ABSTRACT
By virtue of their cardiovascular anatomy, reptiles and amphibians can shunt blood away from the pulmonary or systemic circuits, but the functional role of this characteristic trait remains unclear. It has been suggested that right-to-left (R–L) shunt (recirculation of systemic blood within the body) fuels the gastric mucosa with acidified and CO2-rich blood to facilitate gastric acid secretion during digestion. However, in addition to elevating PCO2, R–L shunt also reduces arterial O2 levels and would compromise O2 delivery during the increased metabolic state of digestion. Conversely, arterial PCO2 can also be elevated by lowering ventilation relative to metabolism (i.e. reducing the air convection requirement, ACR). Based on a mathematical analysis of the relative roles of ACR and R–L shunt on O2 and CO2 levels, we predict that ventilatory modifications are much more effective for gastric CO2 supply with only modest effects on O2 delivery. Conversely, elevating CO2 levels by means of R–L shunt would come at a cost of significant reductions in O2 levels. The different effects of altering ACR and R–L shunt on O2 and CO2 levels are explained by the differences in the effective blood capacitance coefficients.
INTRODUCTION
The ability to shunt blood away from the pulmonary or systemic circulations is a defining character of the reptilian and amphibian cardiovascular systems (Hicks, 1998). However, whilst much is known about the anatomical basis for central vascular shunts and their autonomic regulation, the functional role of bypassing one or the other circulation remains as mysterious as it is debated (Hicks and Wang, 2012). Thus, it remains uncertain as to whether this cardiovascular design is an exquisite adaptation to low ectothermic metabolism and intermittent pulmonary ventilation, or merely an atavistic relict with no particular functional benefits (Hicks and Wang, 2012).
In several species of reptiles and amphibians, the right-to-left (R–L) shunts (i.e. the direct recirculation of systemic venous blood into the arterial systemic circulation) decrease whenever oxygen demands are elevated (Hicks and Wang, 2012). However, in crocodilians, an elevated oxygen consumption associated with digestion may be an exception. A combination of unique anatomical features of the crocodilian cardiovascular system (Hicks, 1998) combined with physiological measurements fostered the idea that increased R–L shunts serve to fuel the gastric mucosa with acidic proton-rich blood during digestion in alligators (Farmer et al., 2008; Gardner et al., 2011; Jones and Shelton, 1993). Central to this proposal is the observation that the crocodilian coeliac artery appears as a continuation of the left aortic arch, which indicates that the stomach is preferentially perfused with CO2-rich blood from the right ventricle (e.g. Jones, 1996; Webb, 1979). In support for elevated (systemic) arterial partial pressure of CO2 (PCO2) governing acid secretion, Farmer et al. (2008) reported slower digestion after surgical removal of the left aorta in alligators. However, a number of other studies show that growth is not affected by similar procedures (Eme et al., 2009, 2010), and it is possible that the slower digestion stems from reduced perfusion of the gastrointestinal organs after occlusion of the left aortic arch (Hicks and Wang, 2012).
Although the cardiovascular system must simultaneously provide for O2 delivery and CO2 removal, the proposition that R–L shunts assist gastric acid secretion has not included considerations of the inexorable reduction in O2 delivery. R–L shunts cause large reduction in arterial O2 levels – whether expressed as partial pressure, O2 concentration or haemoglobin saturation (Wang and Hicks, 1996) – while the effects on arterial PCO2 are predicted to be considerably smaller given the high capacitance coefficient for CO2 in blood. An increased R–L shunt during digestion would therefore also compromise O2 delivery, which seems undesirable given the fourfold elevation in O2 demands during digestion (Busk et al., 2000). In this context, it may be more prudent to elevate arterial PCO2 by means of ventilation [i.e. a lowering of the air convection requirement (ACR) for CO2], a response that has been suggested to compensate for the rise in plasma bicarbonate during digestion (the so-called ‘alkaline tide’; Hicks et al., 2000; Hicks and White, 1992; Wang et al., 2001b). However, decreasing the ACR to elevate CO2 levels will simultaneously lower the lung PO2 and could negatively impact O2 delivery.
