WATER DISSOCIATION AND ACID–BASE

Stewart reminded us of the central role of water in aqueous acid–base equilibria.¹ Mammals are approximately 60% water. It follows that the behaviour of water is fundamental to our understanding of acid–base physiology. Water (simplistically) dissociates as follows:

By the Law of Mass Action, at any equilibrium [H⁺] [OH⁻] = Kw [H₂O], where Kw is the temperature-dependent dissociation constant. Water is a vast proton reservoir, its concentration several orders of magnitude greater than that of its two dissociation products (55.5 M vs. 160 nM at 37 °C). When conditions favour proton release, for example with increased temperature, water dissociates and pH falls. With conditions less favourable, protons return to their source, and pH rises.

An advantage of its numeric predominance is that [H₂O] can be combined with Kw to form a new constant, K’w. The equilibrium equation then simplifies to:

Equation 84.1

THE PaCO₂/PH RELATIONSHIP – THE ACID–BASE ‘WINDOW’ FOR CLINICIANS

About 15 moles of CO₂ are generated daily by aerobic metabolism. CO₂ travels along a partial pressure gradient from its intracellular source (PCO₂ > 50 mmHg) to the atmosphere (PCO₂ = 0.3 mmHg). The primary exit point is the lungs, with transit facilitated by a large, perpetually refreshed blood–air interface. En route, CO₂ equilibrates with all aqueous environments. The PCO₂ in any body fluid is thus an equilibrium value, determined by the interplay between regional CO₂ production, regional blood flow, alveolar perfusion and alveolar ventilation.

Clinicians use the relationship between arterial PCO₂ (PaCO₂) and arterial pH as the acid–base assessment platform. This is appropriate, because the PaCO₂/pH curve is a fundamental physiological property (Figure 84.1). Several factors determine the shape and position of this curve.

Figure 84.1 PCo₂/pH relationships. The solid line shows the normal in vivo PaCO₂/pH relationship. The normal PaCO₂ range is between the filled circles. To the left of the circles there is an increasing acute respiratory alkalosis, and to the right an increasing acute respiratory acidosis. The interrupted curve represents the normal in vitro whole blood relationship, and the dotted curve is the same relationship for separated plasma. A point of commonality exists at PCO₂ = 40 mmHg.

THE PaCO₂/pH RELATIONSHIP IS DEFINED BY SEVERAL SIMULTANEOUS EQUATIONS

In body fluids, pH is a function of water dissociation modified by CO₂, other weak acids and certain electrolytes. All equilibria obey the Laws of Mass Action and Mass Conservation, and must achieve overall electrical neutrality. Non-diffusible ions exert electrochemical forces across membranes, known as Gibbs Donnan effects, which influence the final acid–base result.

Therefore apart from Equation 1, several other equations must be satisfied simultaneously at any equilibrium. They relate to:

1 The interaction of carbon dioxide with water:

By applying the Law of Mass Action and substituting [dissolved CO₂] for [H₂CO₃], the following expression can be derived:

Equation 84.2

This is the Henderson–Hasselbalch equation, where α is the plasma CO₂ solubility coefficient (0.03), and 6.1 is the pKa, the negative logarithm of the dissociation constant. The Henderson–Hasselbalch equation generates the plasma [HCO₃⁻] in blood gas readouts.

2 Bicarbonate dissociation to carbonate. At equilibration:

Equation 84.3

3 Non-volatile weak acid dissociation. Fluid compartments have varying concentrations of non-CO₂ generating (non-volatile) molecules with weak acid properties. In other words, their overall negative charge alters in parallel with pH. In plasma, they consist mainly of albumin and to a lesser extent inorganic phosphate. In red cells haemoglobin predominates. Much smaller concentrations of non-volatile weak acid also appear in interstitial fluid, primarily as phosphate. For convenience, Stewart modelled all non-volatile weak acids in each compartment as having a single anionic form (A⁻) and a single conjugate base form (HA).

By applying the Law of Mass Action:

Equation 84.4

4 Conservation of mass. Stewart termed the total concentration of non-volatile weak acids in any compartment ‘A_TOT’, where A_TOT = [HA] + [A⁻]. A_TOT is an imposed mass constant. It does not vary with pH. A change in pH merely signals a shift in the balance between HA and A⁻.

5 Electrical neutrality, linked to Stewart’s concepts of strong ions and strong ion difference. Certain elements such as Na⁺, K⁺, Ca⁺⁺, Mg⁺⁺ and Cl⁻ exist as completely ionised entities in body fluids. At physiological pH this includes anions with pKa values of 4 or less, for example sulphate, lactate, and β-hydroxybutyrate. Stewart described compounds exhibiting this property as ‘strong ions’. In body fluids there is a surfeit of strong cations, referred to by Stewart as the strong ion difference (SID). In other words, SID = [strong cations] – [strong anions]. Being a ‘charge’ space, SID is expressed in mEq/l. SID calculated from measured strong ions in normal plasma is 42 mEq/l.

