Monday, October 1, 2012

Fractals And Cervical Cancer

In continuing with the theme of preparing for my final paper, I have chosen and article for my article review that uses fractals to find the grade of cervical cancer. Not only is cervical cancer the second most common cancer in women, but it is the third leading cancer related cause of death in women. So, I found this article interesting on so many levels. Not only are they using mathematics to identify the severity of cervical cancer, but the methods used and equations used don't seem that complex. If you would like to take a look at the article, as well as my 1 page review, feel free.   Journal Article 
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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