On the Symmetry of the Bone Structure Density over the Nasopalatine Foramen via Accurate Fractal Dimension Analysis

Bornstein, Michael M.; Fernández–Martínez, M.; Guirao, Juan Luis García; Gómez-García, Francisco; Sánchez, Yolanda Guerrero; López‐Jornet, Pía

doi:10.3390/sym11020202

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…Core flooding using oil Li et al [19] TPG = 0.0747k −1.117 Core flooding using oil Li et al [19] TPG = 0.4k −0.9348 Core flooding using formation water Zeng et al [20] TPG = 0.00965k −0.9738 Core flooding using oil Yang et al [21] On the other hand, fractal theory is an effective tool to characterize the complex pore geometry and structure [22,23]. Yu and Cheng [24] developed a fractal model to evaluate the permeability for both porous particles and porous fabrics media.…”

Section: Tpg Correlationsmentioning

confidence: 99%

Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

Wang

et al. 2020

Symmetry

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Low-permeability porous medium usually has asymmetric distributions of pore sizes and pore-throat tortuosity, thus has a non-linear flow behavior with an initial pressure gradient observed in experiments. A threshold pressure gradient (TPG) has been proposed as a crucial parameter to describe this non-linear flow behavior. However, the determination of this TPG is still unclear. This study provides multi-scale insights on the TPG in low-permeability porous media. First, a semi-empirical formula of TPG was proposed based on a macroscopic relationship with permeability, water saturation, and pore pressure, and verified by three sets of experimental data. Second, a fractal model of capillary tubes was developed to link this TPG formula with structural parameters of porous media (pore-size distribution fractal dimension and tortuosity fractal dimension), residual water saturation, and capillary pressure. The effect of pore structure complexity on the TPG is explicitly derived. It is found that the effects of water saturation and pore pressure on the TPG follow an exponential function and the TPG is a linear function of yield stress. These effects are also spatially asymmetric. Complex pore structures significantly affect the TPG only in the range of low porosity, but water saturation and yield stress have effects on a wider range of porosity. These results are meaningful to the understanding of non-linear flow mechanism in low-permeability reservoirs.

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Section: Tpg Correlationsmentioning

confidence: 99%

Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

Wang

et al. 2020

Symmetry

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“…), as well as in various lines of study in mathematics, physics, and economics, to name a few. In this sense, it should be noted that the study and analysis of fractal patterns have originated highly active lines of research in recent years due to the identification of new fractal structures [ 13 , 14 ]. The basic tool for studying the irregular nature of an object is the so-called fractal dimension (FD), which is a dimensionless topological invariant that provides very useful information on the complexity presented by the object of study when it is examined in different levels of detail.…”

Section: Introductionmentioning

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

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confidence: 99%

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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On the Symmetry of the Bone Structure Density over the Nasopalatine Foramen via Accurate Fractal Dimension Analysis

Cited by 4 publications

References 10 publications

Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

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

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