Transfer Function Analysis of Doppler Waveforms of Lower Extremity

Lee, Hong Gi; Yum, Myung Kul; Kim, Soo Chan

Abstract

BACKGROUND: There are two methods to understand a periodic signal. One is describing it in the time domain, and the other is in the frequency domain. Various methods have been described for analysis of Doppler signals in terms of velocities and they need to be further characterized. Frequency domain analysis involves conventional Fourier transformation and analysis by modeling. In 1980's, Skidmore et al. applied Laplace transformation analysis to the femoral and ankle Doppler waveforms and described the waveforms in terms of damping, stiffness and distal impedance. However, few subsequent studies have been reported by other authors. Further, an appealing feature of frequency function analysis is that it can be used for modeling of the resistive and/or storage property of the circuit. PURPOSE: The purpose of study is to analyze the Doppler waveforms of lower extremity in frequency domain and compare the results with the currently known parameters of pusatility in the time domain.
METHODS
This study includes 119 Doppler waveforms from 7 non-symptomatic limbs and from 18 limbs with symptoms of chronic low extremity ischemia. Each five representative beats of Doppler waveforms were curve-fitted by third-order AR (auto-regressive) model and z-transformed resulting in three representative roots in the z-plane. Maximum velocity (Max), minimum velocity (Min), maximum excursion of the waveform (Max-Min; MaxE), mean velocity (Avg), pulsatility index (PI) and resistive index (RI) were calculated and compared with the values of the roots.
RESULTS
Mostly, the poles of the transfer function were two imaginary and one real poles. Severely diseased waveforms had all three poles in real axis or the imaginary poles approached toward the real axis. The average value of the three poles (Rmean) was 0.5096 ( 0.0967 S.D.) (range: 0.2193~0.7197). The real value of the first pole (R1real) was 0.8957 ( 0.067 S.D.) (range: 0.5964~0.97). The absolute value of imaginary value of the first pole (R1imag) was 0.0998 ( 0.0713 S.D.) (range: 0~0.2336). Significant correlation was observed between 1) Rmean and MaxE (r=0.769), Max (r=0.7498), Avg (r=0.3106), RI (r=0.4378), 2) R1real and MaxE (r=0.5382), Max (r=0.4732), RI (r=0.3629), and 3) R1imag and MaxE (r=0.4785), Max (r=0.3333), Min (r= 0.3703), RI (r=0.5611).
CONCLUSIONS
The position of roots of third-order transfer function of Doppler waveforms seems to correlate with the known parameters of velocity. In addition to these parameters of velocity, transfer function analysis appears to be a useful tool to evaluate the Doppler waveforms. Further studies are needed in relation to clinical manifestation.