Blood Gas Interpretation

Useful information

• With respiratory problems, $p\mathrm{CO}{}_2$ and pH change in different directions
• With metabolic problems, $p\mathrm{CO}{}_2$ and pH change in the same direction

Introduction

• Make sure you understand the difference between oxygenation and ventilation
• Have a good understanding of Acute Respiratory Failure

Approach¹

1. Determine the adequacy of oxygenation
   • Refer to the $S_{\text{p}}\mathrm{O}{}_2$ from the sats probe or $S_{\text{a}}\mathrm{O}{}_2$ as calculated from the ABG or measured from co-oximetry to observe for hypoxaemia
   • Calculate the A-a gradient
     1. Calculate the $F_I\mathrm{O}{}_2$ (see below for calculations and suggested values)
     2. Calculate $P_{\text{A}}\mathrm{O}{}_2$ using the alveolar gas equation which takes the following values for most patients at sea level $$\begin{array}{rl}{P}_{\text{A}}\mathrm{O}{}_2& =F_{\text{I}}\mathrm{O}{}_2\times \left[P_{\text{I}}-P_{\mathrm{H}{}_2\mathrm{O}}\right]-\left(\frac{P_{\text{a}}\mathrm{CO}{}_2}{\text{RQ}}\right)\\ & \approx F_{\text{I}}\mathrm{O}{}_2\times \left[760-47\right]-\left(\frac{P_{\text{a}}\mathrm{CO}{}_2}{0.8}\right)\\ & \approx F_{\text{I}}\mathrm{O}{}_2\times 713-P_{\text{a}}\mathrm{CO}{}_2\times 1.25\end{array}$$
     3. Calculate the A-a gradient
     4. Estimate the adjusted normal A-a gradient $$\text{Normal A-a gradient}\approx \frac{\text{Age}}{4}+4+50\times \left(F_{\text{I}}\mathrm{O}{}_2-0.21\right)$$
     5. Compare the A-a gradient (<10 mmHg normal)
        • If normal, either due to hypoventilation (observe $P_{\text{a}}\mathrm{CO}{}_2$) or low atmospheric pressure
        • If elevated, observe for correction of $\mathrm{O}{}_2$ sats with 100% $F_{\text{I}}\mathrm{O}{}_2$
          • If corrects, suggestive of V/Q mismatch and/or diffusion impairment
          • If doesn’t correct, suggestive of right to left shunt
          • Correlate with history, exam and chest X-ray
   • Calculate the $P_{\mathrm{a}}\mathrm{O}{}_2/F_{\text{I}}\mathrm{O}{}_2$ ratio in ARDS patients where:
     • 300-200 ⇒ mild ARDS with 27% mortality
     • 200-100 ⇒ moderate ARDS with 32% mortality
     • <100 ⇒ severe ARDS with 45% mortality
   • Check for dyshaemoglobinaemia from the co-oximetry
2. Determine pH status (7.35-7.45)
   • pH <7.35: acidaemia: increase in the serum hydrogen ion concentration, lowers the pH
   • pH >7.45: alkalaemia: decreases the hydrogen ion concentration, raises the pH
   • If pH is normal and $\mathrm{HCO}{}_3$ or $P_{\text{a}}\mathrm{CO}{}_2$ is abnormal check the anion gap and the table on mixed disorders below
3. Determine the primary disorder
   • $P_{\text{a}}\mathrm{CO}{}_2$: Determine the respiratory component (35-45 mmHg)
     • $P_{\text{a}}\mathrm{CO}{}_2$ <35 ⇒ ↑ respiratory rate ⇒ alkalotic change
       • If pH >7.45: primary respiratory alkalosis (especially if $\mathrm{HCO}{}_3{}^{-}$ normal)
       • If pH <7.35 and ↓ $\mathrm{HCO}{}_3{}^{-}$: respiratory compensation for metabolic acidosis
     • $P_{\text{a}}\mathrm{CO}{}_2$ >45 ⇒ ↓ respiratory rate ⇒ acidotic change
       • If pH <7.35 and $\mathrm{HCO}{}_3{}^{-}$ normal: hypoventilation
       • If pH >7.45 and ↑ $\mathrm{HCO}{}_3{}^{-}$: respiratory compensation for metabolic alkalosis
   • $\mathrm{HCO}{}_3{}^{-}$: Determine the metabolic component (22-26 mmol/L)
     • $\mathrm{HCO}{}_3{}^{-}$<22 ⇒ acidotic change
       • If pH <7.35: primary metabolic acidosis
       • If pH >7.45: metabolic compensation for respiratory alkalosis
     • $\mathrm{HCO}{}_3{}^{-}$ >26 ⇒ alkalotic change
       • If pH >7.45: primary metabolic alkalaosis
       • If pH <7.35: metabolic compensation for respiratory acidosis
   • If both $P_{\text{a}}\mathrm{CO}{}_2$ and $\mathrm{HCO}{}_3$ are causing the same disturbance (i.e. both acidotic or alkalotic changes) there is co-existing primary respiratory and metabolic disorders
     • There is limited utility in calculating expected compensation
4. Is the compensation adequate
   • If the pH is normal, there is another primary acid/base disorder as compensation will never bring the pH back to adequacy (e.g. if there is respiratory acidosis and the pH is normal, there must also be a primary metabolic alkalosis)
   • Metabolic compensation takes 12 hours - 5 days to take peak effect (generally $\pm 5$ for metabolic compensation formulas)
     • Metabolic acidosis: $P_{\text{a}}\mathrm{CO}{}_2=1.5\times \mathrm{HCO}{}_3+8\pm 2$ (Winter’s formula) or $P\mathrm{a}\mathrm{CO}{}_2=\mathrm{HCO}{}_3+15$
     • Metabolic alkalosis: $P_{\text{a}}\mathrm{CO}{}_2=0.7\times \mathrm{HCO}{}_3+20\pm 5$ or $P_{\text{a}}\mathrm{CO}{}_2=40+0.7\times \left([\mathrm{HCO}{}_3{}^{-}]-24\right)$
