The effect of myoglobin concentration on aerobic dive limit in a Weddell seal

Weddell seals and other marine mammals exhibit physiological adaptations and behavioral strategies that increase dive duration. These include an elevation in total body oxygen stores through increases in blood volume,hematocrit (Hct; the percentage of blood volume occupied by red blood cells)and muscle myoglobin (Mb) concentration. In addition, marine mammals use efficient modes of locomotion (e.g. gliding during descent, stroke-and-glide swimming) that keep oxygen consumption low during diving(Williams et al., 2000; Williams, 2001). For Weddell seals, these physiological adaptations and behavioral strategies result in an aerobic dive limit (ADL) of about 20 min(Davis and Kanatous, 1999;Ponganis et al., 1993a; Kooyman et al.,1980).

If body oxygen stores are the primary physiological limit to dive duration,why are they not larger? During the evolution of marine mammals, what physiological factors may have set the upper limit to blood volume, Hct and muscle Mb concentration? Weddell seals have a blood volume as high as 21% of their body mass (Ponganis et al.,1993), almost three times larger than predicted for a terrestrial mammal of the same size (Stahl,1967). The upper limit to blood volume may be a compromise between increasing oxygen stores and the resultant increase in body mass or abdominal volume.

The Hct of Weddell seals (ca. 60%), which is 1.5-times higher than in most terrestrial mammals, increases blood oxygen stores and maintains convective oxygen transport to organs and tissues as the partial pressure of oxygen in the blood decreases during diving. However, the increased Hct also increases blood viscosity, circulatory resistance and heart work(Elsner and Meiselman, 1995). As a result, the large spleen of Weddell seals sequesters red blood cells,lowers the hematocrit, and decreases blood viscosity when they are at the surface. Only when they begin diving does the spleen contract and release the red blood cells into the circulation, which increases the hematocrit while heart rate is reduced due to the dive response(Hurford et al., 1996). A hematocrit greater than 60% would further increase blood viscosity, increase heart work, and could decrease rather than increase convective oxygen transport. (Hedrick and Duffield, 1986). Consequently, the elevated Hct of Weddell seals and other marine mammals may be at its physiological maximum for optimizing blood oxygen storage and convective oxygen transport.

The concentration of Mb in the skeletal muscles of Weddell seals is about 10-times greater than in most terrestrial mammals(Snyder, 1983). Oxygen bound to Mb represents one-third of the total oxygen store in Weddell seals, so it is a major factor in setting the ADL (Davis and Kanatous, 1999; Kooyman and Ponganis, 1998). However, it is not clear what physical or physiological factors may have set the maximum concentration of muscle Mb. The objective of this study was to model the effects of different muscle Mb concentrations on the ADL of Weddell seals. Specifically, we wanted to know how increasing or decreasing Mb concentration beyond normal levels would affect the ADL. Although lowering the Mb concentration would obviously decrease the ADL, would increasing the concentration automatically increase it? To answer this question, we used a previously published model of convective oxygen transport and tissue oxygen consumption(Davis and Kanatous, 1999). We ran the model at different myoglobin concentrations for various levels of muscular exertion under postabsorptive and postprandial conditions to determine their effect on ADL.

This model considers only dives that are within the seal's ADL(Kooyman et al., 1980;Ponganis et al., 1993a). The term ADL was used in this model to describe the maximum duration of an aerobic dive under specific conditions. The basal contribution of anaerobic metabolism in harbor seals has been shown to constitute approximately 2% of ATP production in a resting state and 1% during active swimming (Davis et al.,1991). For this model, this small basal contribution of anaerobic metabolism is ignored, and tissues are considered aerobic as long as there is no increased reliance on anaerobic metabolism resulting in an increase in blood lactate over resting levels. While terms such as diving lactate threshold (DLT) and calculated aerobic dive limit (cADL) are useful for certain applications (Butler and Jones,1997), they were not applicable to all conditions used to terminate a dive in this model. DLT was not used because increased blood lactate resulting from anaerobic metabolism was not necessary to terminate a dive in this model. The term cADL is historically used to denote a calculation of aerobic dive limit based on total useable oxygen stores divided by whole body metabolism. While this model does calculate an ADL, it does so through modeling of blood flow and metabolism in individual tissues, which can produce vastly different results than whole body calculations in some metabolic states. The rate of oxygen consumption in the tissues is maintained until convective oxygen delivery falls below a critical level and endogenous oxygen stores (skeletal muscle only) are depleted, resulting from a combination of ischemic and hypoxic hypoxia. When any organ (e.g. splanchnic organs) or tissue (e.g. skeletal muscle) no longer has sufficient oxygen to support aerobic metabolism (i.e. the point at which anaerobic energy metabolism commences), then the ADL has been reached and the dive is terminated.

