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The Fractal Nature of Myocardial Blood Flow Emerges from a Whole-Organ Model of Arterial Network
Abstract
Mammalian hearts exhibit a heterogeneous spatial distribution of blood flows, but flows in near-neighbor regions correlate strongly. Also, tracer <sup>15</sup>O-water washout after injection into the inflow shows a straight log-log relationship between outflow concentration and time. To uncover the role of the arterial network in governing these phenomena, morphometric data were used to construct a mathematical model of the coronary arterial network of the pig heart. The model arterial network, built in a simplified three-dimensional representation of tissue geometry, satisfies the statistical morphometric data on segment lengths, diameters and connectivities reported for real arterial networks. The model uses an avoidance algorithm to position successive vascular segments in the network. Assuming flows through the network to be steady, the calculated regional flow distributions showed (1) the degree of heterogeneity observed in normal hearts; (2) spatial self-similarity in local flows; (3) fractal spatial correlations, all with the same fractal dimension found in animal studies; (4) pressure distributions along the model arterial network comparable to those observed in nature, with maximal resistances in small vessels. In addition, the washout of intravascular tracer showed tails with power law slopes that fitted h( t) = at<sup>–α–1</sup> with the exponents α = 2 for the reconstructed networks compared with those from experimental outflow concentration-time curves with α = 2.1 ± 0.3. Thus, we concluded that the fractal nature of spatial flow distribution in the heart, and of temporal intravascular washout, are explicable in terms of the morphometry of the coronary network.
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Most cited references 2
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Power-Law Kinetics of Tracer Washout from Physiological Systems
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25742 J Vasc Res 2000;37:282–296Copyright: All rights reserved. No part of this publication may be translated into other languages, reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, microcopying, or by any information storage and retrieval system, without permission in writing from the publisher. Drug Dosage: The authors and the publisher have exerted every effort to ensure that drug selection and dosage set forth in this text are in accord with current recommendations and practice at the time of publication. However, in view of ongoing research, changes in government regulations, and the constant flow of information relating to drug therapy and drug reactions, the reader is urged to check the package insert for each drug for any changes in indications and dosage and for added warnings and precautions. This is particularly important when the recommended agent is a new and/or infrequently employed drug. Disclaimer: The statements, opinions and data contained in this publication are solely those of the individual authors and contributors and not of the publishers and the editor(s). The appearance of advertisements or/and product references in the publication is not a warranty, endorsement, or approval of the products or services advertised or of their effectiveness, quality or safety. The publisher and the editor(s) disclaim responsibility for any injury to persons or property resulting from any ideas, methods, instructions or products referred to in the content or advertisements.