14.3 Blood Gas & CO-oximetry Derived Calculations

From analyzer numbers to derived indices (III.A.1–2)

Blood gas analyzers report pH, PCO2, PO2 (and often calculated HCO3, BE). CO-oximeters report hemoglobin species fractions. Domain III.A expects the RPFT to compute or select derived values used in clinical review: acid-base primary disorder pattern, alveolar PO2, A-a gradient, oxygen content concepts, and correct use of FO2Hb versus saturation estimates.

You are not writing a full pulmonologist consult, but you must not mis-label FO2Hb as “SpO2,” drop the water-vapor term from PAO2, or ignore that anemia devastates content while PO2 looks normal.

Henderson-Hasselbalch relationship (qualitative mastery)

Conceptually, pH depends on the balance between respiratory component (PaCO2) and metabolic component (HCO3−):

$$pH \propto \log\left(\frac{[HCO_3^-]}{0.03 \times PaCO_2}\right)$$

(Exact constants appear in textbooks; exam literacy is directional.)

Primary disorders (technologist pattern recognition)

Compensation moves the other component to pull pH toward normal—it rarely overshoots to fully normal pH in simple single disorders. Mixed disorders break simple patterns (both CO2 and HCO3 abnormal in same pH direction).

Worked mini-example — primary respiratory acidosis

pH 7.28, PaCO2 58 mmHg, HCO3− 26 mEq/L (near normal).

• Low pH + high PaCO2 + near-normal HCO3− → acute respiratory acidosis pattern.

Worked mini-example — metabolic acidosis with respiratory compensation

pH 7.32, PaCO2 28 mmHg, HCO3− 14 mEq/L.

• Low pH + low HCO3− → metabolic acidosis; low PaCO2 is compensatory hyperventilation, not the primary story.

Exam trap: Calling every low PaCO2 “primary respiratory alkalosis” without looking at pH and HCO3−.

Alveolar gas equation and A-a gradient

Simplified PAO2

A widely taught simplified alveolar oxygen equation:

$$PAO_2 \approx FIO_2 \times (P_{atm} - 47) - \frac{PaCO_2}{R}$$

Where:

• FIO2 — inspired oxygen fraction (0.21 on room air).
• Patm — barometric pressure (mmHg); sea level ~760 mmHg.
• 47 — water vapor pressure at body temperature (mmHg) concept.
• PaCO2 — arterial PCO2 (mmHg), used as a surrogate for PACO2.
• R — respiratory exchange ratio, often assumed 0.8 when not measured (sometimes taught with PaCO2 × 1.25 as equivalent to ÷0.8).

Worked mini-example — room air at sea level

FIO2 0.21, Patm 760, PaCO2 40, R 0.8.

1. PIO2-ish term: 0.21 × (760 − 47) = 0.21 × 713 = 149.7 mmHg.
2. PaCO2/R = 40 / 0.8 = 50.
3. PAO2 ≈ 149.7 − 50 ≈ 100 mmHg.

If measured PaO2 = 85 mmHg, then:

$$A\text{-}a\ gradient = PAO_2 - PaO_2 \approx 100 - 85 = 15\ \text{mmHg}$$

Worked mini-example — elevated FIO2

FIO2 0.40, Patm 760, PaCO2 40, R 0.8.

• 0.40 × 713 = 285
• 285 − 50 = PAO2 ≈ 235 mmHg
• If PaO2 = 120 → A-a ≈ 115 mmHg (widened on O₂—context matters; age and FIO2 expected gradients differ).

Technologist points:

• Enter correct FIO2 and Patm (altitude labs cannot pretend Patm = 760).
• A-a gradient rises with age somewhat; “normal” is not always <10 on every stem—know the calculation first.
• Hypoxemia with normal A-a suggests hypoventilation or low PIO2; hypoxemia with high A-a suggests V/Q mismatch, shunt, diffusion limitation concepts—clinical layer, but calculation must be right first.

