Signal Processing for Quantifying Autoregulation David Simpson Reader
- Slides: 33
Signal Processing for Quantifying Autoregulation David Simpson Reader in Biomedical Signal Processing, University of Southampton ds@isvr. soton. ac. uk
Outline • Preprocessing • Transfer function analysis – Gain, phase, coherence – Bootstrap project • Model fitting • Extracting parameters • Discussion 2
Median filter 5
Median filter • Can not remove wide spikes • Right-shift of signal 6
Smoothing • Bidirectional low-pass (Butterworth) filter, fc=0. 5 Hz • Ignore the beginning! 7
Transfer function analysis (TFA) • Data from Bootstrap Project • Normalized by mean • Not adjusted for Cr. CP Thanks: CARNet bootstrap 8 project for data used
Transfer function analysis (TFA) • Filtered 0. 03 -0. 5 9
Relating pressure to flow Transfer function (frequency response) V(f)=P(f). H(f) Arterial Blood Pressure Input / output model End-tidal p. CO 2 10 Blood Flow Velocity error +
Fourier Series Periodic Signals - Cosine and Sine Waves Period T=1/f 4 2 Sine wave 0 Ph as e Am pli tu de a Cosine wave -2 -4 0 11 t 0. 5 1 time (s) 1. 5 2
Gain 12
Phase 13
Coherence How well are v and p correlated, at each frequency? 14
Power spectral estimation: Welch method An example from EEG 16
Power spectral estimation: Welch method 17
Power spectral estimation: Welch method 18
Power spectral estimation: Welch method 19
Power spectral estimation: Welch method 20
Power spectral estimation: Welch method. Averaging individual estimates TFA analysis: 21 Estimated cross-spectrum between p and v Estimated auto-spectrum of p
Changing window-length T=100 s T=20 s • Frequency resolution: Δf=1/T, T… duration of window 22
Estimating spectrum and cross-spectrum • Frequency resolution: Δf=1/T, T… duration of window • Estimation error: with more windows • Compromise: Longer windows: better frequency resolution, worse random estimation errors • Higher sampling rate increases frequency range • Longer FFTs: interpolation of spectrum, transfer function, coherence … • Window shape: probably not very important 24
Effect of windowlength (M) and number of windows (L) Signal: N=512, fs=128 With fixed N (512), type of window (rectangular), and overlap (50%) M=512 L=? f=? True estimates M=128 L=? f=? M=64 L=? f=? Mean of estimates 25
Critical values for coherence estimates • 3 realizations of uncorrelated white noise Critical value (3 windows, α=5%) 26
Critical values No. of independent windows 27
Modelling Arterial Blood Pressure End-tidal p. CO 2 Adaptive Input / output model Blood Flow Velocity error + 29
Step responses Predicted response to step input (13 recordings, normal subjects) 30
Predicted response to change in pressure 12/2/2020 31
How to quantify autoregulation from model 32
Alternative estimator: FIR filter • • Sampling frequency (2 Hz) Scales are not compatible TFA: not causal Needs pre-processing 33
Change cut-off frequency (0. 03 -0. 8 Hz) 34
ARI Increasing ARI 35
Selecting ARI: best estimate of measured flow 36
Non-linear system identification LNL Model Pressure Linear Non. Linear Filter Static Filter Flow 37
Summary • Proprocessing • TFA – Gain, phase, coherence – Window-length – Critical values for coherence • Issues – What model? – Frequency bands present – How best to quantify autoregulation from model 38
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