Acid-Base physiology: A confused floundering

vivianimbriotis | Feb. 2, 2025, 1:46 a.m.

Do not read this to try to learn acid-base physiology. This is not good didactic content. This is the product of a disturbed and pathological mind. This will be your only warning.

Every moment, you body is trying to kill you. Every molecule of ATP your cells hydrolyze, every amino acid you metabolize, generates acid. There are three systems that prevent you from drying from acidosis:

1. Buffering
2. Respiratory compensation
3. Renal compensation

The acid-base status is determined by the chemical activity of hydrogen in the extracellular fluid. This is determined by a number of interrelated quantities.

1. Carbon dioxide partial pressure
2. Bicarbonate concentration
3. Total nonvolatile weak acids (e.g. albumin, HPO4/PO4-, collectively ATOT)
4. Strong ion difference (fully dissociated cations less fully dissociated anions, SID)
5. Haemoglobin availability (Hb is a potent buffer of H+)

To understand this we first need to understand some prerequisites:

1. Chemical equilibria (aka laws of mass action)
2. Acid-base theory (and honestly not even bronsted-lowry acids are necessary for midwit doctor like myself, let alone lewis acids)
3. Buffering phenomena

Then we will need to understand the regulators of these parameters, which are

1. The lungs
2. The kidney

There are three approaches to measuring these variables to try and determine the cause of an acid base disturbance

1. The Bicarbonate approach (Boston school) - ignores the effect of SID and Hb, but conceptually simple (although 6 rules to memorize)
2. The base excess approach (Copenhagen school) - incorporates information about Hb, fewer rules to memorize, still ignores the SID
3. The physiochemical/Stewart method - Focuses on SID and Atot. Ignores the effect of Hb.

Background: Respiratory control of blood pH

The rate of change of CO2 is the rate of generation of CO2, minus the rate of excretion of CO2.

$$\dot{CO_2} = \dot{CO_2}_{in} - \dot{CO_2}_{out}$$

This equation works regardless of the units. By convention n Australia, these quantities are measured in volume of gas (by the ideal gas law we could equally use partial pressures or moles).

Let's tackle the two right hand side quantities one by one.

(a) CO2 generation

Carbon dioxide production is denoted \dot{V}_CO2. CO2 is produced when oxygen is consumed to oxidize macronutrients. The ratio of oxygen consumed to CO2 generated is called the respiratory quotient.

$$\dot{CO_2}_{in} = \dot{V}_{CO_2} = RQ \cdot \dot{V}_{O_2}$$

The respiratory quotient depends on the maconutrient. This means it is influenced by diet, and also by some drugs (e.g. carnitine palmitoyltransferase inhibitors like perhexiline, which decreases mitochondrial update of fatty acids, reduced the RQ).

But the big influence here is the rate of oxygen consumption. This is increased any time cellular demands for energy are high, so that is in exercise, sepsis, hyperthyroidism, malignant hypertension, and critical illness in general.

(b) CO2 elimination

Let's make some assumptions:

1. There is no atmospheric CO2
2. With each breath, CO2 equilibrates completely across the alveolus (CO2 is highly soluble so by Fick's law this is likely even with a very high respiratory rate)

Then the partial pressure of CO2 in the alveolus equals the partial pressure of CO2 in the blood.

The ideal gas law tells us that the concentration of CO2 in the alveolar gas is directly proportional to its partial pressure (more molecules = more pressure). Double the pressure, double the molecules.

And clearly, the volume of gas in a breath is proportional to the total amount of CO2. For the same partial pressure, if you double the volume of gas, you double the molecules.

The total amount of CO2 eliminated per unit time is just the amount lost per breath, times breaths per unit time (i.e. resp rate):

$$\dot{CO_2}_{out} \propto RR \cdot V_{alveolar} \cdot \rho_aCO_2$$

The volume of alveolar gas is equal to the tidal volume minus all the bits of the tidal volume that aren't in the alveolus (i.e. are in the airways, or are in non-perfused alveoli). We call this non-participatory fraction dead space:

$$\dot{CO_2}_{out} \propto RR \cdot (V_{tidal} - V_{dead}) \cdot \rho_aCO_2$$

And the product of alveolar volume and resp rate is called alveolar ventilation.

$$\dot{CO_2}_{out} \propto \dot{V}_A \cdot \rho_aCO_2$$

The partial pressure of CO2 is itself directly proportional to the total CO2 content in the blood (dear reader, I leave deriving this from the CO2 equilibrium constant as an exercise, xox). So, with K as our constant of proportionality, we have:

$$\dot{CO_2}_{out} = k \cdot [\dot{V}_A \cdot \rho_aCO_2]$$

And we're done.

