Application of fractal geometry techniques to the study of trabecular bone

Majumdar, Sharmila; Weinstein, Robert S.; Prasad, R.R.

doi:10.1118/1.596948

Cited by 117 publications

(64 citation statements)

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“…The FD has been used to describe the complexity of trabecular bone, which has been shown to be useful descriptor of bone quality (Chappard et al,1999(Chappard et al, , 2001Chung et al, 1994;Fazzalari and Parkinson, 1996;Geraets and van der Stelt, 2000;Majumdar et al, 1993;Parkinson and Fazzalari, 2000;Pothuaud et al, 2000) especially the microarchitectural changes seem in osteoporosis (Chappard et al, 1999(Chappard et al, , 2001). Evaluation of both tomographic and microscopic images by this method can identify differences between normal and osteoporotic bone.…”

Section: Discussionmentioning

confidence: 99%

Shannon's entropy and fractal dimension provide an objective account of bone tissue organization during calvarial bone regeneration

Rocha¹,

Adam

Leite

et al. 2008

Microscopy Res & Technique

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The regeneration of compact bone involves the deposition of a poorly organized connective tissue template that remodels into compact lamellar bone. An objective description of this process is difficult because classical histomorphometry is unable to correctly characterize qualitative changes in tissue complexity. In this study, we demonstrated the use of two distinct methods of image texture analysis, the Shannon's entropy [standard error (SE)], and the fractal dimension (FD) to characterize the formation and remodeling of newly formed compact bone within two different polyanionic collagen-elastin matrices. The matrices were implanted in defects created into parietal bones of rats. The SE and FD were calculated for histological images of the experimental groups collected 3, 7, 15, 30, 60, and 365 days postsurgery and for the original bone only at day 365. Results showed that the SE and the FD initially increased and then diminished for all groups from day 3 to day 365 approaching the values of the original bone. These results are consistent with poor tissue organization during early osteogenesis that remodels into an organized lamellar structure, showing that these methods can be valuable tools to describe bone tissue remodeling during the regeneration process of compact bones.

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Section: Discussionmentioning

confidence: 99%

Shannon's entropy and fractal dimension provide an objective account of bone tissue organization during calvarial bone regeneration

Rocha¹,

Adam

Leite

et al. 2008

Microscopy Res & Technique

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“…Morphological parameters are useful to assess variations in trabecular structure (such as loss of trabeculae, their spatial distribution, thickness, and length) to predict fracture risk (Gordon et al, 1998). Fractal analysis has been proposed as a method to evaluate trabecular structure (Majumdar et al, 1993). It measures the complexity of the vertebral bony architecture by examining the relationship between nearest neighbors as a function of spatial resolution.…”

Section: Discussionmentioning

confidence: 99%

Fractal analysis of lumbar vertebral cancellous bone architecture

et al. 2001

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Osteoporosis is characterized by bone mineral density (BMD) decreasing and spongy bone rearrangement with consequent loss of elasticity and increased bone fragility. Quantitative computed tomography (QCT) quantifies bone mineral content but does not describe spongy architecture. Analysis of trabecular pattern may provide additional information to evaluate osteoporosis. The aim of this study was to determine whether the fractal analysis of the microradiography of lumbar vertebrae provides a reliable assessment of bone texture, which correlates with the BMD. The lumbar segment of the spine was removed from 22 cadavers with no history of back pain and examined with standard x-ray, traditional tomography, and quantitative computed tomography to measure BMD. The fractal dimension, which quantifies the image fractal complexity, was calculated on microradiographs of axial sections of the fourth lumbar vertebra to determine its characteristic spongy network. The relationship between the values of the BMD and those of the fractal dimension was evaluated by linear regression and a statistically significant correlation (R = 0.96) was found. These findings suggest that the application of fractal analysis to radiological analyses can provide valuable information on the trabecular pattern of vertebrae. Thus, fractal dimensions of trabecular bone structure should be considered as a supplement to BMD evaluation in the assessment of osteoporosis.

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“…[37][38][39] The five texture parameters used in this study are easy to calculate, and their use in isolation or in combination with BMD was able to distinguish the model type and to quantify the change in the trabecular bone structure. Thus, we see no need for adding additional parameters unless a single new one was able to replace several of the parameters used in this study.…”

Section: Oa-related Changes In Trabecular Bone T Lowitz Et Almentioning

confidence: 99%

Characterization of knee osteoarthritis-related changes in trabecular bone using texture parameters at various levels of spatial resolution—a simulation study

et al. 2014

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Articular cartilage and subchondral bone are the key tissues in osteoarthritis (OA). The role of the cancellous bone increasingly attracts attention in OA research. Because of its fast adaptation to changes in the loading distribution across joints, its quantification is expected to improve the diagnosis and monitoring of OA. In this study, we simulated OA progression-related changes of trabecular structure in a series of digital bone models and then characterized the potential of texture parameters and bone mineral density (BMD) as surrogate measures to quantify trabecular bone structure. Five texture parameters were studied: entropy, global and local inhomogeneity, anisotropy and variogram slope. Their dependence on OA relevant structural changes was investigated for three spatial resolutions typically used in micro computed tomography (CT; 10 lm), high-resolution peripheral quantitative CT (HR-pQCT) (90 lm) and clinical whole-body CT equipment (250 lm). At all resolutions, OA-related changes in trabecular bone architecture can be quantified using a specific (resolution dependent) combination of three texture parameters. BMD alone is inadequate for this purpose but if available reduces the required texture parameter combination to anisotropy and global inhomogeneity. The results are summarized in a comprehensive analysis guide for the detection of structural changes in OA knees. In conclusion, texture parameters can be used to characterize trabecular bone architecture even at spatial resolutions below the dimensions of a single trabecula and are essential for a detailed classification of relevant OA changes that cannot be achieved with a measurement of BMD alone.

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Application of fractal geometry techniques to the study of trabecular bone

Cited by 117 publications

References 0 publications

Shannon's entropy and fractal dimension provide an objective account of bone tissue organization during calvarial bone regeneration

Shannon's entropy and fractal dimension provide an objective account of bone tissue organization during calvarial bone regeneration

Fractal analysis of lumbar vertebral cancellous bone architecture

Characterization of knee osteoarthritis-related changes in trabecular bone using texture parameters at various levels of spatial resolution—a simulation study

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