A One-Dimensional Mathematical Model for Studying the Pulsatile Flow in Microvascular Networks

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Qing Pan ◽  
Ruofan Wang ◽  
Bettina Reglin ◽  
Guolong Cai ◽  
Jing Yan ◽  
...  
Keyword(s):  
Blood Flow ◽  
Pulsatility Index ◽  
Dynamic Models ◽  
Dynamic Properties ◽  
Microvascular Blood Flow ◽  
Integration Scheme ◽  
Microvascular Networks ◽  
Mean Values ◽  
One Dimensional ◽  
Rat Mesentery

Techniques that model microvascular hemodynamics have been developed for decades. While the physiological significance of pressure pulsatility is acknowledged, most of the microcirculatory models use steady flow approaches. To theoretically study the extent and transmission of pulsatility in microcirculation, dynamic models need to be developed. In this paper, we present a one-dimensional model to describe the dynamic behavior of microvascular blood flow. The model is applied to a microvascular network from a rat mesentery. Intravital microscopy was used to record the morphology and flow velocities in individual vessel segments, and boundaries are defined according to the experimental data. The system of governing equations constituting the model is solved numerically using the discontinuous Galerkin method. An implicit integration scheme is adopted to increase computing efficiency. The model allows the simulation of the dynamic properties of blood flow in microcirculatory networks, including the pressure pulsatility (quantified by a pulsatility index) and pulse wave velocity (PWV). From the main input arteriole to the main output venule, the pulsatility index decreases by 66.7%. PWV obtained along arterioles declines with decreasing diameters, with mean values of 77.16, 25.31, and 8.30 cm/s for diameters of 26.84, 17.46, and 13.33 μm, respectively. These results suggest that the 1D model developed is able to simulate the characteristics of pressure pulsatility and wave propagation in complex microvascular networks.

Microvascular blood flow resistance: role of endothelial surface layer

1997 ◽  
Vol 273 (5) ◽  
pp. H2272-H2279 ◽  
Author(s):  
Axel R. Pries ◽  
Timothy W. Secomb ◽  
Helfried Jacobs ◽  
Markus Sperandio ◽  
Kurt Osterloh ◽  
...  
Keyword(s):  
Blood Flow ◽  
Flow Resistance ◽  
Capillary Flow ◽  
Vessel Diameter ◽  
Low Flow ◽  
Microvascular Blood Flow ◽  
Microvascular Networks ◽  
Flow Rates ◽  
Rat Mesentery ◽  
Endothelial Surface

Observations of blood flow in microvascular networks have shown that the resistance to blood flow is about twice that expected from studies using narrow glass tubes. The goal of the present study was to test the hypothesis that a macromolecular layer (glycocalyx) lining the endothelial surface contributes to blood flow resistance. Changes in flow resistance in microvascular networks of the rat mesentery were observed with microinfusion of enzymes targeted at oligosaccharide side chains in the glycocalyx. Infusion of heparinase resulted in a sustained decrease in estimated flow resistance of 14–21%, hydrodynamically equivalent to a uniform increase of vessel diameter by ∼1 μm. Infusion of neuraminidase led to accumulation of platelets on the endothelium and doubled flow resistance. Additional experiments in untreated vascular networks in which microvascular blood flow was reduced by partial microocclusion of the feeding arteriole showed a substantial increase of flow resistance at low flow rates (average capillary flow velocities < 100 diameters/s). These observations indicate that the glycocalyx has significant hemodynamic relevance that may increase at low flow rates, possibly because of a shear-dependent variation in glycocalyx thickness.

Heat-Sterllized Pd Fluid Blocks Leukocyte Adhesion and Increases Flow Velocity in Rat Peritoneal Venules

1996 ◽  
Vol 16 (1_suppl) ◽  
pp. 137-141 ◽  
Author(s):  
Peter Jonasson ◽  
Ulf Bagge ◽  
Anders Wieslander ◽  
Magnus Braide
Keyword(s):  
Cell Culture ◽  
Blood Flow ◽  
Flow Velocity ◽  
Bacterial Infections ◽  
Degradation Products ◽  
Leukocyte Adhesion ◽  
Microvascular Blood Flow ◽  
Leukocyte Rolling ◽  
Rat Mesentery ◽  
Rolling Leukocytes

Data from cell culture experiments indicate that heat sterilization of peritoneal dialysis (PD) fluids produces cytotoxic glucose degradation products. The present vital microscopic study investigated the effects of different sterilization methods on the biocompatibility of PD fluids. Thus, heat-sterilized (commercially obtained and experimentally produced) and filter-sterilized PD fluids (pH = 5.30 5.40; 1.5% glucose) were compared with Tyrode buffer, with respect to the effects on microvascular blood flow velocity and leukocyte adhesion in the rat mesentery. Exteriorization of the mesentery produced a mild inflammation, known from the literature and characterized by the adhesive rolling of leukocytes along venular walls. Superfusion of the mesentery with filter-sterilized PD fluid had no significant effects on leukocyte rolling or flow velocity in venules 25 40 μm in diameter compared with buffer superfusion. Heat-sterilized PD fluid decreased the concentration of rolling leukocytes and increased flow velocity significantly, as compared with buffer and filter-sterilized PD fluid. The results indicate that heat sterilization of PD fluids produces substances that interact with microvascular tone and leukocyte-endothelial adhesion, which hypothetically could impair the acute, granulocyte-mediated defense against bacterial infections.

