Theoretical and Computational Studies on Thrombus Formation and Multiphase Characteristics of Blood Flow
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In this thesis several blood related problems are studied: 1. Malaria-infected, the removal of parasitized red blood cells (pRBCs) using a magnetic force; 2. A new mathematical model for thrombus growth, which incorporates the thrombus-blood interaction, shear induced platelets activation, shear induced platelets embolization and deposited platelets stabilization, is developed, and a successful direct numerical prediction of thrombus formation in an axial blood pump is obtained. According to our knowledge, this is the first time such a study has been performed ; 3. Based on the application of Mixture Theory (or Theory of Interacting Continua), a multiphase model for blood flow is derived, and a new viscosity term, which considers the effect of shear stress and volume fraction of RBCs, is introduced. First, a blood filter system, mPharesis™ system, that will allow the removal of toxic malariainfected, parasitized RBCs (pRBCs or i-RBCs) from circulation using magnetic force is studied. The problem is modeled as a multi-component flow system using CFD-DEM method, where plasma is treated as a Newtonian fluid, the RBCs and pRBCs are modeled as soft-sphere solid particles which move under the influence of the plasma, other RBCs and the magnetic field. The simulation results show that for a channel with nominal height of 100 microns the addition of upstream constriction of 80% improved the stratification by 111% (from 28% to 139%); and a downstream diffuser reduced remixing, hence improved efficiency of stratification to 260%. Second, based on the Sorenson’s model of thrombus formation [1, 2], a new mathematical model describing the process of thrombus growth is developed. In this model the blood is treated as a Newtonian fluid, and the transport and reactions of the chemical and biological species are modeled using CRD (convection-reaction-diffusion) equations. A computational fluid dynamic (CFD) solver for the mathematical model is developed using the libraries of OpenFOAM®. Applying the CFD solver, several representative benchmark problems are studied: rapid thrombus growth in vivo by injecting Adenosine diphosphate (ADP) using iontophoretic method and thrombus growth in rectangular microchannel with crevices. Very good agreements between the numerical and the experimental results validate the model and indicate its potential to study a host of complex and practical problems in the future. Then applying the model, thrombus growth in an axial blood pump is studied. First, the flow field analysis in the blood pump is studied using visualization and numerical simulations. Then applying the thrombus model, a direct prediction of the thrombus growth is performed. The simulation shows a very good agreement with clinical observations. For reducing the computational cost, a dimensionally-reduced model is also developed, based on the complete thrombus model. The dimensionally-reduced model shows good capability to predict the thrombus deposition in blood pump as well. And finally, for describing the multiphase characteristics of blood, using the framework of Mixture Theory, a two-fluid model is applied, where the plasma is treated as a Newtonian fluid and the red blood cells (RBCs) are treated as a shear-thinning fluid. A computational fluid dynamic (CFD) simulation incorporating the constitutive model is implemented using OpenFOAM® where benchmark problems including a sudden expansion and various driven slots and crevices are studied numerically. The numerical results exhibit good agreement with the experimental observations with respect to both the velocity field and the volume fraction distribution of the RBCs.