Computational and Mathematical Methods in Medicine

Volume 2015 (2015), Article ID 242695, 11 pages

http://dx.doi.org/10.1155/2015/242695

## Diagnosis of Lung Cancer by Fractal Analysis of Damaged DNA

^{1}Department of Mechanical Engineering, Faculty of Engineering, Universiti Malaysia Sarawak, 94300 Kuching, Sarawak, Malaysia^{2}Faculty of Biosciences & Medical Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia

Received 23 January 2015; Accepted 24 March 2015

Academic Editor: Alexey Zaikin

Copyright © 2015 Hamidreza Namazi and Mona Kiminezhadmalaie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Cancer starts when cells in a part of the body start to grow out of control. In fact cells become cancer cells because of DNA damage. A DNA walk of a genome represents how the frequency of each nucleotide of a pairing nucleotide couple changes locally. In this research in order to study the cancer genes, DNA walk plots of genomes of patients with lung cancer were generated using a program written in MATLAB language. The data so obtained was checked for fractal property by computing the fractal dimension using a program written in MATLAB. Also, the correlation of damaged DNA was studied using the Hurst exponent measure. We have found that the damaged DNA sequences are exhibiting higher degree of fractality and less correlation compared with normal DNA sequences. So we confirmed this method can be used for early detection of lung cancer. The method introduced in this research not only is useful for diagnosis of lung cancer but also can be applied for detection and growth analysis of different types of cancers.

#### 1. Introduction

Cancers are caused by uncontrollable growth of cells which do not die. Normal cells in the body grow, divide, and finally die (apoptosis) in an orderly path. When the death process of cells breaks down, cancer starts. In case of cancer, cells continue to grow and divide instead of having a programmatic death which results in a bunch of abnormal cells growing out of control.

Lungs are spongy organs in the chest which take in oxygen and release carbon when human inhales and exhales, respectively. Lung cancer begins in the lungs. Lung cancer is a dominant type of cancer which kills many people every year compared to other types of cancer.

When the cell’s gene cannot correct the DNA damage, the lung cancer appears. Inhaling carcinogenic substances is the main reason of lung cancer.

For years some methods have been investigated in order to diagnose the lung cancer. Most of these methods are based on medical theories. Among these methods, employing computed tomography (CT) image analysis is more dominant. By computed tomography of chest Mets et al. derived and validated a model of lung cancer which studies the coronary and aortic calcium volume in lung [1]. Veronesi et al. analyzed computed tomography images of lung in case of smokers and former smokers in order to detect the lung cancer [2]. In another work Jiménez-Bonilla et al. worked on diagnosis of recurrence and assessment of postrecurrence survival in patients with extra cranial non-small cell lung cancer using 18F-FDG PET/CT [3]. See also [4–6]. On the other hand, some researchers have worked on analysis of patients’ DNA for diagnosis lung cancer. An et al. detected tumor-associated aberrant hyper methylation of the* p16* gene in DNA extracted from plasma. Using a modified seminested methylation-specific PCR, they did their experiments on 105 non-small cell lung cancer patients and 92 matched tumor DNA samples [7]. In a recent research, Jelovac et al. detected PIK3CA DNA mutation in plasma of a patient with breast and lung cancers [8]. In another extensive work, Diehn et al. employed deep sequencing for detection of circulating tumor DNA in non-small cell lung cancer [9].

Beside some works done on the prediction and analysis of lung cancer from biological point of view, there are few researches being reported which use mathematical models for diagnosis of lung cancer. McCulloch et al. used mathematical model for developing a model-based CAD algorithm which capture scanner physics and anatomic information. Their model uses multiple segmentation algorithms in order to extract structures in the lungs. Also, they proposed a selection framework which was based on Bayesian statistical model in order to determine the probability of different anatomical events throughout the lung [10]. Kang et al. constructed a diagnostic and prognostic mathematical model of lung cancer. In fact this model integrates let-7 and miR-9 expression into a signalling pathway in order to generate an in silico model for the process of epithelial mesenchymal transition (EMT). They used this model for diagnostic and prognostic biomarkers in lung cancer [11]. In a recent work, Hndoosh suggested a fuzzy mathematical model for detection of lung cancer using a multi-NFclass with confusion fuzzy matrix for accuracy [12].