Organ and tissue masses were based on published values for a 450 kg adult Weddell seal (Fujise et al.,1985; Zapol et al.,1979) as described by Davis and Kanatous in their table 1(Davis and Kanatous, 1999). The resting V̇_O2values for Weddell seal organs and tissues were estimated from the metabolic mass-adjusted V̇_O2for the equivalent organs of a human or rat(Diem and Lentner, 1970; Field et al., 1939; Kety, 1957). The basal, whole body V̇_O2 (897 ml O₂ min^–1 or 2.0 ml O₂min^–1 kg^–1) was calculated by combining individual organ and tissue metabolic rates. The calculated basal metabolic rate was similar to the minimum metabolic rates measured for adult Weddell seals during rest or sleep (Castellini et al., 1992b; Ponganis et al., 1993a; Williams et al., 2004).

Resting heart rate (f_H) (51.5 beats min^–1), cardiac output(V̇b) (42.7 l min^–1)and stroke volume (V_S) (0.83 l) were based on measured values for Weddell seals (Zapol et al.,1979). During a simulated dive, V̇b was varied from 19–131% of resting levels [(see Davis and Kanatous,1999), table 2]. For brevity, we hereafter refer to these percentages of resting, predive V̇b as percent V̇b (e.g. 19%V̇b). When V̇b was below resting levels, most of the reduction resulted from a decrease in f_H (i.e. bradycardia). However, based on studies of seals during forced submergence and voluntary dives (Blix and Folkow,1983; Kjekshus et al.,1982; Ponganis et al.,1990; Sinnet et al., 1978; Zapol et al., 1979), V_S was also reduced as f_H declined. The maximum reduction in V_S in the model was 25% of the resting value and was proportionate to the reduction in f_H. The reduction in cardiac output (i.e. the severity of the dive response) was immediate and remained constant throughout a dive. An`anticipatory' increase in V̇b toward the end of a dive was not included in the model. Except for the brain, where circulation was always maintained at resting levels, we assumed that blood flow to the rest of the body decreased proportionately with V̇b during a dive due to reduced V̇b and peripheral vasoconstriction(Blix et al., 1976; Elsner et al., 1964). Peripheral vasoconstriction was assumed to occur in the large arteries (e.g. the renal artery), making it independent of tissue level metabolic dilators that affect arterioles (White et al.,1973). Because vasoconstriction was assumed to occur high in the vascular tree, blood flow was not adjusted independently to individual tissue beds.

Body oxygen stores were confined to the blood and skeletal muscle in this model, since no oxygen storage capability exists in the splanchnic organs(Dodd et al., 1987) and the heart represents less than 2% of the total muscle mass. We assumed that lung oxygen was not available during a dive due to the complete functional pulmonary shunt that occurs in Weddell seals at pressures greater than 3–5 atmospheres (2280–3800 mmHg; 1 mmHg=0.133 kPa; approximately 30–50 m deep) (Falke et al.,1985; Reed et al.,1994). Even if lung oxygen were available during a dive, it represents only 5% of the total body oxygen store in Weddell seals(Kooyman and Ponganis,1998).