To address the compromise between adequate O2 delivery and arterial acid–base status, we developed an integrated numerical model that can be applied to amphibians and reptiles, to provide a quantitative comparison of the effects of R–L shunting and altered ventilation on blood O2 and CO2 levels.
- ACR
- air convection requirement
- CPaCO2, CPaO2
- concentration of CO2 or O2 in the pulmonary artery
- CPvCO2, CPvO2
- concentration of CO2 or O2 in pulmonary venous return (i.e. left atrium)
- CSaCO2, CSaO2
- concentration of CO2 or O2 in the systemic arterial blood
- CSvCO2, CSvO2
- concentration of CO2 or O2 in systemic venous return (i.e. right atrium)
- Hb
- haemoglobin
- Lshunt
- gas exchange limitation imposed by shunts
- p
- number of Bohr-groups of haemoglobin
- PACO2, PAO2
- partial pressure of CO2 or O2 in the lung gas
- PCO2, PO2
- partial pressure of CO2 or O2 in a given compartment
- PICO2, PIO2
- inspired partial pressure of CO2 or O2
- Q̇LR
- left-to-right shunt flow
- pulmonary blood flow
- right-to-left shunt flow
- systemic blood flow
- total cardiac output
- R–L
- right-to-left shunt
- Rperf
- blood convective/perfusive resistance
- RQ
- respiratory quotient
- Rtot
- total resistance imposed to transport between tissues and the environment
- Rvent
- air convective/ventilatory resistance
- SH
- fractional saturation of haemoglobin with protons
- SO2
- HbO2 saturation
- λ
- blood/gas partitioning coefficient
MATERIALS AND METHODS
Fig. 1A illustrates the model of gas exchange for O2 and CO2 based on mass balances and relationships that express electro-neutrality in blood compartments. The model does not include diffusion limitations or spatial heterogeneities at tissues or lungs, and incorporates a thermodynamically correct description of the Bohr–Haldane effect.
Model illustration and 3D plots showing the effects of alveolar ventilation (and hence ACR) and FRL on PCO2, PO2 and SO2. (A) Illustration of the compartment model with abbreviations as follows: A, lung; Pa, pulmonary arterial blood; Pv, pulmonary venous blood; Sa, systemic arterial blood; Sv, systemic venous blood; T, tissues. For other definitions, see the List of symbols and abbreviations and Table 1. (B–D) 3D plots illustrate how (systemic) arterial PCO2 (B), PO2 (C) and HbO2 saturation (SO2; D) change as a function of the alveolar ventilation (and hence air convection requirement, ACR) and the right-to-left shunt fraction (FRL).
Mass balances
For O2:
(1)
(2)
(3)
(4)
For CO2:
(5)
(6)
(7)
(8)
See Table 1 and the list of symbols and abbreviations for parameter definitions.
Parameter values used in simulations
Concentrations and partial pressures in blood
The concentration of O2 in each blood compartment (CbO2) is the sum of haemoglobin (Hb)-bound O2 [product of blood Hb concentration (CHb), number of O2 binding sites (q=4) and saturation (SO2)] and the physically dissolved O2 [product of physical solubility (αO2) and PO2]:
(9)
To quantify the saturation of Hb with O2 and protons, the Monod–Wyman–Changeux two-state model (Monod et al., 1965) was incorporated where saturation is a function of both PO2 and proton concentration to include the Bohr–Haldane effect.
The total concentration of CO2 in blood (CbCO2) is the sum of the physically dissolved CO2 (αCO2PCO2) and the bicarbonate and carbonate concentration, as quantified by the equilibrium constants of CO2 hydration (K1 and K2) and the proton concentration ([H+], which is related to SO2):
(10)
Electro-neutrality in blood
Equations that express electro-neutrality were derived by conservation of charge, where electro-neutrality in a given blood compartment (subscript i) is given below:
(11)
where SID is the strong-ion difference (Stewart, 1978), Kw is the ionic product of water, βNB is the non-bicarbonate buffer capacity, pHiso is the pH of zero net charge of the buffer groups, SH is the fractional saturation of haemoglobin with protons and p is the number of Bohr-groups of haemoglobin.
