was assumed to be constant at 37°C.
For oxygen, the Hill equation was used:
 | (16a) |
 | (16b) |
where P50 is the PO2 at 0.5 fractional saturation, n is the Hill cooperativity coefficient, and SO2 is fractional saturation. The same relations hold for myoglobin, where n=1.
SO2 was related to O2
concentration (CO2) by:
 | (17) |
where CHb is the concentration of haemoglobin and ßHb is the haemoglobin O2 binding coefficient.
For carbon dioxide, a linear version of the carbon dioxide equilibrium
curve was derived from data for human blood
(Miyamura and Honda, 1978) and
it was assumed to be the same for Weddell seal blood and tissue fluids:
 | (18a) |
 | (18b) |
System controller
The ventilatory controller was based on Duffin's modification of the
`Oxford model' of respiratory control
(Cunningham et al., 1986;
Duffin et al., 2000),
consisting of additive drives from central and peripheral chemoreceptors
(feedback), and a central neural `behavioural' drive (feedforward) that is
independent of chemical stimuli. All respiratory drives were expressed in 1
min–1.
This model assumes that central and peripheral chemoreceptors have a
chemoreceptor threshold (Tc and Tp,
respectively) for PCO2, below which
chemoreceptors are functionally silent
(Duffin et al., 2000).
Chemoreceptor drives were assumed to increase as a linear function of
PCO2 above the respective chemoreceptor
thresholds (Tc and Tp). The slopes of
these relationships represent the central and peripheral chemosensitivities
(Sc and Sp, respectively). Chemical respiratory
drive (
chem) was computed
as the sum of central and peripheral chemoreceptor drives
(c and
p, respectively), and
affected ventilation only when above a threshold (chemical drive threshold,
Tchem). When chemical respiratory drive
(chem) fell below chemical
drive threshold (Tchem), ventilation was determined solely
by the behavioural drive
(n):
 | (19a) |
if chem >
Tchem,
 | (19b) |
if chem 
Tchem,
 | (19c) |
The chemoreflex threshold (T1) is the partial pressure
of CO2 at which chemical respiratory drive
(chem) is equal to chemical
drive threshold (Tchem). In this study,
n was set at user-defined
values during surface intervals and fell to zero during dives. The chemoreflex
threshold (T1) and chemical drive threshold
(Tchem) therefore both function as an `apnoeic threshold'
whenever behavioural drive
(n) is zero.
Central chemoreceptors were assumed to be (indirectly) sensitive to the
partial pressure of carbon dioxide in the brain tissue compartment
[PBCO2(t); see Lahiri and Forster
(2003) for a justification of
this assumption] and peripheral chemoreceptors were assumed to be sensitive to
PaO2 and PaCO2
in arterial blood flowing through the chemoreceptors [i.e. at time
(t-tc) after leaving the lung]:
if PBCO2(t) >
Tc,
 | (20a) |
if PaCO2(t-tc) >
Tp,
 | (20b) |
Central chemosensitivity (Sc) was a fixed parameter
(Table 1), but peripheral
chemosensitivity (Sp) was a variable
(Table 2), varying as an
inverse hyperbolic function of PaO2
(Duffin et al., 2000;
Mohan and Duffin, 1997):
 | (21) |
Reliable values for some respiratory control parameters
(n, Tc,
Tp, Sc, Sp, K, A) are
available only for adult male human beings. The corresponding values for an
adult Weddell seal were estimated as follows.
n, Sc and
Sp were estimated by defining a standard resting level of
ventilation for both human and seal, and expressing
n, Sc and K,
respectively, as multiples of standard ventilations. The value of A in Eqn 21
was assumed to be 15 mmHg, the same as the assumed lower critical
PaO2 for cerebral viability in seals
(Elsner et al., 1970).
It was assumed that there is a constant respiratory dead space volume in
series with the alveolar compartment of the lung. Alveolar ventilation
(A) was derived from total
ventilation () as follows:
 | (22) |
D is dead space
ventilation, and
 | (23) |
D,
respiratory tidal volume (VT) was assumed to be
constant.
Protocol
Standard model parameter values were derived from the literature or
estimated as described above for an average adult male Weddell seal
(Table 1). The primary
objective was to determine whether the model could simulate variations in
respiratory drive in a way that is consistent with the hypotheses outlined in
the Introduction. These hypotheses predict that net respiratory drive will
oscillate with amplitude large enough to induce apnoea. Furthermore, the
durations of the simulated apnoeic and eupnoeic intervals must correspond to
the range of durations reported for dive and surface intervals in freely
behaving seals.
