Wavelet Cross-Correlation to Investigate Regional Variations in Cerebral Oxygenation in Infants Supported on Extracorporeal Membrane Oxygenation

Extracorporeal membrane oxygenation can potentially affect cerebral blood flow dynamics and consequently influence cerebral autoregulation. We applied wavelet cross-correlation (WCC) between multichannel cerebral oxyhemoglobin concentration (HbO2) and mean arterial pressure (MAP), to assess regional variations in cerebral autoregulation. Six infants on veno-arterial (VA) ECMO were studied during sequential changes in the ECMO flows. WCC between MAP and HbO2 for each flow period and each channel was calculated within three different frequency (wavelet scale) bands centered around 0.1, 0.16, and 0.3 Hz chosen to represent low frequency oscillations, ventilation, and respiration rates, respectively. The group data showed a relationship between maximum WCC and ECMO flow. During changes in ECMO flow, statistically significant differences in maximum WCC were found between right and left hemispheres. WCC between HbO2 and MAP provides a useful method to investigate the dynamics of cerebral autoregulation during ECMO. Manipulations of ECMO flows are associated with regional changes in cerebral autoregulation which may potentially have an important bearing on clinical outcome.


Introduction
Extracorporeal membrane oxygenation (ECMO) is a life support system for infants with cardiorespiratory failure. Neurological complications are the largest cause of morbidity and mortality in these patients, with the reported frequency of abnormal neuroimaging ranging from 28 to 52 % [ 1 ] . Initiation of ECMO involves cannulation of the major great vessels-right common carotid artery and internal jugular veinwhich may cause lateralizing cerebrovascular injury. ECMO infants suffer from hypoxia, asphyxia, and hypercarbia which can disrupt cerebral autoregulation, leaving the cerebral microcirculation vulnerable to alterations in blood pressure [ 2 ] .
Methods to assess the status of autoregulation by considering the relationship between spontaneous fl uctuations in MAP and cerebral blood fl ow (CBF) surrogates, such as (HbO 2 ) measured by NIRS, in either the time or frequency domain using Fourier transforms were reported extensively in the literature [ 3 ] . These, conventional methods suffer from the big drawback of averaging out all the potential useful time information, hence treating cerebral autoregulation as a stationary, linear process.
Recent studies have emphasized that cerebral autoregulation is a dynamic process [ 4 ] . The continuous wavelet transform (CWT) possesses the ability to construct a time-frequency representation of a signal that offers time and frequency localization. Latka et al. used CWT to compute a synchronization index between CBF and ABP signals [ 5 ] . Wavelet cross-correlation (WCC) was introduced by Rowley et al. as the cross-correlation between CWT coef fi cients of two time series [ 6 ] . Spectral analysis using wavelets provides a framework for analysis of nonstationary effects in cerebral hemodynamics, thus overcoming the restrictions intrinsic to earlier methods.
Previously we used a dual-channel NIRS system and showed the presence of oscillations related to vasomotion, respiration, and heart rates [ 7 ] . Preliminary results using multichannel NIRS indicate regional variation in cerebral oxygenation [ 8 ] . Here, we investigate the use of WCC as a method to study the concordance between multisite cerebral HbO 2 and mean arterial pressure in order to assess regional variations in cerebral oxygenation in neonates supported on ECMO.

Subjects and Instrumentation
A total of six veno-arterial (VA) ECMO patients, age range 1-16 days, were monitored during sequential changes in the ECMO fl ows. Alterations in the ECMO fl ows refer to successive decrease in the ECMO fl ow by 10 % from the initial fl ow, approximately every 10 min, down to 70 % of the initial fl ow followed by successive increase back to baseline (Fig. 28.2b ). A multichannel NIRS system (ETG-100, Hitachi Medical Ltd., Japan) was used to measure changes in oxy-(HbO 2 ), deoxy-(HHb), and total hemoglobin (HbT) concentrations at 5 Hz. A novel cap was constructed to accommodate the optical sources and detectors (interoptode distance = 3 cm), allowing data to be collected from 12 channels. Multimodal data were collected synchronously including systemic parameters (arterial blood pressure [ABP], heart rate [HR], and arterial oxygen saturation [SpO 2 ]) and ECMO circuit parameters (venous oxygen saturation [SvO 2 ], arterial saturation at the cannula [SaO 2 ]).

