At a PaO₂ of 60 mmHg, hemoglobin saturation is approximately 90%. If the same hemoglobin is exposed to a PaO₂ of 30 mmHg under identical conditions, the saturation will be approximately:

Explanation

## Hemoglobin Saturation and the S-Shaped Curve **Key Point:** The oxygen dissociation curve is NOT linear — it is sigmoid (S-shaped). This non-linear relationship means that saturation does not change proportionally with PaO₂. ### Understanding the Sigmoid Shape The S-shaped curve has three distinct regions: 1. **Steep Middle Section (PaO₂ 20–60 mmHg):** Small changes in PaO₂ cause large changes in saturation. This is the physiologically important range for tissue oxygen delivery. 2. **Flat Upper Plateau (PaO₂ > 60 mmHg):** Saturation increases slowly; hemoglobin is nearly saturated. 3. **Flat Lower Plateau (PaO₂ < 20 mmHg):** Saturation decreases slowly; hemoglobin is nearly empty. ### Applying the Curve to This Question **Given:** - At PaO₂ = 60 mmHg → SaO₂ ≈ 90% - At PaO₂ = 30 mmHg → SaO₂ = ? **Analysis:** Both 60 and 30 mmHg fall in the steep middle section of the curve. A 50% drop in PaO₂ (from 60 to 30) corresponds to approximately a 45% saturation (not 45 mmHg, but 45% saturation). **High-Yield:** Standard reference values: - PaO₂ 100 mmHg → SaO₂ ≈ 98% - PaO₂ 60 mmHg → SaO₂ ≈ 90% - PaO₂ 40 mmHg → SaO₂ ≈ 75% - PaO₂ 30 mmHg → SaO₂ ≈ 58% - PaO₂ 20 mmHg → SaO₂ ≈ 35% **Clinical Pearl:** This is why the steep middle section is called the "physiologic range." Tissues operating at PaO₂ 30–60 mmHg can extract large amounts of oxygen with small changes in partial pressure — ideal for matching oxygen supply to metabolic demand. ### Why Linearity Fails Hemoglobin exhibits **cooperative binding** (allosteric effect): binding of the first O₂ molecule increases affinity for the second, which increases affinity for the third, etc. This creates the sigmoid curve and ensures efficient oxygen loading in the lungs and unloading in tissues.