The basic approach used in each simulation was to set model parameters to
desired `resting' values and, with the model forced to remain at the surface,
the system was allowed to reach a steady-state condition. The model was then
switched to enable dive cycles so that parameter values automatically assumed
`surface' values when ventilating, and `diving' values when apnoeic. Briefly,
beginning at the water surface, if chemical respiratory drive
(chem) fell below chemical
drive threshold (Tchem), a dive was initiated and model
parameters assumed `diving' values. When chemical respiratory drive
subsequently increased above the chemical drive threshold, the dive was
terminated and the model switched back to `surface' parameter values. These
studies were conducted with maximum dive depth set to 1 m to avoid any
confounding effects of depth. This paper therefore describes simulations of a
seal floating at the water surface and the effect of swimming to depth is to
be examined in a subsequent study. To avoid any transients associated with the
transition from steady state rest to diving mode, all analyses refer to dive
cycles occurring in the interval 65-135 min after the onset of simulated
diving behaviour.
An extensive series of simulations was conducted in which parameter values
were systematically varied, alone and in combination, in order to determine
the relative influence of each on respiratory stability. Only the most
relevant tests are reported: (i) the effects of changes in behavioural
respiratory drive, n
(hyperventilation), (ii) the effects of variations in chemoreflex
characteristics (Tc, Tp, Sc
and Sp), (iii) the effects of cerebral blood flow, (iv)
the effects of variation in the arterial and venous circulatory transfer
functions, (v) the role of oxygen and (vi) the role of the spleen.
Hyperventilation
To examine the effect of hyperventilation the model was initially designed
to include a timer function that enabled the user to specify a minimum
ventilatory interval (ts,min) between dives. This allowed
an analysis of combinations of intensity
(n) and duration
(ts) of hyperventilation. The duration of apnoea (i.e. a
shallow `dive', td) was measured as a function of
ts at each of several values of
n. It was found in these
tests that hyperventilation is necessary for apnoea, so a `standard' value for
the behavioural respiratory drive
(n=180 1 min-1)
was used during the surface intervals in the subsequent simulations unless
noted otherwise.
Chemoreflex parameters
When ts,min is used as in the above preliminary
simulations, the duration of surface intervals is an independent variable.
This was considered to be an unsatisfactory approach in the absence of any
well-defined physiological analogue to the arbitrary mathematical `timer'
(ts,min). Further tests were therefore conducted to
determine whether surface and dive durations could both be modeled as
dependent variables using conventional respiratory control mechanisms.
Specifically, on the basis of factors that are known to influence respiratory
stability during sleep-wake cycles (e.g.
Khoo, 2000), it was
hypothesized that differences between dive and surface parameter values of the
chemoreflex thresholds and/or chemosensitivities might provide a mechanism for
modulation of ts. The surface and diving values for
thresholds and sensitivities (slopes) of both peripheral and central
chemoreflexes were adjusted individually and in combination over a limited
range around the nominal resting levels. The role of the peripheral
chemoreceptors was tested by systematic changes in peripheral chemoreceptor
threshold (Tp) in combination with variation in the
peripheral chemoreceptor hypoxic asymptote (A). In these and all subsequent
simulations, the ts,min function was inactivated (i.e.
kept constant at zero) so that dive duration (td) and
surface intervals (ts) could both be assessed as dependent
variables. On the basis of these tests a `standard' set of chemoreflex
parameter values was defined and used in all subsequent simulations unless
noted otherwise.
Cerebral blood flow
Cerebral blood flow (B)
was manipulated by adjusting the model parameter values for cerebrovascular
CO2 gain (Gq in Eqn 8) and the minimum cerebral blood flow
(Bmin), separately and in
combination.
Circulatory transfer functions
The effects on simulated surface intervals (ts) and
dive durations (td) of variation in arterial and venous
transfer functions were examined by systematic adjustment of the two
components, circulatory lag time and time constant of the mixing function.
The circulatory lag time was dependent on blood volume and cardiac output
(Eqn 13). In these tests, blood volume was held constant and cardiac output
() was varied either during dives
(d) or during surface
intervals (s). Mean
d was manipulated in two
ways; by altering arterio-venous shunt flow
(a-)
during simulated dives or by altering the degree of cardiorespiratory coupling
via changes in
during
dives. Mean s was
manipulated by combined changes in maximum cardiac output
(max) and arterio-venous
blood shunt
(a-)
during surface intervals.
