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Could someone kindly provide an explanation on how to solve these equations? The solutions is highlighted in red line 3.(25 ) In a Covid 19

Could someone kindly provide an explanation on how to solve these equations?

The solutions is highlighted in red line

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3.(25 ) In a Covid 19 patient total respiratory system resistance Rrs= 7.7cm H20/(L/sec) and total compliance Crs= 19.6 ml/cm H20 Tidal volume VT= .651 L and respiratory frequency f= 31 breaths/min the inspiratory resistive work Wr= So dy Tinsp Pr at dt Pr=Rrs dV/dt the elastic work in cm H20-L Wel=So Pel dV Pel=V/Crs P=Rrs dV/dt + V/Crs P=Pr+Pel A. The patient is put on a ventilator in volume controlled mode where airflow is constant for the inspiratory duration Tinsp. During expiration ventilator pressure =0. A1(5).Calculate Wr in cm H20 -L for Tinsp= 1/(2*f) A2(5).Calculate Wr in cm H20 -L for Ting=1/(3*f) A3(5). Calculate the elastic work in cm H20-L Wel=So Pel dV Pel=V/C A1. f=31 breaths/min T=60/31=1.94 sec Tinp=1.94/2=.97 sec Flow=.651/.97=.67 L/sec Wr=So (Tinsp Pray dt =.67*7.7*.67*.97=3.35 cm H20-L A2. Tinp=1.94/3=.647 Flow=.651/.647=1.01 L/sec Wr=1.01*7.7*1.01*.647=5.08 cm H20-L A3. Wel= VT^2/2C=.651*.651/(2*.0196)=10.8 cm H20-L B. (5) The patient is put on a ventilator in pressure controlled mode with Tinsp=1/(3f). V(t)=Crs P (1-exp(-t/(Rrs*Crs))Calculate ventilator pressure P for VT=651 ml Ventilator pressure =0 during expiration. Tinsp=.647 sec Rs*C=7.7*.0196=.15 sec .651=.0196*p*(1exp(647/.15))=.0196*p*.987 P=.651/(.0196*.987)=33.7 cm H20 C.(5) Continuous positive airway pressure (PEEP) is often applied during expiration to improve gas exchange. Calculate the additional elastic work per breath required for a PEEP level of 3 cm H20, Crs= 19.6 mL/cm H20 Tidal volume VT= .651 L AWel=3*.651=1.95 cm H20-L

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