Fractal dimension and mechanical properties of human cortical bone

The relationship between primate distal fibula trabecular architecture and arboreality, phylogeny and size

The fibula, despite being traditionally overlooked compared to the femur and the tibia, has recently received attention in primate functional morphology due to its correlation with the degree of arboreality (DOA). Highlighting further fibular features that are associated with arboreal habits would be key to improving palaeobiological inferences in fossil specimens. Here we present the first investigation on the trabecular bone structure of the primate fibula, focusing on the distal epiphysis, across a vast array of species. We collected μCT data on the distal fibula for 21 species of primates, with representatives from most of the orders, and we employed a recently developed approach implemented in the R package 'indianaBones' to isolate the entire trabecular bone underlying an epiphysis or articular facet. After extracting both traditional trabecular parameters and novel topological indices, we tested for the posited relationship between trabecular bone and DOA. To disentangle this effect from others related to body size and phylogenetic relationship, we included a body mass proxy as covariate and employed phylogenetic comparative methods. We ran univariate/multivariate and exploratory/inferential statistical analyses. The trabecular structure of the fibular distal epiphysis in primates does not appear to be associated with the DOA. Instead, it is strongly affected by body mass and phylogenetic relationships. Although we identified some minor trends related to human bipedalism, our findings overall discourage, at this stage, the study of distal fibula trabecular bone to infer arboreal behaviors in extinct primates. We further found that body size distribution is strongly related to phylogeny, an issue preventing us from unravelling the influence of the two factors and that we believe can potentially affect future comparative analyses of primates. Overall, our results add to previous evidence of how trabecular traits show variable correlation with locomotor aspects, size and phylogenetic history across the primate skeleton, thus outlining a complex scenario in which a network of interconnected factors affects the morphological evolution of primates. This work may represent a starting point for future studies, for example, focusing on the effect of human bipedalism on distal fibula trabecular bone, or aiming to better understand the effects of body size and phylogenetic history on primate morphological evolution.

Statistical mechanics of bone damage: a constitutive model

After the elastic regime is surpassed, cortical bone exhibits significant microcracking in its post-elastic mechanical behavior. This work develops a thermodynamically consistent, nonlinear constitutive model based on statistical mechanics, designed to predict the stress-strain relationship and the progression of inter-osteon microcracking. To assess the model's sufficiency, precise tensile and bending tests were performed in comparison to empirical curves that illustrated theoretical predictions of constitutive relationships. Moreover, entropy increases were quantitatively assessed using model parameters refined through experimental data. A large-size sample was utilized, comprising 51 dog-bone-shaped cortical bone specimens from the 4th ribs of various subjects for uniaxial tensile tests, and 15 complete fourth ribs for bending tests. Displacement and strain fields were meticulously recorded using digital image correlation and video analysis. The model demonstrated robustness, accurately fitting the data from all experimental specimens and revealing correlations between constitutive parameters and anthropometric variables. Entropy calculations provide insights into the behavior of the bone under varying strains: microcracking is minimal at low strains with stress nearly proportional to strain, escalating significantly beyond a critical threshold, thus challenging the linear relationship between stress and strain.

Bone ultrasound fractal dimension theory and experimental analysis with application to early osteoporosis prediction in cancellous bone

Fractal analysis and ultrasound techniques are pivotal in assessing osteoporosis by examining the complex structure of cancellous bone. Osteoporosis, marked by reduced bone mass and the degradation of bone microarchitecture, results in greater fragility and a higher risk of fractures. The poroelastodynamic model proposed in this study incorporates the Navier-Stokes equations of linear elasticity and Biot's theory of porous media, allowing the investigation of osteoporosis versus fractal dimension. Some mechanical properties of cancellous bone, such as porosity, density, elasticity, Poisson's ratio, and viscosity of bone marrow within the porous medium, are taken into account in this analysis. Our findings suggest that the fractal dimension of cancellous bone is a critical factor in predicting osteoporosis. Our study incorporates data from 84 women and 49 men to explore how fractal dimension can predict osteoporosis. We found that individuals with osteoporosis consistently exhibit lower fractal dimensions compared to those with normal bone, irrespective of gender or age. Analyzing rib data from three donors, we observed that an increase in fractal dimension correlates with a decrease in Young's modulus. Furthermore, examining lumbar spine data from 22 cadavers, we observed that increased bone mineral density is associated with higher fractal dimensions, while higher bone porosity correlates with reduced bone mineral density. Additionally, considering the attenuation of cancellous bone from 61 women, including 32 with osteoporotic bone and 29 with normal bone, shows that attenuation in normal bone is higher than in osteoporotic bone when accounting for porosity. Therefore, it can be concluded that increased porosity leads to a reduction in fractal dimension. From this study, the fractal dimension emerges as a critical metric in predicting osteoporosis, offering insights into the structural changes within cancellous bone that contribute to its fragility and susceptibility to fractures.

Enhanced Lightweight Structures Through Brachistochrone-Inspired Lattice Design

Lattice structures offer unique mechanical properties and versatility in engineering applications, yet existing designs often struggle to balance performance and material efficiency. This study introduces the brachistochrone curve as a novel framework for optimizing lattice geometries, enhancing mechanical behavior while minimizing material usage. Using finite element simulations and compressive testing of 3D-printed samples, we analyzed the mechanical response of brachistochrone-based (B-) and standard lattice structures (diamond, IWP, gyroid, and BCC). We investigated the scaling behavior of the volume-to-surface area ratio, incorporated fractal dimension analysis, and compared experimental and numerical results to evaluate the performance of B-lattices versus standard designs (S-). Our findings indicate that brachistochrone-inspired lattices enhance mechanical efficiency, enabling the design of lightweight, high-strength components with sustainable material use. Experimental results suggest that B-gyroid lattices exhibit lower stiffness than S-gyroid lattices under small displacements, highlighting their potential for energy absorption applications.

Fractal Analysis of Mandible in Panoramic Radiographs of Patients Received Radiotherapy for Nasopharyngeal Carcinoma

PURPOSE

This study aimed to assess the impact of radiotherapy on the internal structure complexity of mandibular cortical and trabecular bone and to determine the duration required for a return to healthy values post-radiotherapy.

