Change in trabecular architecture as measured by fractal dimension

Berry, Joel L.; Towers, Jeffrey D.; Webber, Richard L.; Pope, Thomas L.; Davidai, Giora; Zimmerman, M. E.

doi:10.1016/0021-9290(95)00113-1

Cited by 14 publications

(7 citation statements)

References 5 publications

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“…In the 2D domain, there has been previous evidence that the FD increased after osteoporosis simulation. For example, Berry et al (1996) decalcified human vertebral bone. Digitized radiographs were made every 30 s and the FD increased from 2 to 3.…”

Section: Discussionmentioning

confidence: 99%

Bone quality assessment based on cone beam computed tomography imaging

Yan

Nackaerts

Duyck

et al. 2009

Clinical Oral Implants Res

134

124

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Section: Discussionmentioning

confidence: 99%

Bone quality assessment based on cone beam computed tomography imaging

Yan

Nackaerts

Duyck

et al. 2009

Clinical Oral Implants Res

134

124

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show abstract

“…In such a case, the fractal dimension may be the other useful descriptor. There are several methods that have been proposed for determining the fractal dimension, including the box‐counting algorithm, (10,17–21) surface area techniques using radiographs, (33) and power spectrum representations of 2D Fourier transforms of radiographs (34,35) . The box‐counting dimension is the one used most in measurements in a number of biological structures and provides a systematic measurement, (17) which is why we used the 3D box‐counting algorithm.…”

Section: Discussionmentioning

confidence: 99%

Effect of Vitamin K₂ on Three‐Dimensional Trabecular Microarchitecture in Ovariectomized Rats

Mawatari

Miura

Higaki

et al. 2000

J of Bone & Mineral Res

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Menatetrenone, a vitamin K 2 with four isoprene units, has been reported to improve osteoporotic bone loss. The purpose of this investigation was to clarify the effect of menatetrenone on the three-dimensional (3D) trabecular microarchitecture in ovariectomized (OVX) rats by using microcomputed tomography (MCT). Forty-two 13-week-old female rats were used and divided into four groups: the OVX (OVX ؉ MK-4) group treated with menatetrenone, the (OVX untreated) group, the sham-operated (Sham ؉ MK-4) group treated with menatetrenone, and the sham-operated group not treated with menatetrenone (Sham untreated) group. OVX rats were fed a calcium-deficient diet. Menatetrenone treatment was begun just after the ovariectomy, and the mean menatetrenone oral intake over the 8-week period was adjusted to 30 mg/kg BW per day. The proximal metaphyseal region of the right tibia was evaluated by dual X-ray absorptiometry (DXA) and MCT. A parametric analysis of the reconstructed trabecular volume was carried out using bone volume fractions, the fractal dimension calculated by the 3D box-counting method, and the connectivity density as determined by topological analysis. Menatetrenone significantly increased the trabecular bone volume, fractal dimension, and connectivity in the OVX ؉ MK-4 group compared with the OVX-untreated group ( p < 0.01). Our results suggest that an 8-week administration of menatetrenone protects against the loss of trabecular bone volume and its connectivity when treatment is begun just after the ovariectomy. Despite this apparent protection, it remains unknown whether it is possible to reestablish trabecular connectivity if therapeutic intervention occurs after the trabecular connectivity has been lost. (J Bone Miner Res 2000;15:1810 -1817)

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“…This results, most likely, from the coexistence of complexity and deterministic chaos (Kolmogorov-Arnold-Moser theorem) within the molecular and energetistic structure of cells [6,7,12]. Consequently, either metabolism [44][45][46], cytoskeletal patterns [47], calcium sequestration [48], tissue morphological patterns in normal or tumor tissues [6,[49][50][51][52][53], or tissue growth [54,55] possess fractal dimension. The fractal dimension reflects the intriguing fact that cells, in spite of the daily experience in the three-dimensional euclidean reality, which approximates geometric reality, are intermediate between two-dimensional surfaces and three-dimensional objects, and possess a fractal structure.…”