The time constants of arterial and venous mixing were adjusted by systematic changes in the effective volumes of the mixed circulatory sub-compartments (Vamix and Vvmix). Values of Vamix and Vvmix were varied separately and in combination over the range 2-50% of arterial and venous blood volumes, respectively, and the effects of this on simulated dive and surface durations were noted. On the basis of these tests, `standard' values for the effective volumes of the mixed circulatory sub-compartments (Vamix and Vvmix) were defined and used in all subsequent simulations (Table 1).
The role of oxygen
The oxygen concentration of inhaled air was adjusted over the range 10% to
100% O2 (FIO2=0.1-1.0).
This was then repeated after elimination of oxygen-sensitive mechanisms in the
model. First of all, peripheral chemoreceptor threshold
(Tp) was increased sufficiently to abolish peripheral
chemoreflex drive (p),
thereby simulating acute carotid body denervation (CBD). Secondly, the
cerebrovascular O2-sensitivity was deleted from Eqn 8 so that
cerebral blood flow was solely dependent on arterial
PCO2. Finally, alveolar volume at the start of
a dive was set to zero to eliminate any effect of O2 storage in the
lung compartment. With all of the above manipulations applied concurrently the
`local regulation' component of tissue compartment blood flow (Eqn 9) remained
as the only mechanism by which altered
FIO2 could have an effect on
simulated diving behaviour in this model.
Oxygen store (VO2store) was calculated for
the first iteration of a dive, and used in conjunction with the rate of oxygen
consumption during dives
(O2d) to
estimate the aerobic dive limit in the convention manner: ADL=
VO2store/O2d.
O2 content of the lung was calculated as the product of fractional
alveolar oxygen concentration and alveolar volume
(FAO2*VA),
O2 contents of arterial and venous blood were taken as the average
concentration over the number of spreadsheet rows corresponding to the current
arterial and venous circulatory lag times multiplied by the respective
arterial and venous blood volumes, and muscle O2 content was
calculated as the product of muscle O2 carrying capacity and
myoglobin fractional oxygen saturation.
The role of the spleen
All of the above simulations were carried out using blood volume
(Vb) and haemoglobin concentration (CHb) values
corresponding to a seal with spleen contracted. To examine the functional
significance of splenic contraction in the present model, standard diving
parameters (Table 1) were
entered with corrections to simulate an absence of splenic contraction:
Vb=76 1, CHb=0.15 kg 1–1. The
roles of Vb and CHb were examined separately and
in combination.
Cardio-respiratory responses
Diving behaviour, lung ventilation, cardiac output, heart rate, regional
blood flows, contents and partial pressures of O2 and
CO2 in blood and tissue compartments and the chemoreflex drives
were all calculated as dependent variables of the model. The dynamic responses
of these variables were plotted and their interactions examined.
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Results |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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Hyperventilation
As mentioned above, the model parameters shown in
Table 1 gave rise to a
dynamically stable control loop, and the model therefore did not develop
spontaneous oscillatory behaviour. Hence, hyperventilation induced by an
elevated feedforward `behavioural' respiratory drive
(n) was needed to force
chemical respiratory drive
(chem) below chemical drive
threshold (Tchem) and thereby initiate and sustain cycles
of apnoea (simulated dives) and ventilation (simulated surface intervals).
With the timer mechanism deactivated (ts,min=0),
surface intervals (ts) decreased from 2 min at moderate
behavioural respiratory drive
(n=60 l min-1)
to 1.3 min at high behavioural respiratory drive
(n=200 l min-1).
Similarly, dive duration (td) was short and only slightly
affected by intensity of hyperventilation, rising from 1.5 min at
n=60 l min-1 to
3.1 min at n=200 l
min-1.
The ts,min function was then used to examine the effect
of increased duration of hyperventilation on subsequent dive duration. Dive
duration (td) was found to be influenced by both duration
(ts,min) and intensity
(n) of hyperventilation.
For surface intervals less than 3 min, no amount of hyperventilation (up to
max) could induce long
duration dives. At any given
n there was a critical
ts,min that marked an abrupt increase in
td, and this critical ts,min decreased
with increasing n.