       • Compensation for a metabolic alkalosis is relatively poor because hypoventilation as a compensation mechanism results in hypoxaemia
     • Easier rule for compensation in metabolic disorders: $P_{\text{a}}\mathrm{CO}{}_2$ is approximately the same as the first two digits of the pH after the decimal point
       • e.g ABG: pH 7.27 / $P_{\text{a}}\mathrm{CO}{}_2$ 25 / $\mathrm{HCO}{}_3{}^{-}$ 11 ⇒ decimals of pH is 27 and $P_{\text{a}}\mathrm{CO}{}_2$ is 25 so approximately equal, hence physiologic compensation is adequate
       • If the $P_{\text{a}}\mathrm{CO}{}_2$ is lower than expected then there is additional respiratory alkalosis and vice versa
   • Respiratory compensation takes 1 - 24 hours to take peak effect (generally $\pm 3$ for respiratory compensation formulas)
     • Respiratory acidosis
       • Acute: $\Delta \mathrm{HCO}{}_3=0.1\times \Delta P\mathrm{a}\mathrm{CO}{}_2$ or $[\mathrm{HCO}{}_3{}^{-}]=24+\frac{P_{\text{a}}\mathrm{CO}{}_2-40}{10}$
       • Chronic: $\Delta \mathrm{HCO}{}_3=0.4\times \Delta P\mathrm{a}\mathrm{CO}{}_2$ or $[\mathrm{HCO}{}_3{}^{-}]=24+4\times \frac{P_{\text{a}}\mathrm{CO}{}_2-40}{10}$
     • Respiratory alkalosis
       • Acute: $\Delta \mathrm{HCO}{}_3=0.2\times \Delta P\mathrm{a}\mathrm{CO}{}_2$ or $[\mathrm{HCO}{}_3{}^{-}]=24-2\times \frac{4-P_{\text{a}}\mathrm{CO}{}_2}{10}$
       • Chronic: $\Delta \mathrm{HCO}{}_3=0.5\times \Delta P\mathrm{a}\mathrm{CO}{}_2$ or $[\mathrm{HCO}{}_3{}^{-}]=24-5\times \frac{4-P_{\text{a}}\mathrm{CO}{}_2}{10}$
5. Calculate the anion gap
   • High anion gap acidosis ⇒ addition of anions (conjugate bases of acids added to serum e.g. ketones or lactate)
     • Severe renal failure can lead HAGMA to excrete phosphate and sulphate in the urine resulting in their accumulation
     • Lactic acidosis, ketoacidosis (DKA, ETOH, starvation), methanol ingestion, ethylene glycol ingestion, toluene inhalation (glue sniffing)
   • Normal anion gap acidosis ⇒ decreased renal $\mathrm{H}{}^{+}$ excretion or loss of $\mathrm{HCO}{}_3$ in urine or GI tract
     • Loss of $\mathrm{HCO}{}_3$: diarrhoea/GI drainage, Type 2 Renal tubular acidosis, Acetazolamide
     • Decreased $\mathrm{H}{}^{+}$ excretion: renal failure, Type 1 Renal tubular acidosis, Type 4 Renal tubular acidosis/Conn syndrome
     • Results in decrease in $\mathrm{HCO}{}_3$ with an increase in $\mathrm{Cl}{}^{-}$ a roughly 1:1 ratio (hence NAGMA sometimes called hyperchloraemic acidosis)
     • Potassium is not included because it tends to influence the result little² however if one insisted, the normal value would be around 16
     $$\mathrm{Anion}\mathrm{Gap}=\mathrm{Na}{}^{+}-\left(\mathrm{Cl}{}^{-}+\mathrm{HCO}{}_3\right)=12\pm 4$$
   • Anion gap unrelated to metabolic acidosis:
     • High anion gap can be due to metabolic alkalosis, hyperphosphataemia
     • Low anion gap can be due to hypoalbuminaemia, ↑ $\mathrm{K}{}^{+}$, ↑ $\mathrm{Ca}{}^{2+}$, ↑ $\mathrm{Mg}{}^{2+}$, Severe lithium toxicity, bromide ingestion (some machines mistake bromine for chlorine; Myaesthenia gravis medications can contain bromine)
   • Adjust anion gap for hypoalbuminaemia³: $${\text{AG}}_{\text{adjusted}}={\text{AG}}_{\text{measured}}+0.25\times (40-[\text{Alb}])$$
6. Delta ratio which should be calculated whenever the anion gap is elevated
   • During a HAGMA there should be a 1:1 gap between the ↑ anion gap and ↓ $\mathrm{HCO}{}_3$
   • Check delta ratio in the presence of a high anion gap metabolic acidosis to determine if it is a pure HAGMA or if there is co-existent normal anion gap metabolic acidosis or metabolic alkalosis
   • The expected delta radio differs by aetiology of HAGMA:
     • Lactic acidosis: 1.6 (1.0 - 2.0) with it initially starting at 1.0 and increasing with time
     • Ketoacidosis: 1.0 (0.8 - 1.2) unless ↓ GFR in which case the ratio may be higher
     • Kidney disease: variable depending on the extent of tubular damage relative to ↓ GFR
     • Methanol, ethylene glycol ingestion: Unknown, probably 1.0 - 2.0
   • Based on the above, the interpretation is made such that if the measured delta ratio is:
     • Lower than the expected range, there is HAGMA and NAGMA
     • Within expected range, there is HAGMA only (although there could be respiratory disorder)
     • Higher than the expected range, there is a HAGMA and metabolic alkalosis
   • A negative delta ratio is possible in the following contexts:
     • High anion gap metabolic acidosis and metabolic alkalosis (can result in a normal or high pH)
     • Mild high anion gap metabolic acidosis and severe chronic respiratory acidosis (usually results in a very low pH)
   $$\mathrm{Delta}\mathrm{Ratio}=\frac{\mathrm{A}{\mathrm{G}}_{\text{adjusted}}-12}{24-\mathrm{HCO}{}_3}=\frac{\mathrm{\Delta AG}}{\mathrm{\Delta }\mathrm{HCO}{}_3}$$
7. Apply corrections to certain measured values

