Fractal Branchings: The Basis of Myocardial Flow Heterogeneities?

Bassingthwaighte, James B.; Beek, Hans van; King, Richard B.

doi:10.1111/j.1749-6632.1990.tb15103.x

Cited by 63 publications

(45 citation statements)

References 12 publications

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“…First, two fundamentally constructed structure-structure scaling laws, volume-diameter (equation (2.1)) and resistance (equation (C 2)), were validated for measured morphometric vascular trees (here and in the study of Huo & Kassab [37]). The premise for the derivation of these scaling laws is that morphometric vascular trees are fractal-like, which obey self-similarity of form, as confirmed by experimental observations from earlier studies [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] (i.e. similar branching ratios in each generation).…”

Section: Physiological Basis Of Scaling Laws In a Vascular Treementioning

confidence: 62%

Intraspecific scaling laws of vascular trees

Huo

Kassab

2011

J. R. Soc. Interface.

124

116

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A fundamental physics-based derivation of intraspecific scaling laws of vascular trees has not been previously realized. Here, we provide such a theoretical derivation for the volumediameter and flow-length scaling laws of intraspecific vascular trees. In conjunction with the minimum energy hypothesis, this formulation also results in diameter -length, flow -diameter and flow-volume scaling laws. The intraspecific scaling predicts the volume -diameter power relation with a theoretical exponent of 3, which is validated by the experimental measurements for the three major coronary arterial trees in swine (where a least-squares fit of these measurements has exponents of 2.96, 3 and 2.98 for the left anterior descending artery, left circumflex artery and right coronary artery trees, respectively). This scaling law as well as others agrees very well with the measured morphometric data of vascular trees in various other organs and species. This study is fundamental to the understanding of morphological and haemodynamic features in a biological vascular tree and has implications for vascular disease.

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Section: Physiological Basis Of Scaling Laws In a Vascular Treementioning

confidence: 62%

Intraspecific scaling laws of vascular trees

Huo

Kassab

2011

J. R. Soc. Interface.

124

116

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“…Studies using artificial networks of vessels based on the known pattern of vessel branching indicate that this self-similarity arises from the dichotomous branching of vessels according to simple recursion rules. 21,22 Heterogeneity of flow has important implications for the measurement of flows in the myocardium. The response of the whole heart to a submaximal perturbation (such as hypoxia) can be misleading, because it will include both responding and nonresponding regions; reliable correlations can be drawn only from the use of sufficiently small tissue samples.23 Clinically, this represents a problem for defining an adequate average flow, eg, determining the adequacy of coronary flow in a patient from a spatially averaged sample.…”

Section: Heterogeneity In the Coronary Microcirculationmentioning

confidence: 99%

Coronary Microcirculation in Health and Disease

Chilian¹

1997

Circulation

206

138

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This article summarizes a 2-day workshop on the coronary microcirculation held in Bethesda, Md, in September 1994 and sponsored by the National Heart, Lung, and Blood Institute of the National Institutes of Health. The workshop explored a variety of topics pertaining to coronary microvascular physiology and pathophysiology. The latest methodologies that are being used to investigate the coronary microvasculature, including endoscopic microscopy of the intramural coronary microvasculature and micro-x-ray computerized tomography, were discussed. The most recent advances in the regulation of the coronary microcirculation-for example, myogenic and flow-dependent responses, K ATP channels, and regional heterogeneity-were reported. The workshop touched on the relation of the microcirculation to clinically important conditions and offered recommendations for future research in this important area. Comparisons are made to recent advances in the peripheral circulation and current gaps in our knowledge concerning the coronary microcirculation. In recent years, research on the coronary microcirculation has made substantial advances, in part as a result of investigations in the peripheral microcirculation but also because of the application of unique methodologies. This research is providing new ways to investigate abnormalities of myocardial perfusion, an area of inquiry that until recently has been limited to examination of coronary pressure-flow relationships.

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“…The model included multiple, parallel flow pathways, identical except for their flow, to describe the effects of regional flow heterogeneity (19). The distribution of flow in the multiple pathways of the model was based on a fractional extrapolation of the regional flow heterogeneity observed by using microspheres in the hearts of normal sheep and baboons (20). The observed input in the left ventricular blood pool, C in (t), is dispersed and delayed during transit through large conduit vessels with transport function h LV , so that the input to the ROI is given by C LV (t) = C in (t) * h LV , where the asterisk denotes convolution.…”

mentioning

confidence: 99%

Regional myocardial blood volume and flow: First‐pass MR imaging with polylysine‐Gd‐DTPA

Wilke

Kroll

Merkle

et al. 1995

Magnetic Resonance Imaging

132

104

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The authors investigated the utility of an intravascular magnetic resonance (MR) contrast agent, poly-L-lysine-gadolinium diethylenetriaminepentaacetic acid (DTPA), for differentiating acutely ischemic from normally perfused myocardium with first-pass MR imaging. Hypoperfused regions, identified with microspheres, on the first-pass images displayed significantly decreased signal intensities compared with normally perfused myocardium (P < .0007). Estimates of regional myocardial blood content, obtained by measuring the ratio of areas under the signal intensityversus-time curves in tissue regions and the left ventricular chamber, averaged 0.12 mL/g ± 0.04 (n = 35), compared with a value of 0.11 mL/g ± 0.05 measured with radiolabeled albumin in the same tissue regions. To obtain MR estimates of regional myocardial blood flow, in situ calibration curves were used to transform first-pass intensity-time curves into content-time curves for analysis with a multiple-pathway, axially distributed model. Flow estimates, obtained by automated parameter optimization, averaged 1.2 mL/min/g ± 0.5 [n = 29), compared with 1.3 mL/min/g ± 0.3 obtained with tracer microspheres in the same tissue specimens at the same time. The results represent a combination of T1-weighted first-pass imaging, intravascular relaxation agents, and a spatially distributed perfusion model to obtain absolute regional myocardial blood flow and volume. Index termsContrast agent, blood pool; Contrast enhancement; Coronary vessels, diseases, 54.76; Heart, flow dynamics; Heart, MR, 51.12143; Model, mathematical; Myocardium, blood supply, 511.12143; Myocardium, MR, 511.12143 NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author ManuscriptA growing body of evidence supports the feasibility of evaluating myocardial perfusion with magnetic resonance (MR) imaging with contrast agents. A variety of intravascular and extracellular MR contrast agents have been studied for delineation of infarcted myocardium (1-3) and for identification of acutely ischemic and reperfused cardiac muscle (4,5). The first-pass MR imaging technique with the extracellular contrast agent gadolinium diethylenetriaminepentaacetic acid (DTPA) has been used to assess myocardial perfusion in patients at rest (6,7) and during pharmacologic stress (8,9). Although experimental (10) and patient studies have demonstrated the suitability of extracellular contrast agents for detecting hypoperfused myocardium, such agents are inherently disadvantageous for flow quantification because they are not confined to a single volume compartment within the tissue. Consequently, first-pass kinetics of an extracellular agent are determined not only by blood flow but by the intravascular and interstitial distribution volumes and by permeability across the capillary wall. This exchange between the vascular and interstitial compartments greatly complicates quantification of tissue blood flow unless it is either very fast or slow compared with flow rates (11).The objective of the present study was to...

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Fractal Branchings: The Basis of Myocardial Flow Heterogeneities?

Cited by 63 publications

References 12 publications

Intraspecific scaling laws of vascular trees

Intraspecific scaling laws of vascular trees

Coronary Microcirculation in Health and Disease

Regional myocardial blood volume and flow: First‐pass MR imaging with polylysine‐Gd‐DTPA

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