scholarly journals Diagnostic Application of Fractal Dimension Analysis of Bone Invasion in Oral Malignancy—A Preliminary Retrospective Study

2020 ◽  
Vol 56 (01) ◽  
pp. 42-45
Author(s):  
Archana M. ◽  
Sadaksharam Jayachandran
Keyword(s):  
Fractal Dimension ◽  
Retrospective Study ◽  
Alveolar Bone ◽  
Bone Structure ◽  
Statistical Significance ◽  
Digital Radiographs ◽  
Box Counting ◽  
Set Inclusion ◽  
Oral Malignancy ◽  
Imagej Software

Abstract Introduction Fractal dimension (FD) analysis gives a numerical measure of the degree of boundary irregularity or surface roughness of an object and is based on quantitative analysis of features in an image. It quantifies the trabecular pattern of bone by analyzing the trabecular bone and bone marrow detecting the early changes in alveolar bone mineral content. The aim of this study is to assess the alveolar bone density by FD analysis in digital orthopantomograms (OPGs) showing bony erosion. Materials and Methods The OPGs of 10 patients from the archives of Department of Oral Medicine and Radiology were included in this retrospective study. The radiographs were selected based on set inclusion and exclusion criteria. FD analysis through box counting (using ImageJ software) was applied to the digital radiographs to establish a noninvasive evaluation of bone structure. The FD values obtained were recorded. Results The FD values were recorded and the data were analyzed. FD values showed statistical significance with p < 0.05. Conclusion With the number of samples analyzed and the results obtained, it can be concluded that FD analysis is an innovative method which can be used for early diagnosis of bony invasion in oral cancer. It can serve as a guide to dental surgeons in identifying the extent of bony invasion and can help in determining the margins of surgical resection of oral malignancy. This will prove to be a useful tool in surgical planning of oral malignancy.

scholarly journals A Comparison between the Implant Stability Quotient and the Fractal Dimension of Alveolar Bone at the Implant Site

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Tomasz Kulczyk ◽  
Agata Czajka-Jakubowska ◽  
Agnieszka Przystańska
Keyword(s):  
Logistic Regression ◽  
Regression Analysis ◽  
Fractal Dimension ◽  
Logistic Regression Analysis ◽  
Linear Correlation ◽  
Alveolar Bone ◽  
Implant Stability ◽  
Implant Stability Quotient ◽  
Digital Radiographs ◽  
Maxilla And Mandible

Objectives. Fractal analysis of the radiographic pattern of bone has been used to evaluate its quantitative properties. However, the relation between initial implant stability and quality of bone remains unclear. The objective of this study was to evaluate RFA values in relation to the fractal dimension of bone where the implant was inserted. Material and Methods. A total of 50 two-stage dental implants were placed in the maxilla and mandible of 32 patients. After implant placement, an implant stability quotient (ISQ) was measured in two perpendicular planes. On intraoral digital periapical radiographs, three 35x35 pixels’ regions of interest (ROIs) were chosen covering the bone adjacent to the neck (ROI 1), middle (ROI 2), and apical (ROI 3) part of the implant, respectively. For every ROI, a fractal dimension (FD) was calculated. A linear correlation, as well as a logistic regression analysis, was used to identify a possible relation between the ISQ and FD values for every ROI in the maxilla and mandible. Results. The ISQ and FD values were found to be correlated at ROI 1 for the maxilla. There was no linear correlation between ISQ and FD values in any of the three ROIs in the mandible. However, logistic regression analysis showed that in ROI 1 and ROI 3 the values of FD and ISQ are statistically important and may be used to express the difference between maxilla and mandible. Conclusion. The fractal dimension of alveolar bone measured from intraoral digital radiographs alone may be an insufficient parameter to determine initial implant stability.