• As an extra step you can determine the consistency of the values from the machine and confirm that the derrived $[\mathrm{HCO}{}_3]$ is correct using:

$$p\mathrm{H}=-{\log }_{10}\left(24\times \frac{Pa\mathrm{CO}{}_2}{[\mathrm{HCO}{}_3]}\times 10^{-9}\right)$$

Additional Details

Differentials

High Anion Gap Metabolic Acidosis

• Mnemonic: KULT
  • Ketoacidosis
    • Diabetes (see: Diabetic ketoacidosis)
    • Starvation
    • Chronic alcoholism
  • Uraemia
    • Renal failure
      • Occurs for 2 reasons:
        • Failure to excrete $\mathrm{H}{}^{+}$ ions in the kidney due to ↓ excretion of $\mathrm{NH}{}_4{}^{+}$ and ↓ excretion of titratable acids (e.g. $\mathrm{H}{}_2\mathrm{PO}{}_4{}^{-}$)
        • Accumulation of unmeasured anions (phosphate, sulphate, urate and hippurate)
      • The anion gap from renal failure rarely exceeds 20 and often co-exists with normal anion gap acidosis
  • Lactic acidosis
    • Increased production of lactate:
      • Problem with $\mathrm{O}{}_2$ delivery (e.g. shock, bowel infarction, hypoxaemia)
      • Problem with $\mathrm{O}{}_2$ utilisation (e.g. genetic enzymatic defects, mitochondrial toxins, thiamine deficiency)
      • Primary production from tumours (e.g. lymphone, leukaemia and multiple myeloma)
      • Increased motor activity (e.g. seizures, vigorous exercise)
    • Decreased clearance (e.g. liver failure or renal failure although noting that renal failure alone is unlikely to cause lactic acidosis)
    • GI absorption of D-Lactate (usually in patients who have undergone either jejunoileal bypass or extensive resection of small bowel)
      • Typically presents as elevated anion gap acidosis that appears after eating and resolves with fasting (clinical appearance of altered mental status)
      • Measured lactate levels are normal unless specifically testing for D-lactate
    • Medications (e.g. paracetamol, anti-retrovirals, beta agonists, 5-flurouracil, halothane, iron, isoniazid, linezolid, nitroprusside, propofol, salicylates, sorbitol, sulfasalazine, valproic acid)
      • There remains disagreement about metformin causing lactic acidosis
    • Toxins (e.g. carbon monoxide, cocaine, cyanide, diethyl ether, ethanol, toxic acidosis)
  • Toxins
    • Methanol
      • Found in windshield wiper fluid, antifreeze, paint remover
      • Presents with vision loss, photophobia, abdominal pain, confusion and lethargy
    • Ethylene glycol
      • Found in antifreeze and liquid coolant
      • Presents with
        • Confusion at <12 hours
        • Heart failure, myocarditis and pulmonary oedema at 24 hours
        • Acute kidney injury at 24-72 hours
      • Also occurs lactic acidosis as glycolate impairs cellular respiration causing lactic acidosis
      • Can be diagnosed via calcium oxalate crystals in the urine (can be quicker to obtain than ethylene glycol level)
    • Ethanol
    • Propylene glycol
      • Used as a solvent for lorazepam, phenobarbital, diazepam, phenytoin
      • Presents with renal failure and unexplained lactic acidosis in a patient who has been on IV infusion of lorazepam for several days
      • Recommended limit of propylene glycol is 69g/day (equivalent to 7mg/hr of lorazepam infusion)
    • Toluene
      • Found in glues/adhesives and paint thinner
      • Acutely presents with euphoria, loss of inhibition, amnesia, slurred speech and ataxia
      • Chronically it can cause cerebellar dysfunction, dementia, rental tubular acidosis, hypokalaemia and renal failure
    • Salicylic acid (aspirin)
    • 5-oxoproline
      • Associated with chronic paracetamol use with additional risk factors including advanced age, malnutrition, chronic illness and alcoholism
      • Symptoms are non-specific
• Approach
  • 
  • Check anion gap and adjust for hypoalbuminaemia
  • Check ABG to ensure acidosis is present (i.e. low bicarb); if no acidosis review causes of ↑ AG w/o acidosis (e.g. hyperphosphataemia, anionic paraprotein)
  • Check lactate and ketones
    • If ↑ lactate, evaluate for hypoperfusion
      • If systemic hypoperfusion it suggests Shock
      • If regional hypoperfusion, probably related to that (e.g. bowel infarct)
      • If nil hypoperfusion consider medical side effect, toxic ingestion or lactate producing malignancy
        • Any altered mental status or Hx of toxic ingestion check: paracetamol level, osmolality + osmololal gap, urine toxicology screen, aspirin level $$\begin{array}{rl}\text{Calculated Osmolality}& =2\times [\mathrm{Na}{}^{+}]+[\mathrm{Glucose}]+[\mathrm{Urea}]\\ \text{Osmolal Gap}& =\text{Measured Osmolality}-\text{Calcualted Osmolality}<10\text{mOsm/kg}\end{array}$$
        • Causes of increased osmolal gap include ethanol, methanol, ethylene glycol and isopropanol ingestion
    • If ↑ ketones, check glucose and alcohol Hx
      • Glucose ≥ 13.9 suggests Diabetic ketoacidosis
      • If Hx of ETOH suggests alcoholic ketoacidosis
  • Check renal function (if above normal)
    • If GFR < 40 and AG ≤ 20 ⇒ renal failure alone is likely cause, otherwise check osmolal gap
  • Check rare aetiologies such as D-lactic acidosis and late presentation of methanol toxicity
• General indications for calculating the osmolal gap are:
  • Suspected posining with unknown toxin
  • Elevated anion gap in the presence of normal lactate, ketones and renal function
  • Unexmplained altered mental status (particularly in an alcoholic or child)
  • Periodic monitoring for patients on high doses of IV lorazepam

