Accuracy and precision of fractal dimension measured on model surfaces

McMurphy, Timothy B.; Harris, Christopher A.; Griggs, Jason A.

doi:10.1016/j.dental.2013.11.015

Cited by 14 publications

(12 citation statements)

References 52 publications

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“…A self-similar object shows the same dimensions in the Z direction scale as those in the X and Y; whereas, for a self-affine object the fractal dimension of the vertical direction is different from the lateral directions [22,23]. The fractal dimension is a measure of global scaling property [20,21].…”

Section: Introductionmentioning

confidence: 99%

Surface roughness and morphology of dental nanocomposites polished by four different procedures evaluated by a multifractal approach

Ţălu

Stach

Lainović

et al. 2015

Applied Surface Science

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Section: Introductionmentioning

confidence: 99%

Surface roughness and morphology of dental nanocomposites polished by four different procedures evaluated by a multifractal approach

Ţălu

Stach

Lainović

et al. 2015

Applied Surface Science

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“…This software provided six algorithms for analyzing surfaces. An experiment was conducted to determine which algorithm provided the most precision in D* values and to calibrate that algorithm on surfaces that were generated with known D* values [17]. The Minkowksi Cover algorithm (MC) was the most precise, and it had a negative bias that could be corrected ( Figure 5).…”

Section: Past Obstaclesmentioning

confidence: 99%

Using fractal geometry to examine failed implants and prostheses

Griggs

2018

Dental Materials

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Objectives: To develop a novel protocol that is precise and accurate for analyzing the fracture surfaces of ceramic specimens using fractal geometry and to demonstrate its use on both clinically retrieved specimens and standard test specimens. Methods: A MathCAD script was written to transfer data from atomic force microscope scans to the FRACTALS software of John Russ. This software provided six algorithms for analyzing surfaces, so an experiment was conducted to determine which algorithm provided the most precision in fractal dimensional increment (D*) values and to calibrate that algorithm on surfaces generated with known D* values. Physical specimens were then tested using the chosen algorithm. These included pure silica glass fractured in deionized water versus nominally identical specimens fractured in saliva. Light body polyvinysiloxane was used to make impressions of Y-TZP fracture surfaces, and replicas were casted using a low-viscosity, low-shrinkage epoxy. Clinically failed Y-TZP dental implants were also examined. In addition, the fracture toughness and D* values of four ceramic materials (silicon nitride, silica glass, Y-TZP, and lithium disilicate glass-ceramic) were tested using standard geometry flexure beam specimens (ISO 6872). Results: The Minkowksi Cover algorithm was the most precise algorithm, and it had a negative bias that was corrected. There was no difference in D* based on water vs. saliva environment (p>0.05), and D* values from the deionized water group had lower standard deviation. The mean D* value obtained from the epoxy replicas 2.247 (0.007) was the same as that obtained from the original Y-TZP specimens 2.245 (0.002) (p=0.43, paired t-test). All scanned areas of the dental implants were fractal in nature, and there was no difference in fractal dimension between the locations near the failure origin and those far from the origin (on the compression curl) (p=0.74, repeated measures ANOVA). There was little scatter in the data collected using the revised protocol on ISO 6872 specimens, and the regression models succeeded in passing through the origin while achieving a good fit to the data (R 2 = 0.99 and 0.95). Significance: The new protocol proved to be a powerful tool in analyzing fracture surfaces of dental ceramic materials.

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“…Fractal and multifractal analyses have been used to quantitatively characterize the 3D rough surfaces in the field of dental materials (Barszczewska‐Rybarek and Krasowska, ; De Oliveira et al, ; McMurphy et al, ; Salerno et al, ; Sánchez and Uzcátegui, ). Furthermore, statistical surface roughness parameters were correlated with fractal dimension of the 3D rough surfaces in different studies (De Oliveira et al, ; Ţălu et al, ).…”

Section: Introductionmentioning

confidence: 99%

Surface micromorphology of dental composites [CE-TZP]-[Al₂O₃] with Ca⁺²modifier

Berezina

Ильичева

Подзорова

et al. 2015

Microsc. Res. Tech.

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The objective of this study was to characterize the three-dimensional (3D) surface micromorphology of the ceramics produced from nanoparticles of alumina and tetragonal zirconia (t-ZrO2) with addition of Ca(+2) for sintering improvement. The 3D surface roughness of samples was studied by atomic force microscopy (AFM), fractal analysis of the 3D AFM-images, and statistical analysis of surface roughness parameters. Cube counting method, based on the linear interpolation type, applied for AFM data was used for fractal analysis. The morphology of non-modified ceramic sample was characterized by the rather big (1-2 μm) grains of α-Al2O3 phase with a habit close to hexagonal drowned in solid solution of t-ZrO2 with smooth surface. The pattern surfaces of modified composite content a little amount of elongated prismatic grains with composition close to the phase of СаСеAl3О7 as well as hexahedral α-Al2O3-grains. Fractal dimension, D, as well as height values distribution have been determined for the surfaces of the samples with and without modifying. It can be concluded that the smoothest surface is of the modified samples with Ca(+2) modifier but the most regular one is of the non-modified samples. A connection was observed between the surface morphology and the physical properties as assessed in previous works.

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Accuracy and precision of fractal dimension measured on model surfaces

Cited by 14 publications

References 52 publications

Surface roughness and morphology of dental nanocomposites polished by four different procedures evaluated by a multifractal approach

Surface roughness and morphology of dental nanocomposites polished by four different procedures evaluated by a multifractal approach

Using fractal geometry to examine failed implants and prostheses

Surface micromorphology of dental composites [CE-TZP]-[Al₂O₃] with Ca⁺²modifier

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Accuracy and precision of fractal dimension measured on model surfaces

Cited by 14 publications

References 52 publications

Surface roughness and morphology of dental nanocomposites polished by four different procedures evaluated by a multifractal approach

Surface roughness and morphology of dental nanocomposites polished by four different procedures evaluated by a multifractal approach

Using fractal geometry to examine failed implants and prostheses

Surface micromorphology of dental composites [CE-TZP]-[Al2O3] with Ca+2modifier

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Product

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Surface micromorphology of dental composites [CE-TZP]-[Al₂O₃] with Ca⁺²modifier