3D box-counting algorithm for calculating fractal dimension of cities

2010 ◽  
Vol 30 (8) ◽  
pp. 2070-2072
Author(s):  
Le-shan ZHANG ◽  
Ge CHEN ◽  
Yong HAN ◽  
Tao ZHANG
Keyword(s):  
Fractal Dimension ◽  
Box Counting ◽  
Counting Algorithm

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

CT Image Analysis on the Meso-Damage of Construction Waste Recycled Brick

2012 ◽  
Vol 588-589 ◽  
pp. 1930-1933
Author(s):  
Guo Song Han ◽  
Hai Yan Yang ◽  
Xin Pei Jiang
Keyword(s):  
Fractal Dimension ◽  
Strain Curve ◽  
Ct Image ◽  
Stress Strain Curve ◽  
Crack Evolution ◽  
Construction Waste ◽  
Box Counting ◽  
Industrial Ct ◽  
Ct Image Analysis ◽  
Box Counting Method

Based on industrial CT technique, Meso-mechanical experiment was conducted on construction waste recycled brick to get the real-time CT image and stress-strain curve of brick during the loading process. Box counting method was used to calculate the fractal dimension of the inner pore transfixion and crack evolution. The results showed that lots of pore in the interfacial transition zone mainly resulted in the damage of the brick. With the increase of stress, the opening through-pore appeared and crack expanded, and the fractal dimension increased.

Outer Cutoff Value for the Box-Counting Method for Fractal Analysis of the Nucleus Using Kirsch Edge Detection

2020 ◽  
pp. 1-8
Author(s):  
Haruhiko Yoshioka ◽  
Kouki Minami ◽  
Hirokazu Odashima ◽  
Keita Miyakawa ◽  
Kayo Horie ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Edge Detection ◽  
Fractal Analysis ◽  
Nuclear Size ◽  
Original Position ◽  
Cytological Diagnosis ◽  
Cutoff Value ◽  
Position Bias ◽  
Box Counting ◽  
Nuclear Rotation

<b><i>Objective:</i></b> The complexity of chromatin (i.e., irregular geometry and distribution) is one of the important factors considered in the cytological diagnosis of cancer. Fractal analysis with Kirsch edge detection is a known technique to detect irregular geometry and distribution in an image. We examined the outer cutoff value for the box-counting (BC) method for fractal analysis of the complexity of chromatin using Kirsch edge detection. <b><i>Materials:</i></b> The following images were used for the analysis: (1) image of the nucleus for Kirsch edge detection measuring 97 × 122 pix (10.7 × 13.4 μm) with a Feret diameter of chromatin mesh (<i>n</i> = 50) measuring 17.3 ± 1.8 pix (1.9 ± 0.5 μm) and chromatin network distance (<i>n</i> = 50) measuring 4.4 ± 1.6 pix (0.49 ± 0.18 μm), and (2) sample images for Kirsch edge detection with varying diameters (10.4, 15.9, and 18.1 μm) and network width of 0.4 μm. <b><i>Methods:</i></b> Three types of bias that can affect the outcomes of fractal analysis in cytological diagnosis were defined. (1) Nuclear position bias: images of 9 different positions generated by shifting the original position of the nucleus in the middle of a 256 × 256 pix (28.1 μm) square frame in 8 compass directions. (2) Nuclear rotation bias: images of 8 different rotations obtained by rotating the original position of the nucleus in 45° increments (0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°). (3) Nuclear size bias: images of varying size (diameter: 190 pix [10.4 μm], 290 pix [15.9 μm], and 330 pix [18.1 μm]) with the same mesh pattern (network width: 8 pix [0.4 μm]) within a 512 × 512 pix square. Different outer cutoff values for the BC method (256, 128, 64, 32, 16, and 8 pix) were applied for each bias to assess the fractal dimension and to compare the coefficient of variation (CV). <b><i>Results:</i></b> The BC method with the outer cutoff value of 32 pix resulted in the least variation of fractal dimension. Specifically, with the cutoff value of 32 pix, the CV of nuclear position bias, nuclear rotation bias, and nuclear size bias were &#x3c;1% (0.1, 0.4, and 0.3%, respectively), with no significant difference between the position and rotation bias (<i>p</i> = 0.19). Our study suggests that the BC method with the outer cutoff value of 32 pix is suitable for the analysis of the complexity of chromatin with chromatin mesh.

