Raw data from the TCD instrument consist of two timecourses of MCAV in cm/s, one each for the LMCA and RMCA at a sampling rate of 1 kHz. Heart rate and/or respiratory oscillations must be filtered out to obtain a clean MCAV timecourse usable for comparison to DCS data. We first obtained the upper and lower envelopes of each timecourse. Then, a lowpass filter of 0.01 Hz was used on all envelopes; measurements were normalized by dividing the entire timecourse by the average baseline MCAV and converting all values to percent change from baseline. Finally, the upper and lower envelopes from both (if available) L/RMCA were averaged together to produce a single TCD timecourse for each subject.

For subjects who did not have TCD measurements, we computed the expected change in MCAV by calibrating a group average of our existing TCD measurements with a group average of their corresponding PETCO2 timecourses. The travel time of the exhaled gas through the sampling tube results in a slight time lag of the PETCO2 timecourse with respect to the TCD curve. This was compounded by a physiological delay in reacting to the hypercapnia. We correct for this by calculating the r2 statistic for linear regression between the TCD timecourse and multiple time-shifted PETCO2 timecourses whose delay time ranged from 1 to 10 s in 1-s increments. The offset time that resulted in the highest r2 statistic between the two timecourses was chosen, and the corresponding linear regression model was then used to calibrate the TCD and shifted PETCO2 data for the 60- to 250-s time interval of the measurement. All subjects chosen with MC fitting based on systemic physiological drift and signal quality criteria (as described below in Sec. 2.4.2) did not have TCD recordings, so expected MCAV values were calculated from the PETCO2 timecourses.

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