Hence, by the Law of Electrical Neutrality:

Equation 84.5

6 Gibbs Donnan forces. These alter equilibria across semipermeable membranes, with electrical gradients balanced against concentration gradients. The plasma compartment (volume 3 l), the erythrocyte compartment (volume 2 l) and the interstitial space (volume 13.5 l) each contains different concentrations of non-diffusible anions, mainly albumin or haemoglobin. Erythrocytes, which harbour most of these trapped negative charges, attract diffusible cations (such as Na⁺, K⁺) from adjacent compartments while repelling diffusible anions (primarily Cl⁻). However, several cations are continually redistributed against the Donnan forces by energy-dependent transmembrane pumps, to prevent cell swelling and haemolysis. Importantly, chloride, the major anion, remains fully susceptible to the Donnan effects.

The trapped anions have weak acid properties. Any pH shift alters their negative charge, driving further ionic redistributions, particularly chloride, between compartments. The net effect is that plasma SID goes up and down with PaCO₂ (Figure 84.2), the origin of the so-called Hamburger effect. Importantly, ionic shifts are confined within the total extracellular space, so that extracellular SID does not alter with PCO₂. This is fortuitous for clinicians, forming the basis of the CO₂ invariance of standard base excess (see below).

Figure 84.2 Gamblegrams of plasma strong and weak ions (in vitro data from CO₂ equilibrated normal blood). On the left, PCO₂ < 20 mmHg; on the right, the same blood with PCO₂ > 200 mmHg. The transition from hypocapnia to hypercapnia increases SIDa, with ionic redistribution between red cells and plasma due to altered Gibbs Donnan forces. There are almost identical increases in SIDe ([A⁻] + [HCO₃⁻]), also known as ‘buffer base’, although [A⁻] actually falls. Note that the SIG, which is SIDa minus SIDe, remains close to zero.

At any equilibrium, Equations 1–5 plus the Donnan equilibria must be satisfied simultaneously. In such a system, pH and HCO₃⁻, as well as CO₃²⁻, A⁻ and OH⁻, cannot be altered directly, only via any of three independent variables imposed on the system but not altered directly by the system. These are SID (total extracellular SID, immune to Gibbs Donnan forces), extracellular A_TOT, and PaCO₂, which is externally regulated by alveolar ventilation. Hence, in arterial blood, pH is defined by PaCO₂, extracellular SID and extracellular A_TOT.

Thus it can be seen that for any individual the PaCO₂/pH relationship is a unique acid–base ‘signature’ (Figure 84.1) and ultimately a complex function of extracellular SID and A_TOT.

WEAK IONS AND BUFFER BASE

SID is a charge space. Weak ions, which arise from variably dissociating conjugate bases, occupy this space. These include H⁺, OH⁻, HCO₃⁻, CO₃²⁻ and A⁻. Their total net charge must always equal SID. However, HCO₃⁻ and A⁻, together known as the ‘buffer base’ anions, take up virtually the entire space on their own (Figure 84.2) since the other ions are measured in either micromoles/l or, in the case of protons, nanomoles/l. SID therefore not only dictates the buffer base concentration but is also numerically identical to it. In other words, SID = [HCO₃⁻] + [A⁻]. This fact, plus Figge’s linear approximations² for calculating A⁻, allows us to simplify Stewart’s equations in plasma, reducing them to three without sacrificing accuracy.³

[Alb] is albumin concentration expressed in g/l. [Pi] is phosphate concentration in mmol/l. PCO₂ is in mmHg. SIDe is effective SID, also known as ‘buffer base’ (Figure 84.2).

SID calculated from measured plasma concentrations of strong ions is termed the ‘apparent’ SID, or SIDa (Figure 84.2). Discrepancies between SIDe and SIDa imply the presence of unmeasured ions in plasma (see below).

ISOLATED CHANGES IN SID AND A_TOT

At any given PaCO₂, a falling SID or a rising A_TOT reduce pH, moving the equilibrium towards a metabolic acidosis. Conversely, a rising SID or a falling A_TOT create a metabolic alkalosis. Many argue that SID and A_TOT act individually and should therefore be regarded as independent metabolic acid–base variables. By this argument we could have a strong ion acidosis or alkalosis combined with either a hyperalbuminaemic (high A_TOT) acidosis or a hypoalbuminaemic (low A_TOT) alkalosis.⁴ However, SID and A_TOT do appear to be linked, with the SID set-point adjusting to A_TOT. In particular, SID seems to fall in hypoalbuminaemia, presumably by renal chloride adjustment.^5,6

HOW ACID–BASE DISTURBANCES AFFECT THE PACO₂/PH RELATIONSHIP

Acute respiratory disturbances move data points along the prevailing PaCO₂/pH curve, to the left in respiratory alkalosis, and to the right in respiratory acidosis (Figure 84.1). In contrast, metabolic disturbances (altered extracellular SID and/or A_TOT) shift the entire curve up or down (Figure 84.3). A down-shifted curve means that the pH at any given PaCO₂ is lower than normal, which – depending on the PaCO₂ – represents either a primary metabolic acidosis or else metabolic compensation for a respiratory alkalosis. With an up-shifted curve, the pH at any given PaCO₂ is higher than normal, signifying either a primary metabolic alkalosis or else compensation for a respiratory acidosis.