Section: Nonlinearity Complexity and Fractal Structurementioning

confidence: 99%

“…Without invalidating molecular findings, complexity offers an alternative, quasi-deterministic interpretation of cellular events underlying phenotype formation and tumorigenesis. The following points need to be emphasized as crucial consequences of the available experimental data: the relationship between genotype and phenotype reflects nonbijective interaction between static and dynamic categories [6,[24][25][26]30,31] leading to nonlinearity of the intra-and intercellular interactions [6,8,9,24], nonlinearity implies the existence of the fractal structure of space of cellular events [6,[44][45][46][47][48][49][50][51][52][53][54][55]. Those features support an holistic rather than a reductionist approach to cellular and cancer biology.…”

Section: Practical Inferencesmentioning

confidence: 99%

On the holistic approach in cellular and cancer biology: Nonlinearity, complexity, and quasi-determinism of the dynamic cellular network

Waliszewski

Molski²,

Konarski³

1998

J. Surg. Oncol.

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A keystone of the molecular reductionist approach to cellular biology is a specific deductive strategy relating genotype to phenotype—two distinct categories. This relationship is based on the assumption that the intermediary cellular network of actively transcribed genes and their regulatory elements is deterministic (i.e., a link between expression of a gene and a phenotypic trait can always be identified, and evolution of the network in time is predetermined). However, experimental data suggest that the relationship between genotype and phenotype is nonbijective (i.e., a gene can contribute to the emergence of more than just one phenotypic trait or a phenotypic trait can be determined by expression of several genes). This implies nonlinearity (i.e., lack of the proportional relationship between input and the outcome), complexity (i.e. emergence of the hierarchical network of multiple cross‐interacting elements that is sensitive to initial conditions, possesses multiple equilibria, organizes spontaneously into different morphological patterns, and is controled in dispersed rather than centralized manner), and quasi‐determinism (i.e., coexistence of deterministic and nondeterministic events) of the network. Nonlinearity within the space of the cellular molecular events underlies the existence of a fractal structure within a number of metabolic processes, and patterns of tissue growth, which is measured experimentally as a fractal dimension. Because of its complexity, the same phenotype can be associated with a number of alternative sequences of cellular events. Moreover, the primary cause initiating phenotypic evolution of cells such as malignant transformation can be favored probabilistically, but not identified unequivocally. Thermodynamic fluctuations of energy rather than gene mutations, the material traits of the fluctuations alter both the molecular and informational structure of the network. Then, the interplay between deterministic chaos, complexity, self‐organization, and natural selection drives formation of malignant phenotype. This concept offers a novel perspective for investigation of tumorigenesis without invalidating current molecular findings. The essay integrates the ideas of the sciences of complexity in a biological context. J. Surg. Oncol. 1998;68:70–78. © 1998 Wiley‐Liss, Inc.

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Change in trabecular architecture as measured by fractal dimension

Cited by 14 publications

References 5 publications

Bone quality assessment based on cone beam computed tomography imaging

Bone quality assessment based on cone beam computed tomography imaging

Effect of Vitamin K₂ on Three‐Dimensional Trabecular Microarchitecture in Ovariectomized Rats

On the holistic approach in cellular and cancer biology: Nonlinearity, complexity, and quasi-determinism of the dynamic cellular network

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Change in trabecular architecture as measured by fractal dimension

Cited by 14 publications

References 5 publications

Bone quality assessment based on cone beam computed tomography imaging

Bone quality assessment based on cone beam computed tomography imaging

Effect of Vitamin K2 on Three‐Dimensional Trabecular Microarchitecture in Ovariectomized Rats

On the holistic approach in cellular and cancer biology: Nonlinearity, complexity, and quasi-determinism of the dynamic cellular network

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Effect of Vitamin K₂ on Three‐Dimensional Trabecular Microarchitecture in Ovariectomized Rats