The arterial blood oxygen saturation (Sa_O2)and venous blood oxygen saturation (Sv_O2) were calculated for the blood of each vascular bed as the quotient of their respective oxygen concentrations (Eqn 6–9) and aβ _BO2 of 348 ml O₂ l^–1blood. The arterial (Pa_O2) and venous(Pv_O2) blood oxygen partial pressures were calculated from their respective Sa_O2 and Sv_O2 using two polynomial equations fitted to the oxy-hemoglobin dissociation curve (P₅₀=26.9 mmHg=0.133 kPa) for adult Weddell seals (Qvist et al., 1981).

Evidence obtained during the forced submergence of harbor seals and Weddell seals indicates that Q̇_B is generally maintained and V̇_BO2 does not decline (Blix and Folkow, 1983; Kerem and Elsner, 1973; Zapol et al., 1979). In this model, we assumed that Q̇_Band V̇_BO2 remained at resting levels during a dive and were independent of V̇b. We also assumed that the minimum Pa_O2 and Pv̄_O2 for normal cerebral metabolism and function were 22 mmHg(Sa_O2=38%) and 18 mmHg(Sv̄_O2=27%),respectively. This is comparable to the average Pa_O2 (24.5±2.86 mmHg; mean ±s.d., N=7) in Weddell seals 2 min before surfacing and to the end tidal P_O2 (24 mmHg) of the first exhalation(assuming that this approximates arterial P_O2)after 17 min aerobic dives (Ponganis et al., 1993a; Qvist et al., 1986). As a result, the model terminated a dive if Pa_O2decreased below 22 mmHg in the model. However, the Pa_O2 of blood perfusing the brain was generally not a consideration in determining ADL.

We assumed that Q̇_H and V̇_HO2 changed proportionately with V̇b(Blix and Folkow, 1983; Blix et al., 1976; Kjekshus et al., 1982). When convective oxygen transport to the myocardium changed during a dive, it was proportional to the change in heart work, and the myocardium always received sufficient blood oxygen to maintain aerobic metabolism.

Q̇_M was also assumed to change proportionately with V̇b. Oxygen transported to the muscles in the blood was always used (up to a maximum E_BO2 of 0.8) before oxygen bound to Mb because of the lower affinity of Hb for oxygen(Schenkman et al., 1997). Oxygen not provided by the blood was obtained from oxymyoglobin stores to meet V̇_MO2requirements. V̇_MO2 was assumed to be independent of Q̇_M as long as the combination of convective oxygen transport and oxymyoglobin stores was sufficient to meet metabolic demand. If at any time the combination of these two were no longer sufficient to maintain aerobic muscle metabolism, the dive was terminated.

Postabsorptive V̇_O2(3.73±0.88 ml O₂ min^–1kg^–1) and postprandial V̇_O2(5.24±0.88 ml O₂ min^–1kg^–1) during aerobic dives were based on indirect calorimetry measurements by Williams et al. for foraging and non-foraging Weddell seals(Williams et al., 2004). We assumed that the average difference in V̇_O2 (1.51 ml O₂ min^–1 kg^–1 or 680 ml O₂ min^–1 for a 450 kg seal) between postabsorptive and postprandial dives of 7–23 min in duration resulted from the metabolic cost of prey warming, digestion, absorption and assimilation, which we refer to as the Heat Increment of Feeding (HIF). This increase in V̇_O2 was added to the postabsorptive V̇_SRCO2 to give a postprandial V̇_SRCO2 of 1234 ml O₂ min^–1 (a 2.2-fold increase). We assumed that the V̇_SRCO2 was maintained as long as: (1) convective oxygen transport was sufficient to support oxygen demand, (2) E_BO2 did not exceed 0.8 and (3) Pa_O2 was greater than 22 mmHg(Kvietys and Granger, 1982; Schlichtig et al., 1992).

