Analysis of vascular pattern and dimensions in arteriolar networks of the retractor muscle in young hamsters

Ellsworth, Mary L.; Liu, Alice J.; Dawant, Benoît M.; Popel, Aleksander S.; Pittman, Roland N.

doi:10.1016/0026-2862(87)90051-3

Cited by 39 publications

(32 citation statements)

References 17 publications

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“…5A-D) are compatible with those in real microvascular networks (Clark, 1991;Ellsworth et al, 1987;Honda and Yoshizato, 1997;Kurz et al, 1995;Less et al, 1997;Lichtenbeld et al, 1996;Lipowsky et al, 1978;Lipowsky and Zweifach, 1974;Pries et al, 1990Pries et al, , 1997Renkin, 1988). Moreover, in our random data samples, we find high pressure and low shear stress in and near the capillary region, because some branches may be (temporarily) not perfused -a situation that frequently occurs in living systems.…”

Section: Hemodynamics and Biomass Distributionsupporting

confidence: 87%

Structural and biophysical simulation of angiogenesis and vascular remodeling

Gödde

Kurz

2001

Developmental Dynamics

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The purpose of this report is to introduce a new computer model for the simulation of microvascular growth and remodeling into arteries and veins that imitates angiogenesis and blood flow in real vascular plexuses. A C؉؉ computer program was developed based on geometric and biophysical initial and boundary conditions. Geometry was defined on a two-dimensional isometric grid by using defined sources and drains and elementary bifurcations that were able to proliferate or to regress under the influence of random and deterministic processes. Biophysics was defined by pressure, flow, and velocity distributions in the network by using the nodal-admittance-matrix-method, and accounting for hemodynamic peculiarities like Fahraeus-Lindqvist effect and exchange with extravascular tissue. The proposed model is the first to simulate interdigitation between the terminal branches of arterial and venous trees. This was achieved by inclusion of vessel regression and anastomosis in the capillary plexus and by remodeling in dependence from hemodynamics. The choice of regulatory properties influences the resulting vascular patterns. The model predicts interdigitating arteriovenous patterning if shear stress-dependent but not pressure-dependent remodeling was applied. By approximating the variability of natural vascular patterns, we hope to better understand homogeneity of transport, spatial distribution of hemodynamic properties and biomass allocation to the vascular wall or blood during development, or during evolution of circulatory systems.

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Section: Hemodynamics and Biomass Distributionsupporting

confidence: 87%

Structural and biophysical simulation of angiogenesis and vascular remodeling

Gödde

Kurz

2001

Developmental Dynamics

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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: 71%

“…Similarly, vascular trees of many organs down to the pre-capillary vessels were also used to verify the scaling power-laws, which are constructed in the Strahler system [30], based on the available literature [6 -19]. The pulmonary arterial tree of rats was obtained from the study of Jiang et al [7]; the pulmonary arterial/ venous trees of cats from Yen et al [8,9]; the pulmonary venous trees of dogs from Gan et al [10]; the pulmonary arterial trees of humans from Singhal et al [11,12] and Huang et al [13]; the pulmonary venous trees of humans from Horsfield & Gordon [14] and Huang et al [13]; the skin muscle arterial tree of hamsters from Bertuglia et al [15]; the retractor muscle arterial tree of hamsters from Ellsworth et al [16]; the mesentery arterial tree of rats from Ley et al [17]; the sartorius muscle arterial tree of cats from Koller et al [18]; the bulbular conjunctiva arterial/venous trees of humans and the omentum arterial tree of rabbits from Fenton & Zweifach [19].…”

Section: Morphometric Vascular Treesmentioning

confidence: 99%

“…The vascular [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], bronchial [20,21] and botanical trees [22][23][24][25] have been found to have fractal-like features. For interspecific scaling, based on three major assumptions in a fractal-like cardiovascular system (i) area-preservation for branching patterns of vessel diameter greater than 1 mm and cubed-law for smaller vessels as well as space-filling branching pattern; (ii) size-invariant capillaries; and (iii) minimum energy loss, West et al [26] proposed a mathematical model referred to as the WBE (West, Brown, and Enquist) model to support the allometric 3/4 scaling law of metabolism.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Quantitative description of the tree-like morphology of distal arteriolar networks shows that vessel number, and their diameter and length follow power-law relationships (Ellsworth et al 1987, Koller et al 1987. The implications are that the networks can be described as fractal structures, i.e., they exhibit self-similarity.…”

Section: Microvascular Architecture and Organizationmentioning

confidence: 99%

Microcirculation and Hemorheology

Popel

Johnson

2005

Annu. Rev. Fluid Mech.

707

641

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Major experimental and theoretical studies on microcirculation and hemorheology are reviewed with the focus on mechanics of blood flow and the vascular wall. Flow of the blood formed elements (red blood cells (RBCs), white blood cells or leukocytes (WBCs) and platelets) in individual arterioles, capillaries and venules, and in microvascular networks is discussed. Mechanical and rheological properties of the formed elements and their interactions with the vascular wall are reviewed. Short-term and long-term regulation of the microvasculature is discussed; the modes of regulation include metabolic, myogenic and shear-stress-dependent mechanisms as well as vascular adaptation such as angiogenesis and vascular remodeling.

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Analysis of vascular pattern and dimensions in arteriolar networks of the retractor muscle in young hamsters

Cited by 39 publications

References 17 publications

Structural and biophysical simulation of angiogenesis and vascular remodeling

Structural and biophysical simulation of angiogenesis and vascular remodeling

Intraspecific scaling laws of vascular trees

Microcirculation and Hemorheology

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