T. Bodnár

On the shear-thinning and viscoelastic effects of blood flow under various flow rates

The aim of this paper is to describe and discuss the results of numerical comparative study performed in order to demonstrate and quantify some of the most relevant non-Newtonian characteristics of blood flow in medium-sized blood vessels, namely its shear-thinning and viscoelastic behavior.The models studied in this work are the classical Newtonian and Oldroyd-B models, as well as their generalized (shear-thinning) modifications. Numerical tests are performed on three-dimensional geometries, namely an idealized axisymmetric stenosis and a realistic stenosed carotid bifurcation reconstructed from medical images. The numerical solution of the system of governing equations is obtained by a finite-volume method on a structured grid. Model sensitivity tests are achieved with respect to the characteristic flow rate to evaluate its impact on the observed non-Newtonian effects.

Numerical simulation of the coagulation dynamics of blood

The process of platelet activation and blood coagulation is quite complex and not yet completely understood. Recently, a phenomenological meaningful model of blood coagulation and clot formation in flowing blood that extends existing models to integrate biochemical, physiological and rheological factors, has been developed. The aim of this paper is to present results from a computational study of a simplified version of this coupled fluid-biochemistry model. A generalized Newtonian model with shear-thinning viscosity has been adopted to describe the flow of blood. To simulate the biochemical changes and transport of various enzymes, proteins and platelets involved in the coagulation process, a set of coupled advection–diffusion–reaction equations is used. Three-dimensional numerical simulations are carried out for the whole model in a straight vessel with circular cross-section, using a finite volume semi-discretization in space, on structured grids, and a multistage scheme for time integration. Clot formation and growth are investigated in the vicinity of an injured region of the vessel wall. These are preliminary results aimed at showing the validation of the model and of the numerical code.

Numerical Study of the Significance of the Non-Newtonian Nature of Blood in Steady Flow Through a Stenosed Vessel

In this paper we present a comparative numerical study of non-Newtonian shear-thinning and viscoelastic blood flow models through an idealized stenosis. Three-dimensional numerical simulations are performed using a finite volume semidiscretization in space, on structured grids, and a multistage Runge-Kutta scheme for time integration, to investigate the influence of combined effects of inertia, viscosity and viscoelasticity in this particular geometry. This work lays the foundation for future applications to pulsatile flows in stenosed vessels using constitutive models capturing the rheological response of blood, under relevant physiological conditions.

Blood coagulation dynamics: mathematical modeling and stability results.

The hemostatic system is a highly complex multicomponent biosystem that under normal physiologic conditions maintains the fluidity of blood. Coagulation is initiated in response to endothelial surface vascular injury or certain biochemical stimuli, by the exposure of plasma to Tissue Factor (TF), that activates platelets and the coagulation cascade, inducing clot formation, growth and lysis. In recent years considerable advances have contributed to understand this highly complex process and some mathematical and numerical models have been developed. However, mathematical models that are both rigorous and comprehensive in terms of meaningful experimental data, are not available yet. In this paper a mathematical model of coagulation and fibrinolysis in flowing blood that integrates biochemical, physiologic and rheological factors, is revisited. Three-dimensional numerical simulations are performed in an idealized stenosed blood vessel where clot formation and growth are initialized through appropriate boundary conditions on a prescribed region of the vessel wall. Stability results are obtained for a simplified version of the clot model in quiescent plasma, involving some of the most relevant enzymatic reactions that follow Michaelis-Menten kinetics, and having a continuum of equilibria.

Spatio-Temporal Modelling of Dust Transport over Surface Mining Areas and Neighbouring Residential Zones