MATERIALS AND METHODS

Panoramic radiographs from patients undergoing radiotherapy for nasopharyngeal carcinoma were analyzed before and after treatment. Four groups were formed based on post-radiotherapy radiography timing (0-6 months, 6-12 months, 12-24 months, and 24-36 months), comprising a total of 59 cases and 118 radiographs. Fractal analysis was conducted on four bilateral regions (ROI) in both trabecular and cortical bone on each radiograph. Additionally, measurements of inferior alveolar canal width and mandibular cortical width were performed. Mean and maximum radiation dose values to the mandible were measured, and their correlation with changes in fractal dimension, inferior alveolar canal width, and mandibular cortical width values was assessed.

RESULTS

Fractal dimension values in regions over trabecular bone showed a statistically significant decrease in all groups, although no significant difference was observed among the four groups. In ROI-4 from cortical bone, a significant fractal dimension decrease was noted in all groups except the 0-6 month group. The magnitude of fractal dimension decrease was higher in the 12-24 and 24-36 month groups compared to the 0-6 month group. inferior alveolar canal width and mandibular cortical width values significantly decreased post-radiotherapy in all groups, with a consistent decrease across the groups.

CONCLUSIONS

Radiotherapy induces a reduction in the internal complexity of trabecular and cortical bone structures in the mandible. Osteoradionecrosis risk persists even three years post-radiotherapy, suggesting a cautious approach to interventional procedures on the bone.

Evaluation of fractal analysis and radiomorphometric measurements of mandibular bone structure in bruxism and non-bruxism paediatric patients

OBJECTIVES

The goal of this examination was to compare the impact of probable sleep/awake bruxism on the mandibular trabecular bone structure by fractal analysis (FA) with digital panoramic radiograph (DPR) and radiomorphometric measurements in paediatric patients with bruxism.

METHODS

The examination included 130 participants with 63 patients with probable sleep/awake bruxism and 67 control groups. Bilateral regions of interest (ROI) in three regions were examined as ROI1: mandibular ramus, ROI2: mandibular angulus, ROI3: anterior to the molar teeth. Radiomorphometric measurements were taken of the mandibular cortical width (MCW), panoramic mandibular index (PMI), and mandibular cortical index (MCI). p < 0.05 was approved for statistical significance.

RESULTS

The ROI-1, ROI-2, and ROI-3 values were defined to be statistically significantly high in the bruxism group (p < 0.05). No significant difference was found between the groups in the other values (p > 0.05). There was no difference in the age and gender for any of the parameters (p > 0.05).

CONCLUSION

In children and adolescents, the mandibular trabecular bone can be affected by bruxism. FA can be used as an auxiliary method for finding the mandibular trabecular differences of patients with bruxism in paediatric dentistry just as it can for adults.

Evaluation of mandibular trabecular bone structure in growing children with Class I, II, and III malocclusions using fractal analysis: A retrospective study

OBJECTIVE

The present study aimed to evaluate the mandibular bone structure of patients with different malocclusions by using fractal dimension (FD) analysis on dental panoramic radiographic images.

MATERIAL AND METHODS

Pre-treatment panoramic radiographic images of 103 patients were included in the study and divided into 3 groups as Class I (group 1: 0

RESULTS

FD values were lower in Class I sagittal skeletal pattern than Class II and III groups in anterior ROI FD, premolar ROI FD, angulus ROI FD, and mean FD values. There were differences between Class I and Class III skeletal patterns (P=0.023 for anterior ROI FD, P=0.016 for premolar ROI FD, P=0.034 for angulus ROI FD, and P=0.014 for mean FD). Class I and II malocclusions differed in anterior ROI FD (P=0.029) and also Classes II and III showed differences in angulus ROI FD (P=0.029).

CONCLUSION

Sagittal skeletal patterns may result in differences in the structure of the mandibular trabecular bone.

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Key Words

• Fractal dimension analysis
• Orthodontics
• Panoramic radiography
• Sagittal skeletal malocclusions

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MESH Headings

• Humans
• Child
• Mandible/diagnostic imaging
• Male
• Female
• Fractals
• Retrospective Studies
• Radiography, Panoramic
• Malocclusion, Angle Class III/diagnostic imaging
• Malocclusion, Angle Class II/diagnostic imaging
• Cancellous Bone/diagnostic imaging
• Malocclusion, Angle Class I/diagnostic imaging
• Malocclusion/diagnostic imaging
• Adolescent
• Cephalometry/methods

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Affiliation(s)

Hümeyra Tercanlı Department of Oral and Maxillofacial Radiology, Faculty of Dentistry, Akdeniz University, 07058 Antalya, Turkey
Esra Bolat Gümüş Department of Orthodontics, Faculty of Dentistry, Akdeniz University, 07058 Antalya, Turkey.

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Efficacy of the CALM® Algorithm in Reducing Motion-Induced Artifacts in CBCT Imaging: A Fractal Dimension Analysis of Trabecular Bone

OBJECTIVE

The primary goal of this investigation was to ascertain the efficacy of the CALM® motion artifact reduction algorithm in diminishing motion-induced blurriness in Cone Beam Computed Tomography [CBCT] images. The assessment was conducted through Fractal Dimension [FD] analysis of the trabecular bone.

METHODS AND MATERIALS

A desiccated human mandible was subjected to Planmeca ProMax 3D® scanning under eight distinct protocols, marked by variations in motion presence [at 5, 10, and 15 degrees] and the deployment of CALM®. In every scan, five distinct regions of interest [ROIs] were designated for FD analysis, meticulously avoiding tooth roots or cortical bone. The FD was computed employing the box-counting method with Image-J 1.53 software.

RESULTS

Our findings reveal that a 5-degree motion does not significantly disrupt FD analysis, while a 10-degree motion and beyond exhibit statistical differences and volatility among the sites and groups. A decreased FD value, signifying a less intricate or "rough" bone structure, correlated with amplified motion blurriness. The utilization of CALM® software seemed to counteract this effect in some instances, reconciling FD values to those akin to the control groups. Nonetheless, CALM®'s efficacy differed across sites and motion degrees. Interestingly, at one site, CALM® application in the absence of motion resulted in FD values considerably higher than all other groups.

