Top

Journal of Cardiovascular Magnetic Resonance

Published in:

Open Access 01-12-2015 | Review

Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation

Authors: Gabriella Captur, Audrey L. Karperien, Chunming Li, Filip Zemrak, Catalina Tobon-Gomez, Xuexin Gao, David A. Bluemke, Perry M. Elliott, Steffen E. Petersen, James C. Moon

Published in: Journal of Cardiovascular Magnetic Resonance | Issue 1/2015

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.

Mandelbrot B. The fractal geometry of nature. Ed. Brickmann, J. Free. Co., San Fr. 1982.

Zouein FA, Kurdi M, Booz GW, Fuseler JW. Applying fractal dimension and image analysis to quantify fibrotic collagen deposition and organization in the normal and hypertensive heart. Microsc Microanal. 2014;20:1134–44.CrossRefPubMed

Squarcina L, De Luca A, Bellani M, Brambilla P, Turkheimer FE, Bertoldo A. Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder. Phys Med Biol. 2015;60:1697–716.CrossRefPubMed

Sandu A, Rasmussen Jr IA, Lundervold A, Kreuder F, Neckelmann G, Hugdahl K, et al. Fractal dimension analysis of MR images reveals grey matter structure irregularities in schizophrenia. Comput Med Imaging Graph. 2008;32:150–8.CrossRefPubMed

Quodbach J, Moussavi A, Tammer R, Frahm J, Kleinebudde P. Assessment of disintegrant efficacy with fractal dimensions from real-time MRI. Int J Pharm. 2014;475:605–12.CrossRefPubMed

Gupta L, Besseling RMH, Overvliet GM, Hofman PA, de Louw A, Vaessen MJ, et al. Spatial heterogeneity analysis of brain activation in fMRI. NeuroImage Clin. 2014;5:266–76.PubMedCentralCrossRefPubMed

Arai TJ, Prisk GK, Holverda S, Sá RC, Theilmann RJ, Henderson AC, et al. Magnetic resonance imaging quantification of pulmonary perfusion using calibrated arterial spin labeling. J Vis Exp. 2011;30(51):2712.

Captur G, Muthurangu V, Cook C, Flett AS, Wilson R, Barison A, et al. Quantification of left ventricular trabeculae using fractal analysis. J Cardiovasc Magn Reson. 2013;15:36.PubMedCentralCrossRefPubMed

Captur G, Lopes LR, Patel V, Li C, Bassett P, Syrris P, et al. Abnormal cardiac formation in hypertrophic cardiomyopathy: fractal analysis of trabeculae and preclinical gene expression. Circ Cardiovasc Genet. 2014;7:241–8.CrossRefPubMed

10.

Captur G, Lopes LR, Mohun TJ, Patel V, Li C, Bassett P, et al. Prediction of sarcomere mutations in subclinical hypertrophic cardiomyopathy. Circ Cardiovasc Imaging. 2014;7:863–7.CrossRefPubMed

11.

Sarkar N, Chaudhuri BB. An efficient differential box-counting approach to compute fractal dimension of image. IEEE Trans Syst Man Cybern. 1994;24:115–20.CrossRef

12.

Aliahmad B, Kumar DK, Sarossy MG, Jain R. Relationship between diabetes and grayscale fractal dimensions of retinal vasculature in the Indian population. BMC Ophthalmol. 2014;14:152.PubMedCentralCrossRefPubMed

13.

Grosgeorge D, Petitjean C, Fares J. Automatic cardiac ventricle segmentation in MR images : a validation study To cite this version. 2010.

14.

Petitjean C, Dacher J-N. A review of segmentation methods in short axis cardiac MR images. Med Image Anal. 2011;15:169–84.CrossRefPubMed

15.

Uemura K, Toyama H, Baba S, Kimura Y, Senda M. Uchiyama a. Generation of fractal dimension images and its application to automatic edge detection in brain MRI. Comput Med Imaging Graph. 2000;24:73–85.CrossRefPubMed

16.

