Single-compartment model of the respiratory system: Pmus(t) = V/C + R · dV/dt (equation of motion). V is the volume above resting lung volume (FRC), C compliance (L per cmH₂O), R airway resistance (cmH₂O per L/s). Muscles apply a half-sine pressure during inspiration; exhalation is passive and decays with time constant τ = R C. Alveolar pressure is Palv = −R dV/dt, pleural pressure Ppl = Palv − V/C. The area of the P-V loop is the work done against resistance.

Gas exchange: the first V_D of each breath only moves dead-space gas, so alveolar ventilation is V̇A = (VT − VD) f and PACO₂ = 863 · V̇CO₂ / V̇A (863 converts STPD fractions to mmHg), with PAO₂ = FIO₂(713) − PACO₂/RQ, RQ = 0.8. The simulation integrates alveolar CO₂ breath by breath with a well-mixed 2.4 L alveolar volume.

Presets mimic obstruction (high R, air trapping), emphysema (high C, little recoil), fibrosis (low C) and exercise. Simplifications: one compartment, linear R and C, no inertia, no chest-wall model, perfect mixing, constant dead space, ventilation-perfusion matching assumed. Educational illustration, not a clinical model.