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fractal dimensions
f
(
h
)
, which is determined by the mass exponent
τ(
q
)
. We apply the
partition-function measure and numerically evaluate the mass exponent
ln
Z
q
(δ)
ln
τ(
q
)
=
(5.94)
δ
for a measured MCAfv time series.
Wes t
et al
.[
32
] measured MCAfv using an ultrasonograph. The 2-MHz Doppler
probes were placed over the temporal windows and fixed at a constant angle and posi-
tion. The measurements were taken continuously for approximately two hours with the
subjects at supine rest. The study sample comprised eight migraineurs and five healthy
individuals. It was checked that those in the migraine group had no illnesses that would
affect cerebral autoregulation. Figure
5.2
(a) shows the averaged exponent and singu-
larity spectrum of the aggregated MCAfv time series for ten measurements of five
(a)
(b)
(a) The average singularity spectrum
f
(
h
)
of healthy subjects (filled circles) for
middle-cerebral-artery blood flow. The spectrum is the average of ten measurements of five
subjects. The solid curve is the best least-square fit of the parameters in (
5.98
) to the data.
(b) The average singularity spectrum
f
(
h
)
of migraineurs (filled circles). The spectrum is the
average of fourteen measurements of eight subjects. The solid curve is the best least-square fit of
the parameters in (
5.98
) to the data [
32
]. Reproduced with permission.
Figure 5.2.