The model was run on a standard spreadsheet program (Quattro Pro for Windows Version 6.0, Novell Applications Group, Orem, UT, USA) for eight levels of V̇b, sixteen levels of V̇_MO2 up to a maximum whole-body V̇_O2 of 10.7 ml O₂ min^–1 kg^–1 and four different Mb concentrations under postabsorptive conditions, which produced 512 combinations. These were then compared to postprandial conditions for the normal and elevated Mb concentration adding an additional 256 combinations. The general procedure was to select a Mb concentration, set the V̇b at a particular level (e.g. 37% of the resting level) and then vary the V̇_MO2 from 1 to 16 times the resting level. This process was then repeated for each Mb concentration and V̇b. V̇_O2 for the four vascular beds and the entire body were calculated for each combination. The ADL was reached and the dive terminated when: (1) any non-muscle organ or tissue did not receive sufficient oxygen through convective oxygen transport to maintain aerobic metabolism, (2) convective oxygen transport and oxymyoglobin stores were no longer sufficient to maintain aerobic muscle metabolism, or (3) when the Pa_O2 fell below 22 mmHg.

The role of V̇b in optimizing the ADL at different levels of muscle metabolism has been described(Davis and Kanatous, 1999). Briefly, the ADL decreases in a non-linear fashion with increasing V̇_MO2 for different levels of V̇b(range=19–131% of resting levels)(Davis and Kanatous, 1999; Davis et al., 2004) (Figs 2, 3). For each level of V̇_MO2, there is an optimal V̇b that gives a maximum ADL,and this optimal V̇b increases (i.e. the dive response is less pronounced) as V̇_MO2 increases[(see Davis and Kanatous,1999), fig. 4 and table 4]. Since the ADL is inversely proportional to V̇_MO2 (assuming a constant level of blood and muscle oxygen depletion), the optimal V̇b decreases as the ADL increases [(see Davis and Kanatous, 1999), fig. 5].

In the postabsorptive state, the resting ADL (28 min) was independent of Mb concentration (Fig. 2). At a resting level of V̇_MO2, the lowest level of convective oxygen transport(V̇b=19%) was still sufficient to supply 97% of the oxygen needed by the skeletal muscle. As a result, very little Mb oxygen (ranging from 21% to 1% of endogenous oxymyoglobin for concentrations from 5 to 108 mg g^–1, respectively) was used while resting submerged, and it was not a factor that limited the ADL (Tables 1, 2, 3, 4). The only way to increase the use of Mb oxygen at rest was to decrease convective oxygen transport even further (i.e. V̇b<19%). However, when we ran the model at a V̇b of 9%, the ADL decreased because convective oxygen transport to the splanchnic organs and kidneys was insufficient. Hence, at rest there was no optimal V̇b that provided sufficient oxygen delivery for the kidneys and splanchnic organs while utilizing more Mb-bound oxygen, regardless of the Mb concentration. As a result, there was no difference in ADL for Mb concentrations of 54 and 108 mg g^–1until V̇_MO2exceeded 3-times resting.

At muscle Mb concentrations of 5 and 27 mg g^–1, the postabsorptive ADL decreased in a curvilinear fashion with increasing V̇_MO2 and whole body V̇_O2. At normal and elevated Mb concentrations, the ADL decreased in a curvilinear fashion with the exception of a common plateau at 24 min for V̇_MO2 of 2- to 3-times resting and 2- to 5-times resting for these two Mb concentrations,respectively (Fig. 2). At these low levels of V̇_MO2, the ADL was limited by blood oxygen stores, and Mb oxygen was not a limiting factor(Tables 3 and 4). These two curves diverge at higher levels of exertion as muscle oxygen stores are consumed and contribute significantly to setting the ADL. Only when V̇_MO2 exceeded 3-times resting did an increase in the Mb concentration above 54 mg g^–1 increase the ADL.

Based on the findings of Williams et al.(Williams et al., 2004), we assumed an average postabsorptive diving V̇_O2 of 3.8 ml O₂ min^–1 kg^–1, which was equivalent to a V̇_MO2 of 5-times resting in our model. At this routine level of diving metabolism, a reduction of Mb concentration from 54 mg g^–1 to 27 mg g^–1 and 5 mg g^–1 reduced the ADL from 18 min to 12.7 min (29% reduction) and 11.0 min (39% reduction), respectively. Doubling the normal Mb concentration increased the ADL 33% from 18 to 24 min(Fig. 2).

