$430 Journal of Biomechanics 2006, Vol. 39 (Suppl 1) Oral Presentations

Ogden-Hill-type constitutive equations, a multi objective quality function and an FE-tool, parameters were determined for the different tissues. For calculating the stress distribution at the test site an FE-model was devel- oped. It was built up by elastic supports consisting of various soft foams with different geometries and a norm body including the previously determined test site. Calculations were made for different material and geometry combinations of the support. The model will be extended with modified slatted frames (micro stimulation) to verify possible benefits of such systems.

T1.15 Biological Flows

T1.15.1 Particle Tracking and Particle Methods for Biological Flows

5838 Mo, 08:15-08:30 (PT) Modelling particle deposition in a turbulent airway model

M.A.I. Khan 1 , X.'~ Luo 1 , F.C.G.A. Nicolleau 2. 1Department of Mathematics, University of Glasgow, Glasgow, UK, 2 Department of Mechanical Engineering, University of Sheffield, Sheffield, UK

Transport and deposition of aerosol particles in a stenotic tube model are studied to investigate the effects of turbulent flow structure on particle deposi- tion. We introduce a novel particle tracking model namely kinematic simulation (KS) [1], which is a Lagrangian model of turbulent dispersion that takes into account the effects of spatio-temporal flow structure on particle dispersion. It is a unified Lagrangian model of one-, two- and indeed multi-particle turbulent dispersion and can easily be used as a Lagrangian sub-grid model for large eddy simulation (LES) code thus enabling complex geometry to be taken into account. To study the effect of small scale flow structure on particle deposition in the stenotic pipe flow we use LES to simulate the flow filed, and KS to model the sub-grid flow structure to generate particle trajectories. Thus the large scales are resolved by the simulation and the small scales are modelled using various sub-grid models. As none of the existing sub-grid models are known to have taken into account the effects of small-scale turbulent flow structures on particle deposition, it is important to use KS's ability to re-model the sub- grid velocity field and thereby incorporate its effect on particle deposition. The parameters of our simulations for LES are the Reynolds number, diameter of the pipe, percentage of stenoses and sub-grid model parameters. For KS the parameters are the energy dissipation rate obtained from LES, the energy spectra, ratio of the largest and smallest sub-grid scales and the total number of modes for the sub-grid velocity field. The turbulent flow features thus obtained are compared with published experimental data [2] in a stenotic pipe. Preliminary results suggest that the particle deposition in the stenotic tube can be greatly affected by the small-scale (sub-grid) turbulent flow structures.

References [1] JCH Fung et al. J Fluid Mech 1992; 236: 281. [2] SA Ahmed et al. J Biomech 1983; 16: 505.

6497 Mo, 08:30-08:45 (PT) Lattice-Boltzmann calculations of blood flow in a fluidised bed: results for the permeability and drag A.K.M. Podias, Y.F. Missirlis. Biomedical Engineering Laboratory, Mechanical Engineering and Aeronautics Department, University of Patras, Rion-Patras, Greece

The flow and transport within fluidised beds depends strongly on particle- particle and fluid-particle interaction. This is the reason that proper closure relations for these two interactions are vital for reliable predictions on the basis of continuum models. In a previous study [Podias A.K.M. and Missirlis '~E (2000), In: Prender- gast EJ., Lee T.C., Carr A..J. (Eds.), Proceedings of the 12 th Conference of the European Society of Biomechanics, Royal Academy of Medicine in Ireland], a model for describing the blood flow field and heparin transport within a heparin-adsorbing device operating as a fluidised bed has been derived and calculated using the Finite Element Method. There, the fluid dynamic interactions between particles in the multi-particle assemblage have been accounted for by employing the so-called sphere-in-cell model [Happel J. (1958), AIChE J. 4, 197]. The present study, demonstrates the use of the lattice-Boltzmann equation (LBE) method in predicting low Reynolds number flow past a mono-dispersed and random assemblage of rigid, fluidised, spherical particles, thereby focusing in the blood-particle interaction relation. The LBE method employed is fully explicit and time-dependent, in which distribution of fluid particles exists at discrete locations in space and move in discrete directions, speeds and intervals of time. Flow quantities such as density and velocity are defined as the appropriate moments over the state space of the distribution values at a given node and time step. The particle distribution dynamics via the application of discrete kinetic theory provides full recovery of the Navier-Stokes continuum fluid equations for the behaviour of the macroscopic fluid properties.

