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The fractal heart — embracing mathematics in the cardiology clinic

Nature Reviews Cardiology volume 14, pages 56–64 (2017)Cite this article

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Abstract

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care.

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Figure 1: Examples of natural fractal phenomena.
Figure 2: Theoretical fractal dimension (FD).
Figure 3: Traditional geometry and spatial fractals.
Figure 4: Cardiology is replete with examples of fractal structures.
Figure 5: Omic-level complexity in the human heart.
Figure 6: Monofractal and multifractal analyses applied to heart-rate variability.

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Acknowledgements

G.C. is supported by the National Institute for Health Research (NIHR) Rare Diseases Translational Research Collaboration for the study of LMNA dilated cardiomyopathy (NIHR RD-TRC, #171603), by the European Society of Cardiology (ESC, EACVI), and by NIHR University College London Hospitals Biomedical Research Centre. A.D.H. received support from the University College London Hospitals NIHR Biomedical Research Centre and the British Heart Foundation relevant to this publication (PG/12/29/29497, CS/15/6/31468, and CS/13/1/30327). J.C.M. is directly and indirectly supported by the University College London Hospitals NIHR Biomedical Research Centre and Biomedical Research Unit at Barts Hospital, respectively.

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Authors and Affiliations

  1. Gabriella Capur is at the UCL Biological Mass Spectrometry Laboratory, Institute of Child Health and Great Ormond Street Hospital, 30 Guilford Street, London WC1N 1EH, UK; and the NIHR University College London Hospitals Biomedical Research Centre, Tottenham Court Road, London W1T 7DN, UK.,

    Gabriella Captur

  2. and the NIHR University College London Hospitals Biomedical Research Centre, Tottenham Court Road, London W1T 7DN, UK.,

    Gabriella Captur

  3. Audrey L. Karperien is at the Centre for Research in Complex Systems, School of Community Health, Charles Sturt University, Albury, NSW 2640, Australia.,

    Audrey L. Karperien

  4. Alun D. Hughes and James C. Moon are at the Institute of Cardiovascular Science, University College London, Gower Street, London WC1E 6BT, UK.,

    Alun D. Hughes

  5. Darrel P. Francis is at the International Centre for Circulatory Health, National Heart and Lung Institute, Imperial College London, London SW3 6LY, UK.,

    Darrel P. Francis

  6. James C. Moon is at the Barts Heart Centre, The Cardiovascular Magnetic Resonance Imaging Unit, St Bartholomew's Hospital, West Smithfield, London, EC1A 7BE, UK.,

    James C. Moon

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Contributions

G.C., A.L.K., and J.C.M. researched data for the article. All the authors discussed the content, wrote the manuscript, and reviewed/edited the article before submission.

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Correspondence to James C. Moon.

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Captur, G., Karperien, A., Hughes, A. et al. The fractal heart — embracing mathematics in the cardiology clinic. Nat Rev Cardiol 14, 56–64 (2017). https://doi.org/10.1038/nrcardio.2016.161

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