Aerial blood gas of a 5 year old child done at sea level gives the following results: pH 7.41, Pa02100 mmHg, and PaCO2 40 mm Hg. The child is being ventilated with 80% oxygen. What is the (A-a) P02
**Core Concept**
The alveolar-arterial oxygen gradient, (A-a) PO2, is a measure of the difference between alveolar oxygen levels and arterial oxygen levels, reflecting gas exchange efficiency across the alveolar-capillary membrane. It is calculated using the alveolar gas equation, which takes into account the partial pressure of oxygen in the alveoli (PAO2) and the partial pressure of oxygen in arterial blood (PaO2). The **alveolar gas equation** is PAO2 = (FiO2 * (Patm - PH2O)) - (PaCO2 / R), where FiO2 is the fraction of inspired oxygen, Patm is atmospheric pressure, PH2O is the partial pressure of water vapor, PaCO2 is the partial pressure of carbon dioxide, and R is the respiratory quotient.
**Why the Correct Answer is Right**
To calculate the (A-a) PO2, we first need to calculate the alveolar oxygen level (PAO2) using the given values: FiO2 = 0.8 (80% oxygen), Patm = 760 mmHg at sea level, PH2O = 47 mmHg, PaCO2 = 40 mmHg, and assuming a respiratory quotient (R) of 0.8. The calculation yields PAO2 = (0.8 * (760 - 47)) - (40 / 0.8) = 599 - 50 = 549 mmHg. Given the PaO2 is 100 mmHg, the (A-a) PO2 = PAO2 - PaO2 = 549 - 100 = 449 mmHg.
**Why Each Wrong Option is Incorrect**
**Option A:** This option would be incorrect because it does not match the calculated (A-a) PO2 based on the given values and the alveolar gas equation.
**Option B:** Similarly, this option is incorrect as it does not align with the calculation.
**Option C:** This option is also incorrect for the same reason, not matching the calculated difference.
**Option D:** This is the correct answer as explained, but let's proceed to the next section for further clarification.
**Clinical Pearl / High-Yield Fact**
A key point to remember is that the normal (A-a) PO2 gradient is less than 10 mmHg in a healthy individual breathing room air. An increased gradient, as seen in this scenario, indicates an issue with gas exchange, which could be due to various conditions affecting the lungs, such as pneumonia, pulmonary edema, or chronic obstructive pulmonary disease (COPD).
**Correct Answer:** Correct Answer: D. 449 mmHg