Dynamic Cerebral Contrast-enhanced Perfusion MRI - Biomedical Signal Analysis: Contemporary Methods and Applications - page 321

In general, a minimal number of clusters is necessary to obtain a
good partition quality of the underlying data set, which leads to a higher
area under the ROC curve. This effect can clearly be seen for subjects 3
and 4. For the data sets of subjects 1 and 2, the cluster number doesn't
seem to play a key role. A possible explanation of this aspect is the large
extent of the infarct area. Thus, even with a smaller number of codebook
vectors, it becomes possible to obtain a good separation of the stroke
areas from the rest of the brain. Any further partitioning, obtained by
increasing the number of codebook vectors, is not of crucial importance
- the area under the curve does not change substantially. Also, for the
patients without evidence of a cerebrovascular disease, the area under
the ROC curve is smaller than that for the subjects with stroke.
Three important aspects remain to be discussed: the interpretation
of the codebook vector, the normalization of the signal time curves, and
the relatively high MTT values.
A codebook vector can be specified as a time series representing
the center (i.e., average) of all the time series belonging to a cluster.
Here, a cluster represents a set of pixels whose corresponding time
series are characterized by similar signal dynamics. Thus, “codebook
vectors” as well as “clusters” are defined in an operational way that
- at a first glance - does not refer to any physiological implications.
However, it is common practice in the literature to conjecture [84] that
similar signal characteristics may be induced by similar physiological
processes or properties, although this cannot be proven definitely. It is
very interesting to observe that the average values for the areas under the
ROC curves seem to be higher for the patients with stroke in comparison
to the patients without stroke. So far, no explanation can be given for
this, but it may be an important subject for further examination in
future work. The different numbers of codebook vectors used for different
subjects can be explained as follows: 16 and 36 codebook vectors were
used for clustering in all data sets. In addition, the optimal number of
clusters was determined by a detailed analysis using several “cluster-
validity criteria”: Kim [138], Calinski, and Harabazs (CH) [39], and
intraclass [97].
In biomedical MRI time series analysis considered here, a similar
problem is faced: It is certainly not possible to interpret all details of
the signal characteristics of the time series belonging to each pixel of the
data set as known physiological processes. Nevertheless, it may be a use-