Avnir D. Applied Mathematics:is the Geometry of Nature Fractal? Science. 1998;279:39–40.CrossRef

17.

Cross SS. The application of fractal geometric analysis to microscopic images. Micron. 1994;25:101–13.CrossRefPubMed

18.

Manera M, Dezfuli BS, Borreca C, Giari L. The use of fractal dimension and lacunarity in the characterization of mast cell degranulation in rainbow trout (Onchorhynchus mykiss). J Microsc. 2014;256:82–9.CrossRefPubMed

19.

Soares F, Janela F, Pereira M, Seabra J, Freire MM. 3D lacunarity in multifractal analysis of breast tumor lesions in dynamic contrast-enhanced magnetic resonance imaging. IEEE Trans Image Process. 2013;22:4422–35.CrossRefPubMed

20.

Zaia A, Eleonori R, Maponi P, Rossi R, Murri R. MR imaging and osteoporosis: Fractal lacunarity analysis of trabecular bone. IEEE Trans Inf Technol Biomed. 2006;10:484–9.CrossRefPubMed

21.

Fiz JA, Monte-Moreno E, Andreo F, Auteri SJ, Sanz-Santos J, Serra P, et al. Fractal dimension analysis of malignant and benign endobronchial ultrasound nodes. BMC Med Imaging. 2014;14:22.PubMedCentralCrossRefPubMed

22.

Bauer WR, Hiller KH, Galuppo P, Neubauer S, Köpke J, Haase A, et al. Fast high-resolution magnetic resonance imaging demonstrates fractality of myocardial perfusion in microscopic dimensions. Circ Res. 2001;88:340–6.CrossRefPubMed

23.

Kam Y, Karperien A, Weidow B, Estrada L, Anderson AR, Quaranta V. Nest expansion assay: a cancer systems biology approach to in vitro invasion measurements. BMC Res Notes. 2009;2:130.PubMedCentralCrossRefPubMed

24.

Cross SS. Fractals in pathology. J Pathol. 1997;182:1–8.CrossRefPubMed

25.

Aldrich PR, Horsley RK, Ahmed YA, Williamson JJ, Turcic SM. Fractal topology of gene promoter networks at phase transitions. Gene Regul Syst Bio. 2010;4:75–82.PubMedCentralCrossRefPubMed

26.

Doubal FN, MacGillivray TJ, Patton N, Dhillon B, Dennis MS, Wardlaw JM. Fractal analysis of retinal vessels suggests that a distinct vasculopathy causes lacunar stroke. Neurology. 2010;74:1102–7.PubMedCentralCrossRefPubMed

27.

Tiraihi A, Tiraihi M, Tiraihi T. Self-organization of developing embryo using scale-invariant approach. Theor Biol Med Model. 2011;8:17.PubMedCentralCrossRefPubMed

28.

Amer ME, Heo M-S, Brooks SL, Benavides E. Anatomical variations of trabecular bone structure in intraoral radiographs using fractal and particles count analyses. Imaging Sci Dent. 2012;42:5–12.PubMedCentralCrossRefPubMed

29.

Doan NT, van Rooden S, Versluis MJ, Buijs M, Webb AG, van der Grond J, et al. An automated tool for cortical feature analysis: Application to differences on 7 Tesla T2 (*) -weighted images between young and older healthy subjects. Magn Reson Med. 2014;00:1–9.CrossRef

30.

Abramyuk A, Hietschold V, Appold S, von Kummer R, Abolmaali N. Radiochemotherapy-induced changes of tumour vascularity and blood supply estimated by dynamic contrast-enhanced CT and fractal analysis in malignant head and neck tumours. Br J Radiol. 2015;88:20140412.CrossRefPubMed

31.

Abramoff MD, Magalhães PJ, Ram SJ. Image Processing with ImageJ. Biophotonics International. 2004;11:36--42.

32.

Yoo TS, Ackerman MJ, Lorensen WE, Schroeder W, Chalana V, Aylward S, et al. Engineering and algorithm design for an image processing Api: a technical report on ITK--the Insight Toolkit. Stud Health Technol Inform. 2002;85:586–92.PubMed

33.

