A Mathematical Model for Estimating Physiological Parameters of Blood Flow through Rotary Blood Pumps

2020 ◽  
Vol 54 (3) ◽  
pp. 163-168
Author(s):  
D. V. Telyshev
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Physiological Parameters ◽  
Blood Pumps ◽  
Flow Through ◽  
Rotary Blood Pumps

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 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.

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.

UNSTEADY RESPONSE OF BLOOD FLOW THROUGH A COUPLE OF IRREGULAR ARTERIAL CONSTRICTIONS TO BODY ACCELERATION

2008 ◽  
Vol 08 (03) ◽  
pp. 395-420 ◽  
Author(s):  
NORZIEHA MUSTAPHA ◽  
SANTABRATA CHAKRAVARTY ◽  
PRASHANTA K. MANDAL ◽  
NORSARAHAIDA AMIN
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Finite Difference ◽  
Stokes Equations ◽  
Computational Study ◽  
Cylindrical Tube ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Body Acceleration ◽  
Flow Through

A two-dimensional (2D) nonlinear mathematical model to study the response of the pulsatile flow of blood through a couple of irregular stenoses influenced by externally imposed periodic body acceleration is developed. The model is 2D and axisymmetric with an outline of the stenosis obtained from the three-dimensional (3D) casting of a mildly stenosed artery. The combined influence of an asymmetric shape and surface irregularities of the constrictions is explored in a computational study of blood flow through arterial stenoses with 48% areal occlusion. The arterial wall is treated as an elastic (moving wall) cylindrical tube having a couple of stenoses in its lumen, while the streaming blood is considered to be Newtonian. Solutions of the time-dependent nonlinear Navier–Stokes equations in the cylindrical coordinate system are obtained using a finite difference method based on the nonuniform and nonstaggered grids. The finite difference approximation helps to estimate the effects of body acceleration on the doubly constricted flow phenomena through several graphical representations quantitatively in order to validate the applicability of the present, improved mathematical model.

scholarly journals Low-flow assessment of current ECMO/ECCO2R rotary blood pumps and the potential effect on hemocompatibility

Critical Care ◽  
2019 ◽  
Vol 23 (1) ◽  
Author(s):  
Sascha Gross-Hardt ◽  
Felix Hesselmann ◽  
Jutta Arens ◽  
Ulrich Steinseifer ◽  
Leen Vercaemst ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Blood Flow ◽  
Shear Stress ◽  
Adverse Effects ◽  
Internal Flow ◽  
Potential Effect ◽  
Low Flow ◽  
Flow Rates ◽  
Blood Pumps ◽  
Rotary Blood Pumps

Abstract Background Extracorporeal carbon dioxide removal (ECCO2R) uses an extracorporeal circuit to directly remove carbon dioxide from the blood either in lieu of mechanical ventilation or in combination with it. While the potential benefits of the technology are leading to increasing use, there are very real risks associated with it. Several studies demonstrated major bleeding and clotting complications, often associated with hemolysis and poorer outcomes in patients receiving ECCO2R. A better understanding of the risks originating specifically from the rotary blood pump component of the circuit is urgently needed. Methods High-resolution computational fluid dynamics was used to calculate the hemodynamics and hemocompatibility of three current rotary blood pumps for various pump flow rates. Results The hydraulic efficiency dramatically decreases to 5–10% if operating at blood flow rates below 1 L/min, the pump internal flow recirculation rate increases 6–12-fold in these flow ranges, and adverse effects are increased due to multiple exposures to high shear stress. The deleterious consequences include a steep increase in hemolysis and destruction of platelets. Conclusions The role of blood pumps in contributing to adverse effects at the lower blood flow rates used during ECCO2R is shown here to be significant. Current rotary blood pumps should be used with caution if operated at blood flow rates below 2 L/min, because of significant and high recirculation, shear stress, and hemolysis. There is a clear and urgent need to design dedicated blood pumps which are optimized for blood flow rates in the range of 0.5–1.5 L/min.

Blood Flow Through Channels and Clearances in Implantable Pumps

2007 ◽  
Author(s):  
Steven W. Day
Keyword(s):  
Medical Devices ◽  
Blood Cells ◽  
Mechanical Design ◽  
Design Criteria ◽  
Design Strategies ◽  
Blood Damage ◽  
Blood Pumps ◽  
Patients With Heart Failure ◽  
Flow Through ◽  
Rotary Blood Pumps

Implantable rotary blood pumps are very effective at supporting patients with heart failure. New designs demonstrate distinct advantages over their predecessor diaphragm type pumps and have generated vast interest in the medical devices community, as demonstrated by hundreds of technical publications and newer commercially available devices. In addition to mechanical design criteria, these pumps share the requirement of moving a relatively large amount of blood through a miniaturized pump without damaging the blood cells. The fluid channels within the impeller are typically 1–3 mm wide and the clearance between the blades, rotating at 2,000–10,000 rpm, and the stationary housing is approximately 100–300μm. This paper gives examples of experimental and numerical methods to characterize the flow field, and a summary of how the flow affects blood cells and design strategies to minimize blood damage.

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