\(N_2\) wash-out method
Subject breathes 100% FIO2
Exhaled nitrogen concentration over time is collected, and integrated to find total exhaled \(N_2\) volume
Dividing by 0.79 (initial \(N_2\_ concentration) gives TLV
Drawbacks: Some \(N_2\) is washed out from blood and tissues (~250mL), only measures ventilated lung volume, leaks will befoul measurement
Helium wash-in method
Inhale gas bolus of known concentration and volume
Hold breath and wait to equilibrate throughout lung volime
Exhale gas
$$C_1 V_{\text{bolus}} = C_2 (\text{FRC} + V_{\text{bolus}})$$
Drawbacks: Helium will dissolve into tissues, only measures ventilated lung
Body Plethysmography
Subject confined in a closed box; airway pressure + box pressure measured
Exhales against closed airway \( \to \ \downarrow V_{\text{Chest}} \ \uparrow V_{box} \ \to \uparrow P_{\text{mouth}} \ \downarrow P_{\text{box}} \)
Measures whole intrathoracic gas volume
Drawbacks: Expensive, immobile equiptment
$$PV = nRT = \text{constant}$$
$$P1_{mouth} = P1_{box} = P_{\text{barometric}}$$
$$P1 V_{box} = P2_{box} (V_{box} + \Delta V)$$
$$\Delta V = V_{box} \frac{P1 - P2_{box}}{P2_{box}}$$
$$P1 FRC = P2_{mouth} (FRC - \Delta V)$$
$$\Delta V = FRC \frac{P1 - P2_{mouth}}{P2_{mouth}}$$
$$FRC \frac{P1 - P2_{mouth}}{P2_{mouth}} = V_{box} \frac{P1 - P2_{box}}{P2_{box}} $$
$$FRC = V_{box} \frac{P1 - P2_{box}}{P1 - P2_{mouth}} \frac{P2_{mouth}}{P2_{box}} $$
$$FRC = V_{box} \frac{\Delta P_{box}}{\Delta P_{mouth}} \frac{P2_{mouth}}{P2_{box}} $$
Because the pressure swings are small compared to barometric pressure, \(\frac{P2_{mouth}}{P2_{box}} \approx 1\) and
$$FRC = V_{box} \frac{\Delta P_{box}}{\Delta P_{mouth}}$$