Morphometry of pig coronary arterial trees

Kassab, Ghassan S.; Rider, C. A.; Tang, Ni; Fung, Y. C.

doi:10.1152/ajpheart.1993.265.1.h350

Cited by 308 publications

(485 citation statements)

References 18 publications

Supporting

Mentioning

469

Contrasting

Order By: Relevance

“…During vascular development, vascular networks remodel into complex networks through dilatation, sprouting, and bridging [5,6,13,15,17]. The large variability in myocardial flow per 100 g tissue that is found indicates variation in anatomical characteristics of the coronary arterial tree [7,16].…”

Section: Introductionmentioning

confidence: 99%

“…Kassab et al [6] and VanBavel and Spaan [15] quantified coronary arterial branching patterns. Kassab et al measured more segments than VanBavel and Spaan, however, Kassab's classification method, based on a modification of Strahler ordering based on diameter (diameter defined Strahler ordering) and a connectivity matrix, was difficult to use for generating trees in our simulation structure.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Relation between branching patterns and perfusion in stochastic generated coronary arterial trees

et al. 2007

View full text Add to dashboard Cite

Biological variation in branching patterns is likely to affect perfusion of tissue. To assess the fundamental consequences of branching characteristics, 50 stochastic asymmetrical coronary trees and one nonstochastic symmetrical branching tree were generated. In the stochastic trees, area growth, A, at branching points was varied: A = random; 1.00; 1.10; 1.13 and 1.15 and symmetry, S, was varied: S = random; 1.00; 0.70; 0.58; 0.50 and 0.48. With random S and A values, a large variation in flow and volume was found, linearly related to the number of vessels in the trees. Large A values resulted in high number of vessels and high flow and volume values, indicating vessels connected in parallel. Lowering symmetry values increased the number of vessels, however, without changing flow, indicating a dominant connection of vessels in series. Both large A and small S values gave more realistic gradual pressure drops compared to the symmetrical non-stochastic branching tree. This study showed large variations in tree realizations, which may reflect real biological variations in tree anatomies. Furthermore, perfusion of tissue clearly depends on the branching rules applied.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Relation between branching patterns and perfusion in stochastic generated coronary arterial trees

et al. 2007

View full text Add to dashboard Cite

show abstract

Section: Blood-tissue Exchange Regionmentioning

confidence: 99%

“…The ratio of RBC to plasma velocity in the blood tissue exchange region was calculated using experimental morphometric data on intramyocardial arterioles and venules from Kassab et al [7], and the reduction in hematocrit as a function of vessel diameter documented by Lipowsky [8], In our model we have represented the blood tissue exchange region as the arterioles and capillaries smaller than 100 µm in diameter because studies by Duling and Berne [9] show significant oxygen loss in the precapillary arterioles. For porcine coronary branching trees of Kassab, flow through the blood tissue exchange region has a relative velocity ratio, V RBC /V pl of 1.2 to 1.9.…”

Section: Blood-tissue Exchange Regionmentioning

confidence: 99%

“…Interregional conductances, defined by the permeability surface area product (PS x ), can be adjusted to accommodate slow diffusional processes. Axial diffusion or dispersion (D x ) smoothes the axial concentration gradients.The ratio of RBC to plasma velocity in the blood tissue exchange region was calculated using experimental morphometric data on intramyocardial arterioles and venules from Kassab et al [7], and the reduction in hematocrit as a function of vessel diameter documented by Lipowsky …”

mentioning

confidence: 99%

See 1 more Smart Citation

Modeling Oxygen and Carbon Dioxide Transport and Exchange Using a Closed Loop Circulatory System

Carlson

Anderson

Raymond

et al.