CONCLUSION

The study indicates that motion, particularly at 10 degrees or more, can considerably impact the FD analysis of trabecular bone in CBCT images. In some situations, the CALM® motion artifact reduction algorithm can alleviate this impact, though its effectiveness fluctuates depending on the site and degree of motion. This underscores the necessity of factoring in motion and the employment of artifact reduction algorithms during the interpretation of FD analysis outcomes in CBCT imaging. More research is necessary to refine the application of such algorithms and to comprehend their influence on different sites under varying motion degrees.

Effect of Fixed and Removable Functional Therapy on Mandibular Anterior Bone Structures: A Fractal Analysis Study

(1) Background and aim: The effects of functional therapies on dentoalveolar and skeletal structures have been investigated in orthodontics for many years. The aim of this retrospective study was to evaluate the changes caused by fixed and removable functional therapy in the mandibular anterior trabecular structures using fractal dimension (FD) analysis. (2) Methods: A total of 60 patients with skeletal and dental class II malocclusion were included in the study and three groups were formed: the untreated control group (CG), the Forsus fatigue-resistant device group (FFRDG), and the Monoblock group (MBG). Bone areas of interest determined in the buccoapical of the mandibular incisors and the symphysis in the lateral cephalometric radiographs taken before (T0) and after (T1) functional therapy were evaluated using FD analysis. The relationship between the FD and IMPA (Incisor Mandibular Plane Angle) angles was evaluated. Parametric and nonparametric tests were used in statistical analysis according to normality distribution. The statistical significance level was determined as p < 0.05. (3) Results: There was no statistically significant difference between the FD values of all groups at T0 (p > 0.05). At T1, buccoapical FD values were significantly lower in FFRDG and MBG compared to the control group (p < 0.05), while symphyseal FD values were not found to be significant (p > 0.05). The IMPA angle was significantly lower in the FFRDG and MBG than in the control group at T0, while it was higher at T1 (p < 0.05). While a significant negative correlation was observed between the IMPA angle and buccoapical FD values in both FFRDG and MBG (p < 0.05), it was not observed with the symphysis FD values (p > 0.05). (4) Conclusions: Trabecular changes caused by functional therapy in the mandibular anterior bone can be evaluated on lateral cephalometric radiographs with FD analysis. It was concluded that orthodontists should ensure controlled changes in the IMPA angle during functional therapy, especially for the decreases in FDs seen in the buccoapical alveolar region due to the forward movement of the mandibular incisors.

Assessment of mandibular trabecular structure and cervical vertebral maturation using fractal analysis

BACKGROUND

Changes in bone trabeculae occur during skeletal maturation. Fractal analysis is a technique for assessing changes in the internal structure of the bone.

OBJECTIVE

The aim of this study was to investigate correlation of bone trabeculation measured on panoramic and lateral cephalometric radiographs with cervical vertebral maturation stages (CVMS).

METHODS

CVMS was evaluated on lateral cephalometric radiographs of 120 individuals aged 6 to 18 years. The subjects were divided into 6 groups (n= 20 each) according to CVMS. On panoramic and lateral cephalometric radiographs, fractal dimension (FD) analyses were performed in mandibular corpus, gonial and condylar regions and cervical vertebral bodies (C2, C3, C4).

RESULTS

FD measurements from the mandibular corpus region bilaterally and C2-C4 vertebral bodies showed significant positive correlations with CVMS (r= 0.418, r= 0.412, r= 0.324, r= 0.304, r= 0.263, respectively). Significant differences were found in the FD values of the right/left mandibular corpus and C2 and C3 vertebrae compared to CVMS (P< 0.001, P< 0.001, P= 0.005, P= 0.019, respectively).

CONCLUSION

Significant positive moderate correlations between the FD values of the right and left mandibular corpus and CVMS suggest that fractal analysis may be useful in determining skeletal maturity stage. The significant FD values obtained from the right/left mandibular corpus, and C2 and C3 vertebra indicate that the complexity of the internal trabecular structure increases with maturation.

Multifractal approach for a biological porous media: Human dentin case

A multifractal characterization to human dentin porosity is made. Micrographs of human dentin samples gotten from scanning electron microscopy (SEM) were studied in order to characterize porosity. We got the generalized dimensions (multifractal moments)D q for pore space and matrix skeleton on gray scale and binary images for samples of both gender. For the case, we found that superficial porosityη s is linked to mass fractal dimensionD 0 in an approximately linear relationship asD 0 ≈ η s + d ¯ for binary images. In addition, probability density distribution (PDD) for pore diameters is found a normal PDD type. Other quantities of interest like mean, standard deviation, maximum and minimum pore diameters, voit ratios, and percentage of chemical composition are reported. RESEARCH HIGHLIGHTS: SEM sample, images and procedure for multifractal analysis are detailed. Micro patterns in grayscale are multifractal and in binary scale are monofractals. Superficial porosity is relate to mass fractal dimension approximately linearly. From the porosity values, voit ratios are determined. Pores diameters obey a normal PDD.

Fractal analysis of the mandible cortical bone: correlation among fractal dimension values obtained by two processing methods from periapical radiograph and micro-computed tomography with cone-beam computed tomography

The objectives of the present study were to assess Fractal Dimension (FD) values in the mandible cortical bone obtained from digital periapical radiographs (DPR), high-resolution microtomography (µCT), and cone-beam computed tomography (CBCT), by two processing methods: binarization (FD.b) and grayscale-based method (FD.f) and, finally, to identify the correlation among these values with other micro-architectural parameters. For this, a prospective study was conducted on 18 healthy individuals (mean age 23 ± 2.4 years old) who underwent third molar extraction. Pre-operative CBCT scans were conducted, bone fragments were removed from the retro-molar region, and DPR and µCT were performed on those bone samples. FD.b and FD.f values were calculated using three parasagittal sections for CBCT, one image for DPR, and three sections for µCT. The 3D bone microarchitecture was analyzed in µCT (voxel size: 19 µm). As a result, FD.b mean values of 1.55 ± 0.02 and 1.80 ± 0.01 were obtained for CBCT and µCT, respectively. Furthermore, FD.f mean values of 1.22 ± 0.12 for DPR, 0.99 ± 0.04 for CBCT, and 1.30 ± 0.07 for µCT were obtained. Both FD.b and FD.f values showed a good agreement. FD.f was negatively correlated with the standard deviation of the mean gray value (p = 0.003) for DPR and intra-cortical bone surface (p = 0.02) for µCT. In conclusion, image processing with or without binarization revealed different values for FD, although showing agreement. The grayscale-based method retrieved FD values correlated with the gray levels and the cortical porous network, which means that FD can be a valuable index for mandibular cortical bone evaluation. FD is associated with mineralization and microarchitecture. Nevertheless, there was no correlation between FD values obtained from low- (DPR) and high-resolution (µCT) X-ray modalities with FD obtained from the in vivo CBCT.

