Here is my 1 page summary of the article:
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Fractal Approach
To Identify The Grade of Cervical Cancer
The above
named article was taken from the World Scientific Journal: Fractals, Vol. 19,
No. 1 (2011) 125-139. This particular article discusses certain methods that
involve using fractals to diagnose grades of cervical cancers. But, in order to
understand what is being discussed, it is important to understand the two main
topics: fractals, and cervical cancer.
Fractal, by
definition, is a geometric pattern that is repeated at
ever smaller scales to produce irregular shapes and surfaces that cannot be
represented by classical geometry. Cervical cancer is described as a disease
caused by the abnormal growth and division of cells that make up the cervix.
Since cancer arises from abnormal cell growth, there have been developments
using mathematics to identify the grades. The most common method used for this
is the Box Counting Method.
The
Box Counting Method is used in conjunction with MATLAB programme to find the
dimensions of the cell variances for normal cells and abnormal cells. This particular method is used because it can
be applied to various sets of dimensions and patterns with or without self-similarity.
The following equation is used to find the fractal dimension (D): D= , where is the number of
boxes of size S needed to cover the structure. The precancerous changes of the
cells in the cervix are described by fractal analysis.
To
compute the actual fractal dimension, there are a few equations to use along
with an algorithm (this will be discussed further in my actual paper). The
image analysis using fractal approaches to characterize the growth of cancerous
cells consists of covering an area with same-size, non-overlapping boxes. The
number of boxes needed to cover the area is then plugged into D=, where D is the fractal dimension, K is a constant, and r
is the size of the boxes. The relationship between r, N(r) is then used to plot
points in a logarithmic scale to obtain D. This relationship helps to indicate
the degree of complexity or dimensions of the fractal.
The Box Counting Method is then used
with HarFA software to show the actual dimension (complexity of a fractal like
structure/the cells growth) and intensity of the cell varies for normal and
abnormal cells. Continuing, there is an Exponential Growth Model, Contact
Model, Epidemic Model and Lacunarity (gap/size distribution of holes), that all
help in determining the grade of the cancer. The Lacunarity finds the
distribution and size of empty domains. For fractal dimensions, the higher the
dimension, the higher the grade of cancer, and vice-versa.
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