Normal Anion Gap Metabolic Acidosis

Primary Issue	GI Problem	Renal Problem
Gain of $\mathrm{H}{}^{+}$ or failure to excrete $\mathrm{H}{}^{+}$	Hyperalimentation (e.g. too fast TPN)	Types 1 and 4 RTA Renal failure Hyperkalaemia
Loss of $\mathrm{HCO}{}_3{}^{-}$	Diarrhoea External pancreatic drainage Ureteral diversion Oral $\mathrm{CaCl}{}_2$ Cholestyramine	Type 2 RTA

• Other causes: Infusion of normal saline or $\mathrm{NH}{}_4\mathrm{Cl}$

Metabolic Alkalosis

Primary Issue	GI Problem	Renal Problem
Loss of $\mathrm{H}{}^{+}$	Vomiting NG suction Congenital chloride diarrhoea	Loop/Thiazide Diuretics Mineralocorticoid Excess Contraction Alkalosis Bartter/Gitelman Syndromes
Gain of $\mathrm{HCO}{}_3{}^{-}$	Milk-alkali syndrome Ingestion of $\mathrm{NaHCO}{}_3{}^{-}$	Contraction Alkalosis

• Contraction alkalosis
  • When intravascular volume depletion occurs → low renal volume perfusion → ↑ aldosterone and angiotensin II → ↑ $\mathrm{Na}$ reabsorption ↑ $\mathrm{HCO}{}_3{}^{-}$ reabsorption, ↑ $\mathrm{K}{}^{+}$ excretion, ↑ $\mathrm{H}{}^{+}$ excretion → metabolic alkalosis
• Diuretics
  • Can result in contraction alkalosis
  • By inhibiting sodium reabsorption proximally in the nephron, more sodium reaches the collecting duct
  • This results in increase in sodium reabsorption and $\mathrm{H}{}^{+}$ excretion (see Diuretics)
• Vomiting/NG suction
  • Volume depletion causing a secondary contraction alkalosis
  • Direct loss of $\mathrm{H}{}^{+}$ in gastric fluids
• Mineralocorticoid excess (suggested by hypertension, hypokaelamia, metabolic alkalosis)
  • Hyperaldosternism (e.g. from primary hyperaldoserism as in Conn’s syndrome or from secondary hyperaldosterism due to elevated from renin as in renal artery stenosis)
  • Cushing’s syndrome (e.g. CRH producing tumour as in bronchial carcinoid tumours, elevated ACTH as in pituitary adenoma termed Cushing’s disease or elevated cortisol in an adrenal adenoma or exogenous use)
• Hypokalaemia
  • Leads to a shift of $\mathrm{K}{}^{+}$ from intracellular to extracellular space in exchange for a shift of $\mathrm{H}{}^{+}$ from extracellular to intracellular space
  • Within the nephron, hypokalaemia stimulates $\mathrm{HCO}{}_3{}^{-}$ reabsorption in the PCT and $\mathrm{H}{}^{+}$ excretion in the CD
• Milk-Alkali syndrome (characterised by hypercalcaemia, metabolic alkalosis and renal insufficiency)
  • Occurs when large amount of calcium and absorbable alkali consumed
  • Common in women taking calcium supplements
• Bartter & Gitelman sydrome (shared features: metabolic alkalosis, hypokalaemia, high renin and aldosterone and lack of hypertension)
  • 

