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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

Clinical application of a fractal analysis for trabecular quantification by CMR in LVNC. It is noteworthy how in healthy hearts, it is the mid-LV that holds the greatest fractal complexity (papillary muscles), a fact that is commonly overlooked as the more intricately trabeculated apex commonly distracts. LVNC = left ventricular noncompaction. Authorization for this adaptation has been obtained both from the owner of the copyright in the original work [8] and from the owner of copyright in the translation or adaptation (JCMR)
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Fig7: Clinical application of a fractal analysis for trabecular quantification by CMR in LVNC. It is noteworthy how in healthy hearts, it is the mid-LV that holds the greatest fractal complexity (papillary muscles), a fact that is commonly overlooked as the more intricately trabeculated apex commonly distracts. LVNC = left ventricular noncompaction. Authorization for this adaptation has been obtained both from the owner of the copyright in the original work [8] and from the owner of copyright in the translation or adaptation (JCMR)

Mentions: Experimenting with fractal analysis of images in the CMR domain, typically involves the in-house development of scripts written for a specific programming environment (e.g., MATLAB, ImageJ [31], Insight Toolkit [ITK] [32], etc.). It may be possible to repurpose already available tools in the form of commercial and open-source fractal plugins and codes [33]. Examples include: Fractalyse (ThèMA, F), Whinrhizo (Regent Instruments Inc.), Image Pro Plus (Media Cybernetics), FDSURFFT (in MATLAB) and Fraclac for ImageJ [34]. Our group started off with Fraclac and then moved to an in-house MATLAB implementation. We applied fractal analysis to CMR cine data for trabecular quantification. In left ventricular noncompaction (n = 30) compared to healthy volunteers (n = 75) fractal analysis (Fig. 7) revealed FD elevation in the apical half of the left ventricle [8] (1.392 ± 0.010 versus 1.235 ± 0.004). When we studied patients at our centre with hypertrophic cardiomyopathy (n = 107), fractal analysis showed abnormally increased apical FD not only in overt disease, but also in sarcomere gene mutation carriers without left ventricular hypertrophy (G + LVH-, 1.249 ± 0.07) compared to controls (1.199 ± 0.05) [9]. In a multi-centre setting high FD was further shown to predict hypertrophic cardiomyopathy sarcomere gene mutation carriage in G + LVH- (n = 73) [10]. Applied to 2547 participants in the population-representative MESA study, fractal analysis was able to provide ethnically-appropriate normal reference ranges for left ventricular endocardial complexity [35].Fig. 7


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)

Clinical application of a fractal analysis for trabecular quantification by CMR in LVNC. It is noteworthy how in healthy hearts, it is the mid-LV that holds the greatest fractal complexity (papillary muscles), a fact that is commonly overlooked as the more intricately trabeculated apex commonly distracts. LVNC = left ventricular noncompaction. Authorization for this adaptation has been obtained both from the owner of the copyright in the original work [8] and from the owner of copyright in the translation or adaptation (JCMR)
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig7: Clinical application of a fractal analysis for trabecular quantification by CMR in LVNC. It is noteworthy how in healthy hearts, it is the mid-LV that holds the greatest fractal complexity (papillary muscles), a fact that is commonly overlooked as the more intricately trabeculated apex commonly distracts. LVNC = left ventricular noncompaction. Authorization for this adaptation has been obtained both from the owner of the copyright in the original work [8] and from the owner of copyright in the translation or adaptation (JCMR)
Mentions: Experimenting with fractal analysis of images in the CMR domain, typically involves the in-house development of scripts written for a specific programming environment (e.g., MATLAB, ImageJ [31], Insight Toolkit [ITK] [32], etc.). It may be possible to repurpose already available tools in the form of commercial and open-source fractal plugins and codes [33]. Examples include: Fractalyse (ThèMA, F), Whinrhizo (Regent Instruments Inc.), Image Pro Plus (Media Cybernetics), FDSURFFT (in MATLAB) and Fraclac for ImageJ [34]. Our group started off with Fraclac and then moved to an in-house MATLAB implementation. We applied fractal analysis to CMR cine data for trabecular quantification. In left ventricular noncompaction (n = 30) compared to healthy volunteers (n = 75) fractal analysis (Fig. 7) revealed FD elevation in the apical half of the left ventricle [8] (1.392 ± 0.010 versus 1.235 ± 0.004). When we studied patients at our centre with hypertrophic cardiomyopathy (n = 107), fractal analysis showed abnormally increased apical FD not only in overt disease, but also in sarcomere gene mutation carriers without left ventricular hypertrophy (G + LVH-, 1.249 ± 0.07) compared to controls (1.199 ± 0.05) [9]. In a multi-centre setting high FD was further shown to predict hypertrophic cardiomyopathy sarcomere gene mutation carriage in G + LVH- (n = 73) [10]. Applied to 2547 participants in the population-representative MESA study, fractal analysis was able to provide ethnically-appropriate normal reference ranges for left ventricular endocardial complexity [35].Fig. 7

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