Comparison of coherence measures for assessment of impaired cerebral
autoregulation
D. De Smet*, J. Vanderhaegen**, G. Naulaers**
and S. Van Huffel*
KATHOLIEKE UNIVERSITEIT LEUVEN, BELGIUM
*DEPARTMENT OF ELECTRICAL ENGINEERING (ESAT-SCD)
**NEONATAL INTENSIVE CARE UNIT, UNIVERSITY HOSPITALS LEUVEN
Introduction
Problem : defective cerebrovascular autoregulation Δ CBF brain injuries
Premature infants : propensity for development because :
• Δ MABP frequent
• Δ MABP Δ CBF in some infants
1st mean to detect defective autoregulation : Δ MABP Δ CBF
Acronyms :
• CBF : Cerebral Blood Flow
• MABP : Mean Arterial blood Pressure 1. Introduction
2. Datasets
3. Preprocessing
4. Sampling frequency 5. Welsh coherence 6. Critical score value 7. In the practice
8. Conclusion
Introduction
But, if Δ SaO
2= 0, then
Δ HbD Δ CBF (hypothesis) 2nd mean to detect defective autoregulation :
Δ MABP Δ HbD with Δ SaO
2= 0
Acronyms :
• HbD : cerebral intravascular oxygenation (=HbO
2-HbR)
• SaO
2: arterial oxygen saturation
Aim : allow correction with medication such that Δ CBF=0 Method: The coherence
coefficient is a
measure of the linear dependence between two signals in the
frequency domain.
1. Introduction 2. Datasets
3. Preprocessing
4. Sampling frequency 5. Welsh coherence 6. Critical score value 7. In the practice
8. Conclusion
Datasets
• More than 50 premature infants with need for intensive care from the hospitals of Zürich, Utrecht, and Leuven.
• MABP, SaO
2, and the NIRS-measured
HbD/rSO2/TOI measured simultaneously in the first days of life.
Acronyms :
MABP : mean arterial blood ressure
HbD : cerebral intravascular oxygenatinon rSO2 : regional oxygen saturation
TOI cerebral tissue oxygenation NIRS : near infrared spectroscopy SaO
2: arterial oxygen saturation 1. Introduction
2. Datasets
3. Preprocessing
4. Sampling frequency 5. Welsh coherence 6. Critical score value 7. In the practice
8. Conclusion
Preprocessing
Each artifact point was deleted (Soul et al. 2007)
Step 1: keep signals within normal ranges
Preprocessing
Step 2: remove artifacts in MABP
Preprocessing
Step 3: remove artifacts in SaO2
Preprocessing
Step 4: remove artifacts in HbD
Preprocessing
Preprocessing makes the coherence growing (S. Van Huffel, iSOTT 08)
Preprocessing has bad consequence on the frequency
content of the signals
Sampling frequency
Condition : sampling frequency (f
s) > signal fluctuation frequency
Cyclical fluctuations in the case of continuously measured signals :
• CBV/HbTot : 2 to 4.7 cycles/min
1and 3 to 6 cycles/min
2(by NIRS)
• MABP : One cycle every 1 to 2.5 min
1f
s> 0.1Hz
Acronyms :
• CBV : cerebral blood volume
• HbTot : total haemoglobin
• MABP : mean arterial blood pressure
_____________________________________________________
[1] von Siebenthal et al., Brain & Development, 1999.
[2] Urlesberger et al., Neuropediatrics, 1998 1. Introduction
2. Datasets
3. Preprocessing 4. Sampling
frequency
5. Welsh coherence 6. Critical score value 7. In the practice
8. Conclusion
Step 1 : divide signal in epochs (C-windows). Divide each C- window in N segments (called H-windows as it is a
highpass filtering)
Welsh coherence
Step 2 : (1) detrend, (2) apply Hanning
windowing, and (3)
compute the PSD/CSD for each H-window
Acronyms :
• P
xy(f) : crosspower spectral density (CSD) of x(t) and y(t) at a given frequency f
• P
xx(f), P
yy(f) : power spectral densities
(PSD) of x(t), respectively y(t)
Step 3 : average the N modified H-windows
Step 4 : keep frequency band of interest (f
Cut: cutoff freq.)
