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Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation.

Captur G, Karperien AL, Li C, Zemrak F, Tobon-Gomez C, Gao X, Bluemke DA, Elliott PM, Petersen SE, Moon JC - J Cardiovasc Magn Reson (2015)

Bottom Line: Many of the structures and parameters that are detected, measured and reported in cardiovascular magnetic resonance (CMR) have at least some properties that are fractal, meaning complex and self-similar at different scales.To date however, there has been little use of fractal geometry in CMR; by comparison, many more applications of fractal analysis have been published in MR imaging of the brain.This review explains the fundamental principles of fractal geometry, places the fractal dimension into a meaningful context within the realms of Euclidean and topological space, and defines its role in digital image processing.It summarises the basic mathematics, highlights strengths and potential limitations of its application to biomedical imaging, shows key current examples and suggests a simple route for its successful clinical implementation by the CMR community.By simplifying some of the more abstract concepts of deterministic fractals, this review invites CMR scientists (clinicians, technologists, physicists) to experiment with fractal analysis as a means of developing the next generation of intelligent quantitative cardiac imaging tools.

View Article: PubMed Central - PubMed

Affiliation: UCL Institute of Cardiovascular Science, University College London, Gower Street, London, WC1E 6BT, UK. gabriella.captur.11@ucl.ac.uk.

ABSTRACT
Many of the structures and parameters that are detected, measured and reported in cardiovascular magnetic resonance (CMR) have at least some properties that are fractal, meaning complex and self-similar at different scales. To date however, there has been little use of fractal geometry in CMR; by comparison, many more applications of fractal analysis have been published in MR imaging of the brain.This review explains the fundamental principles of fractal geometry, places the fractal dimension into a meaningful context within the realms of Euclidean and topological space, and defines its role in digital image processing. It summarises the basic mathematics, highlights strengths and potential limitations of its application to biomedical imaging, shows key current examples and suggests a simple route for its successful clinical implementation by the CMR community.By simplifying some of the more abstract concepts of deterministic fractals, this review invites CMR scientists (clinicians, technologists, physicists) to experiment with fractal analysis as a means of developing the next generation of intelligent quantitative cardiac imaging tools.

No MeSH data available.


Related in: MedlinePlus

Exact self-similar elements cannot always be recognized in naturally occurring fractals. The spiral galaxy (a) is an example of a large-scale fractal in the physical world. Biology is full of fractal objects: from the whorls of molluscs (b), to the woven lattice of human cancellous bone (c); from the branching pulmonary arterial tree (d) to the trabeculated apex of the left ventricle (e). CMR = cardiovascular magnetic resonance
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Fig1: Exact self-similar elements cannot always be recognized in naturally occurring fractals. The spiral galaxy (a) is an example of a large-scale fractal in the physical world. Biology is full of fractal objects: from the whorls of molluscs (b), to the woven lattice of human cancellous bone (c); from the branching pulmonary arterial tree (d) to the trabeculated apex of the left ventricle (e). CMR = cardiovascular magnetic resonance

Mentions: Natural quasi fractal objects, unlike theoretical fractals but much like graphical representations of fractals, are scale invariant across only a limited range of scales. We are surrounded by natural objects that iterate, branch or spiral, spanning a wide range of scales. Some large-scale examples in the physical world include recursing coastlines, branching tree and river networks, and spiralling galaxies (Fig. 1a) and hurricanes. Some small-scale examples in biology include the spirals of a nautilus and whorls of a seashell (Fig. 1b). Small-scale examples in the human body include the lattices of cancellous bone (Fig. 1c), neuronal dendrites, tumor growth patterns, and specifically for the cardiovascular system, branching vascular networks (Fig. 1d), endocardial trabeculae, and the quasi-fractal ordering of collagen and fibrosis in the diseased myocardium as seen by micro-histology [2].Fig. 1


Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation.

Captur G, Karperien AL, Li C, Zemrak F, Tobon-Gomez C, Gao X, Bluemke DA, Elliott PM, Petersen SE, Moon JC - J Cardiovasc Magn Reson (2015)

Exact self-similar elements cannot always be recognized in naturally occurring fractals. The spiral galaxy (a) is an example of a large-scale fractal in the physical world. Biology is full of fractal objects: from the whorls of molluscs (b), to the woven lattice of human cancellous bone (c); from the branching pulmonary arterial tree (d) to the trabeculated apex of the left ventricle (e). CMR = cardiovascular magnetic resonance
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4562373&req=5

Fig1: Exact self-similar elements cannot always be recognized in naturally occurring fractals. The spiral galaxy (a) is an example of a large-scale fractal in the physical world. Biology is full of fractal objects: from the whorls of molluscs (b), to the woven lattice of human cancellous bone (c); from the branching pulmonary arterial tree (d) to the trabeculated apex of the left ventricle (e). CMR = cardiovascular magnetic resonance
Mentions: Natural quasi fractal objects, unlike theoretical fractals but much like graphical representations of fractals, are scale invariant across only a limited range of scales. We are surrounded by natural objects that iterate, branch or spiral, spanning a wide range of scales. Some large-scale examples in the physical world include recursing coastlines, branching tree and river networks, and spiralling galaxies (Fig. 1a) and hurricanes. Some small-scale examples in biology include the spirals of a nautilus and whorls of a seashell (Fig. 1b). Small-scale examples in the human body include the lattices of cancellous bone (Fig. 1c), neuronal dendrites, tumor growth patterns, and specifically for the cardiovascular system, branching vascular networks (Fig. 1d), endocardial trabeculae, and the quasi-fractal ordering of collagen and fibrosis in the diseased myocardium as seen by micro-histology [2].Fig. 1

Bottom Line: Many of the structures and parameters that are detected, measured and reported in cardiovascular magnetic resonance (CMR) have at least some properties that are fractal, meaning complex and self-similar at different scales.To date however, there has been little use of fractal geometry in CMR; by comparison, many more applications of fractal analysis have been published in MR imaging of the brain.This review explains the fundamental principles of fractal geometry, places the fractal dimension into a meaningful context within the realms of Euclidean and topological space, and defines its role in digital image processing.It summarises the basic mathematics, highlights strengths and potential limitations of its application to biomedical imaging, shows key current examples and suggests a simple route for its successful clinical implementation by the CMR community.By simplifying some of the more abstract concepts of deterministic fractals, this review invites CMR scientists (clinicians, technologists, physicists) to experiment with fractal analysis as a means of developing the next generation of intelligent quantitative cardiac imaging tools.

View Article: PubMed Central - PubMed

Affiliation: UCL Institute of Cardiovascular Science, University College London, Gower Street, London, WC1E 6BT, UK. gabriella.captur.11@ucl.ac.uk.

ABSTRACT
Many of the structures and parameters that are detected, measured and reported in cardiovascular magnetic resonance (CMR) have at least some properties that are fractal, meaning complex and self-similar at different scales. To date however, there has been little use of fractal geometry in CMR; by comparison, many more applications of fractal analysis have been published in MR imaging of the brain.This review explains the fundamental principles of fractal geometry, places the fractal dimension into a meaningful context within the realms of Euclidean and topological space, and defines its role in digital image processing. It summarises the basic mathematics, highlights strengths and potential limitations of its application to biomedical imaging, shows key current examples and suggests a simple route for its successful clinical implementation by the CMR community.By simplifying some of the more abstract concepts of deterministic fractals, this review invites CMR scientists (clinicians, technologists, physicists) to experiment with fractal analysis as a means of developing the next generation of intelligent quantitative cardiac imaging tools.

No MeSH data available.


Related in: MedlinePlus