European Radiology

, Volume 27, Issue 4, pp 1537–1546 | Cite as

Fractal analysis of the ischemic transition region in chronic ischemic heart disease using magnetic resonance imaging

  • Florian Michallek
  • Marc Dewey
Computer Applications



To introduce a novel hypothesis and method to characterise pathomechanisms underlying myocardial ischemia in chronic ischemic heart disease by local fractal analysis (FA) of the ischemic myocardial transition region in perfusion imaging.


Vascular mechanisms to compensate ischemia are regulated at various vascular scales with their superimposed perfusion pattern being hypothetically self-similar. Dedicated FA software (“FraktalWandler”) has been developed. Fractal dimensions during first-pass (FDfirst-pass) and recirculation (FDrecirculation) are hypothesised to indicate the predominating pathomechanism and ischemic severity, respectively.


Twenty-six patients with evidence of myocardial ischemia in 108 ischemic myocardial segments on magnetic resonance imaging (MRI) were analysed. The 40th and 60th percentiles of FDfirst-pass were used for pathomechanical classification, assigning lesions with FDfirst-pass ≤ 2.335 to predominating coronary microvascular dysfunction (CMD) and ≥2.387 to predominating coronary artery disease (CAD). Optimal classification point in ROC analysis was FDfirst-pass = 2.358. FDrecirculation correlated moderately with per cent diameter stenosis in invasive coronary angiography in lesions classified CAD (r = 0.472, p = 0.001) but not CMD (r = 0.082, p = 0.600).


The ischemic transition region may provide information on pathomechanical composition and severity of myocardial ischemia. FA of this region is feasible and may improve diagnosis compared to traditional noninvasive myocardial perfusion analysis.

Key Points

A novel hypothesis and method is introduced to pathophysiologically characterise myocardial ischemia.

The ischemic transition region appears a meaningful diagnostic target in perfusion imaging.

Fractal analysis may characterise pathomechanical composition and severity of myocardial ischemia.


Fractals Perfusion imaging Myocardial ischemia Coronary artery disease Microvessels 

Abbreviations and Acronyms


Coronary artery disease


Coronary flow reserve


Coronary microvascular dysfunction


Fractal analysis


Fractal dimension


Invasive coronary angiography


Magnetic resonance imaging


Receiver operating characteristics



We thank B. Herwig for assistance with preparation of the article.

The scientific guarantor of this publication is Prof. Dewey. The authors of this manuscript declare relationships with the following companies:

Prof. Dewey has received grant support from the Heisenberg Program of the DFG for a professorship (DE 1361/14-1), the FP7 Program of the European Commission for the randomised multicentre DISCHARGE trial (603266-2, HEALTH-2012.2.4.-2), the European Regional Development Fund (20072013 2/05, 20072013 2/48), the German Heart Foundation/German Foundation of Heart Research (F/23/08, F/27/10), the Joint Program of the German Research Foundation (DFG) and the German Federal Ministry of Education and Research (BMBF) for meta-analyses (01KG1013, 01KG1110, 01KG1110), GE Healthcare, Bracco, Guerbet, and Toshiba Medical Systems.

Prof. Dewey has received lecture fees from Toshiba Medical Systems, Guerbet, Cardiac MR Academy Berlin, and Bayer (Schering-Berlex).

Prof. Dewey is a consultant to Guerbet and one of the principal investigators of multicentre studies (CORE-64 and 320) on coronary CT angiography sponsored by Toshiba Medical Systems. He is also the editor of Coronary CT Angiography and Cardiac CT, both published by Springer, and offers hands-on workshops on cardiovascular imaging ( Prof. Dewey is an associate editor of Radiology and European Radiology.

Institutional master research agreements exist with Siemens Medical Solutions, Philips Medical Systems, and Toshiba Medical Systems. The terms of these arrangements are managed by the legal department of Charité – Universitätsmedizin Berlin. The multicentre CORE-320 study was supported by a grant from Toshiba Medical Systems. The authors state that this work has not received any funding. No complex statistical methods were necessary for this paper. Institutional review board approval was obtained. Written informed consent was obtained from all subjects (patients) in this study. This article does not contain any studies with animals performed by any of the authors. None of the MR imaging substudy subjects have been previously reported. Methodology: prospective, clinical study, performed at one institution. The authors have filed a patent application for the presented invention (10 2015 217 519.7).

Supplementary material

330_2016_4492_MOESM1_ESM.pdf (234 kb)
ESM 1 (PDF 234 kb)


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Copyright information

© European Society of Radiology 2016

Authors and Affiliations

  1. 1.Charité – Universitätsmedizin Berlin, Institut für RadiologieBerlinGermany

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