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Poster Abstracts

Krzysztof Boryczko^1,2, Witold Dzwinel¹, David A.Yuen²

¹Institute of Computer Science, AGH University of Technology, Kraków, Poland
²Minnesota Supercomputing Institute, University of Minnesota, Minneapolis

Modeling of Blood Flow in Capillary Vessels Using Discrete Particles

We have devised a numerical model based on discrete particles for simulating blood flow and clotting in capillaries with diameters comparable or less than the red blood cell (RBC) size [1,2]. The mesoscopic dynamics of blood are simulated in microscopic capillary vessels about 100mm long and with diameters on the order of 7-10mm. We assume that the plasma consists of fluid particles containing fibrin monomers, while the red blood cells and capillary walls are represented by elastic mesh of .solid. particles. The fluid particles are modeled by using fluid particle model (FPM) in which particles interact with each other with a short-ranged, repulsive dissipative force [3].

Erythrocyte deformability is a critical determinant of blood flow in the microcirculation. Therefore, we model short-time dynamics of RBCs in capillaries assuming different stiffnesses and shapes of the cells. Both biconcave discs.mimicking normal RBCs.and sickle cells.the cells characteristic for rare anemia.are considered. We show that both the red blood cells and walls undergo high stresses and strong deformations during the flow. The rheological properties of flow assuming various stiffness and shapes of RBCs differ considerably. Harder RBCs and sickle cells impede the flow more than normal biconcave cells.

We show also that the discrete-particles model of blood reflects clearly the aggregation properties of the red blood cells flowing in the capillary channels. There is a strong tendency to produce RBC clusters in capillaries. The choking points and other irregularities in geometry considerably increase the clotting effect. We discuss also other clotting factors coming from the fibrinogen. The polymerization of fibrin monomers into hydrated fibrins is modeled by the change of the interactions between fluid particles from repulsive to attractive forces. This process occurs with a probability being an increasing function of the local density. In [4] we show that due to the density fluctuations caused by high acceleration, the fibrin chains are produced within a very short time (0.5 ms). Fibrin aggregation modifies the rheological properties of blood, slows down the incipient flow, and entraps the red blood cells, thus forming dangerous clots. Modeling has been carried out with adequate resolution by using 1 to 10 million particles on multiprocessor systems [5,6]. Discrete particle simulations open a new pathway for modeling the dynamics of complex, viscoelastic fluids at the microscale where both liquid and solid phases are treated with discrete particles.

1. Dzwinel W., Boryczko K., Yuen D.A., .A Discrete-Particle Model of Blood Dynamics in Capillary Vessels,. J Colloid Int Sci, 258/1, 163.173, 2003.
2. Boryczko K., Dzwinel W., Yuen D.A., .Dynamical clustering of red blood cells in capillary vessels,. J Mol. Modeling, 9, 16.33, 2003 (e-paper).
3. Español P., .Fluid particle model,.. Physical Review E 57(3):2930.2948, 1998.
4. Boryczko K., Dzwinel W., Yuen D.A., .Modeling Fibrin Polymerization in Blood Flow with Discrete-Particles,. accepted for publication in Computer Models and Programs in Biomedicine, February 2004.
5. Boryczko K., Dzwinel W., Yuen D.A., .Modeling mesoscopic heterogeneous fluids in irregular geometries on shared memory systems,. Concurrency and Computation: Practice and Experience, submitted in February 2004
6. Boryczko K., Dzwinel W., Yuen D.A., .Clustering Revealed in High-Resolution Simulations and Visualization of Multi-Resolution Features in Fluid-Particle Models,. Concurrency and Computation: Practice and Experience, 15, 101-116, 2003

Poster in PDF format

Witold Dzwinel¹, David A.Yuen², Krzysztof Boryczko^1,2

¹Institute of Computer Science, AGH University of Technology, Kraków, Poland
²Minnesota Supercomputing Institute, University of Minnesota, Minneapolis