Fractals are scale-invariant geometric objects. A scale-invariant object can be self-similar or self-affine. A self-similar object is a union of rescaled copies of itself which is isotropic or uniform in all directions. But in case of self-affine objects, the mechanism is anisotropic or dependent on the direction. Regular fractals have higher self-similarity, but random fractals have a weaker self-similarity.

The class of regular fractals includes many familiar simple objects, such as line intervals, solid squares, and solid cubes, and also many irregular objects. The scaling rules are characterized by “scaling exponents” (dimension). “Simple” regular fractals have integer scaling dimensions. Complex self-similar objects have noninteger dimension. Therefore, it is completely incorrect to define fractals as geometric objects having “fractional” (noninteger) dimension. Fractals may be defined as geometric objects whose scaling exponent (dimension) satisfies the Szpilrajn inequality:where is the scaling exponent (dimension) of the object and is its topological dimension, that is, Euclidean dimension of units from which the fractal object is built. For example, in case of Brownian motion: the path of a particle, a line of dimension one, traveling for a long time over a plane region, eventually covers the entire plane, an entity of dimension two [13].

In case of multifractal system a single fractal dimension cannot describe its dynamics. In this case, a continuous spectrum of exponents is needed [14].

We deal with many multifractal systems in nature such as fully developed turbulence and heartbeat dynamics. In case of using fractal for detection of lung cancer, limited works have been reported which are based on analysis of tumor’s shape using fractal dimension. Miwa et al. found out that the d-FD of intratumoral heterogeneity of FDG uptake can help to differentially diagnose malignant and benign pulmonary nodules. The SUVmax and d-FD obtained from FDG-PET images provide different types of information that are equally useful for differential diagnoses [15]. Lee et al. reported that fractal dimension of carcinoma epithelial architecture can assist in differentiating adenocarcinoma (ADC) from squamous cell carcinoma (SCC) of the lung [16].

In spite of all of these works, no work has been reported which analyses the complexity and correlation of damaged DNA. In this paper we use the concept of fractal dimension and the Hurst exponent in order to analyse the DNA sequences. In order to do this task first we illustrate DNA walk as a random walk and then by introducing the spectra of fractal dimension and the Hurst exponent we compute these parameters for DNA walks extracted from DNA sequences of patients with lung cancer. The multifractality and correlation of patients’ DNA walk are discussed in detail.

#### 2. DNA and Random Motion

A DNA sequence of chromosome in the cell’s nucleus is a combination of four letters. These letters, A, C, G, and T, are the bases adenine, cytosine, guanine, and thymine, respectively. For instance, a DNA sequence is …GTCAGAGCCTATCGTTACG…This string can be written in the form of numbers by assigning 1 for T, 2 for A, 3 for C, and 4 for G, so …4132424331213411234…In fact, the DNA sequence is the root for development of a complete organism.

For years many mathematical methods have been developed in order to study the nature of DNA sequences.

DNA walk plotting is a popular method which generates a planar trajectory of DNA sequences. In this method first the DNA text is converted to a binary sequence and then the DNA walk plot is defined by the cumulative variables [17]. By this consideration, DNA walk can be considered as a random walk (Brownian motion) where each point in the plot can deflect up or down in nucleotide distance.

DNA sequence can be defined by two of six possible combinations which are purines (A+G), pyrimidines (C+T), Imino (A+C), Keto (G+T), Weak (A+T), and Strong (G+C). Combination of pyrimidine tract with purines tract is long known for analysis of DNA [18]. In this research we chose this combination as it helps in better detection of the long dependence property in DNA sequences (see [17, 19]).

Figure 1 shows the one-dimensional DNA walk plot using purine-pyrimidine binary rule. This rule changes purines (A/G) to −1 and pyrimidines (C/T) to +1.