Theory of resistive load detection

During normal breathing the brain sets the required muscle pressure to overcome resistance and elastance and presumably monitors the resultant flow (rate of change of volume). The lag in flow compared to the pressure can be described by a phase angle. When a small resistive load is added the resultant flow is delayed further and the phase angle increases. We postulate that if the change in phase angle exceeds a critical phase lag, the added load is detected. Over a wide range of basal resistances, R, the mathematical analysis predicts that detection occurs if the just noticeable added resistance, delta R, is a constant fraction of the basal resistance. Resistive load detection thus obeys the Weber psychophysical law, delta R/R = constant. This is in accord with previous experimental observations. The theory also predicts that delta R/R increases at low basal resistance in accord with recent experimental observations. Further as yet untested predictions of the theory are that breathing frequency and elastance should affect the Weber relationship.