Cerebral autoregulation in AD and MCI coherence of at least 0.18 were included. Recordings were excluded from further analysis, if nowhere in the frequency range below 0.25 Hz a coherence of 0.18 was reached. From fitting the first 5 seconds of the step response function the autoregulation index (ARI) was determined in the same way as described previ- ously 9. Model description of dCA data The layout of the WKM is shown in figure 1. It consists of two resistors and one capacitor. Resistor Ra represents flow resistance for arterioles distal to the MCA. Rp represents more peripheral resistance in the microcirculation. Cp represents compliance of the microcirculation. The transfer function from pressure ABP to flow CBF can be described in the Laplace domain with equation 1: HWKM ? ? p p (1)CBF1-sRC ABP C p Rp Ra s - R p - Ra whereHWKM is the transfer function between arterial blood pressure (ABP) and cerebral blood flow (CBF).Cp is peripheral compliance,Rp is peripheral resistance, Ra is arterial resistance ands is the Laplace transform variable. Although the model parameters Cp, Rp and Ra are time-invariant system parameters, the trans- fer function of the model in equation 1 describes behaviour in response to blood pressure changes that can be related to the estimated transfer function of dCA calculated through cross spectral analysis. To fit the WKM and convert the measured flow velocity into a flow for the model (CBFV ! CBF) CBFV has to be multiplied by a cross sectional area A. Therefore, an internal MCA diameter of 3 mm was assumed 14, resulting in A of # (1.5)2 = 0.0707 cm2. This assumption obviously introduces noise in the results since not everyone will have a MCA caliber of 3 mm. To estimate WKM parame- ters Ra, Rp and Cp, an error function is minimized iteratively using the “fsolve” function in Matlab with a Levenberg-Marquardt algorithm. g k ?| H TFA ( fi ) | / | HWKM ( fi ) |, k ? 1..8,i ? 4..11 g k ? angle} HTFA ( fi )¡ / angle} HWKM ( fi )¡, k ? 9..16,i ? 4..11 (2) g k ? A » (Ra - R p ) / CVRi, k ? 17 The error function consists of the set of expressions in equation 2 that represent the differences of: 1) TFA and WKM gain in the frequency band from 0.06-0.2 Hz 2) TFA and WKM phase in the frequency band from 0.06-0.2 Hz and 3) CVRi and (Ra+Rp)*A. Consequently, for both gain and phase eight data points (in the frequency range 0.06-0.20 Hz) from the calculated transfer function are com- pared with corresponding frequency WKM values. For CVRi it consists of a 65
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