Evaluation of mandibular osseous structure in patients with mandibular asymmetry: a fractal analysis study

OBJECTIVE

We evaluated the effect of mandibular asymmetry on the trabecular structure of the mandible as measured through fractal analysis (FA).

STUDY DESIGN

We divided a sample of 105 patients with skeletal class I occlusion, cervical vertebral maturation CS6, and skeletal vertical dimension ratios within normal limits into right asymmetric, left asymmetric, and symmetric groups. We performed FA on 6 bilateral regions of interest on panoramic radiographs of the patients and calculated the mean fractal dimension (FD) for each region. We performed the Wilcoxon signed-rank and paired t tests to compare the significance of differences in FD between sides within each group and between groups for all regions. Statistical significance was established at P < .05.

RESULTS

We found statistically significant differences in mean FD values between the right and left condyles of the 2 asymmetric patient groups. The FD was greater in the left condyle of patients with right asymmetry and in the right condyle of patients with left asymmetry. The right condyle had a significantly greater FD in left asymmetric patients than in right asymmetric patients.

CONCLUSIONS

The results of FA indicate that asymmetry is characterized by an increase in the mean FD of the condyle that is responsible for the asymmetry. Fractal analysis can be a valuable diagnostic technique in distinguishing trabecular differences in the condylar areas of asymmetric individuals.

Assessment of correlation between hand-wrist maturation and cervical vertebral maturation: a fractal analysis study

BACKGROUND

To investigate whether fractal dimension (FD) measurements from hand-wrist radiographs and lateral cephalometric radiographs are correlated with each other and with skeletal maturation stages.

METHODS

In this retrospective study conducted on hand-wrist and lateral cephalometric radiographs obtained from patients between 2017 and 2023, hand-wrist maturation stages (HWMS) and cervical vertebral maturation stages (CVMS) of 144 subjects (6 to 17 years of age) were assessed radiographically. The participants were divided into nine groups (n = 16 each) based on HWMS. Fractal analysis was performed on the radiographs of the radius, the middle finger phalanges (proximal, medial and distal), and the cervical vertebral bodies (C2, C3, C4). Mean and standard deviation values, Spearman's and Pearson correlation analyses, one-way ANOVA, Kruskal-Wallis H tests and Mann-Whitney-U test were used to evaluate the data.

RESULTS

Positive correlations were found between the FD values of the radius and HWMS or CVMS (r = .559, P = .001, r = .528 P = .001 respectively). The FD values of the radius were positively correlated with those of all cervical vertebrae (C2, C3, C4), proximal and medial phalanges as well as age. FD values measured from the proximal phalanx, medial phalanx and radius showed significant differences among both HWMS and CVMS (P < .05). HWMS was strongly correlated with CVMS (r = .929, P = .001). Age was strongly correlated with HWMS (r = .795, P = .001) and CVMS (r = .756, P = .001). There was a significant difference in terms of age distribution among HWMS and CVMS (P < .05).

CONCLUSIONS

FD measurements on hand-wrist radiographs can provide useful information for the assessment of skeletal maturation stage. Especially, FD measurements from the radius are important and more reliable to predict skeletal maturation stage.

Relation between mechanical and densimetric properties to fractal dimension in human rib cortical bone

BACKGROUND

Numerous prior studies hypothesized a power-law relationship (E∝ρ^α) between cortical bone Young's modulus (E) and density (ρ) with an exponent 2.3≤α≤3.0, that has not been previously justified in the literature on a theoretical level. Moreover, despite the fact microstructure have been extensively studied, the material correlate of Fractal Dimension (FD) as a descriptor of bone microstructure was not clear in previous studies.

METHODS

This study examined the effect of mineral content and density on the mechanical properties of a large number of human rib cortical bone samples. The mechanical properties were calculated using Digital Image Correlation and uniaxial tensile tests. CT scans were used to calculate the Fractal Dimension (FD) of each specimen. For each specimen, the mineral (f_min), organic (f_org) and water (f_wat) weight fractions were determined. In addition, density was measured after a drying-and-ashing process. Then, Regression Analysis was employed to investigate the relationship between anthropometric variables, weight fractions, density and FD, as well as its impact on the mechanical properties.

FINDINGS

Young's modulus exhibited a power-law relationship with an exponent of α>2.3 when using the conventional density (wet density), but α=2 when using dry density (desecated specimens). In addition, FD increases with decreasing cortical bone density. A significant relationship has been found between FD and density, whereby FD is correlated with the embedding of low density regions in cortical bone.

INTERPRETATION

This study provides a new insight in the exponent value of the power-law relation between Young's Modulus and density, and relates bone behavior with the fragile fracture theory in ceramic materials. Moreover, the results suggest that Fractal Dimension is related to presence of low-density regions.