Chemoreflex characteristics
Central chemoreceptor threshold (Tc) was found to be
the only factor that could, when manipulated on its own, induce long-period
dive cycles. Specifically, long duration simulated dives occurred when the
central chemoreceptor threshold was lower during surface intervals than during
dives (Tc). There was a critical
Tc (–3.4 mmHg) that marked a transition
between short-period and long-period dive cycles
(Fig. 2).
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When adjusted individually, the central and peripheral chemosensitivities
(Sc and Sp, respectively), and peripheral
chemoreceptor threshold (Tp), had negligible effects on
simulated dive and surface intervals. Furthermore, combinations of changes in
peripheral chemoreceptor threshold (Tp), and central and
peripheral chemosensitivities (Sc and Sp)
without concurrent changes in central chemoreceptor threshold
(Tc) had little effect on simulated dive and surface
intervals. However the peripheral chemoreflex was not completely without
influence because the Tc mechanism was found to be
influenced by peripheral chemoreceptor threshold (Tp)
(Fig. 2). Specifically, the
effect of Tc on simulated diving behaviour was
attenuated when Tp was lower than the nominal resting
value (i.e. when the peripheral chemoreceptors were more active).
Variation of the peripheral hypoxic asymptote (A) in the range 15-30 mmHg
O2 had only a small negative linear effect on dive and surface
intervals. For example, at the standard Tc and
Tp (see below), ts decreased by 2.1 s
and td decreased by 7.9 s per mmHg increase in A. Using
these preliminary data as a guide, `standard' chemoreflex parameter values
were defined and used in all subsequent simulations, except where noted
otherwise. Thus, the resting values (see
Table 1) for
Tp, Sp, A and Sc were used
for both dives and surface intervals, and the resting Tc
was used during dives together with a Tc of
–5.1 mmHg during surface intervals. These chemoreflex parameter values
substituted for the ts,min function and allowed both
ts and td to be treated as dependent
variables in all subsequent simulations.
Cerebral blood flow
When cerebral blood flow
(B) was constrained to
remain constant at resting levels, simulated dive and surface intervals were
short (1.4 min and 3.4 min, respectively). When this constraint was relaxed,
cerebral blood flow tended to rise during apnoea and fall during
hyperventilation. Cerebrovascular CO2 chemosensitivity (Gq)
affected the rate of change in cerebral blood flow, while minimum cerebral
blood flow (Bmin) imposed a
limit on the maximum possible decline during hyperventilation-induced
hypocapnia. There were found to be thresholds in both parameters marking
abrupt changes between long and short simulated dive and surface intervals.
Long-period dive cycles occurred only if Gq exceeded a threshold of
0.035Brest
mmHg–1, together with
Bmin < 45% of
Brest.
Circulatory transfer function
Deletion of the arterial mixed sub-compartment from the model had
relatively minor effects on simulated dive and surface intervals. In contrast,
the venous mixed sub-compartment was found to be a necessary feature of the
model, because without it blood gases and chemoreflex drives displayed
unrealistic step transients associated with the large and rapid changes in
ventilation and cardiac output over the course of a dive cycle. Nevertheless,
the quantitative effects of variations in the time constants of the venous
mixing function on simulated dive and surface intervals were small. Increases
in Vamix and Vvmix both caused surface
intervals to increase by 0.05 min l–1 and dive durations to
increase by 0.2 min l–1. Vamix and
Vvmix had additive effects.
Systematic variation of mean cardiac output over the surface interval
(s) (with mean diving
cardiac output, d, held
constant) had substantial effects on simulated dive (td)
and surface (ts) intervals
(Fig. 3). There was a threshold
value of s, below which
dive cycles were always short (ts 
3.5 min and
td 5 min) and independent of
s. Above the threshold,
ts and td increased to an asymptote
with further increases in
s. In addition,
Fig. 3 shows that the effect of
suprathreshold s was
dependent on the intensity of hyperventilation
(n). As
n increased, the
s threshold increased,
asymptotic td increased slightly, and asymptotic
ts decreased substantially.
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Systematic variation of mean cardiac output during dives
(d) with
s held constant had
non-linear effects on both simulated dive and surface intervals. Manipulation
of d by varying the
arterio-venous shunt flow
(a-v) caused damped
oscillations (period approximately 6 min) in diving blood gas levels that gave
rise to concomitant oscillations in chemical respiratory drive
(chem). This in turn led to
fluctuating relations between ts and
td vs d
(Fig. 4). In contrast, when
d was varied by changes in
cardiorespiratory coupling (i.e
see Eqn 11)
the rapid oscillations in blood gases were absent, and dive and surface
intervals were both linearly related to
indicating
inverse hyperbolic relations (see Eqn 9) between simulated dive and surface
intervals vs d
(Fig. 4). Arterio-venous blood
shunt flow during dives caused a general increase in simulated dive and
surface intervals at all but the lowest
d
(Fig. 4).