Respiratory Acidosis

• Alveolar ventilation equation:

$$\begin{array}{rl}{P}_{\text{a}}\mathrm{CO}{}_2& =\frac{{\dot{V}}_{\mathrm{CO}{}_2}\times P_{\text{I}}}{{\dot{V}}_{\text{A}}}\\ & =\frac{{\dot{V}}_{\mathrm{CO}{}_2}\times P_{\text{I}}}{\text{Respiratory Rate}\times (V_{\text{T}}-V_{\text{D}})}\end{array}$$

• Where:
  • ${\dot{V}}_{\mathrm{CO}{}_2}$ is the rate of $\mathrm{CO}{}_2$ production
  • $P_{\text{I}}$ is the total pressure of inspired air
  • ${\dot{V}}_{\text{A}}$ is alveolar ventilation
  • $V_{\text{T}}$ is the tidal volume
  • $V_{\text{D}}$ is the dead space
• It therefore follows that the causes of ↑ $P_{\text{a}}\mathrm{CO}{}_2$ can be due to low respiratory rate, low tidal volume, high dead space or high rate of $\mathrm{CO}{}_2$ production

Respiratory Alkalosis

Patterns of Mixed Disorders with Normal pH

Drug Overdose Changes

• Respiratory alkalosis in the setting of drug overdose can be due to:
  • Aspiration on vomit causing hypoxia induced hyperventilation
  • Aspirin ingestion causing hyperventilation
• Most drug overdose causes respiratory acidosis

A-a Gradient and Oxygenation

• Hypoxia = pathophysiological state of inadequate oxygenation for aerobic metabolism; aetiologies include hypoxaemia, anaemia, dyshaemoglobinaemia, histotoxic hypoxia (e.g. cyanide poisoning)
• Hypoxaemia = ↓ concentration of oxygen in arterial blood
• $P_{\text{a}}\mathrm{O}{}_2$ is the amount of oxygen dissolved in the blood and is measured directly from the ABG (normal >85 mmHg for young adult, child and >75 mmHg for elderly)
• $\mathrm{O}{}_2$ sat commonly refers to the oxygen bound to haemoglobin:
  • $S_{\text{p}}\mathrm{O}{}_2$ is the amount of oxygen bound to haemoglobin as measured from pulse oximetry
  • $S_{\text{a}}\mathrm{O}{}_2$ is the amount of oxygen bound to haemoglobin as calculated from the ABG or measured by co-oximetry
• $P_{\text{A}}\mathrm{O}{}_2$ is the partial pressure of oxygen in the alveolar gas

$\text{A-a gradient}=\underset{\begin{array}{c}\text{Estimated from the}\\ \text{alveolar gas equation}\end{array}}{P_{\text{A}}\mathrm{O}{}_2}-\underset{\begin{array}{c}\text{Measured directly}\\ \text{via ABG}\end{array}}{P_{\text{a}}\mathrm{O}{}_2}$

$P_{\text{A}}\mathrm{O}{}_2=\left(\underset{\begin{array}{c}\text{Fractional concentration}\\ \text{of inspired }\mathrm{O}{}_2\end{array}}{F_{\text{I}}\mathrm{O}{}_2}\times \left(\underset{\begin{array}{c}\text{Total pressure}\\ \text{of inspired air}\end{array}}{P_{\text{I}}}-\underset{\begin{array}{c}\text{Partial pressure}\\ \text{of water vapour}\end{array}}{P_{\mathrm{H}{}_2\mathrm{O}}}\right)\right)-\left(\underset{\begin{array}{c}\text{Arterial }\mathrm{CO}{}_2\\ \text{tension}\end{array}}{P_{\text{a}}\mathrm{CO}{}_2}/\underset{\begin{array}{c}\text{Respiratory}\\ \text{Quotient}\end{array}}{\mathrm{RQ}}\right)$

• At sea level $F_{\text{i}}\mathrm{O}{}_2=21\%$ (when not on oxygen), $P_{\text{I}}=760\text{mm}\mathrm{Hg}$, $P_{\mathrm{H}{}_2\mathrm{O}}=47\text{mm}\mathrm{Hg}$ and for most patients $\text{RQ}=0.8$⁴so the above equation simplifies to: $P_{\text{A}}\mathrm{O}{}_2=150-\frac{P_{\text{a}}\mathrm{CO}{}_2}{0.8}$

Oxygen Supply	Approximate Maximum $F_{\text{I}}\mathrm{O}{}_2$
Room air	0.21
Nasal cannula	0.50
Venturi mask	0.50
Simple face mask	0.60
Non-rebreather	0.80-0.90
Mechanical ventilation	>0.90