Fractal dimension analysis of different mandibular regions in familial Mediterranean fever patients: A cross-sectional retrospective study

Familial Mediterranean fever (FMF) is a genetic condition that may cause loss of bone mineral density (BMD) due to chronic inflammation. Previously, fractal dimension (FD) analysis values of mandibular cortical bone were shown to be lower in osteoporosis. Therefore, FD might be considered as an auxiliary tool to refer patients for dual-energy x-ray absorptiometry (DXA), which is the gold standard for BMD measurement. The purpose of this cross-sectional retrospective study was to evaluate trabecular and cortical microarchitecture of the mandible with FD analysis on panoramic radiographs in a subpopulation of FMF. Also, the effect of colchicine use was investigated. Forty-three FMF patients, aged between 10.8 and 71.2 years, and age- and gender-matched control group consisting of patients, who had no systemic diseases, were included. Demographic information such as age and gender, and colchicine use were recorded. In terms of age, the patients were classified as <30 and 30< years. On each panoramic radiographs five regions of interest were selected on the mandible as: 1- premolar, 2- molar, 3- angular, 4- condylar, and 5- basal cortical bone regions on right (R) and left (L) sides. Statistical significance was accepted at p<0.05 level. Intra- and inter-observer agreements demonstrated good to excellent consistency. In FMF patients, L3 and L4 values were higher, whereas L5 values were lower (p<0.05) than the control group. In terms of age, the difference between groups was insignificant in FMF patients (p>0.05), whereas in control group R3 and L4 values were higher in the 30< age group (p<0.05). Regarding gender and colchicine use, the difference between groups was insignificant (p>0.05). FMF disease might be a candidate for referral to DXA examination based on decreased bone density in the mandibular cortex detected by FD measurements on routine panoramic radiographs. Further studies are warranted to ascertain this relationship.

Fractal Perspective on the Rapid Maxillary Expansion Treatment; Evaluation of the Relationship Between Midpalatal Suture Opening and Dental Effects

OBJECTIVE

This retrospective study investigates the relationship between the midpalatal suture opening and the dental effects of Rapid Maxillary Expansion (RME) treatment using fractal analysis.

METHODS

The participants of this study were selected from the patients who underwent Cone Beam Computed Tomography(CBCT) scans in 2019 and were treated with banded type Maxillary Expander. This study included 20 participants (with a mean age of 10.64±10.64, ranging from 8 to 13 years): 12 males and 8 females. Patients went through CBCT scan and images taken were analyzed using the ImageJ program. The following parameters were measured and analyzed before and after RME treatment: fractal dimensional value of Midpalatal suture(MPS), Distobuccal(DB), Mesiobuccal(MB), Palatal(P), Total distance, Cortical bone and linear values of External maxilla, Internal maxilla, Palatal roots, distance of Central fosses and angular values of Tipping value of 16 and 26. We used Spearman's nonparametric test for non-normal variables to investigate the correlation between changes in MPS and other variables.

RESULTS

The results showed a strong positive correlation between the MPS and Right MB (0.34, p<0.05) and Left MB (0.59, p<0.05) variables and a strong negative correlation between the MPS and the External maxillary variables (-0.53, p<0.05).

CONCLUSION

The results of the study have shown a strong correlation between right and left MB and External Maxilla. RME caused a reduction in buccal alveolar bone thickness and a slight reduction in MPS thickness in growing patients. Therefore, we suggest that fractal analysis can be used to evaluate the skeletal and dental effects of RME in patients.

Interest of Bone Histomorphometry in Bone Pathophysiology Investigation: Foundation, Present, and Future

Despite the development of non-invasive methods, bone histomorphometry remains the only method to analyze bone at the tissue and cell levels. Quantitative analysis of transiliac bone sections requires strict methodologic conditions but since its foundation more 60 years ago, this methodology has progressed. Our purpose was to review the evolution of bone histomorphometry over the years and its contribution to the knowledge of bone tissue metabolism under normal and pathological conditions and the understanding of the action mechanisms of therapeutic drugs in humans. The two main applications of bone histomorphometry are the diagnosis of bone diseases and research. It is warranted for the diagnosis of mineralization defects as in osteomalacia, of other causes of osteoporosis as bone mastocytosis, or the classification of renal osteodystrophy. Bone biopsies are required in clinical trials to evaluate the safety and mechanism of action of new therapeutic agents and were applied to anti-osteoporotic agents such as bisphosphonates and denosumab, an anti-RANKL, which induces a marked reduction of the bone turnover with a consequent elongation of the mineralization period. In contrast, an increased bone turnover with an extension of the formation site is observed with teriparatide. Romosozumab, an anti-sclerostin, has a dual effect with an early increased formation and reduced resorption. Bone histomorphometric studies allow us to understand the mechanism of coupling between formation and resorption and to evaluate the respective role of bone modeling and remodeling. The adaptation of new image analysis techniques will help bone biopsy analysis in the future.

Fractal dimension analysis on CBCT scans for detecting low bone mineral density in postmenopausal women

Purpose

The aim of this study was to compare the fractal dimension (FD) measured at 2 bone sites (second cervical vertebra and mandible) on cone-beam computed tomography (CBCT). The research question was whether FD could serve as an accessory tool to refer postmenopausal women for densitometric analysis. Therefore, the reliability and accuracy of FD were evaluated.

Materials and Methods

In total, 103 postmenopausal women were evaluated, of whom 52 had normal bone mineral density and 51 had osteoporosis, according to dual X-ray absorptiometry of the lumbar spine and hip. On the CBCT scans, 2 regions of interest were selected for FD analysis: 1 at the second cervical vertebra and 1 located at the mandible. The correlations between both measurements, intra- and inter-observer agreement, and the accuracy of the measurements were calculated. A P value less than 0.05 was considered to indicate statistical significance for all tests.

Results

The mean FD values were significantly lower at the mandibular region of interest in osteoporotic patients than in individuals with normal bone mineral density. The areas under the curve were 0.644 (P=0.008) and 0.531 (P=0.720) for the mandibular and vertebral sites, respectively.

Conclusion

FD at the vertebral site could not be used as an adjuvant tool to refer women for osteoporosis investigation. Although FD differed between women with normal BMD and osteoporosis at the mandibular site, it demonstrated low accuracy and reliability.

