Chapter 6 flow) was started, the aorta was cross clamped, cardioplegia was infused and the patient was hemodynamically stabilized. First, paCO2 was set to a hypocapnic level of 30 mmHg and after this was stable for a minute mean CBFV was deter- mined by averaging CBFV over ten seconds. Thereafter, 5 minutes of cyclic changes of indexed pump flow were induced. The flow was manually set to each of the three levels (2.0, 2.4 and 2.8 l/min/m2) upon a verbal command indicating the 6/min rhythm. The 5 minute period was used to evaluate cerebral autoregula- tion. Subsequently, paCO2 was set to a normocapnic level of 40 mmHg respec- tively to a hypercapnic level of 50 mmHg. At every level of paCO2 first ten sec- onds of steady flow were used to determine baseline mean CBFV followed by 5 minutes of cyclic changes of pump flow. The mean CBFV data acquired at each of the three levels of paCO2 were used to calculate CO2R. Data analysis After recording and down sampling of the data, the transfer function yielding coherence, gain and phase shift angle between oscillation in CBFV and ABP was calculated, as described by Gommeret al 17. The transfer functionH(f) was calculated by S ( f ) H ( f ) ? xy , (1) S xx ( f ) whereSxx(f) is the auto spectrum of changes in arterial blood pressure and Sxy(f) is the cross-spectrum between the ABP- and CBFV-signals. For calculating cross- and autospectra also the power spectral densities of ABP and CBFV were calcu- lated. The transfer function magnitude |H(f)| and phase spectrum#(f) were derived from the real partHR(f) and imaginary partHI(f) of the complex transfer function as | H ( f ) |? H R ( f )_ 2 - H I ( f )_2 (2) H ( f ) H( f ) ? arctan I . (3) H R ( f ) The squared coherence function 2(f) was estimated by | S ( f ) |2 i 2 ( f ) ? xy , (4) S xx ( f )S yy ( f ) whereSyy(f) is the auto spectrum of changes in cerebral blood flow velocity. The squared coherence reflects the strength of the linear relationship between ABP and CBFV for each frequency on a scale from 0 to 1. Gain and phase were evalu- ated at 0.1 Hz, because this equals the frequency induced by varying pump flow. The gain is the magnitude of the transfer function between CBFV and ABP and is 106
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