Shunt fractions and blood flows
Total cardiac output (
) is the sum of pulmonary and systemic flows (
and 
, respectively) and the shunt flows (
and 
) are given by total blood flow and the shunt fractions (
and 
). Given the desired general applicability of the model to reptiles with (both R–L and L–R) intra-cardiac shunts, and not just crocodilians with central vascular (R–L) shunts, we derived the following expressions by mass balance, assuming uniformly well-stirred compartments with constant volume where bi-directional shunts can occur independently:
(12)
(13)
However, given the present purpose we only considered unidirectional R–L shunts.
Numerical and analytical solutions
Owing to the simplifying assumptions of the model, at steady-state the pulmonary venous partial pressures of O2 and CO2 (PPvO2 and PPvCO2) are equal to the partial pressures in the lung (PAO2 and PACO2). The total system of 12 equations that express mass balance and electro-neutrality with 12 dependent variables (i.e. partial pressures and proton concentrations in the systemic and pulmonary arterial and venous system for O2 and CO2) was solved numerically in Mathematica (v.10.3, Wolfram Research).
When blood capacitances of O2 and CO2 are assumed constant (approximately true for CO2 and applicable to O2 during hypoxia), the system of equations can be solved analytically, leading to the following solutions:
(14)
(15)
where Rtot is the total resistance imposed to transport from the blood/tissues to the environment equal to the sum of the resistances associated with blood convective/perfusive transport (Rperf) and ventilation (Rvent):
(16)
When only considering unidirectional R–L shunts, the total resistance simplifies to:
(17)
where βb is the blood capacitance coefficient for O2 or CO2. The left part on the right-hand side of Eqn 17 corresponds to Rperf and simplifies to the normal perfusive resistance [
] when there are no shunts, whereas the right part is Rvent. The perfusive resistance (Rperf) can be expressed as the normal resistance without shunts (Rperf,FRL=0) multiplied by a function of the shunt fraction [i.e. f(FRL)=½(2−FRL)/(1−FRL)]:
(18)
While Rvent is the same for O2 and CO2, Rperf and hence Rtot differ given different βb. The gas exchange limitation (Piiper and Scheid, 1972, 1981) imposed by R–L shunts (Lshunt) is given by 1 minus the total resistance without shunts (Rtot, where FRL=0) divided by the total resistance with shunts (i.e. Rtot):
(19)
This can also be expressed by the dimensionless ratio of the normal perfusive to ventilatory resistance without shunts (
):
(20)
where 
is given by the ventilation to perfusion ratio and the blood gas partitioning coefficient (λ=βb/βg) as follows:
(21)
From Eqn 20 it is given that the transport limitation imposed by shunts approaches zero when 
approaches zero (i.e. infinitely high blood flow and partitioning coefficient relative to ventilation). Conversely, the limitation approaches FRL/(2−FRL) when 
approaches infinity (i.e. infinitely high ventilation and low partitioning coefficient relative to blood flow).
RESULTS AND DISCUSSION
The isolated and combined effects of R–L shunts and ACR are illustrated in 3D plots in Fig. 1B–D, where arterial PCO2, PO2 and HbO2 saturation (SO2) are shown as functions of both R–L shunt fraction (FRL) and alveolar ventilation. It is immediately clear that arterial PCO2 increases most steeply when alveolar ventilation is reduced (i.e. reduced ACR), but only moderately when FRL is increased (Fig. 1B). Conversely, both arterial PO2 and SO2 are markedly reduced as the R–L shunt increases, whilst reductions in alveolar ventilation only moderately reduce SO2 (Fig. 1C,D). Thus, our theoretical analysis reveals substantial differences on the influence of R–L shunt and ACR on arterial blood gases, and predicts that ventilatory compensations are much more effective in altering arterial PCO2 than cardiac shunt patterns.
