| Ohm's Law | $\Delta P = FR = P_{aw} - P_{alv} = P_{pl} - PEEP_{total}$ |
|---|---|
| Equation of Motion | $P_{aw} = FR + \frac{V_{t}}{C} + PEEP_{total}$ |
| Compliance | $C = \frac{\Delta V}{\Delta P}$ |
| Natural Decay Equation | $V_i(t)= \frac{V_o}{e^{\frac{t}{RC}}} = \frac{V_o}{e^{\frac{t}{\tau}}}$ |
| Calculating $\Tau$, General Case | $ \tau = \frac{V_t}{F} \Bigg(\frac{PIP - P_{plt}}{P_{plt} - PEEP_{total}}\Bigg) $ |
| Alveolar Gas Equation | $P_AO_2 = F_iO_2(P_{atm}-P_{H_2O}) - \frac{P_aCO_2}{RQ} $, where $RQ = 0.80$ |
$P_AO_2 = F_iO_2(P_{atm}-P_{H_2O}) - \frac{P_aCO_2}{RQ}$
substituting back in to $RQ$ equation: $RQ = \frac{P_ACO_2}{\frac{V_AP_ACO_2}{kVO_2}}= \frac{VO_2}{V_a}k$
$V_T = V_A + V_D$, where $V_A = 350$ and $V_D = 150$
$\frac{V_D}{V_T} = \frac{P_ACO_2 - P_ECO_2}{P_ACO_2}$
Formal measurement of $P_ECO_2$ requires volumetric capnography, which requires a capable ventilator or a dedicated measurement device.
Thankfull, $P_ECO_2 \approx ETCO_2$, so an approimation would $\frac{V_D}{V_T} = \frac{P_ACO_2 - ETCO_2}{P_ACO_2}$
$P_{A}O_2 = F_iO_2(P_{atm}-P_{H_2O}) - \frac{P_AO2}{RQ}$ $\dot{V}_A=k\frac{\dot{V}CO_2}{P_ACO_2}$ $\implies \dot{V}CO2 = \frac{\dot{V}_AP_ACO_2}{k}$
To convert $F_ACO_2$ into $P_ACO_2$, we have $F_ACO_2(P_{atm} - PH_2O = P_ACO_2$ Similarly, using $F_ECO_2$, we can show $P_ECO_2 = F_ECO_2(P_{atm} - P_{H_2O})$
$Volume_{expiredCO2} = Volume_{producedAlvCO2}$
$V_TF_ECO_2 = V_AF_ACO_2$
$V_TF_ECO_2 = (V_T - V_D)F_ACO_2$, and we can convert $F_ACO_2$ into $P_ACO_2$