Computer Vision Techniques for the Diagnosis of Skin Cancer (Series in BioEngineering)
By defining the Hurst exponent and fractal dimension we talk about correlation and complexity of damaged DNA. The analyses of the Hurst exponent and fractal dimensions plots show that DNA walk have smaller values of the Hurst exponent and bigger values of fractal dimension in case of damaged DNA compared to normal DNA. The method used in this research can be applied for analysis and diagnosis of other types of cancer. An example of DNA sequence is. This sequence in letter can be converted to a quaternary number sequence by changing T into 0, A into 1, C into 2, and G into 3, such as.
This genomic sequence is what is contained in the whole set of chromosomes in the nucleus of a single cell. It is a remarkable phenomenon that DNA sequence contained in a cell dictates development of a complete, mature organism from one single cell. Scientists have attempted to decipher the structure and meaning of DNA sequences; however, consensus has not been reached and opinions are diverged.
Various mathematical methods have been applied to investigate the nature of DNA sequences. The chaos game representation of DNA sequences has been reported to produce a unique pattern consistently over different parts of the genome of an organism. From the image generated from the chaos game, characteristics of a DNA sequence can be studied, such as finding association between two letters.
It consists first in converting the DNA text into a binary sequence by coding at a given nucleotide positions and at other positions, and then in defining the graph of the DNA walk by the cumulative variables. A prevalent method for DNA analysis is related to random walk or Brownian motion which led to the discovery of long-range correlation in DNA sequences. The motion of Brownian particle consists of steps of movement in a characteristic length in a random direction; thus, it's also called a random walk. Likewise, DNA sequence can be plotted in a form of time-series, but the x-axis represents an array of DNA sequence instead of time [ 19 ].
This way, the profile of letters can be preserved along the sequence.
Combination of pyrimidine tract with purines tract is long known for analysis of DNA [ 20 ]. In this research we chose this combination as it helps for better detection of the long dependence property in DNA sequences look at [ 19 ]. In the next section by introducing the Hurst exponent we discuss about the correlation of the random walks and in special case the DNA walks.
In order to analyse the behaviour of a DNA walk, the direction of fluctuation deflection from one point to the next point and in a bigger view the correlation of walk should be considered. This behaviour can be studied by computing a time varying parameter, called the Hurst exponent. The Hurst exponent is an indicator of the long term memory of the process and thus, it is the measure of the predictability of the DNA walk.
The Hurst exponent can have any value between 0 and 1, where the value that it gains in each moment determines the behaviour of the next deflection in the signal. If there is no long-range correlation, the walk is a realization of a Brownian motion. Those two processes can be characterized by different values of the Hurst exponent H.
It means that there is absolutely no correlation between any values of the process and it is hard to predict the future of process. The analysis of the Hurst exponent for fractional Brownian motion can be categorized in two ranges. Firstly, if the Hurst exponent has a value between 0 and 0. Secondly, a value of H between 0. This comparison helps us in to find out about the correlation and predictability of damaged versus normal DNA walk.
There are different methods which have been developed to estimate the value of H. Nevertheless, we found out that both methods show similar results which become closer as the DNA sequence becomes longer. The same principle which is applied in case of time series also can be applied to DNA sequence. The calculations are explained here through a sample. From 5 and 8.
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Based on the last discussion the value of H suggests that there exists good persistence in the DNA walk as it is between 0. Then, the slope of the linear graph is the estimated Hurst exponent. In this research we calculate the Hurst exponent in different segments of DNA walk and report a signal-shaped plot for it not only an average value. Using this method we are able to talk about the memory and predictability in the DNA walk.
In this section we explain the fractal dimension as a measure of complexity of the fractals and accordingly DNA walk. The concept of fractal dimension is based on the concept of generalized entropy of a probability distribution, introduced by Renyi [ 23 ]. On the other hand, in case of a DNA walk:. Starting with the letter of order q of the probability w i , the Renyi entropy is:.
Diagnosis of skin cancer by correlation and complexity analyses of damaged DNA
The generalized fractal dimensions of a given DNA walk with the known probability distribution are defined as:. Also, note that for a constant value, all probabilities except one become equal to zero, whereas the remaining probability value equals unity. For a given DNA walk, the function q , corresponding to the probability distribution of walk, is called the fractal spectrum. Indeed, a larger value of the fractal dimension for a given DNA walk corresponds to the presence of more pronounced fluctuations sharper fluctuations, less expected values of the DNA walk than in the DNA walks for which the value of fractal dimension of the same order is less.
Furthermore, DNA walks with a wider range of fractal dimensions can be termed more fractal than DNA walks whose range of fractal dimensions is narrower, so that DNA walks with the zero range are self-similar simple fractals. Now, if the unexpectedness of an event is defined as the inverse of the probability of this event, then steeper spectra correspond to the series in which unexpected values are more dominant, whereas flatter spectra represent those series in which less unexpectedness occurs [ 9 ].
It is noteworthy that patients are in early steps of melanoma cancer. Patients didn't receive any treatment chemotherapy, etc. Before doing the experiments each subject was interviewed by a physician to describe the nature of experiments and then informed consent was obtained from them. It is noteworthy that all procedures were approved by the Internal Review Board of the University. Identity of all subjects remains confidential.
In this research sample were taken from subjects' skin. The extraction yields high quality DNA suitable for further analyses. This procedure creates the DNA walk along genome.
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This may be because the snippet appears in a figure legend, contains special characters or spans different sections of the article. Published online Oct PMID: Hamidreza Namazi , 1 Vladimir V. Kulish , 1 Fatemeh Delaviz , 2 and Ali Delaviz 3. Vladimir V.
Correspondence to: Hamidreza Namazi, gs. Received Sep 12; Accepted Oct 3. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article has been cited by other articles in PMC. Abstract Skin cancer is a common, low-grade cancerous malignant growth of the skin. RESULTS In this section we compute the Hurst exponent and fractal dimension for DNA walks in case of healthy subjects and subjects with skin cancer, and then compare the results for diagnosis of skin cancer.
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Figure 1. Grand average of the Hurst exponent plots for DNA walks of all healthy subjects black curve versus grand average of the Hurst exponent plots for damaged DNA walks of all subjects with skin cancer red curve. Figure 2. Comparison of confidence interval for means of the Hurst exponent As it is clear in the figure, confidence intervals in case of healthy subjects red bar with the variation 0.
Figure 3. Grand average of the spectra of fractal dimension plots for DNA walks for all of healthy subjects black curve versus grand average of the spectra of fractal dimension plots for damaged DNA walks for all of subjects with skin cancer red curve. Figure 4. Comparison of confidence interval for means of Fractal dimensions.
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Figure 5. The Hurst exponent and type of motion In order to analyse the behaviour of a DNA walk, the direction of fluctuation deflection from one point to the next point and in a bigger view the correlation of walk should be considered. Table 1 Probability, number of occurrence bp , and movement of each nucleotide. Nucleotide Probability Number of occurrence bp Movement A 0. Sequence H Reference human beta-cardiac myosin heavy chain gene 0.
Spectra of fractal dimension In this section we explain the fractal dimension as a measure of complexity of the fractals and accordingly DNA walk. Epidemiology and economic burden of non-melanoma skin cancer. Rajpar S, Marsden J. ABC of skin cancer.