The differences in the behaviours of O2 and CO2 upon changing shunt pattern or ACR are also illustrated in Fig. 2A–D, which shows PO2–PCO2 diagrams and similar plots that relate PCO2 and SO2. In Fig. 2B, the dashed line describes steady-state solutions for lung gases and hence also the arterial blood gases in the absence of cardiac shunts (i.e. the mammalian condition). In this case, reductions in ACR cause similar, but reciprocal changes in arterial PO2 and PCO2 as predicted by the respiratory quotient (RQ; set to 1 in the simulations). Conversely, an introduction of R–L shunt at a given ACR causes large reductions in arterial PO2 while arterial PCO2 only increases moderately (full green curve in Fig. 2B). Thus, to produce the same elevation in arterial PCO2 by means of a R–L shunt as by a moderate reduction in ACR (e.g. a reduction from 28 to 20 ml air ml–1 CO2; Fig. 2B), the shunt fraction would have to increase to 0.8, meaning that 80% of the systemic venous return bypasses the lungs (Fig. 2B). Such a large shunt fraction would concomitantly reduce arterial PO2 from more than 120 mmHg to less than 30 mmHg (Fig. 2B) and reduce SO2 from approximately 1.0 to less than 0.5 (Fig. 2A).
PO2–PCO2 diagrams of the solutions comparing the effects of altering ACR and FRL on PCO2, PO2 and SO2. (A–D) Arterial PCO2 as a function of either HbO2 saturation (SO2) (A,C) or PO2 (B,D). In B and D, the dashed black line is the air-line with a slope given by a respiratory quotient (RQ) that describes how PCO2 and PO2 change when altering ACR without shunts, and similarly in A and C, where the ‘air-line’ becomes a curve. In B, the thick green curve originating at the dashed air-line/curve shows solutions when the right-to-left shunt fraction (FRL) is increased at a constant ACR. Note that to produce the same elevation in arterial PCO2 by means of R–L shunt as by a moderate reduction in ACR (e.g. a reduction from 28 to 20 ml air ml–1 CO2), the shunt fraction would have to increase to 0.8 with a concomitant large reduction in arterial PO2 and SO2 (A). (C,D) Solutions for different combinations of FRL (varied 0–0.8) and ACR (varied 12.5–50 ml air ml–1 CO2), where the colour coding indicates increasing PCO2. Here, the thicker curves originating from the air-line/curve show the effects of altering FRL at a given constant ACR. Conversely, the thinner curves originating from the thicker curves show the effects of altering ACR at a given FRL. (E) 3D plot summarizing the effects of altering FRL (thicker curves) and ACR (thinner curves) on both (systemic) venous and arterial blood. The plot is a combination of C and D, where PCO2 is on the vertical z-axis and SO2 and PO2 are on the horizontal x- and y-axes, and therefore also illustrates the effective O2 equilibrium curve. Note that when increasing FRL at a given ACR, the arterial and venous points move down the O2 equilibrium curve with only small elevations in PCO2. Conversely, reducing ACR at a given shunt leads to pronounced elevations of PCO2 but only moderate reductions in SO2.
The complete solutions for different combinations of FRL (varied 0–0.8) and ACR (varied 12.5–50) for arterial blood are given in Fig. 2C,D. The colour coding indicates increasing PCO2 and the thicker lines originating from the air-line (the black dashed line/curve) depict how PO2, PCO2 and SO2 change as FRL is altered at several constant levels of ACR. The thinner curves, originating from the thicker blood curves, represent solutions when ACR is altered at a given constant FRL. By combining the horizontal axes of Fig. 2C,D, the possible solutions are summarized as a 3D diagram with PCO2 on the vertical z-axis and SO2 and PO2 on the horizontal x- and y-axes (Fig. 2E). In this representation, the horizontal x–y plane reflects the effective O2 equilibrium curve. Fig. 2E illustrates that increasing FRL causes large reductions in PO2 of the arterial and venous blood along the O2 equilibrium curve, leading to pronounced SO2 reduction with only moderate elevation of PCO2. Conversely, reducing ACR at a given FRL leads to a large elevation of PCO2 with only moderate reductions in SO2 (thinner upwards-bending curves in Fig. 2E).
