Title: David Simpson
1Signal Processing for Quantifying Autoregulation
- David Simpson
- Reader in Biomedical Signal Processing,
University of Southampton - ds_at_isvr.soton.ac.uk
2Outline
- Preprocessing
- Transfer function analysis
- Gain, phase, coherence
- Bootstrap project
- Model fitting
- Extracting parameters
- Discussion
3Raw Signals
4Beat-averaged Signals
Mean ABP
Mean CBFV
5Median filter
6Median filter
- Can not remove wide spikes
- Right-shift of signal
7Smoothing
- Bidirectional low-pass (Butterworth) filter,
fc0.5Hz - Ignore the beginning!
8Transfer function analysis (TFA)
- Data from Bootstrap Project
- Normalized by mean
- Not adjusted for CrCP
Thanks CARNet bootstrap project for data used
9Transfer function analysis (TFA)
10Relating pressure to flow
Transfer function (frequency response)
V(f)P(f).H(f)
Blood Flow Velocity
Arterial Blood Pressure
-
Input / outputmodel
error
End-tidalpCO2
11Fourier SeriesPeriodic Signals - Cosine and Sine
Waves
Period T1/f
4
Cosine wave
2
Amplitude a
Sine wave
0
Phase ?
-2
t
-4
0
0.5
1
1.5
2
time (s)
12Gain
13Phase
14Coherence
How well are v and p correlated, at each
frequency?
15Periodogram
But randomerror of PSD estimateremainsthe same
16Power spectral estimation Welch methodAn
example from EEG
17Power spectral estimation Welch method
18Power spectral estimation Welch method
19Power spectral estimation Welch method
20Power spectral estimation Welch method
21Power spectral estimation Welch
method.Averaging individual estimates
TFA analysis
Estimated cross-spectrumbetween p and v
Estimated auto-spectrumof p
22Changing window-length
T100s T20s
- Frequency resolution?f1/T, T duration of
window
23PSD
24Estimating 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
25Effect 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
26Critical values for coherence estimates
- 3 realizations of uncorrelated white noise
Critical value (3 windows, a5)
27Critical values
No. of independent windows
28Choosing windowssine-waves at 10, 11.5 and 15 Hz
signal,rectangular window
signal,Hann window
PSD
PSD
Interpolation of PSD using zero-padding
29Modelling
Blood Flow Velocity
Arterial Blood Pressure
-
Adaptive Input / outputmodel
error
End-tidalpCO2
30Predicted response to step input (13 recordings,
normal subjects)
Step responses
31Predicted response to change in pressure
32How to quantify autoregulation from model
33Alternative estimator FIR filter
- Sampling frequency (2 Hz)
- Scales are not compatible
- TFA not causal
- Needs pre-processing
34Change cut-off frequency (0.03-0.8Hz)
35ARI
Increasing ARI
36Selecting ARI best estimate of measured flow
37Non-linear system identification
LNL Model
Non- Linear
Pressure
Flow
Linear
Linear
Filter
Filter
Static
38Summary
- Proprocessing
- TFA
- Gain, phase, coherence
- Window-length
- Critical values for coherence
- Issues
- What model?
- Frequency bands present
- How best to quantify autoregulation from model