(c) Putting it together

All our hard work yields this beauty:

$$\dot{CO_2} = [RQ \cdot \dot{V}_{O_2}] - k \cdot [\dot{V}_A \cdot \rho_aCO_2]$$

Here we have a differential equation of the form:

$$\dot{y} = a - b \cdot y$$

Which we can solve with separation of variables like so:

$$\frac{1}{a - b \cdot y} \frac{dy}{dt} = 1$$

$$\int \frac{1}{a - b \cdot y} dy = \int 1 dt$$

A quick u-substitution yields

$$ - \frac{1}{b} \ln{|a - b \cdot y|} = t + c$$

Being a little naughty and letting our (arbitrary) c absorb the b constant,

$$ \ln{|a - b \cdot y|} = - bt + c$$

$$ y = \frac{a}{b} \pm \frac{e^{c}}{b} e^{-bt}$$

If we only care about the steady state, though, then we can let t trend to infinity and...

$$ y = \frac{a}{b}$$

What did these letters stand for again? Oh yeah,

$$CO_2 = \frac{RQ \cdot \dot{V}_{O_2}}{k \dot{V}_A}$$

Or, for short,

$$CO_2 \propto \frac{\dot{V}_{CO_2}}{\dot{V}_A}$$

This means that total body CO2 is proportional to:

1. VO2 (increased in sepsis, exercise, malignant hyperthermia, other hypermetabolic states)
2. The respiratory quotient (increased with high-fat diets)

And inversely proportional to:

1. The respiratory rate
2. The alveolar volume (increased with higher tidal volume, decreased with higher dead space)

The neural circuit here is straightforward negative feedback:

1. Central and peripheral chemoreceptors detect elevated pH and paCO2
2. This signals the respiratory pattern generator in the medulla to increase tidal volume and resp rate
3. This restores homeostasis

Or, to make it even simpler: in health, the lungs can set the CO2 to whatever the brain wants.

Background: Renal control of blood pH

The kidneys control pH through three mechanisms:

(a) In the proximal tubule, reabsorbing bicarbonate along with sodium

This occurs due to the activity of carbonic anhydrase in the proximal tubule.

1. CO2 inside the cell dissociates into bicarb and hydrogen (CA)
2. Hydrogen and sodium are antiported apically, reabsorbing sodium and pumping out hydrogen (NHE3)
3. tubular hydrogen reacts with filtered bicarbonate to form CO2 and water (CA)
4. the CO2 diffuses back into the cell to begin the cycle again
5. meanwhile, sodium is pumped out basally but Na/K ATPase, and bicarbonate is pumped basally by sodium symport (NBCe1A)

This process continues until no more tubular bicarbonate remains to fuel step (3). The net effect of this is to reabsorb sodium and bicarbonate, without reabsorbing any chloride.

This process is disrupted in proximal RTA, or by a carbonic anhydrase inhibitor

(b) Freely filtering, and actively secreting, phosphates, suphates, and other "titratable acids"

1. Conjugate bases like phosphate, sulphate, and creatine are freely filtered.
2. The sodium-hydrogen antiport described can also bind hydrogen to these buffers, resulting in a little bit of hydrogen loss and sodium reabsorption (without chloride reabsorption).

This process is quantitatively unimportant.

(c) Most importantly, generating de novo ammonium and excreting it along with chloride

1. Urea (from glutamine) is converted to ammonium in the epithelium of the PCT.
2. Ammonium is then reabsorbed in the medulla by masquerading as potassium, taking the place of the potassium ion in symport with sodium and chloride via the furosemide-sensitive NKCC2 transport in the ascending limb of the loop of Henle.
3. Ammonium is then excreted in the distal collecting duct, and with it an equimolar amount of chloride.

The process of manufacturing ammonium consumes a hydrogen ion. The net effect is loss of hydrogen and of chloride, without any sodium loss.

This process is disrupted in distal RTA, or in the presence of hyperkalaemia, which competes with ammonium for NKCC2 excretion in the loop of Henle.

All three processes are under direct negative feedback from ECF pH.

Approach 1: Boston

The Boston school of thought is derived directly from the Henderson-Hasselbalch equation.

