Quantitation of the renal arterial tree by fractal analysis

Cross, Simon S.; Start, R. D.; Silcocks, Paul; Bull, A D; Cotton, D. W. K.; Underwood, James

doi:10.1002/path.1711700412

Cited by 66 publications

(30 citation statements)

References 17 publications

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“…The basic idea to build such a method stems from the complexity of living being and fractal nature of many physioanatomic structures [31] . Seve ral structures and functions of human body have got fractal properties [62,72,73] . Trabecular bone, in addition to be a good model for fractal analysis in biological structures, offers the opportunity of analyzing fra ctal lacunarity [74] .…”

Section: Bone Structurementioning

confidence: 99%

Fractal lacunarity of trabecular bone and magnetic resonance imaging: New perspectives for osteoporotic fracture risk assessment

Alimazighi¹

2015

WJO

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Osteoporosis represents one major health condition for our growing elderly population. It accounts for severe morbidity and increased mortality in postmenopausal women and it is becoming an emerging health concern even in aging men. Screening of the population at risk for bone degeneration and treatment assessment of osteoporotic patients to prevent bone fragility fractures represent useful tools to improve quality of life in the elderly and to lighten the related socio-economic impact. Bone mineral density (BMD) estimate by means of dualenergy X-ray absorptiometry is normally used in clinical practice for osteoporosis diagnosis. Nevertheless, BMD alone does not represent a good predictor of fracture risk. From a clinical point of view, bone microarchitecture seems to be an intriguing aspect to characterize bone alteration patterns in aging and pathology. The widening into clinical practice of medical imaging techniques and the impressive advances in information technologies together with enhanced capacity of power calculation have promoted proliferation of new methods to assess changes of trabecular bone architecture (TBA) during aging and osteoporosis. Magnetic resonance imaging (MRI) has recently arisen as a useful tool to measure bone structure in vivo . In particular, high-resolution MRI techniques have introduced new perspectives for TBA characterization by non-invasive non-ionizing methods. However, texture analysis methods have not found favor with clinicians as they produce quite a few parameters whose interpretation is difficult. The introduction in biomedical field of paradigms, such as theory of complexity, chaos, and fractals, suggests new approaches and provides innovative tools to develop computerized methods that, by producing a limited number of parameters sensitive to pathology onset and progression, would speed up their application into clinical practice. Complexity of living beings and fractality of several physio-anatomic structures suggest fractal analysis as a promising approach to quantify morphofunctional changes in both aging and pathology. In this particular context, fractal lacunarity seems to be the proper tool to characterize TBA texture as it is able to describe both discontinuity of bone network and sizes of bone marrow spaces, whose changes are an index of bone fracture risk. In this paper, an original method of MRI texture analysis, based on TBA fractal lacunarity is described and discussed in the light of new perspectives for early diagnosis of osteoporotic fractures.

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Section: Bone Structurementioning

confidence: 99%

Fractal lacunarity of trabecular bone and magnetic resonance imaging: New perspectives for osteoporotic fracture risk assessment

Alimazighi¹

2015

WJO

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“…28) Fractal geometric analysis has been applied in the analysis of neuronal dendritic arborizations, 29) vascular heterogeneity in the heart, 30) formation of human retinal blood vessels in the kidney, 31) the structure of the bronchial tree, 32,33) and the distribution and quantification of arterial blood vessels in the kidney. 34,35) Recently, in the field of pathology, fractal dimensions of the histological structure of colorectal polyps 17) and cell growth patterns in human malignant tumors 36) have been reported. Cross et al 17) have suggested that the fractal dimension is a better way of quantitating polyp shape and is a useful morphometric discriminant among diagnostic categories.…”

Section: Discussionmentioning

confidence: 99%

Three‐dimensional Reconstruction and Fractal Geometric Analysis of Serrated Adenoma