• Variation of $F_{\text{I}}\mathrm{O}{}_2$ with flow rate and respiratory rate for nasal prongs:
  • 
  • Can be estimated with the following formula (use 0.03 for patients with increased respiratory rate and 0.05 for patients with normal respiratory rate):
  • $F_{\text{I}}\mathrm{O}{}_2\approx 0.21+(0.03\to 0.05)\times \underset{(\text{L}/\text{min})}{\text{Flow rate}}$
• Variation of $F_{\text{I}}\mathrm{O}{}_2$ with respiratory rate
  • High flow systems are able to meet the patient’s full inspiratory flow requirement (i.e. $F_{\text{I}}\mathrm{O}{}_2$ is independent of respiratory rate) (e.g. venturi mask, HFNP, mechanical ventilation)
  • Low flow systems are not able to meet the full inspiratory flow requirement (i.e. $F_{\text{I}}\mathrm{O}{}_2$ varies with respiratory rate)
• The normal A-a gradient increases with age⁵ and can be calculated by the following equation when there is no supplemental oxygen: $\text{Normal A-a gradient}=\left(\frac{\text{Age}}{4}\right)+4$
• Due to physiological shunting caused by supplemental oxygen, the adjust A-a gradient can be approximated by:

$$\text{Adjust Normal A-a gradient}\approx \left(\frac{Age}{4}+4\right)+50\times \left(F_{\text{I}}\mathrm{O}{}_2-0.21\right)$$

NOTE

If a patient has both a low $P_{\text{a}}\mathrm{CO}{}_2$ and a low $P_{\text{a}}\mathrm{O}{}_2$, then the A-a gradient must be elevated

• If the A-a gradient is normal then the cause of the hypoxaemia must be either:
  • Hypoventilation (i.e. ↑ $P_{\text{a}}\mathrm{CO}{}_2$)
  • Low $P_{\text{I}}$ (e.g. extreme altitudes)
• If the A-a gradient is elevated then the cause of the hypoxaemia must be either:
  • V/Q mismatch
  • Shunt (i.e. there exists perfused alveoli with zero ventilation e.g. cardiac shunts, lobar pneumonia ARDS)
    • Importantly when $F_{\text{I}}\mathrm{O}{}_2$ is increased, there is an increase in the A-a gradient as $P_{\text{a}}\mathrm{O}{}_2$ can not be further increased
  • Impaired diffusion

Simple Example

Question: A 56 year old man with a history of CAD, HTN, and 60 pack years of smoking, presents to the ER with a productive cough and dyspnea x 3 days. On exam, his RR=28 and 02 sat = 81% on room air. His breaths are shallow and with pursed lips. ABG: pH: 7.31 / $P_{\text{a}}\mathrm{CO}{}_2$ 60 / $P_{\text{a}}\mathrm{O}{}_2$ 57 on room air Answer:

1. Check A-a gradient

$$\begin{array}{rl}{P}_{\text{A}}\mathrm{O}{}_2& =\left[F_{\text{I}}\mathrm{O}{}_2\left(P_{\text{I}}-P_{\mathrm{H}{}_2\mathrm{O}}\right)\right]-\left(\frac{P_{\text{a}}\mathrm{CO}{}_2}{\text{RQ}}\right)\\ P_{\text{A}}\mathrm{O}{}_2& =150-\left(\frac{60}{0.8}\right)=75\text{mmHg}\\ \text{A–a gradient}& =75-57=18\text{mmHg}\end{array}$$

2. Estimate normal A-a gradient $(\text{Age}/4)+4=(56/4)+4=18\text{mmHg}$
3. Normal A-a gradient with high $P_{\text{a}}\mathrm{CO}{}_2$ indicates a COPD exacerbation

Harder Example

Question: An 80 y/o man with COPD, presents to the ER with progressive dyspnea and cough for 3 days. He appears acutely uncomfortable, and his sitting up, leaning forward with his hands on his knees. Vitals: T=36.9°C, HR=104, BP=135/80, RR=30, 02 saturation=95% on Venturi mask set at 30%. ABG: pH: 7.28 / $P_{\text{a}}\mathrm{CO}{}_2$ 80 / $P_{\text{a}}\mathrm{O}{}_2$ 80 on 30% $F_{\text{I}}\mathrm{O}{}_2$ Answer:

1. Check A-a gradient

$$\begin{array}{rl}{P}_{\text{A}}\mathrm{O}{}_2& =\left[F_{\text{I}}\mathrm{O}{}_2\left(P_{\text{I}}-P_{\mathrm{H}{}_2\mathrm{O}}\right)\right]-\left(\frac{P_{\text{a}}\mathrm{CO}{}_2}{\text{RQ}}\right)\\ & =\left[0.30\times (760-47)\right]-\frac{80}{0.8}=114\text{mmHg}\\ \text{A-a gradient}& =114-80=34\text{mmHg}\end{array}$$

2. Estimate adjusted normal A-a gradient

$$\begin{array}{rl}\text{Normal A-a gradient}& \approx \left(\text{(}Age)/4\right)+4+50\left(F_{\text{I}}\mathrm{O}{}_2-0.21\right)\\ & \approx \left(80/4\right)+4+50\times (0.30-0.21)\approx 0.29\text{mmHg}\end{array}$$

3. Pretty much normal A-a gradient with high $P_{\text{a}}\mathrm{CO}{}_2$ indicates an acute COPD exacerbation

Harder Example

Question: A 64 y/o man with a history of CAD, presents to the ER with sudden onset of dyspnea 1 hour ago. He is in moderate respiratory distress, with rapid, shallow breaths. Current vitals: T=36.2 °C HR=115, BP=95/40, RR=30, O2 saturation=100% on 6L via nasal prongs. ABG: pH 7.54 / $P_{\text{a}}\mathrm{CO}{}_2$ 28 / $P_{\text{a}}\mathrm{O}{}_2$ 143 on 6L $\mathrm{O}{}_2$ via NP Answer:

1. Check the A-a gradient

$$\begin{array}{rl}{F}_{\text{I}}\mathrm{O}{}_2& \approx 0.21+(0.03\times 6)=0.39\\ P_{\text{A}}\mathrm{O}{}_2& =\left[F_{\text{I}}\mathrm{O}{}_2\left(P_{\text{I}}-P_{\mathrm{H}{}_2\mathrm{O}}\right)\right]-\left(\frac{P_{\text{a}}\mathrm{CO}{}_2}{\text{RQ}}\right)\\ & =243\text{mmHg}\\ \text{A-a gradient}& =243-143=100\text{mmHg}\end{array}$$

2. Estimate adjusted normal A-a gradient

$$\begin{array}{rl}\text{Normal A-a gradient}& \approx \left(\text{Age}/4\right)+4+50\left(F_{\text{I}}\mathrm{O}{}_2-0.21\right)\\ & \approx 29\text{mmHg}\end{array}$$

3. Abrupt changes in A-a gradient without symptoms suggestive of hypertensive emergency or mucous plugging can be explained by pulmonary embolism or acute coronary syndrome with secondary pulmonary oedema

Harder Example

• Increase in A-a gradient with increase $F_{\text{I}}\mathrm{O}{}_2$ suggests right to left shunting
• Patient appears to be due to intrapulmonary right to left shunting in a patient with septic shock (most likely severe sepsis and acute lung injury/ARDS secondary to endocarditis)

Other Measures of Oxygenation

• $P_{\text{a}}\mathrm{O}{}_2/F_{\text{I}}\mathrm{O}{}_2$ Ratio
  • Used in ICU setting to measure severity of hypoxaemia
  • Normal: $100\text{mm}\mathrm{Hg}/0.21=476\text{mm}\mathrm{Hg}$
  • Abnormal:
    • 200-300 mm$\mathrm{Hg}$ ⇒ gas exchange abnormal
    • <200 mm$\mathrm{Hg}$ ⇒ severe abnormality (e.g. more suggestive of ARDS)

Effect of Altitude

• Higher altitudes will only decrease $P_{\text{I}}$ in the alveolar gas equation (no effect on $F_{\text{I}}\mathrm{O}{}_2$ or $P_{\mathrm{H}{}_2\mathrm{O}}$)
• $P_{\text{a}}\mathrm{CO}{}_2$ usually decreases at high altitudes due to hypoxia-driven hyperventilation

VBG Vs ABG

$$\begin{array}{rl}\text{Arterial pH}& \approx \text{Venous pH}+0.03\\ P_{\text{a}}\mathrm{CO}{}_2& \approx P_{\text{V}}\mathrm{CO}{}_2-4\end{array}$$

• While VBGs are not useful for oxygenation status, they can probably substitute for ABGs in most analyses of acid base
  • Treger, R., Pirouz, S., Kamangar, N., Corry, D., 2010. Agreement between Central Venous and Arterial Blood Gas Measurements in the Intensive Care Unit. Clin J Am Soc Nephrol 5, 390–394. https://doi.org/10.2215/CJN.00330109

Effect of Temperature on ABG

• Higher temperature → more gas dissolved in blood

12345 Rule

• Respiratory acidosis :: For every 10 mmHg rise in PaCO2, there should be 1 increase in $\mathrm{HCO}{}_3{}^{-}$ for acute and 4 increase in chronic
• Respiratory alkalosis :: For every 10mmHg rise in PaCO2, there should be 2 decrease in $\mathrm{HCO}{}_3{}^{-}$ for acute and 5 decrease in chronic

	Acute	Chronic
Respiratory Acidosis	↑ $[\mathrm{HCO}{}_3{}^{-}]$	↑ by 4 $[\mathrm{HCO}{}_3{}^{-}]$
Respiratory Alkalosis	↓ by 2 $[\mathrm{HCO}{}_3{}^{-}]$	↓ by 5 $[\mathrm{HCO}{}_3{}^{-}]$

Anion Gap

• Given by the formula:

$$\mathrm{Anion}\mathrm{Gap}=\mathrm{Na}{}^{+}-(\mathrm{Cl}{}^{-}+\mathrm{HCO}{}_3{}^{-})$$

• The normal value varies between machine and technique used (4-12 if measured by ion selective electrode or 8-16 if measured by flame photometry)
• If AG >30 mmol/L then metabolic acidosis is invariably present
• Importantly albumin is the major unmeasured anion and contributes most to the anion gap value, so in hypoalbuminaemia patients may appear as a normal anion gap acidosis but actually have a high anion gap acidosis

$$\mathrm{Corrected}\mathrm{Anion}\mathrm{Gap}=\mathrm{Measured}\mathrm{Anion}\mathrm{Gap}+\frac{40-\mathrm{Albumin}}{4}$$

• Additionally, you can correct for phosphate as well because hypophosphateaemia also lowers the expected anion gap

$$\mathrm{Corrected}\mathrm{Anion}\mathrm{Gap}=0.25\times \mathrm{Albumin}+1.5\times \mathrm{PO}{}_4{}^{3-}$$

• High anion gap metabolic acidosis :: Accumulation of organic acids or impaired $\mathrm{H}{}^{+}$ excretion
• Normal anion gap metabolic acidosis :: Loss of $\mathrm{HCO}{}_3{}^{-}$ from ECF See: https://litfl.com/anion-gap/