Computed Tomography as a Characterization Tool for Engineered Scaffolds with Biomedical Applications

The ever-growing field of materials with applications in the biomedical field holds great promise regarding the design and fabrication of devices with specific characteristics, especially scaffolds with personalized geometry and architecture. The continuous technological development pushes the limits of innovation in obtaining adequate scaffolds and establishing their characteristics and performance. To this end, computed tomography (CT) proved to be a reliable, nondestructive, high-performance machine, enabling visualization and structure analysis at submicronic resolutions. CT allows both qualitative and quantitative data of the 3D model, offering an overall image of its specific architectural features and reliable numerical data for rigorous analyses. The precise engineering of scaffolds consists in the fabrication of objects with well-defined morphometric parameters (e.g., shape, porosity, wall thickness) and in their performance validation through thorough control over their behavior (in situ visualization, degradation, new tissue formation, wear, etc.). This review is focused on the use of CT in biomaterial science with the aim of qualitatively and quantitatively assessing the scaffolds’ features and monitoring their behavior following in vivo or in vitro experiments. Furthermore, the paper presents the benefits and limitations regarding the employment of this technique when engineering materials with applications in the biomedical field.

Mechanical properties and in vitro cytocompatibility of dense and porous Ti-6Al-4V ELI manufactured by selective laser melting technology for biomedical applications

The Ti-6Al-4V alloy is the most common biomaterial used for bone replacements and reconstructions. Despite its advantages, the Ti-6Al-4V has a high stiffness that can cause stress-shielding. In this work, we demonstrated that the selective laser melting (SLM) technology could be used to fabricate porosity in Ti-6Al-4V extra low interstitial (ELI) to reduce its stiffness while improving cell adhesion and proliferation. With a porosity of 14.04%, the elastic modulus of the porous Ti-6Al-4V ELI was reduced to 80 GPa. The compressive stress and the 3-point-bending flexural tests revealed that the porous Ti-6Al-4V ELI possessed a brittle characteristic. The additional pores within the beams of the lattice structures of porous Ti-6Al-4V ELI increased its surface arithmetic average roughness, R_a = 3.94 μm. The in vitro cytocompatibility test showed that the SLM printing process and the post-processes did not cause any toxicity in the MC3T3-E1 cells. The in vitro cell proliferation test also showed that the porous Ti-6Al-4V ELI increased the proliferation rate of osteogenic induced MC3T3-E1 cells on Day 7. The findings from this study would provide engineers and researchers with both the mechanical information and biological understanding of SLM printed porous Ti-6Al-4V ELI, and SLM printed dense Ti-6Al-4V ELI towards biomedical applications.

Trabecular and cortical mandibular bone investigation in familial adenomatous polyposis patients

Mandibular cortical and trabecular bone abnormalities in patients with familial adenomatous polyposis (FAP) were evaluated using dental panoramic radiographs (DPR) radiomorphometric indices and fractal dimension (FD). Sixty DPRs from 15 FAP patients and 45 healthy controls were evaluated. FAP group was composed of 33.3% females and 66.6% males, age_mean = 37.2 years (SD 15.79). The non-FAP group was paired by gender and sex. The parameters analyzed were: FD of the trabecular bone in four regions of interest (ROI), mandibular cortical index (MCI) and width (MCW). FD values were lower for the FAP group. Statistically significance differences were shown by ROI 2 and 3 anteriorly to the mental foramen bilaterally, p = 0.001, and p = 0.006. The ROI 1 and 4, at the mandibular angle trabeculae, indicated statistical significances on the right side (p = 0.036) and no differences on the left side (p = 0.091). There was no significant difference in MCI and MCW when the groups were compared, MCW (L) p = 0.247, and MCW (R) p = 0.070. Fractal values of FAP patients' mandibular trabecular bone were lower than healthy controls. The radiomorphometric indices MCI and MCW were not useful for analyzing the cortical bone pattern. Therefore, FD is a promising tool for detection of abnormal bone structure in DPRs and for supporting the appropriate referral of FAP patients.

Investigation of mandibular fractal dimension on digital panoramic radiographs in bruxist individuals

OBJECTIVE

This study aimed to evaluate changes in mandibular trabecular bone structure in bruxism using fractal analysis on digital panoramic radiographs obtained with automatic dosing.

STUDY DESIGN

In this prospective study, fractal analysis was performed on radiographs of 126 bruxists and 126 non-bruxists. Eight paired mandibular regions of interest were selected: the bilateral condylar and gonial regions, and the bilateral dentate regions between the apical areas of the first molar and second premolar and between the first premolar and canine. Fractal dimensions (FDs) were calculated at each site.

RESULTS

Mean FD values in the bilateral gonial regions of the bruxists were significantly lower than those of controls (P ≤ .049). In both groups, FD values of the right dentate region anterior to the mental foramen were significantly lower than those on the left side (P ≤ .042). Females exhibited significantly lower FD values in both condylar regions in both groups (P ≤ .039) and in the right dentate regions in the controls (P ≤ .022). Correlations between age and FD in all regions were positive but nonsignificant in both groups (P > .05).

CONCLUSIONS

FD values of mandibular trabecular bone are affected by bruxism in the gonial region and by laterality and sex differences in the condylar and dentate regions.

Prediction of mechanical properties of human rib cortical bone using fractal dimension

A large number of post mortem human subjects was used to investigate the relation between the micro-structure of rib cortical bone and the mechanical properties using Fractal Dimension. Uniaxial tensile tests were performed on coupons of rib cortical bone. Tensile strength, yield stress, Young's Modulus, maximum strain, and work to fracture were determined for each coupon. Fractal dimension was computed using CT images and Digital Image Correlation procedures. A highly significant effect of fractal dimension in the mechanical properties was found. In addition, the variation in mechanical properties was found to be adequately represented by Generalized Extreme Value type distributions.

Is there any predictive bone parameter for implant stability in 2-dimensional and 3-dimensional radiologic images?

OBJECTIVES

This ex vivo study aimed to compare radiomorphometric parameters between 2-dimensional (2-D) and 3-dimensional (3-D) radiographs and evaluate the influence of preoperative radiologic bone parameters on the clinical outcomes of implant stability.

STUDY DESIGN

Implant recipient sites in fresh bovine blocks were evaluated on panoramic radiographs for gray value (GV), fractal dimension (FD), number of connected trabeculae (Co), and density of connected trabeculae (CoD). Cone beam computed tomography (CBCT) scans were evaluated for trabecular thickness (TbTh), cortical thickness (CTh), degree of anisotropy (DA), FD, and Co. Insertion torque (IT) and implant stability quotient (ISQ) were measured.

