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 Table of Contents  
Year : 2015  |  Volume : 27  |  Issue : 3  |  Page : 354-358

Fractal analysis in oral leukoplakia

Department of Oral Medicine and Radiology, Career Postgraduate Institute of Dental Sciences and Hospital, Lucknow, Uttar Pradesh, India

Date of Submission21-Nov-2014
Date of Acceptance19-Nov-2015
Date of Web Publication25-Nov-2015

Correspondence Address:
Prashant Bhai Pandey
C/o Dr. A. B. Pandey, G IIA, Krishna Apartment, Narendra Nagar, Rewa - 486 001, Madhya Pradesh
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/0972-1363.170448

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Introduction: Fractal analysis (FA) quantifies complex geometric structures by generating a fractal dimension (FD), which can measure the complexity of mucosa. FA is a quantitative tool used to measure the complexity of self-similar or semi-self-similar structures. Aim and Objective: The study was done to perform the FA of oral mucosa with keratotic changes, as it is also made up of self-similar tissues, and thus, its FD can be calculated. Results: In oral leukoplakia, keratinization increases the complexity of mucosa, which denotes fractal geometry. We evaluated and compared pretreated and post-treated oral leukoplakia in 50 patients with clinically proven oral leukoplakia and analyzed the normal oral mucosa and lesional or keratinized mucosa in oral leukoplakia patients through FA using box counting method. Conclusion: FA using the fractal geometry is an efficient, noninvasive prediction tool for early detection of oral leukoplakia and other premalignant conditions in patients.

Keywords: Fractal analysis, fractal dimension, keratinization, premalignant

How to cite this article:
Pandey PB, Kandakurti S, Saxena VS, Tripathi P, Pamula R, Yadav M. Fractal analysis in oral leukoplakia. J Indian Acad Oral Med Radiol 2015;27:354-8

How to cite this URL:
Pandey PB, Kandakurti S, Saxena VS, Tripathi P, Pamula R, Yadav M. Fractal analysis in oral leukoplakia. J Indian Acad Oral Med Radiol [serial online] 2015 [cited 2022 May 17];27:354-8. Available from: https://www.jiaomr.in/text.asp?2015/27/3/354/170448

   Introduction Top

Fractal analysis (FA) was introduced by Mandelbrot in 1983. [1] It is a mathematical model for the description of many complex biological geometric structures. [2] The word "fractal" is derived from the Latin word "fractus" which means "fracture" or "broken." It has been used to name a geometry that deals with self-similar forms and is different from typical geometries taught in schools like Euclidean and Cartesian geometries. [3],[4] Fractal theory offers methods for describing the complexity and irregularity of anatomic structures that comprise organs, tissues, and cells considered as fractal objects. Fractal objects have properties that include self-similarity, scale independence, complexity, and infinite length or detail. [2] Based on this concept, it is possible to identify the shape and structure of an object which is not identifiable, using FA, and they are expressed numerically using fractal dimension (FD). Biofractals are the fractal textures/contours in biology whose properties aid in the classification of biological and medical data and images. [2] The FD depends on the methodological and experimental parameters involved, such as diversity of subjects, image acquisition, type of image, image quality, its processing, FA methods, including the algorithm and specific calculation used. [2] In other words, FD increases or decreases according to the complexity of the object. [4] Fractal geometry and analysis has found plenty of applications in several branches of dentistry by tracing digital image analysis.

