Wei-Tao Wu

Multi-Constituent Simulation of Thrombus Deposition

In this paper, we present a spatio-temporal mathematical model for simulating the formation and growth of a thrombus. Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus (solid) phase. The transport and reactions of 10 chemical and biological species are incorporated using a system of coupled convection-reaction-diffusion (CRD) equations to represent three processes in thrombus formation: initiation, propagation and stabilization. Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: in vivo thrombus growth in an injured blood vessel and in vitro thrombus deposition in micro-channels (1.5 mm × 1.6 mm × 0.1 mm) with small crevices (125 μm × 75 μm and 125 μm × 137 μm). For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally. Based on the success with these two benchmark problems, which have very different flow conditions and biological environments, we believe that the current model will provide useful insight into the genesis of thrombosis in blood-wetted devices, and provide a tool for the design of less thrombogenic devices.

Fully developed flow of a drilling fluid between two rotating cylinders

In this paper, we study the fully developed Couette flow of a drilling fluid, and explore the effects of concentration and shear-rate-dependent viscosity. The one-dimensional form of the governing equations, as well as the boundary conditions are made dimensionless and a parametric study is performed by varying the dimensionless numbers.

Heat transfer and flow of a slag-type non-linear fluid: Effects of variable thermal conductivity

In this paper, we study the effects of variable thermal conductivity on the flow and heat transfer in a slag-type non-linear fluid down a vertical wall. The constitutive relation for the heat flux vector is assumed to be the Fouriers law of conduction with a variable thermal conductivity which includes the second order effects of the volume fraction. We numerically solve the non-dimensional form of the governing equations to study the effects of various dimensionless numbers on the velocity, temperature and volume fraction. The results indicate that the thermal conductivity plays a major role in the temperature distribution. Also, for certain values of the dimensionless numbers, minor differences are observed in the velocity and volume fraction distribution compared with the case of constant thermal conductivity.

High fidelity computational simulation of thrombus formation in Thoratec HeartMate II continuous flow ventricular assist device.

Continuous flow ventricular assist devices (cfVADs) provide a life-saving therapy for severe heart failure. However, in recent years, the incidence of device-related thrombosis (resulting in stroke, device-exchange surgery or premature death) has been increasing dramatically, which has alarmed both the medical community and the FDA. The objective of this study was to gain improved understanding of the initiation and progression of thrombosis in one of the most commonly used cfVADs, the Thoratec HeartMate II. A computational fluid dynamics simulation (CFD) was performed using our recently updated mathematical model of thrombosis. The patterns of deposition predicted by simulation agreed well with clinical observations. Furthermore, thrombus accumulation was found to increase with decreased flow rate, and can be completely suppressed by the application of anticoagulants and/or improvement of surface chemistry. To our knowledge, this is the first simulation to explicitly model the processes of platelet deposition and thrombus growth in a continuous flow blood pump and thereby replicate patterns of deposition observed clinically. The use of this simulation tool over a range of hemodynamic, hematological, and anticoagulation conditions could assist physicians to personalize clinical management to mitigate the risk of thrombosis. It may also contribute to the design of future VADs that are less thrombogenic.

Channel Flow of a Mixture of Granular Materials and a Fluid

In this paper, we consider the three dimensional flow of granular materials and a viscous fluid in a channel. We use Mixture Theory to treat this problem as a two-component system [1]: One component is the solid particles (granular materials), such as sand, coal particles or red blood cells; the solid particles are modeled as a generalized Reiner-Rivlin type fluid derived by Massoudi [2], which not only considers the effects of volume fraction but also has a viscosity which is shear rate dependent. The other component, the host fluid, is assumed to behave as a linear viscous fluid, such as water, oil or plasma. For the interaction forces, the effect of different hindrance functions for the drag force is studied; moreover a generalized form of the expression for the hindrance function is suggested. For studying this two-component system numerically, a three dimensional CFD solver based on OpenFOAM® has been developed. Applying this solver, a specific problem (blood flow) has been studied for which our numerical results and experimental data [3] show good agreement.Copyright

Study of Blood Flow in Micro-Channels Using Mixture Theory

It is known that in large vessels (whole) blood behaves as a Navier-Stokes (Newtonian) fluid; however, in a vessel whose characteristic dimension (e.g., a diameter in the range of 20 to 500 microns) is about the same size as the characteristic size of the blood cells, blood behaves as a non-Newtonian fluid, exhibiting complex phenomena, such as shear-thinning, stress relaxation, the Fahraeus effect, the plasma-skimming, etc.. Using the framework of mixture theory an Eulerian-Eulerian two phase model is applied to model blood flow, where the plasma is treated as Newtonian fluid and the RBCs are treated as shear thinning fluid.[5]Copyright

Flow of Granular Materials Modeled as a Generalized Reiner-Rivlin Type Fluid

In this paper we use a non-linear constitutive model for flowing granular materials developed by Massoudi [1] which not only considers the effect of volume fraction but also has a viscosity which is shear rate dependent. This model is a generalization of Reiner’s model [2] derived for wet sand. Specifically we study the simple shear flow of granular materials between two horizontal plates, with the lower plate fixed and the upper plate moving at a constant speed. Numerical solutions are presented for various dimensionless parameters.Copyright