RESULTS

GV was significantly correlated with all parameters in 2-D and 3-D images except FD in 2-D and Co in 3-D, and with all surgical parameters (P ≤ .029). Co and CoD values on panoramic radiographs had significant correlation with TbTh, CTh, and DA values on CBCT images (P < .001). All 2-D parameters and TbTh and CTh in the CBCT data were significantly correlated with IT only (P ≤ .047). Only GV was correlated with ISQ measurements (P ≤ .029).

CONCLUSIONS

GV, Co, and CoD values on panoramic radiographs reflect the architecture of trabecular bone and the thickness of cortical bone, and might help predict implant stability in clinical situations.

A 3D Bioprinted Pseudo-Bone Drug Delivery Scaffold for Bone Tissue Engineering

A 3D bioprinted pseudo-bone drug delivery scaffold was fabricated to display matrix strength, matrix resilience, as well as porous morphology of healthy human bone. Computer-aided design (CAD) software was employed for developing the 3D bioprinted scaffold. Further optimization of the scaffold was undertaken using MATLAB® software and artificial neural networks (ANN). Polymers employed for formulating the 3D scaffold comprised of polypropylene fumarate (PPF), free radical polymerized polyethylene glycol- polycaprolactone (PEG-PCL-PEG), and pluronic (PF127). Simvastatin was incorporated into the 3D bioprinted scaffolds to further promote bone healing and repair properties. The 3D bioprinted scaffold was characterized for its chemical, morphological, mechanical, and in vitro release kinetics for evaluation of its behavior for application as an implantable scaffold at the site of bone fracture. The ANN-optimized 3D bioprinted scaffold displayed significant properties as a controlled release platform, demonstrating drug release over 20 days. The 3D bioprinted scaffold further displayed formation as a pseudo-bone matrix, using a human clavicle bone model, induced with a butterfly fracture. The strength of the pseudo-bone matrix, evaluated for its matrix hardness (MH) and matrix resilience (MR), was evaluated to be as strong as original bone, having a 99% MH and 98% MR property, to healthy human clavicle bones.

Ontogenetic changes to bone microstructure in an archaeologically derived sample of human ribs

There is considerable variation in the gross morphology and tissue properties among the bones of human infants, children, adolescents, and adults. Using 18 known-age individuals (n_female  = 8, n_male  = 9, n_unknown  = 1; birth to 21 years old), from a well-documented cemetery collection, Spitalfields Christ Church, London, UK, this study explores growth-related changes in cortical and trabecular bone microstructure. Micro-CT scans of mid-shaft middle thoracic ribs are used for quantitative analysis. Results are then compared to previously quantified conventional histomorphometry of the same sample. Total area (Tt.Ar), cortical area (Ct.Ar), cortical thickness (Ct.Th), and the major (Maj.Dm) and minor (Min.Dm) diameters of the rib demonstrate positive correlations with age. Pore density (Po.Dn) increases, but age-related changes to cortical porosity (Ct.Po) appear to be non-linear. Trabecular thickness (Tb.th) and trabecular separation (Tb.Sp) increase with age, whereas trabecular bone pattern factor (Tb.Pf), structural model index (SMI), and connectivity density (Conn.D) decrease with age. Sex-based differences were not identified for any of the variables included in this study. Some samples display clear evidence of diagenetic alteration without corresponding changes in radiopacity, which compromises the reliability of bone mineral density (BMD) data in the study of past populations. Cortical porosity data are not correlated with two-dimensional measures of osteon population density (OPD). This suggests that unfilled resorption spaces contribute more significantly to cortical porosity than do the Haversian canals of secondary osteons. Continued research using complementary imaging techniques and a wide array of histological variables will increase our understanding of age- and sex-specific ontogenetic patterns within and among human populations.

Use of Micro-Computed Tomography for Bone Evaluation in Dentistry

Micro computed tomography (µCT) follows the same principle of computed-tomography used for patients, however providing higher-resolution. Using a non-destructive approach, samples can be scanned, and each section obtained is used to build a volume using tridimensional reconstruction. For bone analysis, it is possible to obtain information about the tissue's microarchitecture and composition. According to the characteristics of the bone sample (e.g. human or animal origin, long or irregular shape, epiphysis or diaphysis region) the pre-scanning parameters must be defined. The resolution (i.e. voxel size) should be chosen taking into account the features that will be evaluated, and the necessity to identify inner structures (e.g. bone channels and osteocyte lacunae). The region of interest should be delimited, and the threshold that defines the bone tissue set in order to proceed with binarization to separate the voxels representing bone from the other structures (channels, resorption areas, and medullary space). Cancellous bone is evaluated by means of the trabeculae characteristics and their connectivity. The cortex is evaluated in relation to the thickness and porosity. Bone mineral density can also be measured, by the amount of hydroxyapatite. Other parameters such as structure-model-index, anisotropy, and fractal dimension can be assessed. In conclusion, intrinsic and extrinsic determinants of bone quality can be assessed by µCT. In dentistry, this method can be used for evaluating bone loss, alterations in bone metabolism, or the effects of using drugs that impair bone remodeling, and also to assess the success rate of bone repair or surgical procedures.

Cortical Fractal Analysis and Collagen Crosslinks Content in Femoral Neck After Osteoporotic Fracture in Postmenopausal Women: Comparison with Osteoarthritis

The femoral neck (FN) has been previously characterized by thinner cortices in osteoporotic fracture (HF) when compared to hip osteoarthritis (HOA). The purposes of this study were to complete the previous investigations on FNs from HF and HOA by analyzing the complexity of the cortical structure and to approach the intrinsic properties of cortical bone by assessing the collagen crosslink contents. FN samples were obtained during arthroplasty in 35 postmenopausal women (HF; n = 17; mean age 79 ± 2 years; HOA; n = 18; mean age 66 ± 2 years). The cortical fractal dimension (Ct.FD) and lacunarity (Ct.Lac) derived from high-resolution peripheral quantitative tomography (isotropic voxel size: 82 μm) images of FN by using Ctan software and Fraclac running in ImageJ were analyzed. The collagen crosslinks content [pyridinoline, deoxypyridinoline, pentosidine (PEN)] were assessed in cortical bone. Ct.FD was significantly lower (p < 0.0001) in HF than HOA reflecting a decreased complexity and was correlated to the age and BMD. In two sub-groups, BMD- and age-matched, respectively, Ct.FD remained significantly lower in HF than HOA (p < 0.001). Ct.Lac was not different between HF and HOA. PEN content was two times higher in HF than HOA (p < 0.0001) independently of age. In conclusion, FN with HF was characterized by a less complex cortical texture and higher PEN content than HOA. In addition to the decreased bone mass and BMD previously reported, these modifications contribute to the lower bone quality in HF than HOA in postmenopausal women.

