Differential negative resistance in a one-mass model of the larynx with supraglottal resistance

The steady flow calculations of Conrad [Conference on Physiology and Biophysics of Voice, Iowa (1983)], show that the larynx can manifest a differential negative resistance, i.e., translaryngeal pressure can decrease as flow rate increases. These calculations were based on the one-mass model of Flanagan and Landgraf [IEEE Trans. Audio Electroacoust. AU-16, 57–64 (1968)] with added supraglottal resistance. If the spring acting on the mass is changed from linear to nonlinear, the differential negative resistance becomes bounded by two regions of positive differential resistance. As nonlinear stiffness increases, differential negative resistance disappears. The one-mass model plus supraglottal resistance can be described as an N-type, flow-controlled nonlinear resistance, QNLR. It is well known in electronics and elsewhere that a QNLR in a series resonant circuit can transform de power to oscillatory power [e.g., Ph. le Corbeiller, Proc. Inst. Elec. Eng. 79, 361–378 (1936)]. The system can be usefully analyzed in terms of van der Pol's equation which gives the oscillation condition, the frequency, rate of build-up, limiting amplitude and efficiency. The analysis shows that differential negative resistance is a necessary condition for oscillation.