Signal_processing_for_quantifying_autoregulation - Cerebral ...

pancakesbootAI and Robotics

Nov 24, 2013 (3 years and 9 months ago)

85 views

David Simpson

Reader in Biomedical Signal Processing,

University of Southampton

ds@isvr.soton.ac.uk


Signal Processing for

Quantifying Autoregulation

Outline


Preprocessing


Transfer function analysis


Gain, phase, coherence


Bootstrap project


Model fitting


Extracting parameters


Discussion



2

5

Median filter

0
10
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-10
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10
20
time (s)
cm/s
blood flow velocity


original
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12
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-10
0
10
20
time (s)
cm/s
blood flow velocity


original
median filtered
Median filter

6

18
18.2
18.4
-10
0
10
20
time (s)
cm/s
blood flow velocity


original
median filtered

Can not remove wide spikes


Right
-
shift of signal

0
10
20
-10
0
10
20
time (s)
cm/s
blood flow velocity


original
median filtered
Smoothing

7

0
5
10
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20
25
2
4
6
8
time (s)
cm/s
filtered velocity


original
median filtered
0
10
20
-10
0
10
20
time (s)
cm/s
blood flow velocity


original

Bidirectional low
-
pass

(Butterworth) filter, fc=0.5Hz


Ignore the beginning!

Transfer function analysis (TFA)

8

0
50
100
150
200
250
300
-15
-10
-5
0
5
10
15
20
25
time (s)
%
raw signals


p
v

Data from Bootstrap Project


Normalized by mean


Not adjusted for CrCP

Thanks: CARNet bootstrap
project for data used

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100
200
300
-5
0
5
10
15
time (s)
%
raw signals


p
v
Transfer function analysis (TFA)

9


Filtered 0.03
-
0.5

Relating pressure to flow

10

Input / output

model

Arterial Blood

Pressure

Blood Flow

Velocity

End
-
tidal

pCO2

+

-

error

V(f)=P(f).H(f)

Transfer function (frequency response)

11

Fourier Series

Periodic Signals
-

Cosine and Sine Waves

)
2
cos(
.
)
(




ft
a
t
x
0

0.5

1

1.5

2

-
4

-
2

0

2

4

time (s)

Period T=1/f

Cosine wave

Sine wave

t

Gain

12

0
0.1
0.2
0.3
0.4
0
1
2
3
frequency (Hz)
gain
TFA
Phase

13

0
0.1
0.2
0.3
0.4
-2
0
2
frequency (Hz)
phase
TFA
Coherence

14

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

0
0.1
0.2
0.3
0.4
0.2
0.4
0.6
0.8
frequency (Hz)
|coherence|
TFA
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Power spectral estimation:

Welch method

An example from EEG

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1
-1
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1
time (s)
signal
x
window
x.window
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0.4
-1
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1
time (s)
signal
Detail
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40
0.01
0.02
0.03
frequency (Hz)
PSD
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Power spectral estimation:

Welch method

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0.5
1
-1
0
1
time (s)
signal
x
window
x.window
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0.6
-1
0
1
time (s)
signal
Detail
0
20
40
0.01
0.02
0.03
0.04
frequency (Hz)
PSD
18

Power spectral estimation:

Welch method

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0.5
1
-1
0
1
time (s)
signal
x
window
x.window
0.6
0.8
-1
0
1
time (s)
signal
Detail
0
20
40
0.01
0.02
0.03
0.04
frequency (Hz)
PSD
19

Power spectral estimation:

Welch method

0
0.5
1
-1
0
1
time (s)
signal
0.8
1
1.2
-1
0
1
time (s)
signal
Detail
0
20
40
0.02
0.04
0.06
frequency (Hz)
PSD
20

Power spectral estimation:

Welch method

0
0.5
1
-1
0
1
time (s)
signal
1
1.2
1.4
-1
0
1
time (s)
signal
Detail
0
20
40
0.05
0.1
0.15
frequency (Hz)
PSD
21

Power spectral estimation:

Welch method.

Averaging individual estimates

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20
30
40
0.05
0.1
0.15
frequency (Hz)
PSD
TFA analysis:

Estimated cross
-
spectrum

between p and v

Estimated auto
-
spectrum

of p

0
0.1
0.2
0.3
0.4
1
2
3
frequency (Hz)
gain
TFA
Changing window
-
length

22

T=100s

T=20s

0
0.1
0.2
0.3
0.4
-2
0
2
frequency (Hz)
phase
TFA

Frequency resolution:

Δ
f=1/T,

T… duration of window

Estimating spectrum and cross
-
spectrum


Frequency resolution:

Δ
f=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

0
10
20
30
1
2
3
4
frequency [Hz]
PSD
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Effect of
windowlength (M) and
number of windows (L)

Signal: N=512, f
s
=128

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


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30
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10
frequency [Hz]
PSD
M=512

L=?


f=?


M=128

L=?


f=?

0
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20
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0.5
1
1.5
frequency [Hz]
PSD
M=64

L=?


f=?


True

estimates

Mean of

estimates

Critical values for coherence estimates

26

0
0.5
1
1.5
2
0.2
0.4
0.6
0.8
frequency (Hz)
coherence

3 realizations of uncorrelated white noise

Critical value (3 windows,
α
=5%)

0
0.1
0.2
0.3
0.4
0.2
0.4
0.6
0.8
frequency (Hz)
|coherence|
TFA
Critical values

27

0
20
40
0.2
0.4
0.6
0.8
no. windows
C
2
crit


10%
5%
1%
No. of

independent

windows

Modelling

29

Adaptive

Input / output

model

Arterial Blood

Pressure

Blood Flow

Velocity

End
-
tidal

pCO2

+

-

error

30

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

-2
0
2
4
6
8
-1
-0.5
0
0.5
1
1.5
time (s)
%
Step responses


Predicted response to

change in pressure

24 November 2013

31

-10
-5
0
5
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-1
0
1
2
time (s)
pressure pulse response
How to quantify autoregulation from
model

32

Mx
Pha
Coh
ARI
H1
L
NL
L
NL
L
NL
L
NL
0
20
40
60
80
100
120
+
+
*
*
o
o
*
+
o
o
A7
A1.5
PCS
FVS
o
*
*
o
%
Autoregulatory Parameter

SDn

Inter-subject variability

mSDn

Intra-subject variability
Alternative estimator: FIR filter

33


Sampling frequency (2 Hz)


Scales are not compatible


TFA: not causal


Needs pre
-
processing

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0.1
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1
2
3
frequency (Hz)
gain


TFA
FIR filter
-10
-5
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-1
0
1
time (s)
impulse response


TFA
FIR
Change cut
-
off frequency (0.03
-
0.8Hz)

34

-10
-5
0
5
10
0
0.5
1
time (s)
impulse response


TFA
FIR
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0.1
0.2
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0.4
0
1
2
3
frequency (Hz)
gain


TFA
FIR filter
ARI

35

0
5
10
0
0.5
1
time (s)
%/%
step responses
Increasing ARI

Selecting ARI:

best estimate of measured flow

36

30
40
50
60
-5
0
5
time (s)
v


measured
estimated
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Non
-
linear system identification

LNL Model

Linear

Non
-

Linear

Linear

Pressure

Flow

Filter

Filter

Static

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