Advances in Experimental Medicine and Biology

View full text Add to dashboard Cite

The binding and buffering of O 2 and CO 2 in the blood influence their exchange in lung and tissues and their transport through the circulation. To investigate the binding and buffering effects, a model of blood-tissue gas exchange is used. The model accounts for hemoglobin saturation, the simultaneous binding of o 2 CO 2 . H + , 2,3-DPG to hemoglobin, and temperature effects [1,2]. Invertible Hill-type saturation equations facilitate rapid calculation of respiratory gas redistribution among the plasma, red blood cell and issue that occur along the concentration gradients in the lung and in the capillary-tissue exchange regions. These equations are well-suited to analysis of transients in tissue metabolism and partial pressures of inhaled gas. The modeling illustrates that because red blood cell velocities in the flowing blood are higher than plasma velocities after a transient there can be prolonged differences between RBC and plasma oxygen partial pressures. The blood-tissue gas exchange model has been incorporated into a higher level model of the circulatory system plus pulmonary mechanics and gas exchange using the RBC and plasma equations to account for pH and CO 2 buffering in the blood. IntroductionThe exchange of O 2 and CO 2 between the tissue and vasculature depends on adequate delivery and removal of these gases. Oxygen delivery begins with inhalation of ambient air into the airspaces of the lung, transport to the blood from the alveoli, transport through the arterial system, and then exchange between the blood and the peripheral tissue. In a closed circulatory system, venous blood returns to the lungs where CO 2 is expired. Quantifying O 2 and CO 2 transport requires accounting for their solubility in plasma, RBCs and tissue as well as their binding and release from the hemoglobin (Hb) in the RBCs and, in addition, for O 2 only, its binding to myoglobin in tissue. Hemoglobin dissociation curves were developed that described the fraction of O 2 and CO 2 bound to Hb in the steady state as a function of P O2 , P CO2 . pH, 2,3-DPG and temperature [1], These expressions were used to describe the steady state transport of O 2 and CO 2 as well as H + and HCO 3 − in a blood-tissue exchange model with convective transport and axial diffusion in the capillary along with exchange and metabolism in the surrounding tissue region [2].The model presented in this study accounts for ventilatory exchange between outside air and lung alveoli, exchange with alveolar capillary blood, convective transport in arteries, the exchange in tissue capillaries and arterioles, and return of venous blood to the lungs. The model describes transport of O 2 and CO 2 to tissue as influenced by respiration rate, composition of inspired gas, H + and CO 2 production and O 2 consumption in tissue and buffering in the blood. A feature of biophysical interest but modest physiological importance is the persistence of disequilibria between plasma and RBC P O2 due to the higher velocities of RBC than plasma. This difference in velocity ...

show abstract

Morphometry of human coronary arterial trees

1998

View full text Add to dashboard Cite

Background: Some groups, including ours, have been generating arterial tree models using constrained constructive optimization (CCO). Arterial trees have been grown to arbitrary resolution without input of anatomical data. We performed this study to learn about the shortcomings that might have resulted from neglecting the anatomical data in CCO models.Methods: In a total of 450 segments obtained from 4 human cast hearts, the ratio of bifurcating daughter segment radii (0 Ͻ S bif ϭ r(2)/r(1) Ͻ 1) was examined, which corresponds to the split of the total flow of the mother segment. For any complete bifurcation, where the radii of the parent segments and the radii of daughters were known, the area expansion ratio was computed (A exp ϭ [r(1) 2 ϩ r(2) 2 ]/ r(parent) 2 ).Results: The bifurcating ratio was found to be distributed in a nonnormal fashion, with a median of 0.76. The average area expansion ratio A exp , characterizing the change of cross-sectional area of the vasculature from proximal to distal, was 0.93 Ϯ 0.26. The 'rate of branching' (d(i)/(d(0)) was defined by the segment diameter relative to the diameter of the root segment. Averaging the rate of branching over segments within each bifurcation level resulted in a decreasing function of bifurcation level.Conclusions: This article provides new experimental data on branching geometry of coronary arteries (i.e., the trees evaluated in this study are purely delivering rather than conveying). Based on these facts, we suggest that the analytical bifurcation law in CCO might be replaced by the bifurcation rule obeyed on a stochastic basis only. Anat.

show abstract

Morphometry of pig coronary arterial trees

Cited by 308 publications

References 18 publications

Relation between branching patterns and perfusion in stochastic generated coronary arterial trees

Relation between branching patterns and perfusion in stochastic generated coronary arterial trees

Modeling Oxygen and Carbon Dioxide Transport and Exchange Using a Closed Loop Circulatory System

Morphometry of human coronary arterial trees

Contact Info

Product

Resources

About