Respiratory Mechanics · Equation of Motion Simulator

Pressure waveforms across three modes

Curves integrated from the equation of motion: (Paw − PEEP) + Pmus = R · Flow + V/C. Adult parameters: C = 60 mL/cmH₂O, R = 5 cmH₂O/(L/s), τ = 0.3 s.

Spontaneous breathing

P_aw = 0 · alveolar drops below atmospheric on inspiration · pleural swings −5 to ~−13

Controls
14 /min
8 cmH₂O
Airway (P_aw)
Alveolar (P_alv)
Pleural (P_pl)
Muscles drop pleural pressure → alveolar drops below atmospheric → flow enters lungs. At end-inspiration flow is zero, so P_alv returns to 0.

CPAP

P_aw clamped at PEEP · alveolar drops below PEEP on inspiration · patient does the work

Controls
8 cmH₂O
16 /min
8 cmH₂O
Airway (P_aw)
Alveolar (P_alv)
Same physiology as spontaneous, just shifted up by PEEP. WOB unchanged. Higher effort → larger alveolar dip → larger tidal volume.

Pressure support + PEEP

Machine ramps P_aw to PEEP + PS · alveolar lags behind by τ = R·C

Controls
5 cmH₂O
12 cmH₂O
14 /min
0.2 s
Airway (P_aw)
Alveolar (P_alv)
Alveolar approaches PIP via 1−e^(−t/τ). Crank up rate or PEEP to see alveolar fail to reach baseline → auto-PEEP.
The math behind the curves
(P_aw − PEEP) + P_mus = R · Flow + V/C
Flow = [(P_aw − PEEP) + P_mus − V/C] / R
P_alv = P_aw − R · Flow
τ = R × C = 5 × 0.06 = 0.3 s
Spontaneous
P_aw = 0
P_mus drives flow inward
P_alv: −3 to −5 on inspiration
P_alv: +2 to +4 on expiration
CPAP
P_aw = PEEP
P_mus still drives flow
P_alv dips below PEEP on insp
WOB unchanged from baseline
PSV
P_aw = PEEP+PS during insp
P_mus = 0 (machine takes over)
P_alv approaches PIP via 1−e^(−t/τ)
Expiratory decay: e^(−t/τ)
Single-compartment linear model. Forward Euler integration at 10 ms timesteps. Increasing R or decreasing C lengthens the time constant; increasing PEEP raises baseline without changing τ. Disease states (low C in ARDS, high R in COPD) and viscoelastic effects are not modeled.