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.

scholarly journals Unsteady solute dispersion in blood rheology with reversible phase exchange at the artery wall

2018 ◽  
Vol 7 (2) ◽  
pp. 750
Author(s):  
D S Sankar ◽  
Nurul Aini Jaafar ◽  
Yazariah Yatim
Keyword(s):  
Blood Flow ◽  
Diffusion Coefficient ◽  
Blood Rheology ◽  
Expansion Method ◽  
Casson Fluid ◽  
Longitudinal Diffusion ◽  
Flowing Fluid ◽  
Derivative Series ◽  
Flow Through ◽  
Reversible Phase

The effect of reversible phase exchange between the flowing fluid and wall tissues of arteries in the unsteady dispersion of solute in blood flow through a narrow artery is analysed mathematically, modelling the blood as Casson fluid. The resulting convective diffusion equation along with the initial and boundary conditions is solved analytically using the derivative series expansion method. The expressions for the negative asymptotic phase exchange, negative asymptotic convection, longitudinal diffusion coefficient and mean concentration are obtained. It is noted that when the solute disperses in blood flow through a narrow artery, the negative exchange coefficient, the negative convection coefficient increase and the longitudinal diffusion coefficient decreases with the increase of the Damköhler number and partition coefficient.

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.

MATHEMATICAL MODELING OF BLOOD FLOW IN A POROUS VESSEL HAVING DOUBLE STENOSES IN THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD

2011 ◽  
Vol 04 (02) ◽  
pp. 207-225 ◽  
Author(s):  
J. C. MISRA ◽  
A. SINHA ◽  
G. C. SHIT
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Mathematical Model ◽  
Blood Flow ◽  
Shear Stress ◽  
External Magnetic Field ◽  
Volumetric Flow Rate ◽  
Hematocrit Level ◽  
Flow Through ◽  
The Mathematical Model

In this paper, a mathematical model has been developed for studying blood flow through a porous vessel with a pair of stenoses under the action of an externally applied magnetic field. Blood flowing through the artery is considered to be Newtonian. This model is consistent with the principles of ferro-hydrodynamics and magnetohydrodynamics. Expressions for the velocity profile, volumetric flow rate, wall shear stress and pressure gradient have been derived analytically under the purview of the model. The above said quantities are computed for a specific set of values of the different parameters involved in the model analysis. This serves as an illustration of the validity of the mathematical model developed here. The results estimated on the basis of the computation are presented graphically. The obtained results for different values of the parameters involved in the problem under consideration, show that the flow is appreciably influenced by the presence of magnetic field and the rise in the hematocrit level.

scholarly journals The Relationship Between Cerebral Blood Flow and the EEG in Normals

1980 ◽  
Vol 7 (3) ◽  
pp. 195-198 ◽  
Author(s):  
Devidas Menon ◽  
Zoltan Koles ◽  
Allen Dobbs
Keyword(s):  
Blood Flow ◽  
Low Frequency ◽  
Weight Percent ◽  
Initial Slope ◽  
Inhalation Technique ◽  
Frequency Components ◽  
Flow Through ◽  
Gamma Rhythms ◽  
The Subject ◽  
The Relationship

SUMMARY:Using the Xel33 inhalation technique, measurements of the blood flow to the left and right parietal and temporal regions of the cerebrum were obtained in 5 healthy individuals while simultaneously recording their EEGs. Up to 3 measurements were obtained from each of the subjects the first while they were mentally at rest and the others while they were engaged in prescribed forms of mental activity. Relationships between the measured blood flow through grey matter, initial slope index, relative grey weight, percent grey flow and power in the delta, delta-theta, alpha, beta and gamma rhythms of the EEG were examined. The results showed that for the subject group as a whole there was a strong correlation between the power present in the low frequency components of EEG and the grey flow and relative grey weight parameters of blood flow. On an individual basis, the observed relationships were highly variable particularly at high flow rates and at low relative grey weights, but became much more definitive at low flows and high weights. The results as they relate to previous work of this kind are discussed.

scholarly journals MATHEMATICAL ANALYSIS OF UNSTEADY MHD BLOOD FLOW THROUGH PARALLEL PLATE CHANNEL WITH HEAT SOURCE

2020 ◽  
Vol 5 (1) ◽  
pp. 40-50
Author(s):  
M.V. Surseh ◽  
P. Sekar
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Numerical Model ◽  
Heat Source ◽  
Prandtl Number ◽  
Mathematical Analysis ◽  
Parallel Plate ◽  
Flow Through ◽  
Fractional Differential ◽  
Plate Channel

A mathematical model of flimsy blood move through parallel plate channel under the action of a connected steady transverse attractive field is proposed. The model is subjected to warm source. Expository articulations are gotten by picking the hub speed; temperature dispersion and the typical speed of the blood rely upon y and t just to change over the arrangement of fractional differential conditions into an arrangement of normal differential conditions under the conditions characterized in our model. The model has been breaking down to discover the impacts of different parameters, for example, Hart-mann number, warm source parameter and Prandtl number on the hub speed, temperature circulation, and the ordinary speed. The numerical arrangements of pivotal speed, temperature conveyances, and typical speed are demonstrated graphically for better comprehension of the issue. Subsequently, the present numerical model gives a straightforward type of pivotal speed, temperature circulation and typical speed of the bloodstream so it will help not just individuals working in the field of Physiological liquid elements yet in addition to the restorative professionals.

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