Chapter 5 systolic values, but for simplicity only mean will be mentioned. To create equi- distant time series for flow velocity and blood pressure repetitively 3rd order polynomial functions were fitted to 4 subsequent mBP and mCBFV beat-to-beat values which were then resampled at 5Hz 8. To correct for unknown TCD insonation angles and to allow inter-individual comparison, absolute blood flow velocity was transformed into changes relative to the value at the onset of stimulation. Also for blood pressure this transform to relative changes was performed. Subsequently, to suppress non stimulus related changes, ensemble averages over all stimulation cycles were calculated. For each subject the ensemble average mCBFV during the “On” phase of the stimulation cycle is fitted as the output signal of two different control systems. First, only the visual evoked response RG model was applied. Second, in order to incorporate the effect of blood pressure on the mCBFV response, the averaged blood pressure response was used as a second input for a new two input - one output model. Parameters of both models were determined by a least square fitting technique using Matlab’s lsqcurvefit function (Levenberg-Marquardt algorithm) minimizing the fit error between the averaged mCBFV response and the model output. The RG model was described by the second order proportio- nal-derivative model as proposed by Rosengartenet al 21. The transfer function in the Laplace domain is given in equation 1 where! represents an undamped natural frequency, a damping ratio, Tv a rate time and K a gain. K μ (1 -T μ s) H RG ? 2 |V (1)s - 2 μ μ s - 1 y 2 y 40 35 30 25 20 15 10 5 step stimulus NVC 00 50 100 150 200 250 40 35 + 2530 20 + 15 10 blood pressure CA 05 0 50 100 150 200 250 2 3 1 . 5 2 1 1 0 . 5 0 1 - 0 2 - - 0 . 5 3 - 0 5 2 0 0 2 0 5 1 0 0 1 0 5 0 - 1 - 1 . 5 - 2 - 2 . 5 2 5 0 2 0 0 1 5 0 1 0 0 5 0 0 Figure 1 2-input 1-output RGCA model combining NVC response to stimulus and CA response to blood pressure. 84
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