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# proefschrift gommer inhoud met kaft.indd

Chapter 5
regulation is described by parameters T for oscillation time and D for damping
ratio. K2 equals the parameter K from Tieckset al 29 and T and D are identical
to their parameters T and D.
Eventually, fitting the VEFR reponses results in the parameters K, Tv,! and for
the RG model and additionally in K3, K2, T and D for the RGCA model. From the
step response function of the RGCA model also the autoregulatory index ARI can
be estimated 29. Because, in the traditional RG model usually systolic values for
cerebral blood flow velocity are used, results will be reported both for mean and
systolic values of blood pressure and cerebral blood flow velocity.
Parameter reliability
The Matlab routine used to estimate the NVC parameters computes the Jacobian
matrix which can be used to quantify the reliability of the parameter estimates.
The Jacobian (J) contains all first-order partial derivatives (" pi#" MSDi, i =1...4) of
the parameters pi with respect to the residual vectorMSD, which is the mean
squared difference between fit and measured response. In case of the 4 parameter
RG model an NVC response (stimulus on duration of 40 seconds at 5 Hz) yields a
4 by 201J matrix. Together with theMSD, the 4 by 4 covariance matrix of the
parameter coefficient estimates (Cov) is calculated according to equation 3.
Cov =MSD * (JT*J)-1 (3)
withJT the transposed Jacobian Matrix.
The 95% confidence bounds (C) for the fitted parameters are now given by
equation 4.
C =p ± t*$S (4)
p is the vector of the 4 fitted Rosengarten parameters, t depends on the confi-
dence level and is computed using the inverse of Student’s t cumulative distribu-
tion function and equals 1.96 for 95% confidence bounds.S is a vector of the
diagonal elements of the estimated covariance matrix of the fitted parameters.
The relative width of the confidence bounds (%CP), expressed as a percentage of
the estimated parameter, is a measure for the precision of the parameter estima-
tion and can be used for sensitivity analysis, i.e. when confidence bounds are
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proefschrift gommer inhoud met kaft.indd

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