User Tools
resources:formulae
Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| resources:formulae [2023/12/22 20:15] – admin | resources:formulae [2024/06/05 17:46] (current) – [Equation of Motion] admin | ||
|---|---|---|---|
| Line 3: | Line 3: | ||
| ==== Foundational Equations ==== | ==== Foundational Equations ==== | ||
| - | ^ Ohm's Law | $\Delta P = FR = P_{aw} - P_{alv} = P_{pl} - PEEP_{total}$ | + | ^ Ohm's Law | $\Delta P = FR = P_{aw} - P_{alv} = P_{pl} - PEEP_{total}$ |
| - | ^ Equation of Motion | + | ^ Equation of Motion |
| - | ^ Compliance | + | ^ Compliance |
| - | ^ Natural Decay Equation | + | ^ Natural Decay Equation |
| - | ^ Calculating $\Tau$, General Case | $ \tau = \frac{V_t}{F} \Bigg(\frac{PIP - P_{plt}}{P_{plt} - PEEP_{total}}\Bigg) $ | | + | ^ Calculating $\Tau$, General Case | $ \tau = \frac{V_t}{F} \Bigg(\frac{PIP - P_{plt}}{P_{plt} - PEEP_{total}}\Bigg) $ |
| - | ^ Alveolar Gas Equation | + | ^ Alveolar Gas Equation |
| + | ^ Mech Power, VC | ${MP}_{VC} = 0.098 \cdot RR \cdot V_t[PIP-\frac{1}{2}(P_{plat}-PEEP)]$ | ||
| + | ^ Mech Power, PC | ${MP}_{VC} = 0.098 \cdot RR \cdot V_t[PEEP + \Delta P_{insp}(1-e^{\frac{-T_{insp}}{RC}})]$ | ||
| + | ===== Respiratory Equations ===== | ||
| + | ==== Mechanical Power ==== | ||
| + | === Volume Control === | ||
| + | ${MP}_{VC} = 0.098 \cdot RR \cdot V_t[PIP-\frac{1}{2}(P_{plat}-PEEP)] \approx \frac{MV(P_{peak}+PEEP+\frac{Q_{insp}}{6})}{20}$ | ||
| + | |||
| + | ===Pressure Control === | ||
| + | ${MP}_{VC} = 0.098 \cdot RR \cdot V_t[PEEP + \Delta P_{insp}(1-\exp(\frac{-T_{insp}}{RC}))]$ | ||
| + | |||
| + | ${MP}_{VC} = 0.098 \cdot RR \cdot V_t[PEEP + \Delta P_{insp}(1-e^{\frac{-T_{insp}}{RC}})] \approx 0.098 \cdot RR \cdot V_t(PEEP + \Delta P_{insp})$ | ||
| * [[https:// | * [[https:// | ||
| + | |||
| ==== Alveolar Gas Equation==== | ==== Alveolar Gas Equation==== | ||
| $P_AO_2 = F_iO_2(P_{atm}-P_{H_2O}) - \frac{P_aCO_2}{RQ}$ | $P_AO_2 = F_iO_2(P_{atm}-P_{H_2O}) - \frac{P_aCO_2}{RQ}$ | ||
| Line 20: | Line 32: | ||
| + | ==== Shunt Equation (Berggren Equation)==== | ||
| + | $$\frac{Q_s}{Q_t} = \frac{C_{C_{O_2}} - C_{a_{O_2}}}{C_{C_{O_2}} - C_{v_{O_2}}}$$ | ||
| + | |||
| + | where: | ||
| + | * $Q_s=$ pulmonary physiology shunt $(\frac{mL}{min})$ | ||
| + | * $Q_t=$ cardiac output $(\frac{mL}{min})$ | ||
| + | * $C_{C_{O_2}} = $ end-pulmonary-capillary oxygen content | ||
| + | * $C_{a_{O_2}} = $ arterial oxygen content | ||
| + | * $C_{v_{O_2}} =$ mixed venous oxygen content | ||
| + | |||
| + | So, you will need an ABG and a true mixed VBG (art line + SGC). | ||
| + | |||
| + | === Derivation === | ||
| ==== Dead Space Fraction ==== | ==== Dead Space Fraction ==== | ||
| $\frac{V_D}{V_T} = \frac{P_ACO_2 - P_ECO_2}{P_ACO_2}$ | $\frac{V_D}{V_T} = \frac{P_ACO_2 - P_ECO_2}{P_ACO_2}$ | ||
| Line 65: | Line 90: | ||
| $P_{aw} = \dot VR + \frac{V_t}{C} + PEEP_{total} + P_{musc}$ | $P_{aw} = \dot VR + \frac{V_t}{C} + PEEP_{total} + P_{musc}$ | ||
| + | ==== CPET Testing==== | ||
| + | ===Heart rate reserve | ||
| + | $HRR = HR_{achieved}^{max} - HR_{predicted}^{peak}$, | ||
| + | |||
| + | where $HR_{predicted}^{peak} = 220 - age$ | ||
| + | |||
| + | ===Slope of work efficiency=== | ||
| + | $m(work_e) = \frac{\Delta VO_2}{\Delta WR}$ | ||
| + | |||
| + | ===Slope of heart rate rise=== | ||
| + | $\frac{\Delta HR}{\Delta VO_2}$ | ||
| ===== CARDS ===== | ===== CARDS ===== | ||
| $TPG = mPAP - PCWP$ | $TPG = mPAP - PCWP$ | ||
resources/formulae.1703276139.txt.gz · Last modified: 2023/12/22 20:15 by admin
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
