Fractal Dimension of Trabecular Bone Projection Texture Is Related to Three-Dimensional Microarchitecture

Pothuaud, Laurent; Benhamou, Claude-Laurent; Porion, Patrice; Lespessailles, Éric; Harba, Rachid; Levitz, Pierre

doi:10.1359/jbmr.2000.15.4.691

Cited by 151 publications

(82 citation statements)

References 48 publications

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“…TBS is an analytical tool that performs graylevel texture measurements on DXA image of the LS and thereby captures information relating to trabecular microarchitecture (14,15). Previous studies have demonstrated that TBS correlates with three-dimensional bone microarchitecture parameters, such as connectivity density and trabecular number, and negatively with trabecular separation (16,17).…”

Section: Introductionmentioning

confidence: 99%

Treatment of acromegaly increases BMD but reduces trabecular bone score: a longitudinal study

Godang

Olarescu

Bollerslev

et al. 2016

European Journal of Endocrinology

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Context: Bone turnover is increased in acromegaly. Despite normalization of bone turnover after treatment, the risk for vertebral fractures remains increased. Gonadal status, but not BMD, is correlated with vertebral fractures. Trabecular bone score (TBS) is related to bone microarchitecture. Objective: The aim of this study is to assess the longitudinal change in TBS and BMD following treatment for acromegaly. Results: Following treatment, the mean TBS decreased by 3.0 (±7.0) %, whereas the BMD at the lumbar spine (LS) increased by 3.2 (±4.9) % (both P < 0.01). The changes in BMD LS and TBS were not correlated (P = 0.87). The TBS change was found to be −4.5 % (±6.7; P = 0.003) in men and −0.3 % (±6.8; P = 0.85) in women (P = 0.063 for interaction men vs women). The mean BMD LS increased in men +4.2 g/cm 2 (±4.3; P < 0.001), but not in women +1.5 g/ cm 2 (±5.6; P = 0.36); (P = 0.073 for interaction). BMD increased in the ultradistal radius and total body (both P < 0.01).The increase in BMD LS was associated with a decrease in P1NP and CTX-1 (P < 0.001) and with lower P1NP and CTX-1 at the follow-up (P < 0.02). Conclusion: Treatment of acromegaly affects TBS and BMD at LS in different manners. The reduction of bone turnover markers predicts the increase in BMD but not the decrease in TBS. The DXA changes were more pronounced in men. Alterations in trabecular bone architecture may explain the persistent fracture risk despite the increase in BMD after disease control.

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Section: Introductionmentioning

confidence: 99%

Treatment of acromegaly increases BMD but reduces trabecular bone score: a longitudinal study

Godang

Olarescu

Bollerslev

et al. 2016

European Journal of Endocrinology

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“…(22) gives: Equation (22) links fractal dimension to porosity as found in another published research work, where fractal dimension has been shown to be a function of porosity and connectivity (Pothuaud et al 2000).…”

Section: Theorymentioning

confidence: 94%

A mathematical determination of the pore size distribution and fractal dimension of a porous sample using spontaneous imbibition dynamics theory

Amadu

Pegg

2018

J Petrol Explor Prod Technol

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Wallace sandstone has been extensively used by the construction industry for a long time in Nova Scotia. Apart from oxide analysis and a few strength-related parameter data found on some websites, petrophysical data regarding pore-sized distribution and fractal dimension are lacking. In the petroleum engineering literature, the spontaneous imbibition dynamics mechanism has been modeled where imbibition time has been linked to imbibition rise. One of the models links imbibition time to imbibition rise through a group of parameters that integrate the fractal dimension and sediment tortuosity. Based on the assumption of a bundle of parallel capillary tubes model found in the petrophysical literature, we have used the spontaneous imbibition model to derive an equation that links fractal dimension to porosity and permeability. Using literature source data on Wallace sandstone core samples, we have calculated the fractal dimension and pore size distribution using our equation. Results show that this sandstone has a significant level of heterogeneity. Calculation using another literature source data shows that our equation calculates fractal dimensions that are closer to those reported for the capillary pressure method. Although the assumption of bundle of parallel capillary tubes leads to deviations in calculated fractal dimensions using literature source data with experimentally determined porosity, permeability and fractal dimensions, our equation calculates meaningful values of fractal dimensions. Graphical abstract

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“…As an example, the stress asymmetry and micropolar effects indeed have been experimentally observed in bone mechanics [20]. Given the fact that bone is fractally structured [21], a fractal micropolar continuum model could be developed. Overall, the field equations resulting from the fractal micropolar continuum can be solved quantitatively, as demonstrated on several wave propagation problems, e.g., Ref.…”

Section: M(w)mentioning

confidence: 96%

Comment on “Hydrodynamics of fractal continuum flow” and “Map of fluid flow in fractal porous medium into fractal continuum flow”

Ostoja–Starzewski

2013

Phys. Rev. E

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In two recent papers [Phys. Rev. E 85, 025302(R) (2012) and Phys. Rev. E 85, 056314 (2012)], the authors proposed fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. While in general providing a certain advancement of continuum mechanics modeling of fractal media to fluid flows, some results and statements to previous works need clarification. We first show that the nonlocal character those authors alleged in our paper [Proc. R. Soc. A 465, 2521 (2009)] actually does not exist; instead, all those works are in the same general representation of derivative operators differing by specific forms of the line coefficient c 1 . Next, the claimed generalization of the volumetric coefficient c 3 is, in fact, equivalent to previously proposed product measures when considering together the separate decomposition of c 3 on each coordinate. Furthermore, the modified Jacobian proposed in the two commented papers does not relate the volume element between the current and initial configurations, which henceforth leads to a correction of the Reynolds' transport theorem. Finally, we point out that the asymmetry of the Cauchy stress tensor resulting from the conservation of the angular momentum must not be ignored; this aspect motivates a more complete formulation of fractal continuum models within a micropolar framework.

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Fractal Dimension of Trabecular Bone Projection Texture Is Related to Three-Dimensional Microarchitecture

Cited by 151 publications

References 48 publications

Treatment of acromegaly increases BMD but reduces trabecular bone score: a longitudinal study

Treatment of acromegaly increases BMD but reduces trabecular bone score: a longitudinal study

A mathematical determination of the pore size distribution and fractal dimension of a porous sample using spontaneous imbibition dynamics theory

Comment on “Hydrodynamics of fractal continuum flow” and “Map of fluid flow in fractal porous medium into fractal continuum flow”

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