Mancardi D, Varetto G, Bucci E, Maniero F, Guiot C. Fractal parameters and vascular networks: facts & artifacts. Theor Biol Med Model. 2008;5:12.PubMedCentralCrossRefPubMed

34.

A. K. FracLac for ImageJ. http://rsb.info.nih.gov/ij/plugins/fraclac/FLHelp/Introduction.htm. 1999–2013.

35.

Captur G, Zemrak F, Muthurangu V, Petersen SE, Li C, Bassett P, et al. Fractal analysis of myocardial trabeculations in 2547 subjects: the Multi-Ethnic Study of Atherosclerosis. Radiology 2015:Epub ahead of print.

36.

Bossuyt PM. The STARD Statement for Reporting Studies of Diagnostic Accuracy: Explanation and Elaboration. Clin Chem. 2003;49:7–18.CrossRefPubMed

37.

Sado DM, Flett AS, Moon JC. Novel imaging techniques for diffuse myocardial fibrosis. Future Cardiol. 2011;7:643–50.CrossRefPubMed

38.

Eke A, Herman P, Kocsis L, Kozak LR. Fractal characterization of complexity in temporal physiological signals. Physiol Meas. 2002;23:R1–38.CrossRefPubMed

39.

Bossuyt PM, Reitsma JB, Bruns DE, Gatsonis CA, Glasziou PP, Irwig LM, et al. The STARD statement for reporting studies of diagnostic accuracy: explanation and elaboration. Ann Intern Med. 2003;138:W1–12.CrossRefPubMed

40.

Li C, Huang R, Ding Z, Gatenby JC, Metaxas DN, Gore JC. A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI. IEEE Trans Image Process. 2011;20:2007–16.CrossRefPubMed

41.

Zemrak F, Ahlman MA, Captur G, Mohiddin SA, Kawel-Boehm N, Prince MR, et al. The relationship of left ventricular trabeculation to ventricular function and structure over a 9.5-year follow-up. J Am Coll Cardiol. 2014;64:1971–80.CrossRefPubMed

42.

Somasundaran P. Encyclopedia of surface and colloid science. Volume 4. Boca Raton, FL: CRC Press, Taylor & Francis Group; 2006:6675.

Title: Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation
Authors: Gabriella Captur
Audrey L. Karperien
Chunming Li
Filip Zemrak
Catalina Tobon-Gomez
Xuexin Gao
David A. Bluemke
Perry M. Elliott
Steffen E. Petersen
James C. Moon
Publication date: 01-12-2015
Publisher: BioMed Central
Published in: Journal of Cardiovascular Magnetic Resonance / Issue 1/2015
Electronic ISSN: 1532-429X
DOI: https://doi.org/10.1186/s12968-015-0179-0

Keynote webinar | Spotlight on sleep in brain health

Springer Medicine

Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation

Abstract

Keynote webinar | Spotlight on sleep in brain health

Springer Medicine

Abstract

Please log in to get access to this content

Other articles of this Issue 1/2015

Influence of phase correction of late gadolinium enhancement images on scar signal quantification in patients with ischemic and non-ischemic cardiomyopathy

Mechanism of decreased sensitivity of dobutamine associated left ventricular wall motion analyses for appreciating inducible ischemia in older adults

Pulmonary artery to aorta ratio for the detection of pulmonary hypertension: cardiovascular magnetic resonance and invasive hemodynamics in heart failure with preserved ejection fraction

Positive contrast high-resolution 3D-cine imaging of the cardiovascular system in small animals using a UTE sequence and iron nanoparticles at 4.7, 7 and 9.4 T

Detection of elevated right ventricular extracellular volume in pulmonary hypertension using Accelerated and Navigator-Gated Look-Locker Imaging for Cardiac T1 Estimation (ANGIE) cardiovascular magnetic resonance

Quantification of LV function and mass by cardiovascular magnetic resonance: multi-center variability and consensus contours