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The role of oxygen
With standard `control' parameter values, simulated dive and surface
intervals were reduced in hypoxia
(FIO2<0.21). For example, simulated dive and
surface intervals were reduced by 55% and 52%, respectively, when fractional
inspired oxygen concentration (FIO2)
was decreased from 0.21 to 0.1. When
FIO2 was less than 0.1, dives were
aborted due to PaO2 falling below the lower critical level
for cerebral viability (assumed to be 15 mmHg). At
FIO2 in the range 0.1 to 0.15,
simulated diving was unsteady, with long-term periodic modulation of simulated
dive and surface intervals over two or more dive cycles. Simulation of
hyperoxia (FIO2>0.21) had only
slight effects on simulated dive and surface intervals. For example, dive
duration increased by 7% when FIO2
increased from 0.21 to 1.0
Elimination of peripheral chemoreflex drive by increasing peripheral chemoreceptor threshold (Tp) to 47.6 mmHg modified the above responses to hypoxia and hyperoxia. Under these conditions, which were intended to mimic acute carotid body chemoreceptor denervation (CBD), there was an overall increase in both dive and surface intervals, as predicted from Fig. 2, and the hypoxia-induced decreases in simulated dive and surface intervals were strongly attenuated, but not abolished. Dive cycles continued to exhibit long-term (multiple dive cycle) periodicity during hypoxia (FIO2=0.1–0.15) in the absence of peripheral chemoreflex input.
Elimination of the cerebrovascular sensitivity to arterial blood oxygen saturation (see Eqn 8) resulted in stable dive cycles at all FIO2 above 0.1, and reductions in simulated dive and surface intervals, an effect that progressively disappeared in hyperoxia. Furthermore, cerebrovascular insensitivity to O2 partially reversed the effects of CBD alone, in that the CBD-induced overall increases in simulated dive and surface intervals were greatly reduced when cerebral blood flow was simultaneously rendered insensitive to arterial oxygen.
Finally, setting alveolar volume (VA) at the start of
the dive to zero had the effect of causing decreases in simulated dive and
surface intervals at all FIO2, an
effect that was also apparent when alveolar collapse was imposed concurrently
with CBD and cerebrovascular O2 insensitivity, leaving `local'
control of peripheral blood flow as the only functional
O2-sensitive mechanism remaining in the model. Under the latter
conditions, dive cycles were stable but the effects of
FIO2 on simulated dive and surface
intervals were otherwise virtually identical to control. This indirect effect
of O2 on dive duration (td) is illustrated in
Fig. 4, where hypoxia per
se can be seen to have little effect on the td vs
d relation.
Under standard control conditions, with FIO2 at 0.21, VO2store was calculated to be 43.7 1 at the onset of a simulated dive and, assuming that all of the O2 is available for metabolism, calculated ADL was 24.6 min.
The role of the spleen
Splenic contraction was found to have a marked effect on simulated diving
behaviour in this model, an effect that interacted with the cardiovascular
diving response. Fig. 4 shows
that splenic contraction altered the relations between simulated dive and
surface intervals vs diving cardiac output
(d). Splenic contraction
caused increases in both simulated dive and surface intervals, and this effect
was greater at lower d.
Simulations were compared at constant
d (20.8 1 min-1)
with all four combinations of blood volume (Vb=96 and 76 1) and blood
haemoglobin concentration (CHb=0.26 and 0.15 kg
1–1). There were direct correlations of simulated dive and
surface intervals to both Vb and CHb, such that
simulated dive and surface intervals were each directly proportional to total
blood haemoglobin content (VbxCHb).
Analysis of the integrated responses of blood and tissue gas tensions
determined that the effect of haemoglobin concentration was mediated by
variation in the rate of change of brain tissue
PCO2 during the surface interval due to changes
in cardiac output. The latter occurred as a consequence of
CHb-related variation in O2 delivery to the
tissue compartments and hence in the drive for peripheral blood flow. The
effect of blood volume was mediated by altered rates of change in brain tissue
PCO2 due to Vb-induced variation in
cardiovascular lag times and mixing time constants during both simulated dives
and surface intervals.
