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David Simpson Reader in Biomedical Signal Processing, University of Southampton

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

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David Simpson Reader in Biomedical Signal Processing, University of Southampton

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  1. Signal Processing for Quantifying Autoregulation David Simpson Reader in Biomedical Signal Processing, University of Southampton ds@isvr.soton.ac.uk

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

  3. Median filter

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

  5. Smoothing • Bidirectional low-pass (Butterworth) filter, fc=0.5Hz • Ignore the beginning!

  6. Transfer function analysis (TFA) • Data from Bootstrap Project • Normalized by mean • Not adjusted for CrCP Thanks: CARNet bootstrap project for data used

  7. Transfer function analysis (TFA) • Filtered 0.03-0.5

  8. Relating pressure to flow Transfer function (frequency response) V(f)=P(f).H(f) Blood Flow Velocity Arterial Blood Pressure - Input / outputmodel + error End-tidalpCO2

  9. Fourier SeriesPeriodic Signals - Cosine and Sine Waves Period T=1/f 4 Cosine wave 2 Sine wave Amplitude a 0 Phase  -2 t -4 0 0.5 1 1.5 2 time (s)

  10. Gain

  11. Phase

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

  13. Power spectral estimation: Welch methodAn example from EEG

  14. Power spectral estimation: Welch method

  15. Power spectral estimation: Welch method

  16. Power spectral estimation: Welch method

  17. Power spectral estimation: Welch method

  18. Power spectral estimation: Welch method.Averaging individual estimates TFA analysis: Estimated cross-spectrumbetween p and v Estimated auto-spectrumof p

  19. Changing window-length T=100s T=20s • Frequency resolution:Δf=1/T, T… duration of window

  20. 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

  21. Effect of windowlength (M) and number of windows (L)Signal: N=512, fs=128 M=128 L=? f=? With fixed N (512), type of window (rectangular), and overlap (50%) True estimates M=512 L=? f=? M=64 L=? f=? Mean of estimates

  22. Critical values for coherence estimates • 3 realizations of uncorrelated white noise Critical value (3 windows, α=5%)

  23. Critical values No. of independent windows

  24. Modelling Blood Flow Velocity Arterial Blood Pressure - Adaptive Input / outputmodel + error End-tidalpCO2

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

  26. Predicted response to change in pressure

  27. How to quantify autoregulation from model

  28. Alternative estimator: FIR filter • Sampling frequency (2 Hz) • Scales are not compatible • TFA: not causal • Needs pre-processing

  29. Change cut-off frequency (0.03-0.8Hz)

  30. ARI Increasing ARI

  31. Selecting ARI: best estimate of measured flow

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

  33. 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

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