Estimates of the local velocity distributions and permeability are obtained for wide ranges of physical and kinematic conditions. Results on the dynamics of the flow in terms of the resulting drag coefficient are also obtained and discussed. The predicted permeability and drag coefficient is compared with theoretical estimates from the literature and with our experimental results [Po- dias A.K.M. and Missirlis '~E (2002), In: R. Bedzinski, C. Pezowicz, K. Scigala (Eds.), ACTA of Bioengineering and Biomechanics: Proceedings of the 13th Conference of the European Society of Biomechanics, Wroclaw, Poland].

5071 Mo, 08:45-09:00 (P7) Particle simulations of blood flow in vein with many red blood cells K. Nagayana. Department of Mechanical Information Science & Technology Kyushu Institute of Technology, lizuka, Japan

Particle simulations of blood flow in vein with red blood cells were carried out. This model considers plasma as fluid particles with viscous forces and red blood cell as elastic particles using springs for surface and fluid particles inside. Vein is modeled as solid particles. 2D and 3D simulations are carried out. In 2D flow between parallel walls, more than 30 RBCs are simulated for cases with and without narrow position assuming thrombus. Between parallel walls, RBCs tend to turn parallel to the flow direction and flows away from the wall to reduce flow resistance. With narrow position, interactions among red blood cells increased. At very low Re number region, recirculation was not appear, and RBC was not captured around narrow position. The model also extended to simplified case with thrombus formation, and the preliminary results were obtained. As thrombus grew, flow resistance increased and blood flow rate decreased. Three dimensional particle simulations of blood flow with red blood cell are also carried out. First plasma flow was tested comparing with theoretical Pouiseille flow. Red blood cell shape was modeled as sphere at first, and removing plasma particles inside, the shape change is checked. And finally, blood flow with blood cell inside the vein was simulated for cases from one RBC to several RBCs. In case of a RBC flowing at center of the vein, parachute type deformation was observed. In case of several RBCs, their interaction was studied.

6576 Mo, 09:00-09:15 (P7) Three-dimensional simulations of microscopic blood flow using SPH method N. Tanaka, Y. Hayakawa, T. Masuzawa. Department ef Mechanical Engineering, Ibaraki University, Hitachi, Japan

We have developed microscopic blood model based on the smoothed particle hydrodynamics (SPH) method. In the model, plasma fluid is discretized by SPH particles, and a red blood cell (RBC) is expressed by internal SPH particles surrounded by elastic membrane (structure) particles. In addition, a new interaction model between fluid particles and structure particles has been developed in order to prevent an internal particle from getting out of the membrane. This model is also applicable to the interaction between fluid particles and wall particles for preventing a fluid particle from moving into wall. For verifying the model, we numerically analyzed the three-dimensional tank- tread motion of an RBC under a constant shear field. The numerical results can well reproduce behaviors of RBC. We also analyzed another numerical example of blood flow in stenosed vessel. The results show that a RBC flexibly changes its shape according to the vessel geometry and moves past the narrow vessel part. Finally, the numerical results were visualized by the recent ray-tracing technique for the purpose of realistic representation.

6790 Mo, 09:15-09:30 (P7) Simulation study on effects of elastic red blood cells on primary thrombogenesis using particle method K.-i. Tsubota, H. Kamada, S. Wada, T. Yamaguchi. Department ef Bioengineering and Robotics, Graduate School of Engineering, Tohoku University, Sendal, Japan

A novel computer simulation approach using particle method was proposed to analyze the formation of primary thrombus due to platelet aggregation in the blood flow. Platelets, elastic red blood cells (RBCs) and plasma fluid, which are main components of blood, were modeled by discrete particles. The platelet aggregation to the injured vessel wall was expressed by introducing an attractive force transferred from the injured wall to the platelets. The solid- like mechanical properties of the primary thrombus consisting of aggregated platelets were expressed by spring force acting between the adhered platelet particles. The particles for the RBC membrane were connected with their neighboring membrane particles by stretch/compression and bending springs. Being subjected to an incompressible viscous flow governed by Navier-Stokes (N-S) equations, the motion of all the particles was solved by using the MPS method. The forces induced by the springs that act on the particles for the