Harmonic distortion from nonlinear systems with broadband inputs: applications to lung mechanics

We present a simple index, extended harmonic distortion (kd), to represent the degree of system nonlinearity under sparse pseudorandom noise inputs (SPRN). The frequencies in a SPRN waveform are neither harmonics nor sums or differences of the other component frequencies. Expressed by percentage, the kd is the square root of the ratio of output power at non-input frequencies to the total output power. We evoke three simple corrections to recover the true kd under imperfect SPRN inputs. Simulations on two block-structured nonlinear models (Wiener and Hammerstein) demonstrate the necessity and effectiveness of these corrections especially for the Wiener-type nonlinearity. By applying kd to pressure-flow data of dog lungs, we found that the nonlinear harmonic interactions from a lung arise primarily from its tissues most likely the processes governing the tissue stiffness. This nonlinearity, assessed from kd, is stronger at higher tidal volumes and enhanced (but to a lesser degree) during bronchoconstriction. We conclude that since the kd approach avoids the necessity for multiple-input measurements and lengthy data records, it may be useful for tracking the dynamic variations in nonlinearities of a physiological system.