Oral leukoplakia (OL) is a premalignant lesion described as "a predominant white lesion of the oral mucosa which cannot be defined as any other known lesion" [5] [Figure 1]. The term "leukoplakia" was first used by Schwimmer in 1877. OL is regarded to be a premalignant or, synonymously, a potentially malignant or precancerous lesion. In this study, we attempted to evaluate the FD of oral mucosa in OL, as FD also increases as keratinization/complexity of mucosa increases, i.e. along with the progression of lesion [Figure 2], and it can be an effective noninvasive prognostic tool to measure the progression/regression of the lesion.
Figure 1: Grayish white patch on the buccal mucosa showing typical cracked mud-like appearance of oral leukoplakia

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Figure 2: Histopathological picture of oral leukoplakia showing dysplastic changes

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Aim and objectives

Aim of our study was to evaluate the FDs of OL by measuring the FD of normal oral mucosa and lesional mucosa, i.e. keratinized mucosa in OL patients, using FA. The FD of keratinized mucosa was calculated and compared in pretreated and post-treated OL to analyze the progression or regression of the lesion following treatment.

   Materials and Methods Top

This study was conducted in the Department of Oral Medicine and Radiology. A total of 50 individuals consisting of males and females were included in the study group in which the subjects had been clinically diagnosed and histopathologically confirmed as OL. The patients' clinical profile including gender and age was recorded and digital images of normal and lesional mucosa were taken [Figure 3]a with Sony cyber-shot digital camera (model no. DHC-H200). The digital images obtained were then preprocessed by cropping in a manner involving both normal and keratinized mucosa according to the regions of interest (ROIs) of size 86 × 124 pixels [Figure 3]b. With the help of ImageJ software version 1.47 compatible with personal computer with a configuration including Windows 7 operating system, Intel Pentium CPU, and 32 BIT operating system, the digital images were processed and analyzed. Firstly, the ROI images, i.e. 16-bit direct digital images, were converted to 8-bit images [Figure 3]c because only 8-bit images can be segmented with ImageJ. The obtained digital images were segmented to binary in a similar way described by White and Rudolph. [6] ROIs were then duplicated [Figure 3]d and blurred by a Gaussian filter with diameter 35 pixels [Figure 3]e. This step removed all the fine-scale and medium-scale structures and retained only larger variations in density. The resulting blurred image was then subtracted from the original [Figure 3]f] and 128 was added to the result at each pixel location [Figure 3]g. This generates an image of value 128 regardless of the initial intensity of the image. The image was then made binary [Figure 3]h, thresholding on a brightness value of 128. To reduce noise, binary images were eroded [Figure 3]i, and dilated once [Figure 3]j and processed as skeletonized image [Figure 3]k. The FD of all skeletonized images obtained from the image processing procedure was calculated using box counting method. A graph plotted between box count and box size showed the resultant FD value [Figure 3]l. The change of FD of oral mucosa and lesional/keratinized mucosa was calculated and compared.
Figure 3: Steps involved in image processing in fractal analysis: (a) Digital image of buccal mucosa of a patient diagnosed with oral leukoplakia (b) Cropped image showing regions of interest of size 86 × 12 pixels (c) Cropped image converted into 8-bit image (d) Duplicated image (e) Blurred image obtained by adding Gaussian fi lter with a diameter of 35 pixels (f) Subtracted image (g) Added image, with brightness value of 128 at each pixel location (h) Binary image (i) Eroded image with reduced noise (j) Dilated image (k) Skeletonized image (l) Plot between box count and box size, showing the value of fractal dimension

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   Results Top

Digital images of different patients and having the same ROI were taken. The results of all 50 patients were tabulated [Table 1] and statistical analysis was done using the unpaired t test. Confidence interval was 95% (0.510611-0.666612). The mean difference between the two groups and standard error of difference were found to be 0.588612 and 0.039, respectively [Table 2]. The P value obtained was 0.0001. Thus, by conventional criteria, this difference is considered to be extremely statistically significant. The difference in FDs between pretreated and post-treated lesions was observed and was suggestive of decrease in complexity/keratinization of the lesion following treatment, i.e. regression of the lesion.
Table 1: Value of fractal dimension of 50 patients in pretreatment and post-treatment groups

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Table 2: Mean value, standard deviation, SEM value, and no. of samples

