Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation.
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.
UCL Institute of Cardiovascular Science, University College London, Gower Street, London, WC1E 6BT, UK. gabriella.captur.11@ucl.ac.uk.|Division of Cardiovascular Imaging, The Heart Hospital, part of University College London NHS Foundation Trust, 16-18 Westmoreland Street, London, W1G 8PH, UK. gabriella.captur.11@ucl.ac.uk.
Gabriella
G
Captur
Centre for Research in Complex Systems, School of Community Health, Charles Sturt University, Albury, NSW 2640, Australia. akarperien@yahoo.com.
Audrey L
AL
Karperien
Department of Radiology, University of Pennsylvania, Philadelphia, PA, USA. li_chunming@hotmail.com.
Chunming
C
Li
Division of Cardiovascular Imaging, The Heart Hospital, part of University College London NHS Foundation Trust, 16-18 Westmoreland Street, London, W1G 8PH, UK. filip.zemrak@gmail.com.|Cardiovascular Biomedical Research Unit, Barts and the London School of Medicine and Dentistry, Queen Mary University of London, London, UK. filip.zemrak@gmail.com.
Filip
F
Zemrak
Division of Imaging Sciences & Biomedical Engineering, King's College London, London, UK. catactg@gmail.com.
Catalina
C
Tobon-Gomez
Circle Cardiovascular Imaging Inc., Panarctic Plaza, Suite 250, 815 8th Avenue SW, Calgary, AB T2P 3P2, Canada. gavin@circlecvi.com.
Xuexin
X
Gao
Radiology and Imaging Sciences, National Institutes of Health Clinical Center, Center Drive, Bethesda, MA, USA. bluemked@cc.nih.gov.
David A
DA
Bluemke
UCL Institute of Cardiovascular Science, University College London, Gower Street, London, WC1E 6BT, UK. perry.elliott@ucl.ac.uk.|Division of Cardiovascular Imaging, The Heart Hospital, part of University College London NHS Foundation Trust, 16-18 Westmoreland Street, London, W1G 8PH, UK. perry.elliott@ucl.ac.uk.
Perry M
PM
Elliott
Division of Cardiovascular Imaging, The Heart Hospital, part of University College London NHS Foundation Trust, 16-18 Westmoreland Street, London, W1G 8PH, UK. s.e.petersen@qmul.ac.uk.|Cardiovascular Biomedical Research Unit, Barts and the London School of Medicine and Dentistry, Queen Mary University of London, London, UK. s.e.petersen@qmul.ac.uk.
Steffen E
SE
Petersen
UCL Institute of Cardiovascular Science, University College London, Gower Street, London, WC1E 6BT, UK. j.moon@ucl.ac.uk.|Division of Cardiovascular Imaging, The Heart Hospital, part of University College London NHS Foundation Trust, 16-18 Westmoreland Street, London, W1G 8PH, UK. j.moon@ucl.ac.uk.
James C
JC
Moon
D000818:Animals; D002318:Cardiovascular Diseases / Q000175:diagnosis* / Q000473:pathology / Q000503:physiopathology; D002319:Cardiovascular System / Q000473:pathology / Q000503:physiopathology; D017709:Fractals; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D019028:Magnetic Resonance Imaging, Cine / Q000379:methods*; D008955:Models, Cardiovascular; D011237:Predictive Value of Tests; D011379:Prognosis