Projects focusing on spatio-temporal modelling of the living environment need to manage a wide range of terrain measurements, existing spatial data, time series, results of spatial analysis and inputs/outputs from numerical simulations. Thus, GISs are often used to manage data from remote sensors, to provide advanced spatial analysis and to integrate numerical models. In order to demonstrate the integration of spatial data, time series and methods in the framework of the GIS, we present a case study focused on the modelling of dust transport over a surface coal mining area, exploring spatial data from 3D laser scanners, GPS measurements, aerial images, time series of meteorological observations, inputs/outputs form numerical models and existing geographic resources. To achieve this, digital terrain models, layers including GPS thematic mapping, and scenes with simulation of wind flows are created to visualize and interpret coal dust transport over the mine area and a neighbouring residential zone. A temporary coal storage and sorting site, located near the residential zone, is one of the dominant sources of emissions. Using numerical simulations, the possible effects of wind flows are observed over the surface, modified by natural objects and man-made obstacles. The coal dust drifts with the wind in the direction of the residential zone and is partially deposited in this area. The simultaneous display of the digital map layers together with the location of the dominant emission source, wind flows and protected areas enables a risk assessment of the dust deposition in the area of interest to be performed. In order to obtain a more accurate simulation of wind flows over the temporary storage and sorting site, 3D laser scanning and GPS thematic mapping are used to create a more detailed digital terrain model. Thus, visualization of wind flows over the area of interest combined with 3D map layers enables the exploration of the processes of coal dust deposition at a local scale. In general, this project could be used as a template for dust-transport modelling which couples spatial data focused on the construction of digital terrain models and thematic mapping with data generated by numerical simulations based on Reynolds averaged Navier-Stokes equations.

Numerical Simulations of Blood Flow in a Stenosed Vessel under Different Flow Rates using a Generalized Oldroyd‐B Model

The present paper discusses the influence and importance of the application of generalized Newtonian and generalized viscoelastic models to blood flow simulations. A simple shear‐thinning viscosity model together with a Oldroyd‐B model for the viscoelastic part of the stress was applied to a simplified test case of stenosed vessel. The direct comparison between results of Newtonian and non‐Newtonian flows is presented for various flow rates. The aim of the study is to test the applicability of the presented numerical method to this type of flows.

Numerical Modelling of Pollution Dispersion in 3D Atmospheric Boundary Layer

The main goal of this work is to present the applicable models and numerical methods for solution of flow and pollution dispersion in 3D Atmospheric Boundary Layer (ABL). Mathematical models are based on the system of Reynolds averaged Navier-Stokes equations and its simplifications. The sets of governing equations are completed by the transport equations for passive impurities and potential temperature. A simple algebraic turbulent closure model is used. The thermal stability phenomenon is taken into account. For each mathematical model a numerical scheme based on finite-difference or finite-volume discretization is proposed and discussed. Some results of numerical tests are presented for pollution dispersion from point sources and flows over simple geometries.

Mathematical Models for Blood Coagulation

This chapter presents an overview and introduction to blood coagulation models. The historical exposure of the development of classical coagulation modeling theories is followed by a basic overview of blood coagulation biochemistry. The recent developments of cell-based models are explained in detail to demonstrate the current shift from the classical cascade/waterfall models. This phenomenological overview is followed by a survey of available mathematical concepts used to describe the blood coagulation process at various spatial scales including some of the related biophysical phenomena. A comprehensive survey of basic literature is provided for each of these topics.

Application of compact finite-difference schemes to simulations of stably stratified fluid flows

Abstract This paper presents a comparison of the results of numerical simulations obtained by two different numerical methods for one specific case of stably stratified incompressible flow. The focus in this paper is on the numerical results obtained using some of the compact finite-difference discretizations introduced in the paper [1] . The numerical scheme itself follows the principle of semi-discretisation, with high order compact discretisation in space, while the time integration is carried out by the Strong Stability Preserving Runge–Kutta scheme. Results are compared against the reference solution obtained by the AUSM finite volume method. The test case used to demonstrate the capabilities of selected numerical methods represents the flow of stably stratified fluid over low, smooth, hill-like wall mounted obstacle.

Numerical Simulation of Flow and Pollution Dispersion in the Area of Opencast Coal Mine

This paper presents some of the results of numerical simulation of flow and pollution dispersion in the proximity of coal deposit placed in the area of opencast coal mine. The mathematical model is based on Reynolds averaged Navier‐Stokes equations for incompressible flows. Turbulent closure of the model is obtained by simple algebraic turbulence model. The numerical solution is carried out by the semi‐implicit finite‐difference scheme. The 3D results are presented for the flow in real terrain including simulated obstacles. Model sensitivity is studied with respect to simulated obstacle size and shape.