Abstract: The colonic tissue is a complicated dynamic system
and the colonic activities it generates are composed of irregular
segmental waves, which are referred to as erratic fluctuations or spikes.
They are also highly irregular with subunit fractal structure. The
traditional time-frequency domain statistics like the averaged
amplitude, the motility index and the power spectrum, etc. are
insufficient to describe such fluctuations. Thus the fractal
box-counting dimension is proposed and the fractal scaling behaviors
of the human colonic pressure activities under the physiological
conditions are studied. It is shown that the dimension of the resting
activity is smaller than that of the normal one, whereas the clipped
version, which corresponds to the activity of the constipation patient,
shows with higher fractal dimension. It may indicate a practical
application to assess the colonic motility, which is often indicated by
the colonic pressure activity.
Abstract: Migration in breast cancer cell wound healing assay
had been studied using image fractal dimension analysis. The
migration of MDA-MB-231 cells (highly motile) in a wound healing
assay was captured using time-lapse phase contrast video microscopy
and compared to MDA-MB-468 cell migration (moderately motile).
The Higuchi fractal method was used to compute the fractal
dimension of the image intensity fluctuation along a single pixel
width region parallel to the wound. The near-wound region fractal
dimension was found to decrease three times faster in the MDA-MB-
231 cells initially as compared to the less cancerous MDA-MB-468
cells. The inner region fractal dimension was found to be fairly
constant for both cell types in time and suggests a wound influence
range of about 15 cell layer. The box-counting fractal dimension
method was also used to study region of interest (ROI). The MDAMB-
468 ROI area fractal dimension was found to decrease
continuously up to 7 hours. The MDA-MB-231 ROI area fractal
dimension was found to increase and is consistent with the behavior
of a HGF-treated MDA-MB-231 wound healing assay posted in the
public domain. A fractal dimension based capacity index has been
formulated to quantify the invasiveness of the MDA-MB-231 cells in
the perpendicular-to-wound direction. Our results suggest that image
intensity fluctuation fractal dimension analysis can be used as a tool
to quantify cell migration in terms of cancer severity and treatment
responses.
Abstract: In this paper, we have developed a method to
compute fractal dimension (FD) of discrete time signals, in the
time domain, by modifying the box-counting method. The size
of the box is dependent on the sampling frequency of the
signal. The number of boxes required to completely cover the
signal are obtained at multiple time resolutions. The time
resolutions are made coarse by decimating the signal. The loglog
plot of total number of boxes required to cover the curve
versus size of the box used appears to be a straight line, whose
slope is taken as an estimate of FD of the signal. The results
are provided to demonstrate the performance of the proposed
method using parametric fractal signals. The estimation
accuracy of the method is compared with that of Katz, Sevcik,
and Higuchi methods. In addition, some properties of the FD
are discussed.