Iseki

Endoh²,

Hiwatashi

et al. 2002

Japanese Journal of Cancer Research

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Serrated adenoma (SA) is a relatively newly defined entity of colorectal neoplasm first characterized by Longacre and Fenoglio-Preiser in 1990. This lesion is characterized by a complicated serrated edge of crypts. In this study, we performed three-dimensional (3-D) reconstruction, including 3-D distribution patterns of Ki-67-positive cells and fractal dimension of SA, in order to evaluate the nature of the complicated architecture, including its possible morphogenesis. We studied nine colonoscopic polypectomy specimens including three SAs, three tubular adenomas (TAs), and three hyperplastic polyps (HPs). Sixty serial tissue sections per case were stained alternately with hematoxylin and eosin (H&E) and Ki-67 immunostain. Each serial image was then digitized for 3-D computer analysis and the distribution pattern of Ki-67-positive cells was evaluated. Ki-67-immunostained sections were also subjected to 2-D quantitative morphometric study. In addition, the fractal dimensions of images from H&E-stained sections were examined using a box-counting method. Results of the 3-D reconstruction study demonstrated that glandular budding and branching were more frequent in SA than in TA or HP. These findings were confirmed quantitatively by the results of fractal geometric analysis of these polyps (fractal dimension:1.34 ± ± ± ±0.08 for SA, 1.23 ± ± ± ±0.07 for TA, and 1.28 ± ± ± ±0.12 for HP). Ki-67-positive cells in HP were localized mainly in the bottom of crypts and those in TA were diffusely distributed, while Ki-67-positive cells in SA were mainly aggregated in the depressed sites of serrated epithelia. These findings were also confirmed quantitatively using 2-D morphometry. These distribution patterns of the proliferative zone of SA are considered to contribute to the formation of the characteristic serrated epithelia and the complicated morphological appearance of SA.

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“…Whether a given network has fractal characteristics should not be taken a priori, but as a hypothesis that requires empirical validation. An abundant literature has been devoted to the fractal properties of biological features (see, for a review, Losa 15 ), among them the pattern of the vascular network 10,13,16,17 , which have been described as a combination of scale-invariant and scale-specific patterns17. What it is important to notice is that these kinds of structural analysis of vascular networks are grounded on physicomathematical concepts and tools.…”

Section: Form and Function Of Vascular Networkmentioning

confidence: 99%

Theoretical Analysis of the Vascular System and its Relation to Adrian Bejan's constructal Theory

Roux¹,

Marhl²

2017

JTAVR

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Basically, the main function of the cardiovascular system is to provide oxygen and other nutriments to the tissues, achieved by the pumping action of the heart and the subsequent blood flow through the tree-like vasculature. Classically, in the physical and mathematical analysis of the relationship between form and function of vascular systems, form is given first. The constructal theory, first proposed by Adrian Bejan in 1996, is a thermodynamic principle according to which flow systems, such as watersheds and vascular networks, evolve so that they gain more global performance over time. There are two major points about the constructal theory. The first one is that it provides a unifying concept of form and function, in which the configuration is not postulated, but is to be discovered. The second one is that it is presented as a unifying physical concept of evolution of organic and inorganic flow systems. By comparing non-living (watersheds) and living (vasculature) systems, we show that the processes of morphological "change upon time" in watersheds and those of developmental morphogenesis and evolutionary modifications through generations in a population are not equivalent. Mechanistic explanations in biology include physico-mathematical models but, from the biological point of view, the epistemic value of the constructal law is not its unifying power by subsumption of biological processes under a general nomological principle, but, to the contrary, to provide an idealized physicomathematical model of living systems that is embedded in general mechanistic explanatory frameworks of biological processes such as development and evolution.

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Quantitation of the renal arterial tree by fractal analysis

Cited by 66 publications

References 17 publications

Fractal lacunarity of trabecular bone and magnetic resonance imaging: New perspectives for osteoporotic fracture risk assessment

Fractal lacunarity of trabecular bone and magnetic resonance imaging: New perspectives for osteoporotic fracture risk assessment

Three‐dimensional Reconstruction and Fractal Geometric Analysis of Serrated Adenoma

Theoretical Analysis of the Vascular System and its Relation to Adrian Bejan's constructal Theory

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