A novel approach to improve the accuracy of the box dimension calculations: Applications to trabecular bone quality

Fernández–Martínez, M.; Sánchez, Yolanda Guerrero; López‐Jornet, Pía

doi:10.3934/dcdss.2019105

Cited by 7 publications

(8 citation statements)

References 13 publications

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“…The fractal dimension is a mathematical value that is common for each structure and measures in some way the internal similarity of such an object, particularly in the case of the biological structures used in the study for the present work. The fractal dimension in the current work has been computed via the so-called “box-counting technique”, modified using our algorithm, which was introduced in [ 38 ].…”

Section: Discussionmentioning

confidence: 99%

Use of the Fractal Dimension to Differentiate Epithelium and Connective Tissue in Oral Leukoplakias

Sánchez

García

Chamorro-Petronacci

et al. 2022

Cancers

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Background: Oral leukoplakia (OL) is considered one of the most common potentially malignant oral disorders (OPMD), with a verified increased risk of developing oral cancer. The identification of the dysplasia grade (low–high) is the only consolidated factor used to evaluate this risk. The objective of this study was to verify the role of the fractal dimension (FD) in assessing this dysplasia. Methods: To begin, 29 OL and 10 normal oral mucosa (NOM) biopsies were retrieved for FD analysis of the epithelial (dime) and the connective (dimc) tissue. Results: In the OL group, the median value of dime is higher (1.67, IQR = 0.12) than for the NOM group (1.56, IQR = 0.08), with statistically significant differences (Wilcoxon test, p = 0.0031). There were no differences in relation to dimc. Significant differences were observed between the non-dysplasia vs. high-grade (p = 0.0156) and low-grade vs. high-grade (p = 0.0049) groups. No significant differences were identified in relation to dimc for the different degrees of dysplasia. For a cut-off point of 1.44 of dime, a specificity of 96.6% was obtained, a sensitivity of 100%, and an AUC = 0.819 (p = 0.003). Conclusions: FD at the level of the epithelium may be used as a diagnostic tool in OL.

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Section: Discussionmentioning

confidence: 99%

Use of the Fractal Dimension to Differentiate Epithelium and Connective Tissue in Oral Leukoplakias

Sánchez

García

Chamorro-Petronacci

et al. 2022

Cancers

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“…Hopefully, the digital technology has brought to dentistry several advances, both in the preoperative (scanners) and surgical (computer assisted implantology) fields [10]. In fact, the development of imaging techniques such as cone beam computed tomography (CBCT in the sequel) has allowed a proper display of such structures [11], thus being consolidated as an appropriate resource to extract valuable information from high resolution images [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…It is noteworthy that our fractal dimension calculations were carried out by an accurate procedure described in Section 2 (cf. [12,13,19]).…”

mentioning

confidence: 99%

“…With this aim, a novel algorithm especially designed to accurately calculate the fractal dimension of binary CBCTs was applied (cf. [12,13]). With this aim, all the 400 CBCTs of maxillary sinuses were assigned to one of two subgroups.…”

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confidence: 99%

“…The calculations involving the fractal dimensions of the binary CBCTs were performed by means of the following expression (cf. [12,13,20]):…”

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confidence: 99%

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Anatomical Considerations and Study of the Fractal Dimension around the Posterior Superior Alveolar Artery

et al. 2020

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The Posterior Superior Alveolar Artery (PSAA) provides vascular support to molars, gingiva, and maxillary sinus. A tear of the PSAA may cause profuse hemorrhages which may lead to complications at a surgical level. As such, it becomes crucial to anatomically analyse several features regarding the PSAA as well as the area surrounding it. In this paper, we are particularly interested in the study of the complexity of the periodontal tissue structure which appears close to the location of the PSAA. A total amount of 400 cone beam computed tomography (CBCT) scans (two per subject) were performed to explore the presence of the PSAA, the thickness of the Schneider’s membrane, and the existence of septa. Several parameters were evaluated including the location of the artery in the maxillary sinus, the distance from the PSAA to the alveolar ridge, the thickness of the membrane, the diameter of the cavities produced by the septa, and the fractal dimension of the trabecular tissue that surrounds the PSAA. They were found strong linear relationships between Distal and Central Measures (a Pearson’s R 2 = 0.9952 ), Mesial and Central Measures ( R 2 = 0.9950 ), and Distal and Mesial Measure ( R 2 = 0.997 ). We hypothesised that the loss of dental pieces would imply a distinct complexity of the trabecular tissue structure surrounding the PSAA. In this way, a p-value equal to 0.001 was provided by the Mann-Whitney test, which supports our hypothesis. Furthermore, the mean of the fractal dimensions of the group of edentulous patients (equal to 1.56 ) was found to be lower than the one of the group of non-edentulous patients (equal to 1.61 ) with small standard deviations in both cases. Our study suggests that accurate calculations of the fractal dimension combined with the use of CBCT do provide valuable information regarding the area that surrounds the PSAA.

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Representation of aggregates from their two-dimensional images for primary particles of different sizes

Wang,

Ajalova,

Kolan

et al. 2025

Powder Technology

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A novel approach to improve the accuracy of the box dimension calculations: Applications to trabecular bone quality

Cited by 7 publications

References 13 publications

Use of the Fractal Dimension to Differentiate Epithelium and Connective Tissue in Oral Leukoplakias

Use of the Fractal Dimension to Differentiate Epithelium and Connective Tissue in Oral Leukoplakias

Anatomical Considerations and Study of the Fractal Dimension around the Posterior Superior Alveolar Artery

Representation of aggregates from their two-dimensional images for primary particles of different sizes

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