scholarly journals Microvascular Blood Flow and Oxygenation in the Rat Mesentery during Hemorrhagic Hypotension (HH)

2007 ◽  
Vol 21 (6) ◽  
Author(s):  
Luciana N Torres ◽  
Ivo P Torres Filho ◽  
Roland N Pittman ◽  
Aleksander S Golub
Keyword(s):  
Blood Flow ◽  
Microvascular Blood Flow ◽  
Hemorrhagic Hypotension ◽  
Rat Mesentery

Relationship between structural and hemodynamic heterogeneity in microvascular networks

1996 ◽  
Vol 270 (2) ◽  
pp. H545-H553 ◽  
Author(s):  
A. R. Pries ◽  
T. W. Secomb ◽  
P. Gaehtgens
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Topological Structure ◽  
Blood Rheology ◽  
Experimental Information ◽  
Microvascular Networks ◽  
Rat Mesentery ◽  
Hemodynamic Characteristics ◽  
Flow Through ◽  
The Relationship

The relationship between structural and hemodynamic heterogeneity of microvascular networks is examined by analyzing the effects of topological and geometric irregularities on network hemodynamics. Microscopic observations of a network in the rat mesentery provided data on length, diameter, and interconnection of all 913 segments. Two idealized network structures were derived from the observed network. In one, the topological structure was made symmetric; in another a further idealization was made by assigning equal lengths and diameters to all segments with topologically equivalent positions in the network. Blood flow through these three networks was simulated with a mathematical model based on experimental information on blood rheology. Overall network conductance and pressure distribution within the network were found to depend strongly on topological heterogeneity and less on geometric heterogeneity. In contrast, mean capillary hematocrit was sensitive to geometric heterogeneity but not to topological heterogeneity. Geometric and topological heterogeneity contributed equally to the dispersion of arteriovenous transit time. Hemodynamic characteristics of heterogeneous microvascular networks can only be adequately described if both topological and geometric variability in network structure are taken into account.

A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree

2007 ◽  
Vol 292 (6) ◽  
pp. H2623-H2633 ◽  
Author(s):  
Yunlong Huo ◽  
Ghassan S. Kassab
Keyword(s):  
Blood Flow ◽  
Large Scale ◽  
Stokes Equations ◽  
Energy Losses ◽  
Type Model ◽  
Pulsatile Blood Flow ◽  
Arterial Tree ◽  
Main Trunk ◽  
Mean Values ◽  
One Dimensional

Using a frequency-domain Womersley-type model, we previously simulated pulsatile blood flow throughout the coronary arterial tree. Although this model represents a good approximation for the smaller vessels, it does not take into account the nonlinear convective energy losses in larger vessels. Here, using Womersley's theory, we present a hybrid model that considers the nonlinear effects for the larger epicardial arteries while simulating the distal vessels (down to the 1st capillary segments) with the use of Womersley's Theory. The main trunk and primary branches were discretized and modeled with one-dimensional Navier-Stokes equations, while the smaller-diameter vessels were treated as Womersley-type vessels. Energy losses associated with vessel bifurcations were incorporated in the present analysis. The formulation enables prediction of impedance and pressure and pulsatile flow distribution throughout the entire coronary arterial tree down to the first capillary segments in the arrested, vasodilated state. We found that the nonlinear convective term is negligible and the loss of energy at a bifurcation is small in the larger epicardial vessels of an arrested heart. Furthermore, we found that the flow waves along the trunk or at the primary branches tend to scale (normalized with respect to their mean values) to a single curve, except for a small phase angle difference. Finally, the model predictions for the inlet pressure and flow waves are in excellent agreement with previously published experimental results. This hybrid one-dimensional/Womersley model is an efficient approach that captures the essence of the hemodynamics of a complex large-scale vascular network. The present model has numerous applications to understanding the dynamics of coronary circulation.

1715-P: Impaired Postprandial Adipose Tissue Microvascular Blood Flow in Healthy People with a Family History of Type 2 Diabetes

Diabetes ◽  
2020 ◽  
Vol 69 (Supplement 1) ◽  
pp. 1715-P
Author(s):  
KATHERINE ROBERTS-THOMSON ◽  
RYAN D. RUSSELL ◽  
DONGHUA HU ◽  
TIMOTHY M. GREENAWAY ◽  
ANDREW C. BETIK ◽  
...  
Keyword(s):  
Type 2 Diabetes ◽  
Blood Flow ◽  
Adipose Tissue ◽  
Family History ◽  
Healthy People ◽  
Microvascular Blood Flow ◽  
History Of
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