Right-to-left shunt has modest effects on CO₂ delivery to the gut during digestion, but compromises oxygen delivery

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 (P_CO2) 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 P_CO2 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 P_CO2 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 P_O2 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.

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.

See Table 1 and the list of symbols and abbreviations for parameter definitions.

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 P_O2 and proton concentration to include the Bohr–Haldane effect.

where SID is the strong-ion difference (Stewart, 1978), K_w is the ionic product of water, β_NB is the non-bicarbonate buffer capacity, pH_iso is the pH of zero net charge of the buffer groups, S_H is the fractional saturation of haemoglobin with protons and p is the number of Bohr-groups of haemoglobin.

However, given the present purpose we only considered unidirectional R–L shunts.

Owing to the simplifying assumptions of the model, at steady-state the pulmonary venous partial pressures of O₂ and CO₂ (P_PvO2 and P_PvCO2) are equal to the partial pressures in the lung (P_AO2 and P_ACO2). 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).

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 F_RL/(2−F_RL) when approaches infinity (i.e. infinitely high ventilation and low partitioning coefficient relative to blood flow).

The isolated and combined effects of R–L shunts and ACR are illustrated in 3D plots in Fig. 1B–D, where arterial P_CO2, P_O2 and HbO₂ saturation (S_O2) are shown as functions of both R–L shunt fraction (F_RL) and alveolar ventilation. It is immediately clear that arterial P_CO2 increases most steeply when alveolar ventilation is reduced (i.e. reduced ACR), but only moderately when F_RL is increased (Fig. 1B). Conversely, both arterial P_O2 and S_O2 are markedly reduced as the R–L shunt increases, whilst reductions in alveolar ventilation only moderately reduce S_O2 (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 P_CO2 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 P_O2–P_CO2 diagrams and similar plots that relate P_CO2 and S_O2. 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 P_O2 and P_CO2 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 P_O2 while arterial P_CO2 only increases moderately (full green curve in Fig. 2B). Thus, to produce the same elevation in arterial P_CO2 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 P_O2 from more than 120 mmHg to less than 30 mmHg (Fig. 2B) and reduce S_O2 from approximately 1.0 to less than 0.5 (Fig. 2A).

The complete solutions for different combinations of F_RL (varied 0–0.8) and ACR (varied 12.5–50) for arterial blood are given in Fig. 2C,D. The colour coding indicates increasing P_CO2 and the thicker lines originating from the air-line (the black dashed line/curve) depict how P_O2, P_CO2 and S_O2 change as F_RL 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 F_RL. By combining the horizontal axes of Fig. 2C,D, the possible solutions are summarized as a 3D diagram with P_CO2 on the vertical z-axis and S_O2 and P_O2 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 F_RL causes large reductions in P_O2 of the arterial and venous blood along the O₂ equilibrium curve, leading to pronounced S_O2 reduction with only moderate elevation of P_CO2. Conversely, reducing ACR at a given F_RL leads to a large elevation of P_CO2 with only moderate reductions in S_O2 (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 (β_b) (alternatively expressed as differences in blood gas partitioning coefficients, λ). This is illustrated in Fig. 3, showing the limitation imposed on gas exchange by F_RL (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 F_RL 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 β_b). Therefore, owing to the high β_b, CO₂ is less limited by shunts than O₂, although the differences may become less distinct in deep hypoxia where the effective β_b 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.

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 P_CO2 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 P_O2 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 P_CO2 rather than the ineffective mean of regulation by central vascular shunts.