Fractal and Convolutional Analysis for Deep Atmospheric Turbulence Using Machine Learning

2021 ◽  
Author(s):  
Nicholas Dudu ◽  
Arturo Rodriguez ◽  
Gael Moran ◽  
Jose Terrazas ◽  
Richard Adansi ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Atmospheric Turbulence ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Counting Method ◽  
Data Set ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Self Similar ◽  
Box Counting Method

Abstract Atmospheric turbulence studies indicate the presence of self-similar scaling structures over a range of scales from the inertial outer scale to the dissipative inner scale. A measure of this self-similar structure has been obtained by computing the fractal dimension of images visualizing the turbulence using the widely used box-counting method. If applied blindly, the box-counting method can lead to misleading results in which the edges of the scaling range, corresponding to the upper and lower length scales referred to above are incorporated in an incorrect way. Furthermore, certain structures arising in turbulent flows that are not self-similar can deliver spurious contributions to the box-counting dimension. An appropriately trained Convolutional Neural Network can take account of both the above features in an appropriate way, using as inputs more detailed information than just the number of boxes covering the putative fractal set. To give a particular example, how the shape of clusters of covering boxes covering the object changes with box size could be analyzed. We will create a data set of decaying isotropic turbulence scenarios for atmospheric turbulence using Large-Eddy Simulations (LES) and analyze characteristic structures arising from these. These could include contours of velocity magnitude, as well as of levels of a passive scalar introduced into the simulated flows. We will then identify features of the structures that can be used to train the networks to obtain the most appropriate fractal dimension describing the scaling range, even when this range is of limited extent, down to a minimum of one order of magnitude.

scholarly journals Changes in alveolar bone support induced by the Herbst appliance: a tomographic evaluation

2016 ◽  
Vol 21 (2) ◽  
pp. 95-101 ◽  
Author(s):  
João Paulo Schwartz ◽  
Taisa Boamorte Raveli ◽  
Humberto Osvaldo Schwartz-Filho ◽  
Dirceu Barnabé Raveli
Keyword(s):  
Bone Loss ◽  
Alveolar Bone ◽  
Statistical Significance ◽  
Alveolar Bone Loss ◽  
T Test ◽  
Bone Thickness ◽  
Herbst Appliance ◽  
Bone Level ◽  
Dependent Samples ◽  
Mandibular Incisors

ABSTRACT Objective: This study evaluated alveolar bone loss around mandibular incisors, induced by the Herbst appliance. Methods: The sample consisted of 23 patients (11 men, 12 women; mean age of 15.76 ± 1.75 years), Class II, Division 1 malocclusion, treated with the Herbst appliance. CBCT scans were obtained before treatment (T0) and after Herbst treatment (T1). Vertical alveolar bone level and alveolar bone thickness of mandibular incisors were assessed. Buccal (B), lingual (L) and total (T) bone thicknesses were assessed at crestal (1), midroot (2) and apical (3) levels of mandibular incisors. Student's t-test and Wilcoxon t-test were used to compare dependent samples in parametric and nonparametric cases, respectively. Pearson's and Spearman's rank correlation analyses were performed to determine the relationship of changes in alveolar bone thickness. Results were considered at a significance level of 5%. Results: Mandibular incisors showed no statistical significance for vertical alveolar bone level. Alveolar bone thickness of mandibular incisors significantly reduced after treatment at B1, B2, B3, T1 and significantly increased at L2. The magnitude of the statistically significant changes was less than 0.2 mm. The changes in alveolar bone thickness showed no statistical significance with incisor inclination degree. Conclusions: CBCT scans showed an association between the Herbst appliance and alveolar bone loss on the buccal surface of mandibular incisors; however, without clinical significance.

Sign in / Sign up

Export Citation Format

Share Document