For all four Mb concentrations, the optimal V̇b (i.e. the V̇b that gave the maximum ADL) increased as muscular exertion increased (Fig. 3). The optimal V̇b increased more quickly with increasing levels of exertion (i.e. the slope of the trend line was greater) for low muscle Mb concentrations compared to normal and elevated Mb concentrations. As Mb increased, the optimum V̇b for each level of V̇_MO2 decreased. For example, at the average diving V̇_MO2 of 5-times resting, the optimal V̇b at Mb concentrations of 5, 27, 54 and 108 g Mb kg^–1 were 75%, 56%,37% and 19% of resting levels, respectively. As Mb increases, V̇b and muscle blood flow must decrease(i.e. more pronounced dive response) for the muscle to fully use this Mb bound oxygen.

At a V̇_MO2 of 5-times resting for normal and elevated Mb concentrations, convective oxygen transport at the optimal V̇b was insufficient to support the aerobic metabolic needs of the muscle. As a result, muscle Mb oxygen stores were used from the beginning and throughout the dive (Fig. 4). In contrast,the optimal V̇b for reduced Mb concentrations was greater (i.e. less pronounced dive response), resulting in increased convective oxygen transport to the muscles and a delay in the use of Mb oxygen until well into the dive (7 min and 1.33 min for Mb concentrations of 5 and 27 mg g^–1, respectively). With optimal matching of V̇b to V̇_MO2, almost all myoglobin oxygen was consumed at this routine level of exertion regardless of myoglobin concentration.

Under postprandial conditions, the ADL decreased at all levels of exertion because of the increased oxygen consumption of the splanchnic organs associated with prey warming, digestion and assimilation. At a routine V̇_MO2 of 5-times resting and normal Mb concentration, the postprandial ADL (12 min) was 33%less than under postabsorptive conditions(Fig. 5). The convective oxygen transport needed by the splanchnic organs required a V̇b that was not optimal for the complete use of muscle oxygen at a routine diving V̇_MO2 of 5-times resting. Not until V̇_MO2 exceeded 7-times resting did this level of perfusion allow for complete utilization of muscle oxygen stores, and Mb oxygen became limiting to the ADL(Fig. 5 and Table 5). As a result, doubling the Mb concentration did not increase the ADL until the level of muscular exertion exceeded 7-times resting. Diving at routine levels of muscular exertion in a postprandial state resulted in convective oxygen transport and not oxy-myoglobin limiting the ADL. Based on the results from our model,digesting and assimilating food while diving decreased the ADL for two reasons: (1) increased splanchnic consumption of blood oxygen and (2) the increased convective oxygen transport needed by the splanchnic organs resulted in a V̇b that was not optimal for the complete use of muscle oxygen. As a result, the model indicated that there was no advantage in having a higher than normal myoglobin concentration during postprandial dives at routine levels of V̇_MO2.

Due to myoglobin's high affinity for oxygen (p50=2–3 mmHg)(Schenkman et al., 1997)compared to Hb (p50=27 mmHg) (Qvist et al., 1981), it is an endogenous oxygen store for muscle only. To use this source of oxygen, the muscle must become hypoxic by reducing convective oxygen transport. This not only decreases the muscle P_O2 so that the oxygen dissociates from myoglobin, but also reserves more blood oxygen for other tissues. The first publication using this model (Davis and Kanatous, 1999) showed the importance of adjusting cardiac output and convective oxygen transport to muscle according to the level of exertion,so that the total oxygen available in the muscle and blood was used by the end of a dive. As the level of muscular exertion increased, the dive response was less pronounced and convective oxygen transport to skeletal muscle (and other peripheral organs and tissues) increased. To maximize the ADL, both oxygen stores had to be depleted simultaneously so that neither was singly responsible for limiting aerobic dive duration.

In a postabsorptive resting state, the ADL was independent of Mb concentration from 5–108 mg myoglobin g^–1 muscle(Fig. 2). The model showed that the V̇b needed to maintain resting metabolism in the splanchnic organs (19%) resulted in an over-perfusion of the skeletal muscle so that almost all (97%) of the oxygen used by the muscles at rest was supplied by convective oxygen transport in the blood. Greater utilization of Mb oxygen would require less convective oxygen transport to skeletal muscle. However, further reduction in V̇b (9%) resulted in insufficient convective oxygen transport to the splanchnic organs and reduced the ADL.

