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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.


The 3D FD (between 2 and 3) of the grayscale cine is computed using the differential box-counting algorithm that takes 3D pixel intensity information into account. In the standard box-counting method applied to binary images as either outlines or filled silhouettes, intensity information is lost as foreground pixels are contrasted from the background pixels to derive the 2D FD (range 1 – 2). For the same original image and considering only the mantissa, it is usually the case that the binary FD is greater than the grayscale equivalent. Furthermore, the FD of the filled binary mask would usually be nearer to 2 when compared to the FD of the equivalent binary outline as the FD of the filled areas massively outweigh the FD of the edges. Abbreviations as in Fig. 2
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Fig4: The 3D FD (between 2 and 3) of the grayscale cine is computed using the differential box-counting algorithm that takes 3D pixel intensity information into account. In the standard box-counting method applied to binary images as either outlines or filled silhouettes, intensity information is lost as foreground pixels are contrasted from the background pixels to derive the 2D FD (range 1 – 2). For the same original image and considering only the mantissa, it is usually the case that the binary FD is greater than the grayscale equivalent. Furthermore, the FD of the filled binary mask would usually be nearer to 2 when compared to the FD of the equivalent binary outline as the FD of the filled areas massively outweigh the FD of the edges. Abbreviations as in Fig. 2

Mentions: The mathematical details of a fractal analysis are generally taken care of by software, but this is typically preceded by some medical image preparation. It may be necessary to generate the needed image format (e.g., grayscale, binary or red-green-blue (RGB) data type) or to remove image complexity unrelated to the feature to be measured. For example, a short-axis cine slice may carry signal originating from the myocardium, blood-myocardial boundary, blood pool, and surrounding tissues, all of which are measurable, either separately or together. To be able to measure the quasi-fractal properties of an endocardial contour (the blood-myocardial boundary) some image transformation would be needed in order to extract its relevant pattern, in particular its binary outline. In a segmented image, derived according to a fixed thresholding rule, the meaning of each single pixel is reduced to the binary logic of existence (pixel present/foreground) and nonexistence (pixel absent/background). Typically, the FD of a binary filled object (e.g., the binary mask of the blood pool) is greater than that of its binary outlined counterpart (e.g., the edge image of the endocardial contour), and the FD of such binary images (whether filled or outlined) will be generally greater than the equivalent FD [11] of the original grayscale object (Fig. 4) [12].Fig. 4


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)

The 3D FD (between 2 and 3) of the grayscale cine is computed using the differential box-counting algorithm that takes 3D pixel intensity information into account. In the standard box-counting method applied to binary images as either outlines or filled silhouettes, intensity information is lost as foreground pixels are contrasted from the background pixels to derive the 2D FD (range 1 – 2). For the same original image and considering only the mantissa, it is usually the case that the binary FD is greater than the grayscale equivalent. Furthermore, the FD of the filled binary mask would usually be nearer to 2 when compared to the FD of the equivalent binary outline as the FD of the filled areas massively outweigh the FD of the edges. Abbreviations as in Fig. 2
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig4: The 3D FD (between 2 and 3) of the grayscale cine is computed using the differential box-counting algorithm that takes 3D pixel intensity information into account. In the standard box-counting method applied to binary images as either outlines or filled silhouettes, intensity information is lost as foreground pixels are contrasted from the background pixels to derive the 2D FD (range 1 – 2). For the same original image and considering only the mantissa, it is usually the case that the binary FD is greater than the grayscale equivalent. Furthermore, the FD of the filled binary mask would usually be nearer to 2 when compared to the FD of the equivalent binary outline as the FD of the filled areas massively outweigh the FD of the edges. Abbreviations as in Fig. 2
Mentions: The mathematical details of a fractal analysis are generally taken care of by software, but this is typically preceded by some medical image preparation. It may be necessary to generate the needed image format (e.g., grayscale, binary or red-green-blue (RGB) data type) or to remove image complexity unrelated to the feature to be measured. For example, a short-axis cine slice may carry signal originating from the myocardium, blood-myocardial boundary, blood pool, and surrounding tissues, all of which are measurable, either separately or together. To be able to measure the quasi-fractal properties of an endocardial contour (the blood-myocardial boundary) some image transformation would be needed in order to extract its relevant pattern, in particular its binary outline. In a segmented image, derived according to a fixed thresholding rule, the meaning of each single pixel is reduced to the binary logic of existence (pixel present/foreground) and nonexistence (pixel absent/background). Typically, the FD of a binary filled object (e.g., the binary mask of the blood pool) is greater than that of its binary outlined counterpart (e.g., the edge image of the endocardial contour), and the FD of such binary images (whether filled or outlined) will be generally greater than the equivalent FD [11] of the original grayscale object (Fig. 4) [12].Fig. 4

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.