Mathematical modeling and spectrum analysis of the physiological patello-femoral pulse train produced by slow knee movement

A mathematical model for knee vibration signals, in particular the physiological patello-femoral pulse (PFP) train produced by slow knee movement, is presented. It demonstrated that the repetition rate of the physiological PFP train introduces repeated peaks in the power spectrum, and that it affects the spectrum mainly at low frequencies. The theoretical results also show that the spectral peaks at multiples of the PFP repetition rate become more evident when the variance of the interpulse interval (IPI) is small, and that these spectral peaks shift toward higher frequencies with increasing PFP repetition rates. To evaluate the mathematical model, a simulation algorithm which generate PFP signals with adjustable repetition rate and IPI variance was developed. Results of simulations and analysis of signals recorded from human subjects support the mathematical model´s prediction that the IPI statistics play a very significant role in determining the low-end power spectrum of the physiological PFP signal. Evidence is presented to show that ignoring these IPI statistics will affect the interpretation of the spectrum.