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   Discussion Top

Keratinization is a process in which the dividing cells are in self-similar forms as shown by histopathological slide and, thus, represents the same clinical picture. Changes also occur at the level of basement membrane, which could be shown by histopathological examination when the lesion gets converted into nonhomogenous form or carcinoma in situ. The boundary forms between lesional mucosa and normal mucosa show high turnover and also show self-similar shape or semi-self-similar shape, thus representing fractal geometry. The decrease in FD after treatment suggests reduction in complexity of the lesion, which means resolution of the lesion. FD analysis of the OL has been introduced as an alternative method to investigate the prognosis of the leukoplakia lesions. Previously, no other study had been done using this concept in assessing healing of leukoplakia. We took a small step to explore this concept. The basic concept of fractal geometry holds that we do not live in a Euclidean world of points, straight angles, rectangles, and cubes as largely created by man. Natural objects are often rough and are not well described by the ideal constructs of Euclidean geometry. An important characteristic of fractal geometry is the property of "self-similarity." Fractal images are similar in statistical sense, at all levels of magnification or scale. As a fractal image is viewed at higher and higher magnifications, the amount of detail is constant. This is equivalent to stating that any measured length is proportional to the resolvable length. In principle, a theoretical or mathematically generated fractal is self-similar over an infinite range of scales. Natural fractal images, however, have a limited range of self-similarity. [7]

We took this concept of self-similarity for keratinized mucosal structure in OL. Leukoplakia is a premalignant lesion and has the potential to transform into carcinoma; therefore, assessment of its progression is of important value. FA is one of the important tools that can be used for investigation, diagnosis, and treatment planning. Thus, if we get the digital image of the same ROIs as those in pretreatment digital image, then by using FA, we can compare and determine the progression or healing of the lesion. The concept of self-similarity for oral mucosa structure has been used for the first time in our study. The results are encouraging, but further studies and research are required to explore this concept. [7] Limitations of the study are certain factors which include less knowledge of digital images and computer applications, as the software used in this study is technique sensitive. There should be more and more studies of such type, so that newer methods can come into play to diagnose and treat lesions.

   Conclusion Top

FA can be an effective and noninvasive diagnostic and prognostic tool for various premalignant lesions and conditions, e.g. leukoplakia, lichen planus, SLE, etc. FD varies according to the complexity of the lesion, and is economical, less time consuming, and an accurate tool for measuring the progression of premalignant lesions like OL. It can play a major role in the community settings by establishment of an effective methodology for education and training on the frontline.

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Conflicts of interest

There are no conflicts of interest.

   References Top

Kang HU, Jeong SW, Jo BH, Kim YD, Kim SS. Observation of trabecular changes of the mandible after orthognathic surgery using fractal analysis. J Korean Assoc Oral Maxillofac Surg 2012;38:2-96.  Back to cited text no. 1
Elena PA, Talu S, Talu M, Giovanzana S, Craciun C. Fractal Analysis of Healthy Human Periodontium. Ann Rom Soc Cell Biol 2012;17:45-8.  Back to cited text no. 2
Jolley L, Majumdar S, Kapila S. Technical factors in fractal analysis of periapical radiographs. Dentomaxillofac Radiol 2006;35:393-7.  Back to cited text no. 3
Ivan S, Gladys U. Fractals in dentistry. J Dent 2011;39:273-92.  Back to cited text no. 4
Ribeiro AS, Salles PR, da Silva TA, Mesquita RA. A review of the nonsurgical treatment of oral leukoplakia. Int J Dent 2010;2010:186018.  Back to cited text no. 5
White SC, Rudolph DJ. Alterations of the trabecular pattern of the jaws in patients with osteoporosis. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 1999;88:628-35.  Back to cited text no. 6
Freny K, Siddhartha SV. Fractals in forensics. J Indo Pacific Acad Forensic Odontol 2011;2:16-21.  Back to cited text no. 7


  [Figure 1], [Figure 2], [Figure 3]

  [Table 1], [Table 2]

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