At a routine diving V̇_MO2 of 5-times resting, the postabsorptive ADL increased with higher Mb concentrations(Fig. 2). In addition, Mb concentration was negatively correlated with optimal V̇b for a dive(Fig. 3). Higher Mb concentrations (54 and 108 mg g^–1) required a greater reduction in cardiac output (more profound dive response). The resultant reduction in convective oxygen transport to muscles decreased the muscle P_O2 (i.e. made the muscle hypoxic) so that myoglobin oxygen was used throughout the dive(Fig. 4).

At a V̇_MO2 of 1 to 7-times resting in a postprandial state, the V̇b required to maintain the elevated aerobic metabolism in the splanchnic organs resulted in an over-perfusion of the skeletal muscle, which caused the incomplete use of Mb oxygen stores(Table 5). Inefficient use of muscle oxygen stores as well as increased use of blood oxygen for digestion and assimilation resulted in blood oxygen limiting the ADL in the postprandial state until V̇_MO2exceeded 7-times resting (Fig. 5 and Table 5). As a result, the doubling of Mb concentration did not increase the ADL under postprandial conditions until the level of V̇_MO2 exceeded 7-times resting, which is 40% higher than the routine level of exertion.

The results of this model showed that an increase in the Mb concentration increased the ADL at a routine diving V̇_MO2 under postabsorptive conditions (Fig. 2). However, for the same V̇_MO2 under postprandial conditions, the convective oxygen transport needed for digestion and assimilation required a V̇b which resulted in an over-perfusion of the muscle and incomplete use of muscle oxygen stores at routine levels of exertion (i.e. <7 times resting V̇_MO2)(Fig. 5 and Tables 5, 6). Castellini et al. stressed the importance of integrating physiology and behavior in considering the biology of diving (Castellini et al.,1992a). To determine what selective pressures might affect myoglobin concentration, it is important to consider the way Weddell seals routinely dive.

Davis et al. classified Weddell seal dives into four types(Davis et al., 2003). Type 1 were feeding dives with a mean duration of 15.0 min, and these accounted for 14% of all dives made and 29% of total time submerged. Given the assumptions regarding HIF, the postprandial ADL (12 min) at a routine level of exertion calculated by our model agrees well with average duration of feeding dives reported (Davis et al., 2003). Types 2 and 3 dives were relatively short in duration (mean=3.6 min and 7.9 min, respectively) and were rarely associated with feeding. Together these dives accounted for 72% of dives being made. The average duration of these dive types are well below our estimated postabsorptive ADL of 18 min and are not limited by the physiological constraints of the oxygen stores, but by behavior.

Type 4 dives were long in duration (average=24.7 min), appeared to be exploratory (non-feeding) dives, and accounted for 14% of all dives. This dive type exceeds our estimated postabsorptive ADL of 18 min and relies significantly on anaerobic metabolism. Our model indicates that an increased myoglobin concentration would prolong aerobic metabolism for this type of dive. However, these long duration dives rarely occur in free-diving Weddell seals (Kooyman, 1980).