Data Analysis
Mean arterial pressure (MAP) was obtained by trapezoid integration of ABP every 0.2 s, equivalent to sampling frequency of 5 Hz. The time series of MAP and HbO 2 were divided into sections representing each ECMO fl ow period ( Fig. 28.3c). Each section of data was then high and low pass fi ltered at 0.008 and 1 Hz.
An approximate relationship between the scale a in the wavelet domain and frequency in the Fourier transform, f a , can be computed as [ 5 ] : where f c is the center frequency and d t is the sampling period. Wavelet analysis was performed on HbO 2 data. WCC and synchronization index, g , were used as methods to investigate the relation between MAP and HbO 2 . The complex Morlet wavelet was used to calculate the CWT coef fi cients for MAP and HbO 2 using the MatLab wavelet toolbox function cwt . The central frequency ( f c ) and bandwidth ( f b ) of the complex Morlet wavelet were both chosen as 1 in order to be in agreement with previous methods [ 5,6 ] . A scale range with unit spacing from 5 to 100, representing frequencies 0.008-1 Hz was used to obtain two complex time series, MAP ( , ) W t a and 2 HbO ( , ) W t a for each fl ow period A-G and across each of the 12 channels.
The WCC between MAP and HbO 2 in each channel and for each fl ow was obtained using the equation below [ 6 ] : in which R X , Y ( s 1, s 2, a , t ) denotes the cross-correlation of the wavelet coef fi cients of the series s 1 and s 2 at a scale a and for a relative time shift t and R X , X ( s 1, a , 0) denotes the autocorrelation of the time series s 1 for zero time shift. WCC( a , t ) represents the cross-spectral power in the two time series (shifted relative to each other by t ) as a fraction of the total power in the two time series. WCC ranges from 0 to 1. At a given wavelet scale, WCC = 1 would indicate that the coef fi cients of the two wavelet transforms are related to each other by a simple scaling factor, suggesting strong synchronization at this frequency [ 6 ] . The phase difference between the two time series, MAP and HbO 2 was also calculated using the circular mean, ΔΦ( ) α , of the instantaneous phase difference between the two signals D F ( a , t ) over the duration of a test segment [ 5 ] For each time series pair at each fl ow period and for each channel, the maximum value of WCC( a , t ) was found within three scale bands: a i = 5 < a < 20 ( f ai = 0.25 Hz < f a < 1 Hz), a ii = 20 < a < 40 ( f aii = 0.13 Hz < f a < 0.25 Hz), a iii = 40 < a < 80 ( f aiii = 0.06 Hz < f a < 0.13 Hz). These bands were chosen to overlap with respiration rate (RR), ventilation rate (VR), and slow M-waves, respectively. The maximum circular mean, D F max , were also calculated within each scale band, for each fl ow period and each channel. Student's t -test was then used to analyze the statistical signi fi cance of the differences in the group mean of each of these variables between channels. , 29 ( f a = 0.17 Hz) and a relatively weaker peak at scale 55 ( f a = 0.09 Hz). WCC for patient 2 at baseline fl ow shows a relatively weak peak at a scale 34 ( f a = 0.15 Hz). As with patient 1 correlation between MAP and HbO 2 becomes stronger at minimum fl ow with the peak at scale 34 spreading to higher Mayer-waves related scales and another peak occurring at scale 10 ( f a = 0.5 Hz). These peaks appear shifted from zero time lag in agreement with Rowley et al. [ 6 ] .

Results
In general, WCC between MAP and HbO 2 revealed three distinct peaks within three scale regions. The fi rst peak typically occurs at a scale of around 14 (0.36 Hz), the second at a scale around 30 (0.16 Hz) and the third at a scale around 50 (0.1 Hz). These peaks could correspond to the RR, VR, and Mayer-waves, respectively.

Discussion and Conclusions
WCC between HbO 2 and MAP provides a useful method to investigate the dynamics of cerebral autoregulation. Cerebral autoregulation on ECMO is poorly studied, since there have been no easy noninvasive methods to study and interpret complex cerebral physiological process. Our results showed a relationship between WCC and ECMO fl ow in the grouped data of six patients. These differences were statistically signi fi cant between right and left hemispheres, especially when the fl ows were weaned sequentially. Modest manipulations of ECMO fl ows are associated with regional changes in cerebral autoregulation which may potentially have an important bearing on clinical outcome.