EXAMPLE

Question A 48 y/o alcoholic man is found unconscious in his apartment, soiled with vomit. He was last seen leaving a party 6 hrs prior. ABG: pH 7.17 / $P_{\text{a}}\mathrm{CO}{}_2$ 65 / $\mathrm{HCO}{}_3{}^{-}$ 22 / Na: 136 / Cl 98 / Albumin 16 What disorders are present? Solution

1. pH suggestive of acidaemia
2. $P_{\text{a}}\mathrm{CO}{}_2$ elevated suggestive of respiratory acidosis
3. Check compensation. $\mathrm{HCO}{}_3{}^{-}$ should increase by 1 for every 10 $P_{\text{a}}\mathrm{CO}{}_{2}40\pm 3$ ⇒ $24+2.5\pm 3$ ⇒ lowest allowed value is 23.5, therefore additional metabolic acidosis present
4. Calculate anion gap: $\text{AG}=136-(98+22)=16$. ${\text{AG}}_{\text{adjusted}}={\text{AG}}_{\text{measured}}+0.25\times (40-16)=22$ ⇒ high anion gap metabolic acidosis
5. Calculate delta ratio: $\Delta \text{AG}/\Delta \mathrm{HCO}{}_3{}^{-}=10/2=5$ which is higher than expected irrespective of the aetiology so there is also a metabolic alkalosis present
6. Respiratory acidosis (from intoxication from central respiratory depression) + high anion gap metabolic acidosis (from alcoholic ketoacidosis) + metabolic alkalosis (from vomiting)

Corrected Values

• $\mathrm{Na}{}^{+}$ for glucose
  • In patients with marked hyperglycaemia, the elevated serum glucose raises the serum tonicity (as the glucose cannot enter cells) which pulls water out of cells and expands the extracellular water compartment – thereby lowering the concentration of sodium
  • The corrected serum sodium can be calculated, which represents what the serum sodium concentration would be if the glucose level was reduced back to normal
  • If the corrected sodium is in a normal range – the patient does not have a concurrent hypotonic hyponatraemia

$$\mathrm{Corrected}\mathrm{Na}{}^{+}=\mathrm{Na}{}^{+}+1.5\times \frac{\mathrm{glucose}-5.5}{5.5}\approx \mathrm{Na}{}^{+}+\frac{\mathrm{glcuose}-5}{3}$$

• $\mathrm{K}{}^{+}$ for pH (acidaemia causes hyperkalaemia)
  • For each 0.1 pH drop below 7.4, $\mathrm{K}{}^{+}$ rises by 0.6 mmol/L
  • e.g. For a patient with a $\mathrm{K}{}^{+}$ of 4 mmol/L at pH 7.2, the corrected $\mathrm{K}{}^{+}$ is 2.8, hence the patient is hypokalaemic and $\mathrm{K}{}^{+}$ should be monitored and replaced as pH is corrected
  • This occurs because of the exchange of $\mathrm{H}{}^{+}$ ions for $\mathrm{K}{}^{+}$ ions across the cell membrane which may cause the appearance of hyperkalaemia on serum potassium levels but the patient is actually net hypokalaemic
  • Correcting for potassium in alkalaemia (i.e. alkalaemia causing hypokalaemia) is not often done as the change is quantitatively smaller

$$\mathrm{Corrected}\mathrm{K}{}^{+}=\mathrm{K}{}^{+}-0.6\times \frac{7.4-\mathrm{pH}}{0.1}$$

• Correcting $\mathrm{Ca}{}^{+}$ for albumin, however evidence demonstrates that formulas actually perform worse than uncorrected calcium levels

$$\mathrm{Corrected}\mathrm{Calcium}=0.8\times (40-\mathrm{Albumin})+\mathrm{Ca}{}^{2+}$$

Easily Figuring Out Direction of Compensation

• One must just look at the Henderson-Hasselbach equation to determine that for the pH to remain the same, the $\mathrm{HCO}{}_3{}^{-}$ must move in the same direction as $P_{\text{a}}\mathrm{CO}{}_2$ and vice versa

$$\mathrm{pH}=6.1+\log \left(\frac{[\mathrm{HCO}{}_3{}^{-}]}{0.03\times P_{\text{a}}\mathrm{CO}{}_2}\right)$$

Sources

• https://litfl.com/acid-base-disorders/
• The A-a Gradient (ABG Interpretation - Lesson 16) - YouTube

Useful resources

• https://onepagericu.com/acid-base

Footnotes

1. This is the approach for the ‘Boston’ approach or standard approach ↩

2. In July 2019, Jeremy Cohen (the CICM Chair of the Second Part Exam) issued a decree via the official college newsletter, stating that “unless otherwise specified in the question stem, anion gap calculations should be made without inclusion of potassium or correction to albumin.” ↩

3. Although apparently the evidence for this was from Figge in 1998 and is flawed (see: Mythbusting: Correcting the anion gap for albumin is not helpful) ↩

4. With the exception being patients with extreme diets (e.g. severe anorexia) ↩

5. The normal A-a gradient also increases with higher $F_{\text{I}}\mathrm{O}{}_2$ and may be >100 mmHg in an elderly patient on 100% $\mathrm{O}{}_2$ ↩