Assessment of the trabecular structure of mandibular condyles in patients with temporomandibular disorders using fractal analysis

OBJECTIVES

The aim of this study was to evaluate changes in the trabecular structure of the mandibular condyle in patients with temporomandibular disorders (TMDs) using fractal analysis.

STUDY DESIGN

A total of 100 patients ages 18 to 73 years were clinically assessed using the Diagnostic Criteria for Temporomandibular Disorders. The control group was age- and sex-matched with the patient group. Panoramic radiographs were obtained using a Kodak 8000 digital device with 73 kVp and 5 mA fixed parameters. The degree of degeneration in the mandibular condyles was calculated. Regions of interest (84 × 84 pixels) were selected within the cortical boundary of the mandibular condyle, and the fractal dimension (FD) was calculated using ImageJ version 1.48.

RESULTS

Radiographic degenerative changes were more frequently present and more severe in the patient group (P < .001). The mean value of FD was 1.22 ± 0.06 in the patient group and 1.25 ± 0.06 in the control group (P = .001). A significant decrease in FD was observed (P = .001) in the left temporomandibular joints of the patient group, whereas a nonsignificant decrease in FD was observed in the right temporomandibular joints (P = .073) as degenerative changes increased.

CONCLUSIONS

Lower FD values were associated with more severe degenerative changes in the patient group. The trabecular structure of condyles in patients with TMD exhibited decreased complexity when erosive and sclerotic changes were evident. As a result, fractal analysis enhanced the use of panoramic radiography in detecting degenerative changes in patients with TMD.

Avalanche criticality during compression of porcine cortical bone of different ages

Crack events developed during uniaxial compression of cortical bones cut from femurs of developing pigs of several ages (4, 12, and 20 weeks) generate avalanches. These avalanches have been investigated by acoustic emission analysis techniques. The avalanche energies are power-law distributed over more than four decades. Such behavior indicates the absence of characteristic scales and suggests avalanche criticality. The statistical distributions of energies and waiting times depend on the pig age and indicate that bones become stronger, but less ductile, with increasing age. Crack propagation is equally age-dependent. Older pigs show, on average, larger cracks with a time distribution similar to those of aftershocks in earthquakes, while younger pigs show only statistically independent failure events.

Characterization of trabecular bone density with ultra-short echo-time MRI at 1.5, 3.0 and 7.0 T--comparison with micro-computed tomography

The goal of this study was to test the potential of ultra-short echo-time (UTE) MRI at 1.5, 3.0 and 7.0 T for depiction of trabecular bone structure (of the wrist bones), to evaluate whether T2* relaxation times of bone water and parametric maps of T2* of trabecular bone could be obtained at all three field strengths, and to compare the T2* relaxation times with structural parameters obtained from micro-computed tomography (micro-CT) as a reference standard. Ex vivo carpal bones of six wrists were excised en bloc and underwent MRI at 1.5, 3.0 and 7.0 T in a whole-body MR imager using the head coil. A three-dimensional radial fat-suppressed UTE sequence was applied with subsequent acquisitions, with six different echo times TE of 150, 300, 600, 1200, 3500 and 7000 µs. The T2* relaxation time and pixel-wise computed T2* parametric maps were compared with a micro-computed-tomography reference standard providing trabecular bone structural parameters including porosity (defined as the bone-free fraction within a region of interest), trabecular thickness, trabecular separation, trabecular number and fractal dimension (Dk). T2* relaxation curves and parametric maps could be computed from datasets acquired at all field strengths. Mean T2* relaxation times of trabecular bone were 4580 ± 1040 µs at 1.5 T, 2420 ± 560 µs at 3.0 T and 1220 ± 300 µs at 7.0 T, when averaged over all carpal bones. A positive correlation of T2* with trabecular bone porosity and trabecular separation, and a negative correlation of T2* relaxation time with trabecular thickness, trabecular number and fractal dimension, was detected (p < 0.01 for all field strengths and micro-CT parameters). We conclude that UTE MRI may be useful to characterize the structure of trabecular bone, comparable to micro-CT.

Fractal dimension and mandibular cortical width in normal and osteoporotic men and women

OBJECTIVE

To verify whether fractal dimensions (FD) on the mandibular trabecular and cortical bone and mandibular cortical width (MCW) differ between patients with normal bone mineral density (BMD) and osteoporosis.

STUDY DESIGN

In this retrospective study, 133 dental panoramic radiographs from men aged >60 years and postmenopausal women with a bone densitometry report of the lumbar spine and hip classified as either normal or osteoporotic were selected. Fractal dimensions of five standardized trabecular and cortical mandibular regions of interest and mandibular cortical width were measured on the panoramic radiographs by an experienced oral radiologist, blinded to the densitometric diagnosis. The following statistical analyses were performed: ANOVA and a forward logistic stepwise regression to verify associations between dental panoramic measurements and the densitometric diagnosis. P values less than .05 indicated statistical significance.

MAIN OUTCOME MEASURES

Fractal dimension and mandibular cortical width.

RESULTS

Differences were found in the FD values on mandibular cortical bone and MCW between patients with normal BMD and with osteoporosis, but not in the FD values of trabecular bone. The odds of having lower mean values of MCW and FD on cortical bone were 2.16, 3125 and 1005 times in osteoporotic patients, respectively, compared with patients with normal BMD.

CONCLUSION

The values of FD analysis on mandibular cortical bone and MCW were lower in women with osteoporosis. A well-adjusted logistic regression model showed that cortical bone measurements might be considered as auxiliary tools to referring patients for DXA exam.