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A. M. Artoli, A. G. Hoekstra and P. M. A. Sloot

Simulation of a systolic cycle in a realistic model of a Human Artery with the Lattice Boltzmann BGK method. A. M. Artoli, A. G. Hoekstra and P. M. A. Sloot. Section Computational Science Institute Informatics Faculty of Science University of Amsterdam The Netherlands

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A. M. Artoli, A. G. Hoekstra and P. M. A. Sloot

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  1. Simulation of a systolic cycle in a realistic model of a Human Artery with the Lattice Boltzmann BGK method A. M. Artoli, A. G. Hoekstra and P. M. A. Sloot Section Computational Science Institute Informatics Faculty of Science University of Amsterdam The Netherlands http://www.science.uva.nl/research/scs Emails: [artoli, alfons, sloot]@science.uva.nl

  2. Overview • Motivation • Introduction • Benchmark • 3D systolic flow in a tube • Velocity and Shear stress • Accuracy • The Real Thing • From MRA to LB grid • Simulations • Results • Ongoing research

  3. Cardiovascular diseases are the main cause of human death. Atherogenesis grows at locations of complex geometry and complex flow behavior. Planned vascular surgeries need to guarantee better HDs Why Hemodynamics? Aorta with a bypass

  4. Why Modeling? • Measurements are either • Not possible • Invasive • of limited accuracy • Time consuming

  5. Why the Real thing? • Geometrical models are more than simple. • Anatomy is patient dependent. • Imaging techniques and segmentation algorithms are developing.

  6. Why Simulations? • Simulations can be • Possible • non-invasive • Accurate • More informative • adaptive • Interactive

  7. Why LBM? • Cartesian Grid • Implementation is easy • Parallelism is direct. • Shear stress can be “measured” • Real time Interactive simulations are possible.

  8. The Lattice Boltzmann BGK

  9. Hydrodynamics • NS can be derived in the limit of low Mach number • Density • r = sum of the distributions over all directions =  fi • Pressure • Pressure = rx (speed of sound )2 • Velocity • it is momentum / mass

  10. The stress tensor • The LBM can be used to calculate the local components of the stress tensor in fluid flows WITHOUT a need to estimate velocity gradients. This has two benefits over conventional CFD methods : Increasing accuracy and decreasing computational cost. • where is the dissipative part of the momentum tensor , which can be obtained during the collision operation, without a need to take the derivatives.

  11. Systolic cycle • Analytical solutions 1. Pressure is differentiated to get the flow rate 2. Flow rate is Fourier transformed 3. Analytical solution is the Linear combinations of oscillatory Womersley solutions

  12. Benchmarks • Systolic flow in a tube

  13. Low a a = 2.8, Re= 10

  14. High a a = 16, Re = 2000

  15. Flow characteristics • There is a Phase lag between the pressure and the fluid motion. • At low a, steady Poiseuille flow is obtained. • At high a, we have the annular effect: • Profiles are flattened. • The phase lag increases towards the center. • The shear stress is very low near the center and reasonably high at the walls.

  16. Boundary Conditions • Walls • Bounce-Backs • Curved: compute fractional distance from nearest fluid, interpolate or extrapolate. • Inlet and Outlets • Periodic • Velocity • Pressure • No flux

  17. BBL Vs BBC • Bounce Back • Curved

  18. 0.125 0.1 0.075 0.05 v E 0.025 0 -0.025 -0.05 0 50 100 150 200 250 300 350 w BBL and BBC at Fixed Mach No. BBL BBC1 BBC2

  19. Influence of the Mach number and the BC BBL BBC

  20. Mach x Knudsen

  21. Convergence Vs Mach No.

  22. The Real Thing:From MRA voxels to LBM fi s LBM grid voxel Suggested bypass MRA segmented

  23. Velocity Profiles

  24. Shear Stress

  25. Ongoing Research • Comparison with Experiments • Simulations on a fly • Use of Incompressible models • Fluid-structure interaction

  26. LBGK Limitations • For fast convergence, Relatively High Mach no. is needed  Compressibility errors D3Q19  D3Q19i • Grid resolution of MRA ~1mm •  subgrid models may be needed • LBGK Thermodynamic inconsistency • Non-ideal gas models are encouraged

  27. Conclusions • Blood flow simulation is possible with LBGK with acceptable accuracy and performance . • Simulations of Blood flow in arteries with LBGK are accurate enough for surgical planning if accurate reconstruction of the arteries are used. • BBL may perform better than some BBCs at Low Mach numbers. • LBM is a suitable CHD solver. • Hemodynamic constrains need to be controlled cautiously. • Interpolation schemes may not work nicely at high Womersley numbers.

  28. Thanks!

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