It appears that dives of the type and duration in which an increase in myoglobin concentration would increase the ADL are rare under normal diving behavior. While an increase in myoglobin would prolong aerobic metabolism during some long duration, postabsorptive dives, it does not appear to limit the ADL in the majority of natural dives (i.e. Types 1, 2 and 3). Weddell seals make the majority of their feeding dives in bouts of many dives with short recovery periods on the surface(Castellini et al., 1992a; Kooyman et al., 1980). As a result, many of these feeding dives probably occur in the postprandial condition. Davis et al. observed (Davis et al., 1983) that the plasma of Weddell seals became very lipemic during deep foraging dives, indicating that the digestion and intestinal absorption of fat was occurring during the 5–6 h foraging session. Increased energy expenditure for digestion during diving is added to the metabolic costs for locomotion and basal metabolism(Williams et al., 2004). This increased metabolism for digestion and assimilation is also thought to reduce the ADL of southern elephant seals during foraging bouts(McConnell et al., 1992). Digestion not only increases oxygen consumption, but also influences the optimal management of the muscle and blood oxygen stores. Our model indicated that diving with the additional metabolic cost of HIF causes blood oxygen to limit the ADL rather than myoglobin oxygen (i.e. myoglobin stores may not be completely used). We hypothesize that myoglobin concentration is optimized for the type and duration of dives routinely made by Weddell seals, and that a further increase may not increase the ADL of most free-ranging dives. Whether physiological constraints associated with the dive response and convective oxygen transport have limited the concentration of myoglobin in muscles remains uncertain, but our model does suggest a possible influence during the evolution of Weddell seals and other long duration divers. In addition, the model indicates that the calculated ADL is more complex than simply the quotient of the available oxygen stores and estimated metabolic rate.

 
• ADL

  aerobic dive limit

 
• cADL

  calculated aerobic dive limit

 
• Ca_O2

  arterial blood oxygen concentration (ml O₂^–1 blood)

 
• Cbv_O2

  cerebral venous blood oxygen concentration (ml O₂l^–1 blood)

 
• Chv_O2

  coronary venous blood oxygen concentration (ml O₂l^–1 blood)

 
• Cmv_O2

  skeletal muscle venous blood oxygen concentration (ml O₂l^–1 blood)

 
• Csrcv_O2

  splanchnic, renal, cutaneous and other peripheral tissue venous blood oxygen concentration (ml O₂ l^–1 blood)

 
• Cv̄_O2

  mixed venous blood oxygen concentration (ml O₂l^–1 blood)

 
• Cv_O2

  venous blood oxygen concentration (ml O₂l^–1 blood)

 
• DLT

  diving lactate threshold

 
• E_BO2

  extraction coefficient of oxygen from blood[(Ca_O2–Cv_O2)/Ca_O2]

 
• f_H

  heart frequency (beats min^–1)

 
• Hb

  hemoglobin

 
• Hct

  hematocrit

 
• HIF

  heat increment of feeding

 
• Mb

  myoglobin

 
• Pa_O2

  arterial blood oxygen partial pressure (mmHg)

 
• P_O2

  oxygen partial pressure (mmHg)

 
• Pv_O2

  venous blood oxygen partial pressure (mmHg)

 
• Q̇

  blood flow rate (l min^–1)

 
• Q̇ _B

  brain blood flow (l min^–1)

 
• Q̇ _H

  heart blood flow (l min^–1)

 
• Q̇ _M

  skeletal muscle blood flow (l min^–1)

 
• Q̇ _O2

  convective oxygen transport in the blood (ml O₂min^–1)

 
• Q̇ _SRC

  splanchnic, renal, cutaneous and other peripheral tissue blood flow (l min^–1)

 
• Sa_O2

  arterial blood oxygen saturation (%)

 
• Sv̄_O2

  mixed venous blood oxygen saturation (%)

 
• Sv_O2

  venous blood oxygen saturation (%)

 
• V̇b

  cardiac output (l min^–1)

 
• V̇ B_O2

  brain oxygen consumption rate (ml O₂min^–1)

 
• V̇ _CRSO2

  splanchnic, renal, cutaneous and other peripheral tissue oxygen consumption rate (ml O₂ min^–1)

 
• V̇ _HO2

  heart oxygen consumption rate (ml O₂min^–1)

 
• V̇ _MO2

  skeletal muscle oxygen consumption rate (ml O₂min^–1)

 
• V̇ _O2

  rate of oxygen consumption (ml O₂min^–1)

 
• V_S

  stroke volume (l)

 
• βBO2

  capacitance coefficient of oxygen in blood (ml O₂l^–1 blood)

We thank T. M. Williams for supplying data used in the completion of this model. We also thank T. M. Williams and S. B. Kanatous for helpful comments during drafting of this manuscript.