In this paradigm

1. The lungs set the CO2
2. The kidneys/liver/GIT set the bicarbonate

The main problem is that CO2 also affects the bicarbonate, even without the kidneys doing anything at all (e.g. an increase in CO2 will immediately increase bicarbonate by driving the equilibrium to the right). This means that the bicarbonate is affected by

1. Primary metabolic acidoses or alkaloses
2. Actual renal compensation for chronic primary respiratory acidosis or alkalosis
3. Acute changes in the CO2 which do not really represent any compensation by another organ system

This system therefore relies on a set of observational rules:

1. If you think the pathology is primarily metabolic, then you calculate the expected CO2 with Winter's formula. If the CO2 deviates from this, then there is a superimposed respiratory process
2. If you think the process is primarily respiratory, you apply the appropriate 1-2-4-5 rule (e.g. for a 10mmHg increase in CO2, acutely the bicarbonate increases by 1, chronically the bicarbonate increases by 4)
3. If there is a significant discrepancy between the expected and the actual value, then there is a mixed process.

Approach 2: Copenhagen

The Copenhagen school of thought tries to isolate the effects of the kidneys and the lungs. It defines two special quantities, called the "base excess" and "standard base excess". In this paradigm

1. The lungs set the CO2
2. The kidneys/liver/GIT set the base excess

Here's how you make a base excess:

1. get a unit volume of plasma
2. set the pCO2 around the plasma to 40mmHg
3. wait for the plasma to equilibrate
4. now add acid to the sample until the pH is exactly physiological (i.e. 7.4)
5. how much acid did you add? that's the base excess

Of course, the blood gas machine uses an algorithm to estimate this quantity.

The standard base excess is a little fancier. The idea is the same, but instead of being concerned with a unit volume of plasma, the quantity concerns a unit volume of ECF. What's the difference? Haemoglobin.

Since haemoglobin is a potent buffer, but is only available to the plasma, the plasma base excess (and indeed bicarbonate) are a biased estimate of the ECF base excess/bicarbonate, which is what we really care about. The standard base excess uses the blood gas analyser's estimate of the Hb to adjust the base excess estimate.

The advantage of this system is that it fully separates the respiratory and metabolic components, such that an acute respiratory disturbance does not affect the SBE. It also reduces cognitive burden because the normal value of the SBE is 0, +/- 3.

Of course, we still need to assess the adequacy of compensation in chronic respiratory disturbances and metabolic disturbances. There's only three rules to know:

In a chronic resp disturbance, the SBE is 0.4 * the change in the PaCO2

In a metabolic alkalosis, the change in CO2 is 0.6 * the SBE

In a metabolic acidosis, the change in CO2 is equal to the SBE

Approach 3: Stewart

The Stewart approach is a reimaginging of acid-base physiology from first principles of chemistry. It eschews focusing on bicarbonate and hydrogen, as these quantities cannot be directly regulated by the body.

(For example, if a cell pumps out hydrogen ions, then the rate of autoionization of water inside the cell will increase by LCP, driving pH back down to near the previous value; similarly, if the kidneys pump out bicarbonate, this will increase the rate of dissociation of CO2 into bicarbonate).

This all sounds very complicated. Luckily, there are a few independent variables in the system that are no subject to equilibria like this, and Stewart's contention is that these are what is actually regulated by the body (all else is consequent).

1. The strong ion difference SID (all the strong, i.e. completely dissociated, cations less all the strong anions)
2. The total quantity of acids ATOT (meaning the sum of all acids and their conjugate bases)
3. The PaCO2 (which is directly set by the lungs)

In this paradigm:

1. The lungs set the CO2
2. The kidneys / GIT set the SID
3. The ATOT is set by the kidney (which is health excretes weak acids like phosphate) and the liver (because the most ubiquitous weak acid is albumin)

The best intuition pump for this is to go back to the Henderson-Hasselbalch equation. The pH remains under direct physiological control. But it is the combination of the SID and ATOT that determine the bicarbonate concentration (and therefore the pH).

This is because of electroneutrality. The total amount of anions and cations has to remain constant.

Decreasing the SID adds strong anions (usually chloride or lactate) to the left. Only weak acids, like bicarbonate, can escape to become other compounds, since the strong ions have to remain dissociated. To maintain electroneutrality, bicarbonate is forced into being carbonic acid.

Similarly, changes in the quantities of total acid, e.g. changes in albumin, will change how much conjugate base is competing with bicarbonate for anion-space. This is how a hypoalbuminaemia causes a metabolic alkalosis.

In reality, these factors are not JUST acting on bicarbonate, but on all the weak acids in the body fluids.

This approach does not consider the effect of haemoglobin and also does not consider adequacy of compensation (which is an evolved biological process that cannot be estimated from first principles).