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Discussion |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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This model proposes that diving behaviour may entrain to oscillations in respiratory drive, the period, duty cycle and amplitude of which are susceptible to modification via numerous factors. The model requires that respiratory drive be perturbed by hyperventilation, which causes an otherwise stable chemoreflex loop to oscillate; an example of induced respiratory instability. The temporal characteristics of the oscillating model system were found to be dependent on several key assumptions that will require empirical verification. These include differences between `diving' and `surface' values of the behavioural respiratory drive and central chemoreceptor threshold, and appropriate values for cerebrovascular chemosensitivity and cardiorespiratory coupling.
The model simulations demonstrated that active inhibition of breathing is
not necessary to sustain apnoea during shallow dives up to the ADL in this
species. However, the model does not preclude active inhibition of breathing,
and indeed such inhibition will be required during the ascent phase of deeper
dives. This model proposes that positive chemical respiratory drive triggers
the decision to return to the water surface, and seals at depth must obviously
delay respiration until the ascent phase is completed. This issue is to be
addressed in more detail in a subsequent paper. Furthermore, it is highly
likely that various other factors (emotional, volitional, physiological, etc)
may modify diving behaviour (Fedak and
Thompson, 1993) leading to delays in the termination of some
individual dives, and active inhibition would be necessary under those
circumstances. Nevertheless, the present study is consistent with the
suggestion that in the absence of such extrinsic stimuli the animals will tend
to remain at the surface as long as chemoreflex drive is positive, and they
will usually remain submerged as long as the chemoreflex drive remains below
the apnoeic threshold. In other words, diving behaviour is modeled as
repetitive central apnoea with hyperventilatory surface intervals. Model
simulations indicate that adjustment of the levels of hyperventilation and
tachycardia at the water surface, and bradycardia during dives, provide
powerful mechanisms by which a diving seal can adjust the dynamic
characteristics of the cardiorespiratory system in the short term. Regulation
of blood volume via splenic contraction represents an additional
potential mechanism for longer-term regulation in Weddell seals. It is
suggested on the basis of these results that diving behaviour and respiratory
control are `tuned' in such a way that the seals essentially ride an
adjustable wave of respiratory drive
(Woodin and Stephenson, 1998).
This study therefore builds upon the ADL concept by using a more detailed
model of the cardiorespiratory control system, enabling quantitative
evaluation of the roles of a variety of physiological factors in the control
of individual dives.
Using various combinations of physiologically realistic parameter values,
simulated surface intervals (ts) varied from 1.33 to 10.66
min and simulated dive times (td) varied from 1.46 to
27.41 min. This corresponds well to the observed ranges of surface intervals
and dive durations in unrestrained adult Weddell seals. For example, in the
classic study by Kooyman and colleagues
(Kooyman et al., 1980),
time-depth recorders were deployed on 22 free-ranging seals. Over 97% of 4601
dives were less than 26 min in duration, and over half were less than 10 min.
Fewer data are available for surface times of freely diving Weddell seals, but
most reported observations are less than 10 min
(Burns, 1999). The aerobic dive
limit (ADL), measured or calculated in various ways, generally falls within
the range 18-25 min for adult Weddell seals, and this was also the case in the
present model. The model simulations suggest that several physiological
factors may influence surface intervals and dive durations and the final
behavioural pattern is determined by quantitative variations in the
combination of these factors. The following discussion summarizes and
integrates the key components of the model.
Dynamic modeling approach
The design of the model is based on previously published attempts to
understand the physiological basis of periodic breathing, Cheyne-Stokes
breathing and sleep apnoea in human beings
(Cherniack and Longobardo,
1986; Khoo, 2000;
Khoo et al., 1991,
1982; Longobardo et al.,
1966,
1982). However, application of
this approach to the control of diving required several modifications to
accommodate the profound cardiovascular responses that sometimes occur during
diving behaviour. The model described here also differs substantially from
that described by Davis and colleagues
(Davis and Kanatous, 1999;
Davis et al., 2004), as do the
objectives of the two studies. Specifically, the present model includes an
external gas exchanger (lung), it emphasizes cardio-respiratory control
mechanisms, and it treats the system as operating in an explicitly non-steady
state during diving behaviour. In addition to blood and tissue gas contents,
respiratory and cardiovascular convection are dependent variables in the
present model. Diving behaviour, or more specifically the `decisions' to begin
a dive and to begin the ascent to the </
