Digital Signal Processing Reference
In-Depth Information
where
α>
0 is an unknown proportionality constant. Based on equation
(11.2), the concentration-time curves (CTCs) are obtained from the
signal PTCs.
Conventional data analysis was performed by computing MTT,
rCBV, and rCBF parameter maps employing the relations (e.g. [299],
[11], [240])
MTT =
τ
rCBV =
c
(
τ
)
dτ,
c
(
τ
)
dτ
c
(
τ
)
dτ
·
rCBF =
rCBV
,
MTT
.
(11.3)
Methods for analyzing perfusion MRI data require presumptive
knowledge of contrast-agent dynamics based on theoretical ideas of
contrast-agent distribution that cannot be confirmed by experiment
(e.g., determination of relative CBF, relative CBV, or MTT compu-
tation from MRI signal dynamics). Although these quantities have been
shown to be very useful for practical clinical purposes, their theoretical
foundation is weak, as the essential input parameters of the model cannot
be observed directly. On the other hand, methods for absolute quantifi-
cation of perfusion MRI parameters do not suffer from these limitations
[200]. However, they are conceptually sophisticated with regard to theo-
retical assumptions and require additional measurement of arterial input
characteristics, which sometimes may be dicult to perform in clinical
routine diagnosis. At the same time, these methods require computa-
tionally expensive data postprocessing by deconvolution and filtering.
For example, deconvolution in the frequency domain is very sensitive to
noise. Therefore, additional filtering has to be performed, and heuris-
tic constraints with regard to smoothness of the contrast-agent residual
function have to be introduced. Although other methods, such as singu-
lar value decomposition (SVD), could be applied, a gamma variate fit
[213, 265] was used in this context.
The limitations with regard to perfusion parameter computation-
based equations (11.3) are addressed in the literature (e.g., [281], [220]).
Evaluation of the clustering methods
This section is dedicated to presenting the algorithms and evaluating
the discriminatory power of unsupervised clustering techniques. These
are Kohonen's self-organizing map (SOM), fuzzy clustering based on
deterministic annealing, the “neural gas” network, and the fuzzy
c
-
means algorithm. These techniques are according to grouping image
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