Oxygen content (CaO2) concept

Arterial oxygen content is how much O2 is in the blood, not merely how high the PO2 is.

Conceptual equation:

$$CaO_2 \approx (1.34 \times [Hb] \times SO_2) + (0.003 \times PaO_2)$$

Where:

• 1.34 mL O2 per g Hb (some texts use 1.36 or 1.39—know the structure, use lab constants).
• [Hb] in g/dL.
• SO2 as fraction (e.g., 0.97) from appropriate saturation measure.
• 0.003 × PaO2 — dissolved O2, usually small at ordinary PO2.

Worked mini-example — anemia with “normal” PO2

Hb 7 g/dL, SO2 0.97, PaO2 95 mmHg.

• Bound ≈ 1.34 × 7 × 0.97 ≈ 9.1 mL/dL
• Dissolved ≈ 0.003 × 95 ≈ 0.3
• CaO2 ≈ 9.4 mL/dL (low)

Compare normal-ish Hb 15 g/dL at same SO2/PO2 → bound ≈ 1.34 × 15 × 0.97 ≈ 19.5, total ~19.8 mL/dL.

Exam gold: Severe anemia → content hypoxia risk even when SpO2 and PaO2 look acceptable. Domain III wants that conceptual calculation, not a shrug that “sats are fine.”

CO-oximetry: FO2Hb vs SpO2 vs estimated SaO2 (III.A.2)

What co-oximetry measures

Multiwavelength CO-oximetry / hemoximetry partitions hemoglobin into species, commonly:

Functional saturation concepts (O2Hb / (O2Hb + HHb)) differ from fractional oxyhemoglobin (O2Hb / total Hb including dyshemoglobins).

SpO2 and calculated SaO2 are not the same as FO2Hb

Worked mini-example — carbon monoxide exposure

CO-ox: FO2Hb 78%, FCOHb 18%, MetHb 1%, HHb 3% (illustrative).

• Pulse ox might still read ~90%+ misleadingly depending on device/situation.
• Calculated sat from PO2 alone might look near normal if PaO2 is normal.
• FO2Hb 78% reveals reduced oxygen-carrying oxyhemoglobin fraction; CaO2 falls.

Technologist rule: When dyshemoglobin is suspected (smoke inhalation, known CO exposure, nitrate/drug MetHb risk, sat gap), select CO-oximetry results and report FO2Hb and dyshemoglobin fractions, not SpO2 alone as the gold saturation.

Saturation gap concept

Large difference between calculated O2 sat and measured FO2Hb/functional sat prompts co-ox evaluation. Domain III.A.2 is about recognizing which number to report for oxygen-binding status.

Putting ABG-derived calculations on the report

1. Verify sample validity (II.C)—air bubble, delay, temperature—before trusting derived math.
2. Report pH, PCO2, PO2, HCO3−/BE as configured.
3. Compute/select PAO2 and A-a when ordered or SOP-required, with stated FIO2 and Patm.
4. When Hb and sat available, understand content implications for severe anemia.
5. Attach CO-ox panel when indicated; label FO2Hb distinctly from SpO2.
6. For acid-base, ensure calculated HCO3− consistency with measured pH/PCO2 (machine flags).

RPFT vignettes

Vignette A: Room air, Patm 760, PaCO2 80, PaO2 50. PAO2 ≈ 0.21×713 − 80/0.8 ≈ 150 − 100 = 50; A-a ≈ 0. Hypoxemia with normal A-a fits pure hypoventilation pattern conceptually.

Vignette B: PaO2 55, PAO2 100 → A-a 45 widened—do not call this pure hypoventilation without looking at PaCO2.

Vignette C: SpO2 98%, FO2Hb 82%, COHb 15%—report co-ox fractions; do not certify “normal oxygenation” from SpO2 alone.

Link forward

Exercise, walk-test, resistance, muscle pressures, provocation PC20, and serial change math complete Domain III.A calculations in section 14.4.