Fig 1.
The time series on the left is used to calculate the DCSx time series on the right. DCSx is calculated only during segments when the mean arterial pressure had a range greater than 5 mmHg. The dashed red line indicates threshold set at 0.4 and the red dots indicate DCSx values above this threshold. %DCSx, the percentage of DCSx values above 0.4 of the total time DCSx is calculated, 66.5% for this segment.
Fig 2.
The process to determine the wavelet coherence.
First the data is segmented into 20-minute sections, and then artifacts are identified and removed before normalization. The continuous wavelet transform is performed, and the coherence is then calculated (Red box). To determine if the coherence is significant, coherence data is generated from surrogate data (Blue box). Using the surrogate data, a threshold is applied to the coherence data and the area under the curve (AUC) is then calculated. (For details of surrogate data, see Fig 4).
Fig 3.
An example of how the wavelet coherence is calculated.
First the continuous wavelet transform (middle) of the rBF and MAP time series (left) is calculated. Using the wavelet coherence equation and the continuous wavelet transform, the coherence vs frequency is calculated (right). The red boxes in the middle figures and red shade in the right figure denote the 0.05 to 0.1 Hz range that is used in the analysis.
Fig 4.
An example of how the surrogate data is used for determining whether coherence at each frequency is due to noise or not.
First the time series for both rBF and MAP are randomized using the iterative amplitude adjusted Fourier transform (left). Using these time series and the wavelet coherence equation (Eq 1), the coherence is calculated for the surrogate data (middle). This is done 1000 times to generate a distribution. Using signals at 0.09 Hz as an example, the right uppermost figure shows the distribution of coherence values and determination of the 95th percentile of coherence at that frequency. The actual coherence is then compared to the 95th percentile of surrogate at each frequency and if greater, it is considered significant (bottom right). Values that are above the threshold are determined as significant coherence values and are highlighted as the red bolded line and those in the shaded region are used for the WCOH calculation.
Table 1.
Demographic data of the eleven patients under VA ECMO monitored for this study.
Table 2.
Measurement timing and neurologic assessment with GCS.
Table 3.
Percentage of total time each parameter was calculated for each subject.
Fig 5.
Boxplots comparing DCS-derived CA measures between neuroinjured and uninjured patients determined by CT.
(a) Boxplots comparing WCOH. Neuroinjured group had a significantly higher coherence compared to uninjured for both the left (p-value = 0.041) and right (p-value = 0.041) hemispheres. (b) Boxplots comparing the %DCSx. Neuroinjured group did not show a significantly higher %DCSx compared to uninjured for the left (p-value = 0.073) and right (p-value = 0.268) hemispheres. Significance was computed using a one-tailed Wilcoxon rank-sum test. Red data point indicates subject 11 who was diagnosed with a microhemorrhage in the right hemisphere.
Fig 6.
Logistic regression and ROC curves.
Logistic regression for (a) WCOH left hemisphere, (b) %DCSx left hemisphere, (c) WCOH right hemisphere, and (d) %DCSx right hemisphere are presented in the top row. Hollow black circles at 0 represent values for patients with no neurological injuries, while filled circles at 1 represent values for patients with neurological injuries. ROC curves for (e) WCOH left hemisphere, (f) %DCSx left hemisphere, (g) WCOH right hemisphere, and (h) %DCSx right hemisphere are shown in the bottom row. ROC plots false positive rate (1-specificity) against the true positive rate (sensitivity). Each parameter’s area under the curve (AUC) and maximum Youden’s J index values are reported.