David Simpson

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Signal Processing for Quantifying Autoregulation

• David Simpson
• Reader in Biomedical Signal Processing,
  University of Southampton
• ds_at_isvr.soton.ac.uk

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Outline

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

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Raw Signals
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Beat-averaged Signals
Mean ABP
Mean CBFV
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Median filter
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Median filter

• Can not remove wide spikes
• Right-shift of signal

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Smoothing

• Bidirectional low-pass (Butterworth) filter,
  fc0.5Hz
• Ignore the beginning!

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Transfer function analysis (TFA)

• Data from Bootstrap Project
• Normalized by mean
• Not adjusted for CrCP

Thanks CARNet bootstrap project for data used
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Transfer function analysis (TFA)

• Filtered 0.03-0.5

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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
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Fourier SeriesPeriodic Signals - Cosine and Sine
Waves
Period T1/f
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Cosine wave
2
Amplitude a
Sine wave
0
Phase ?
-2
t
-4
0
0.5
1
1.5
2
time (s)
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Gain
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Phase
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Coherence
How well are v and p correlated, at each
frequency?
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Periodogram
But randomerror of PSD estimateremainsthe same
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Power spectral estimation Welch methodAn
example from EEG
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Power spectral estimation Welch method
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Power spectral estimation Welch method
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Power spectral estimation Welch method
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Power spectral estimation Welch method
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Power spectral estimation Welch
method.Averaging individual estimates
TFA analysis
Estimated cross-spectrumbetween p and v
 
Estimated auto-spectrumof p
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Changing window-length
T100s T20s

• Frequency resolution?f1/T, T duration of
  window

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PSD
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Estimating spectrum and cross-spectrum

• Frequency resolution?f1/T, T duration of
  window
• Estimation error ? with more windows
• CompromiseLonger 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

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Effect of windowlength (M) and number of windows
(L)Signal N512, fs128
M128 L? ?f?

• With fixed N (512), type of window (rectangular),
  and overlap (50)

True
estimates
M512 L? ?f?
M64 L? ?f?
Mean of estimates
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Critical values for coherence estimates

• 3 realizations of uncorrelated white noise

Critical value (3 windows, a5)
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Critical values
 
No. of independent windows
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Choosing windowssine-waves at 10, 11.5 and 15 Hz
signal,rectangular window
signal,Hann window
PSD
PSD
Interpolation of PSD using zero-padding
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Modelling
Blood Flow Velocity
Arterial Blood Pressure
-
Adaptive Input / outputmodel

error
End-tidalpCO2
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Predicted response to step input (13 recordings,
normal subjects)
Step responses
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Predicted response to change in pressure
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How to quantify autoregulation from model
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Alternative estimator FIR filter

• Sampling frequency (2 Hz)
• Scales are not compatible
• TFA not causal
• Needs pre-processing

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Change cut-off frequency (0.03-0.8Hz)
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ARI
Increasing ARI
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Selecting ARI best estimate of measured flow
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Non-linear system identification
LNL Model
Non- Linear
Pressure
Flow
Linear
Linear
Filter
Filter
Static
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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