Morphometry of Cat’s Pulmonary Arterial Tree

Yen, R. T.; Zhuang, Fengyuan; Fung, Y. C.; Ho, Hirzel; Tremer, Herta M.; Sobin, Sidney S.

doi:10.1115/1.3138469

Cited by 62 publications

(53 citation statements)

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“…Thus one unique aspect of this method for constructing an asymmetrical tree is that the tree can be constructed with this morphometric relationship predetermined. 1), versus the number of vessels in an order, N(j), which is a form of the data available from several morphometric studies of pulmonary arterial trees (9,17,22,39,44), is depicted (triangles on dashed lines in Figs. 1-3).…”

Section: Methodsmentioning

confidence: 99%

Branching exponent heterogeneity and wall shear stress distribution in vascular trees

Karau¹,

Krenz

Dawson

2001

American Journal of Physiology-Heart and Circulatory Physiology

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is the parent vessel diameter and D 2 and D 3 are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance of uniform shear stress. A mean z of 3 has been considered confirmation of such a control mechanism. The objective of the present study was to evaluate the consequences of a heterogeneous distribution of z values about the mean with regard to this uniform shear stress hypothesis. Simulations were carried out on model structures otherwise conforming to the criteria consistent with uniform shear stress when z ϭ 3 but with varying distributions of z. The result was that when there was significant heterogeneity in z approaching that found in a real arterial tree, the coefficient of variation in shear stress was comparable to the coefficient of variation in z and nearly independent of the mean value of z. A systematic increase in mean shear stress with decreasing vessel diameter was one component of the variation in shear stress even when the mean z ϭ 3. The conclusion is that the influence of shear stress in determining vessel diameters is not, per se, manifested in a mean value of z. In a vascular tree having a heterogeneous distribution in z values, a particular mean value of z (e.g., z ϭ 3) apparently has little bearing on the uniform shear stress hypothesis. mathematical model; pulmonary arterial tree; vascular morphometry; Murray's Law; complexity SHEAR STRESS on the vascular endothelial surface is a physiologically transducible force that influences vascular function in several ways. In the short term, shear stress affects vessel tone, and, in the longer term, it affects the vascular architecture generated during the vasculo-and angiogenesis and vascular remodeling associated with vascular adaptation and disease (3,4,7,20,21,33). Thus there has been considerable interest in the concept that the form of a vascular network reflects shear stress optimization operating during the network construction and maintenance. The complexity of vascular tree structures, in terms of both the branching network and the local contour of the vessel wall (1, 4), contributes to the difficulty in evaluating this concept. One simplification that has been used as a reference point in such evaluations is "Murray's Law," which provides a vascular design criterion for minimizing the power required to operate a distribution network constructed of cylindrical vessels with convective transport via Poiseuille flow (34). According to Murray's Law, power is minimized if flow throughout the network is proportional to the cube of the vessel diameters. This is also a condition that can produce uniform shear stress throughout the network. Thus shear stress control over vessel diameter would appear to be a means of developing and/or maintaining optimal vascular structure (23,28,29,38,45,47). One implication of Murray's Law is that, for a bif...

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Section: Methodsmentioning

confidence: 99%

Branching exponent heterogeneity and wall shear stress distribution in vascular trees

Karau¹,

Krenz

Dawson

2001

American Journal of Physiology-Heart and Circulatory Physiology

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“…11. 6,72,73,75,76 Recently, Burrowes et al 77 have begun to merge measurements providing detailed descriptions of the geometry of the large vessels obtained from volumetric CT, with statistically based models of the small-scale vascular structure. These studies have contributed significantly to the understanding of the flow distribution within the pulmonary circulation.…”

Section: Functional Implicationsmentioning

confidence: 99%

“…11 Various mathematical modeling studies have focused on understanding the impact of arterial network properties on the control of vascular pressure and flow in the pulmonary circulation. 6,[72][73]74 Many of these studies have relied on morphometric data for the pulmonary arterial tree, i.e., the number, length, and diameter of pulmonary vessels and their connectivity, that exist in varying detail as statistical extrapolations of actual morphometric measurements, e.g., Fig. 11.…”

Section: Functional Implicationsmentioning

confidence: 99%

“…80 Under network topology assumptions involving the number and connective structure of the various size resistors (that is, the morphometric data), and ignoring additional losses due to the disruption of stream lines at bifurcations, the pulmonary vascular pressure, resistance, and flow computations translate into familiar Kirchoff current and voltage law calculations. 6,7,[72][73]74,81 Biomechanical properties of pulmonary arteries are thought to play an important role in determining the vascular pressure distribution within the lung. The extension of the concept of vascular resistance, (19), to idealized distensible vessels is discussed in Fung [80].…”

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confidence: 99%

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Lung Circulation Modeling: Status and Prospect

Clough

Audi²,

Molthen³

et al. 2006

Proc. IEEE

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Mathematical modeling has been used to interpret anatomical and physiological data obtained from metabolic and hemodynamic studies aimed at investigating structure-function relationships in the vasculature of the lung, and how these relationships are affected by lung injury and disease. The indicator dilution method was used to study the activity of redox processes within the lung. A steadystate model of the data was constructed and used to show that pulmonary endothelial cells may play an important role in reducing redox active compounds and that those reduction rates can be altered with oxidative stress induced by exposure to high oxygen environments. In addition, a morphometric model NOT THE PUBLISHED VERSION; this is the author's final, peer-reviewed manuscript. The published version may be accessed by following the link in the citation at the bottom of the page. 2 of the pulmonary vasculature was described and used to detect, describe,and predict changes in vascular morphology that occur in response to chronic exposure to low-oxygen environments, a common model of pulmonary hypertension. Finally, the model was used to construct simulated circulatory networks designed to aid in evaluation of competing hypotheses regarding the relative contribution of various morphological and biomechanical changes observed with hypoxia. These examples illustrate the role of mathematical modeling in the integration of the emerging metabolic, hemodynamic, and morphometric databases. Proceedings of the IEEE,

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“…Morphometric data have generally been obtained from plastic corrosion casts [60,63,66,67,68,76,79,82], and data obtained using imaging methods are becoming available [62,70,75]. The data consist of measurements of diameters lengths and numbers of vessels, and are commonly summarized by binning according to some ordering scheme [4,66,68].…”

Section: Morphometrymentioning

confidence: 99%

Fluctuations, Noise and Scaling in the Cardio-Pulmonary System

et al. 2003

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The structure and the functioning of cardio-pulmonary system is complex and statistical physics appear to be suitable for their characterization. In this review, we examine scaling in cardio-pulmonary physiology. The focus will be on the interpretation of scaling behaviors and their relation to structure-function in the normal and diseased cardio-pulmonary system. First, we overview fluctuations and scaling in respiratory rate variability in terms of a neural network model. Next, we analyze fluctuations in human heartbeat dynamics under healthy and pathologic conditions using wavelets and multifractal approaches. We then discuss avalanche behavior of airway openings as well as scaling behavior of crackling sound generated during the process of airway openings. We also examine the relationship between the observed scaling properties and the design features of the pulmonary vascular tree. Finally, we show how the network failure of lung tissue structure leads to emphysema, a leading cause of respiratory disability and death worldwide.

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Morphometry of Cat’s Pulmonary Arterial Tree

Cited by 62 publications

References 0 publications

Branching exponent heterogeneity and wall shear stress distribution in vascular trees

Branching exponent heterogeneity and wall shear stress distribution in vascular trees

Lung Circulation Modeling: Status and Prospect

Fluctuations, Noise and Scaling in the Cardio-Pulmonary System

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