Welsh coherence
Step 5 : compute average
amplitude of spectrum in
the frequency band of
interest
REMARK 1 The FFT (fast Fourier
transform) supposes the signals are periodical
REMARK 2 A complete period of the signal should be contained in a each H-window REMARK 3
The higher the value of N, the lower the
variance of the estimates of the spectra (SNR grows)
Problem : if N is too large, then the
amplitude of the spectra diminishes
1N close to 8
2,3_____________________________________________________
[1] De Smet., Unpublished, 2007.
[2] Kay, Prentice Hall, 1988 (book).
[3] Taylor, Circulation, 1998.
Welsh coherence
1. Introduction 2. Datasets
3. Preprocessing
4. Sampling frequency 5. Welsh coherence 6. Critical score value 7. In the practice
8. Conclusion
REMARK 4
All parameters satisfy
• TH acts as a highpass filer
• The ratio TH/TC should be in the range of 0.5
1or smaller
REMARK 5
The ratio THOver/TH should be equal to 0.5 if a Hanning window was applied to the H-windows prior to the periodogram average
2.
_____________________________________________________
[1] De Smet., Unpublished, 2007.
[2] Carter, IEEE Trans. on Audio and Electroacoustics, 1973.
Welsh coherence
1. Introduction 2. Datasets
3. Preprocessing
4. Sampling frequency 5. Welsh coherence 6. Critical score value 7. In the practice
8. Conclusion
Consequence : TC= TH(N+1)/2
TH and TH/TC are the sole parameters we really can choose
But … REMARK 6 TH have to satisfy :
• TH < TC
• TH > 10s
1,2Acronyms :
• TC : duration of C-window (calculation window)
• TH : duration of H-window (highpass filtering window)
• N : number of averages in the Welsh method
_____________________________________________________
[1] von Siebenthal et al., Brain & Development, 1999.
[2] Urlesberger et al., Neuropediatrics, 1998
Welsh coherence
1. Introduction 2. Datasets
3. Preprocessing
4. Sampling frequency 5. Welsh coherence 6. Critical score value 7. In the practice
8. Conclusion
Critical Score Value
The critical score value (CSV) is the value above which the amplitude of coherence witnesses a significant linear concordance between the input signals.
Possible value for CSV are :
• CSV=0.5
1• or
2Acronyms :
: significance level (e.g. 0.05) : to be chosen
• d : 2.83*TC/TH (for Hanning window) : TH to be chosen
• F : F hypothesis test
The significance level greatly influences the CSV, in the case that the remainder parameters are unchanged!!
_____________________________________________________
[1] De Boer et al., Med. Biol. Eng. Comput., 1985.
[2] Taylor et al., Circulation, 1998 1. Introduction
2. Datasets
3. Preprocessing
4. Sampling frequency 5. Welsh coherence 6. Critical score value 7. In the practice
8. Conclusion
Critical Score Value
Problem : this formula doesn’t take into account THOver (and thus N) that also has an influence on the amplitude of the coherence spectrum
1Solution : keep working with CSV=0.5 (two signals based on 50% shared variance), and calibrate
2mean COH (on all infants) on mean correlation coefficient (COR)
+ look at the range of COH and COR.
_____________________________________________________
[1, 2] De Smet., Unpublished 1. Introduction
2. Datasets
3. Preprocessing
4. Sampling frequency 5. Welsh coherence 6. Critical score value 7. In the practice
8. Conclusion
Morren 1 Soul 2 Wong 3 Optimization fs 6Hz
(0.2Hz) 2Hz
(O.4Hz) 1Hz >0.1Hz
(von Siebenthal, Urlesberger)
TC 30min 10min 20min TH(N+1)/2
TCOver 10min 0min 0min E.g. : TC/2
N 217 3 5 close to 8 or calibr.
TH 12min 5min 10min > 2.5min
(von Siebenthal) THOver 11min55s 2.5min 7.5min TH/2 if Hanning
(Carter)
fCut 0.01Hz 0.04Hz 0.02Hz <0.05Hz
(von Siebenthal, Urlesberger, Nyq.)
CSV 0.5 0.77
(Taylor)
0.5 0.5 with calibr. or Taylor’s CSV
In the practice
[1] Morren et al., Proc. of the Intern. Conf. of IEEE, 2001.
[2] Soul et al., Pediatric Research, 2007.
[3] Wong et al., Pediatrics, to be published.