The different effects of altering ACR and R–L shunt on O2 and CO2 is explained by the differences in blood capacitance coefficients (βb) (alternatively expressed as differences in blood gas partitioning coefficients, λ). This is illustrated in Fig. 3, showing the limitation imposed on gas exchange by FRL (Eqn 21). Here, the ratio of the normal perfusive to ventilatory resistance without shunts (
) is varied from a physiologically relevant range for O2 and CO2 (colour coded), and the asymptotic relationship between the limitation and FRL for 
approaching infinity and 
=0 is given by the black curve and the horizontal axis. Fig. 3 emphasizes that at a given shunt fraction, the gas species mostly limited by the shunt is the one with the highest blood to air convective resistance (
) and hence the lowest λ (i.e. lowest βb). Therefore, owing to the high βb, CO2 is less limited by shunts than O2, although the differences may become less distinct in deep hypoxia where the effective βb for O2 increases. The same conclusion was made by Wagner (1979) when considering the effects of lung shunts on O2 versus CO2 exchange. Besides the differences in effects of shunts on O2 and CO2, Fig. 3 also illustrates that the limitation in general is predicted to increase when overall 
is high and vice versa.
Simplified analytic solution of the model that illustrates the limitation imposed on gas exchange by shunts (Lshunt, Eqn 21) as a function of the right-to-left shunt fraction (FRL) for different values of the ratio of the perfusive to ventilatory resistance without shunts (
, Eqn 22, colour coded). The asymptotic limitations when 
approaches infinity or zero are plotted. As a consequence of higher blood capacitance coefficient (βb) and hence blood/gas partitioning coefficient (λ), 
for O2 is higher than for CO2 and hence O2 uptake will be more limited by a given shunt.
If digestion is facilitated by supplying the gut with blood with higher CO2 levels, our model predicts that this is best mediated by reducing ACR instead of increasing R–L shunt. Elevating CO2 levels by increasing R–L shunt would come at the cost of pronounced reductions in O2 levels, producing hypoxemia at a time at which O2 demand may be elevated fourfold above resting (e.g. Busk et al., 2000). Conversely, reductions of ACR entail much smaller reductions in O2 delivery, but provide for an effective elevation of PCO2 that compensates for the alkaline tide during digestion (Wang et al., 2001a). Furthermore, these postprandial reductions in ACR are well known in reptiles (Hicks et al., 2000; Overgaard et al., 1999; Secor et al., 2000) and PO2 remains high during digestion in all animals studied, including alligators (Busk et al., 2000; Hartzler et al., 2006; Overgaard et al., 1999).
For many reptiles and amphibians, digestion is associated with large elevations in oxygen demands and an increased need to secrete gastric acid with resulting challenges to blood acid–base balance. Our theoretical approach clearly demonstrates that reliance on R–L shunting to meet the digestive demands conflicts significantly with increased metabolic demands of the digestive organs, and cannot provide adequate compensation for the alkaline tide. In contrast, ventilatory regulation, through reductions in ACR, addresses all the physiological challenges simultaneously, i.e. blood acid–base regulation, increased CO2 delivery to the gastric mucosa without sacrificing O2 delivery. Thus, while our theoretical model obviously does not provide information on the actual physiological responses of living animals, it would certainly seem that natural selection should favour efficient ventilatory regulation on arterial PCO2 rather than the ineffective mean of regulation by central vascular shunts.
FOOTNOTES
Competing interests
The authors declare no competing or financial interests.
Author contributions
This analysis results from numerous discussions over the past decade involving all the authors. C.L.M. constructed the model used in the manuscript on the basis of previous simpler attempts. The manuscript was written by H.M. and T.W. with continuous input and final approval of all co-authors.
Funding
This study was funded by the Danish Research Council (Natur og Univers, Det Frie Forskningsråd).
- Received September 12, 2016.
- Accepted December 6, 2016.
- © 2017. Published by The Company of Biologists Ltd
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