Signal Processing for Quantifying Autoregulation David Simpson Reader

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Signal Processing for Quantifying Autoregulation David Simpson Reader in Biomedical Signal Processing, University of

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

Outline • Preprocessing • Transfer function analysis – Gain, phase, coherence – Bootstrap project • Model fitting • Extracting parameters • Discussion 2

Median filter 5

Median filter 5

Median filter • Can not remove wide spikes • Right-shift of signal 6

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

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 •

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

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

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

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

Gain 12

Phase 13

Phase 13

Coherence How well are v and p correlated, at each frequency? 14

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 An example from EEG 16

Power spectral estimation: Welch method 17

Power spectral estimation: Welch method 17

Power spectral estimation: Welch method 18

Power spectral estimation: Welch method 18

Power spectral estimation: Welch method 19

Power spectral estimation: Welch method 19

Power spectral estimation: Welch method 20

Power spectral estimation: Welch method 20

Power spectral estimation: Welch method. Averaging individual estimates TFA analysis: 21 Estimated cross-spectrum between

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

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

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

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

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

Critical values No. of independent windows 27

Modelling Arterial Blood Pressure End-tidal p. CO 2 Adaptive Input / output model Blood

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

Step responses Predicted response to step input (13 recordings, normal subjects) 30

Predicted response to change in pressure 12/2/2020 31

Predicted response to change in pressure 12/2/2020 31

How to quantify autoregulation from model 32

How to quantify autoregulation from model 32

Alternative estimator: FIR filter • • Sampling frequency (2 Hz) Scales are not compatible

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

Change cut-off frequency (0. 03 -0. 8 Hz) 34

ARI Increasing ARI 35

ARI Increasing ARI 35

Selecting ARI: best estimate of measured flow 36

Selecting ARI: best estimate of measured flow 36

Non-linear system identification LNL Model Pressure Linear Non. Linear Filter Static Filter Flow 37

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

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