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resources:formulae [2024/01/02 13:42] – adminresources:formulae [2025/05/09 09:46] (current) – [CPET Testing] admin
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 ==== 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                | $P_{aw} =  FR + \frac{V_{t}}{C} + PEEP_{total}$                                                          | +^ Equation of Motion                | $P_{aw} =  FR + \frac{V_{t}}{C} + PEEP_{total}$                                               | 
-^ Compliance                        | $C = \frac{\Delta V}{\Delta P}$                                                                          | +^ Compliance                        | $C = \frac{\Delta V}{\Delta P}$                                                               | 
-^ Natural Decay Equation            | $V_i(t)= \frac{V_o}{e^{\frac{t}{RC}}} = \frac{V_o}{e^{\frac{t}{\tau}}}$                                  | +^ 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) $                        | +^ 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 $RQ = 0.80$ | +^ Alveolar Gas Equation             | $P_AO_2 = F_iO_2(P_{atm}-P_{H_2O}) - \frac{P_aCO_2}{RQ} $, where $RQ = 0.80$                  | 
-^ Mech Power, VC| ${MP}_{VC} = 0.098 \cdot RR \cdot V_t[PIP-\frac{1}{2}(P_{plat}-PEEP)]$ | +^ Mech Power, VC                    | ${MP}_{VC} = 0.098 \cdot RR \cdot V_t[PIP-\frac{1}{2}(P_{plat}-PEEP)]$                        | 
-^ Mech Power, PC| |+^ Mech Power, PC                    | ${MP}_{VC} = 0.098 \cdot RR \cdot V_t[PEEP + \Delta P_{insp}(1-e^{\frac{-T_{insp}}{RC}})]$  |
  
 ===== Respiratory Equations ===== ===== Respiratory Equations =====
 ==== Mechanical Power ==== ==== Mechanical Power ====
-${MP}_{VC} = 0.098 \cdot RR \cdot V_t[PIP-\frac{1}{2}(P_{plat}-PEEP)] \approx \frac{VE(P_{peak}+PEEP+\frac{Q_{insp}}{6})}{20}$+=== 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://xlung.net/en/mv-manual/basic-modes-of-mechanical-ventilation | Vent Waveforms]]   * [[https://xlung.net/en/mv-manual/basic-modes-of-mechanical-ventilation | Vent Waveforms]]
  
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 +==== 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 ====
 $\frac{V_D}{V_T} = \frac{P_ACO_2 - P_ECO_2}{P_ACO_2}$ $\frac{V_D}{V_T} = \frac{P_ACO_2 - P_ECO_2}{P_ACO_2}$
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 $P_{aw} = \dot VR + \frac{V_t}{C} + PEEP_{total} + P_{musc}$  $P_{aw} = \dot VR + \frac{V_t}{C} + PEEP_{total} + P_{musc}$ 
  
 +==== 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 ===== 
 $TPG = mPAP - PCWP$ $TPG = mPAP - PCWP$
  
 $SVR =\frac{MAP-CVP}{CO}\cdot80$ $SVR =\frac{MAP-CVP}{CO}\cdot80$
 +
 +$PVR = \frac{mPAP - PCWP}{CO}\cdot80$
  
 $CO = LVOT_{area}\cdot LVOT_{VTI}\cdot HR$ $CO = LVOT_{area}\cdot LVOT_{VTI}\cdot HR$
resources/formulae.1704202946.txt.gz · Last modified: by admin

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