Figure 84.3 PaCO₂/pH curve shifts and associated SBE values (mEq/l). Alterations in metabolic acid–base status shift the curve down (SBE increasingly negative) or up (SBE increasingly positive).

TEMPERATURE CORRECTION OF BLOOD GAS DATA – ‘ALPHA-STAT’ VERSUS ‘PH-STAT’ APPROACHES

Blood gas analysers operate at 37 °C. Their software can convert pH and gas tensions to values corresponding to the patient core temperature for interpretation and action. This is the ‘pH-stat’ approach. The alternative isto act on values as measured at 37 °C – the ‘alpha-stat’ approach.

‘Alpha’ is the ratio of protonated imidazole to total imidazole on the histidine moieties in protein molecules. At 37 °C, under normal acid–base conditions, the mean intracellular pH is 6.8 (the neutral pH at 37 °C). Alpha is then approximately 0.55. Maintaining alpha close to 0.55 preserves enzyme structure and function, and is thus a fundamental goal.

‘Alpha-stat’ logic is best illustrated by considering blood in a blood gas syringe. When placed on ice, the PCO₂ falls as its solubility coefficient increases. Water dissociation is reduced, due to the hypocapnia and to the temperature-induced decrease in K’w. Consequently, there is a progressive alkalaemia, which on rewarming in the blood gas analyser reverts immediately. Throughout these phenomena, alpha stays constant. The reason is that the fall of the imidazole pKa with temperature is about half the fall in pK’w.

Hence, a simple way to keep alpha at 0.55 in hypothermia is to maintain uncorrected PaCO₂ and pH measurements in their 37 °C reference ranges.^7,8 This mimics the hypothermic physiology of ectothermic (cold-blooded) animals. Similar arguments apply in fever, the more common intensive care unit (ICU) scenario. Many intensivists follow the alpha-stat approach, whatever the core temperature.

Those who favour the pH-stat approach argue that it is more consistent with the physiology of hibernating endothermic mammals, and that it allows better maintenance of cerebral perfusion in hypothermia.⁹ This approach was used during an influential trial of mild hypothermia following out-of-hospital cardiac arrest.¹⁰

RENAL PARTICIPATION IN ACID–BASE

In the absence of renal function, there is a progressive metabolic acidosis. About 60 mEq of strong anions, particularly sulphate, but also hippurate and others, are produced daily as metabolic end-products. These accumulate in renal failure, reducing extracellular SID. So does free water, which brings sodium concentrations closer to chloride, again reducing SID. Hyperphosphataemia contributes by increasing A_TOT, although in acute renal failure this is commonly offset by coexistent hypoalbuminaemia.¹¹

Traditionally, renal acid–base homeostasis is described in terms of resorption of filtered bicarbonate primarily in the proximal tubule, and excretion of fixed acids through titration of urinary buffers, particularly phosphate, and through excretion of ammonium, primarily in the distal tubule.¹²

From the physical chemical perspective, the traditional analysis of renal acid–base homeostasis is misleading, since it is based on H⁺ or HCO₃⁻ ‘balances’. H⁺ and HCO₃⁻ are dependent variables, responsive exclusively to PCO₂, SID and A_TOT, and not subject to ‘in versus out’ balance sheets. The physical chemical explanation is simple. The kidneys regulate extracellular SID via urinary SID, the principal tool being tubular NH₄⁺ acting as an adjustable cationic partner for tubular Cl⁻ and other urinary strong anions.¹³ The kidneys also modify A_TOT via phosphate excretion, which is a totally different concept from that of ‘titratable acidity’.

ACID–BASE ASSESSMENT – THE TWO ‘SCHOOLS’

By convention, acid–base disorders are divided into respiratory (PaCO₂) and metabolic (non-PaCO₂). PaCO₂ is the undisputed index of respiratory acid–base status. Two ‘schools’, Boston and Copenhagen, separated by a large ocean,¹⁴ have formed around the identification and quantification of metabolic acid–base disturbances. Both succeed as navigation systems, if used correctly.

Stewart’s concepts neither invalidate nor supplant the traditional approaches,^15–17 but rather help us to understand their physiological basis, evaluate their relative merits, and extend their utility.¹⁸ SID by itself is not a reliable measure of metabolic acid–base status, for three reasons:

For a pure metabolic index to succeed, it must integrate the effects of extracellular SID and A_TOT, irrespective of the PaCO₂. The best of these (in the author’s opinion) is standard base excess, the flagship of the Copenhagen school. However, Boston school devotees can navigate quite successfully using empiric plasma bicarbonate-based ‘rules of thumb’.