Fluid Particles in Modelling of Colloids and Suspensions

When mesoscopic features embedded within macroscopic phenomena in polymers are coupled with microstructural dynamics and boundary singularities, the complex multiresolution behavior observed in polymer dynamics are difficult to capture with the continuum models [1]. Therefore, the approaches based on the Navier-Stokes and the Cahn-Hillard equations, which use partial differential equations, become useless when employed in microscopic and mesoscopic scales. They must be augmented with discretized atomistic microscopic models, such as molecular dynamics (MD), to provide an effective solver across the diverse scales with different physics. The two-level fluid particle model [2] is a discrete-particle method, which is a mesoscopic version of the molecular dynamics (MD) technique combined with fluid particle method (FPM). Unlike in MD, where the particles represent atoms and molecules, in our model they represent both colloidal beds and fluid particles. The fluid particles mimic the .lumps of fluid,. which interact with each other, not only via central conservative forces as it is in MD, but with non-central, dissipative, and stochastic forces as well.

We show that by using discrete-particles we can model realistic behavior of such the mesoscopic phenomena such as the thin-film evoluation in mesoscale [3], mixing instabilities in suspensions [4,5], phase separation [6], creation of colloidal arrays [7] and colloidal aggregates [8]. The modeled multiresolution patterns and qualitative behavior of mesoscopic features are amazingly similar to the results found in laboratory experiments and predicted by the theory. The combination of two different types of interactions, postulated by the DLVO theory, represents realistic interactions between colloidal beds and defines dissipative and random interactions acting between fluid particles, resulting in spontaneous creation of many multiresolutional structures. They represent a single micelle, colloidal crystals, large-scale colloidal aggregates up to scales of hydrodynamic instabilities [9] and the macroscopic phenomenon involving the clustering of red blood cells in capillaries. We can summarize the computationally homogeneous discrete particle model in the following hierarchical scheme [1,2]: non-equilibrium molecular dynamics (NEMD), dissipative particle dynamics (DPD), fluid particle model (FPM), smoothed particle hydrodynamics (SPH), and thermodynamically consistent DPD. The large scale-simulations involving up to 10 million fluid particles in three dimensions were carried out on a broad range of parallel systems including an IBM SP multicomputer, SGI/Origin ccNUMA multiprocessor, IBM/Regatta, and SGI/Altix machines, resulting in an efficient and universal discrete-particle algoritms and codes [10,11,12]. A powerful toolkit over the grid can be formed from these discrete particle schemes to successfully model multiple-scale phenomena such as biological vascular and mesoscopic porous-media systems.

References:

1. Dzwinel W., Alda W., Yuen, D.A., Mol. Simul., 22, 397.418, 1999.
2. Dzwinel W., Yuen D.A., Boryczko K., J Mol. Modeling, 8, 33.45, 2002.
3. Dzwinel W., Yuen D.A., Mol. Simul., 22, 369.395, 1999.
4. Dzwinel W., Alda W., Pogoda M., Yuen D.A., Physica D, 137, 157.171, 2000.
5. Dzwinel W., Yuen D.A., Int. J. Mod Phys.C, 12/1, 91.118, 2001.
6. Dzwinel W., Yuen D.A., Int. J. Mod Phys.C, 11/1, 1.25, 2000.
7. Dzwinel W., Yuen D.A.,  J Colloid Int Sci, 225, 179.190, 2000.
8. Dzwinel W., Yuen D.A., Int. J. Mod Phys.C, 11/5, 1037.1067, 2000.
9. Dzwinel W., Yuen D.A., J Colloid Int Sci, 247, 463.480, 2002.
10. Boryczko K., Dzwinel W., Yuen D.A., Concurr&Comput: Practice and Experience, 14, 1.25, 2002.
11. Boryczko K., Dzwinel W., Yuen D.A., Concurr&Comput: Practice and Experience, 15, 101.116, 2003.
12. Boryczko K., Dzwinel W., Yuen D.A., Concurr&Comput: Practice and Experience, submitted Feb. 2004.

Poster in PDF format