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# FSI of impedance pump by Idit Avrahami

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the dynamic of fluid and structure waves along a flexible tubes allow valveless and bladeless pumping at specific exitation frequrncies. the presentation describes different medical applications for this pump and the numerical method to analyse its capabilities
by Dr. Idit Avrahami

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### FSI of impedance pump by Idit Avrahami

1. 1. Fluid and Structure Tango in Biomedical Research Idit Avrahami, Afeka ISMBE, I.Avrahami, Afeka
2. 2. Fluid-Structure Interaction (FSI) The unknown motion of the structure is a BC for the flow, and vice versa 2 ISMBE, I.Avrahami, Afeka
3. 3. Fluid-Structure Interaction (FSI)1. Separate the problem to: – structural domain (S) – fluid domain (F)2. Solve each domain separately3. The interactions occurs along the interfaces 3 ISMBE, I.Avrahami, Afeka
4. 4. Governing EquationsFor the fluid domain For the solid domain ∇⋅U = 0 DU && & MU + CU + KU = Rρ = −∇p + μ∇ 2 U DtFor moving boundaries U = u f − ug Interactions at the interfaces Vf = Us n ⋅ τ f = n ⋅ τs 4 ISMBE, I.Avrahami, Afeka
5. 5. Numerical Methods for solving the PDEMeshing: Divide each domain into elementsDiscretization: Approximate the PDE into a set of algebraic equations (FVM/ FEM)Moving Mesh in the fluid domain: ALE (Arbitrary Lagrangian Eulerian ) approach is used to adjust the mesh to the boundary motion Afeka ISMBE, I.Avrahami, 5
6. 6. Impedance Pump based on resonance wave dynamics Flexible graft Pincheroutflow Fluid Impedance mismatch (anastomosis) 6 ISMBE, I.Avrahami, Afeka
7. 7. Pressure waves in Elastic Tube A local periodic pressure imposed in an elastic tube produces pressure waves that travel along the tube in the wave speed of: Eh C= ρd 7 ISMBE, I.Avrahami, Afeka
8. 8. Wave Reflection• A local excitation in a specific frequency produces periodic waves in the domain• The waves travel along the domain and reflected by the reflection site• The reflected waves are combined with the traveling waves• At specific frequency (natural freq. and its harmonics) the reflected waves are added to the traveling waves and the waves are enhanced – this is resonance 8 ISMBE, I.Avrahami, Afeka
9. 9. 9ISMBE, I.Avrahami, Afeka
10. 10. Resonance Wave Pumping Channelthickness 200 μm 10 (Rinderknecht et al., 2005) ISMBE, I.Avrahami, Afeka
11. 11. Experimental Model (Hickerson et al., 2005) ISMBE, I.Avrahami, Afeka
12. 12. Numerical ModelFull fixation Full fixation Imposed harmonic Stress free dY=dZ=0 dY=dZ=0 motion Y Fluid-structure interface, Contact surface no slip conditions ZStress- Stress- Axisymmetricfree BC free BC BC ISMBE, I.Avrahami, Afeka
13. 13. Symmetric Excitation => no net flow 13 ISMBE, I.Avrahami, Afeka
14. 14. Asymmetric Excitation (Avrahami & Gharib,2008, JFM) 14 ISMBE, I.Avrahami, Afeka
15. 15. Typical Transient Flow Rate Positive outlet flow rate 400 Instantaneous Flow The average Bulk Flow 300 flow rate over aFlow rate (cm /sec) cycle in the3 200 100 periodic phase is the 0 Pump Bulk -100 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 Flow Time (sec) 15 ISMBE, I.Avrahami, Afeka
16. 16. Effect of Excitation Point (Rinderknecht, et al., 2005, JMM) ISMBE, I.Avrahami, Afeka 16
17. 17. Effect of Pinching Parameters 1.5 Numerical simulation 1.4 1.0 Non-dimensional flow rate Experiments 1.2Normalized flow rate (Hickerson, 2005) 0.5 1.0 0.0 0.8 0.6 -0.5 0.4 -1.0 0.2 -1.5 2 4 6 8 10 12 0.0 Axial location along the tube (cm) 0 20 40 60 80 100 Pinching amplitude (%) 2.5 Numerical simulation 200 2.0 150 Non-dimensional Flow Rate F lo w (m L /m in ) Experiments (Hickerson, 2005) 100 1.5 50 1.0 0 -50 0.5 -100 -150 0.0 -200 -0.5 0 5000 10000 15000 20000 25000 0 20 40 60 80 100 Duty-Cycle (%) Pressure (dyn/cm2) 17 ISMBE, I.Avrahami, Afeka
18. 18. Effect of Pinching Frequency 300 Resonant 0 . 0 0 1 2 Bulk flow-rate Frequencies 11.5 Hz 6 Hz FFT 0 . 0 0 1 250Flow rate (cm /sec) Natural 0 . 0 0 0 8 Frequency 2003 0 . 0 0 0 6 150 0 . 0 0 0 4 100 Natural 0 . 0 0 0 2 Frequency 50 0 2 7 12 Frequency (Hz) 18 ISMBE, I.Avrahami, Afeka FSI in BME, I. Avrahami, Afeka
19. 19. Active Bypass GraftUsing resonance wave pumpingImpedance pump t G ra f y Stenosis ar ter nar y Coro 19 ISMBE, I.Avrahami, Afeka (Avrahami & Gharib, 2005, BMES)
20. 20. The Numerical Model Pincher 3D model based on physiological geometry Dacron GraftArtery φ 2 mm Anastomosis 450 90% stenosis (Avrahami & Gharib, 2005, BMES) ISMBE, I.Avrahami, Afeka 20
21. 21. Resonance Wave Pumping • Maximal flow is found at natural frequency 150 5E 10 - Bulk flow 140 Natural 4. 5E 10 - Dacron Graft 130 D=3mm 4E 10 - frequency 120 3. 5E 10 - L= 12 cmFR (ml/min) 110 3E 10 - 100 2. 5E 10 - Duty-cycle=50% 90 2E 10 - 80 1. 5E 10 - Pinch amp =20% 70 1E 10 - => 60 5E 11 - frequency=100 Hz 50 0 25 50 75 100 125 150 Frequency (Hz) 21 ISMBE, I.Avrahami, Afeka (Avrahami & Gharib, 2005, BMES)
22. 22. Wall Shear Stress at the Anastomosis without pump with pump 22 ISMBE, I.Avrahami, Afeka (Avrahami & Gharib, 2005, BMES)
23. 23. Graft Anastomosis Toe Downstream Artery 120 Graft Anastomosis Toe 100 Downstream arteryWall shear stress (dyne/cm2) 80 60 40 20 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 23 Time (sec) ISMBE, I.Avrahami, Afeka
24. 24. Additional Support Pump pump On Cavo-pulmonary Intra - Aortic supportconnection support for Pump Fontan procedure (Loumes et al., 2008) (Avrahami et al., 2006) 24 ISMBE, I.Avrahami, Afeka
25. 25. Micro-Pumpfor mixing and heat removal Max Flow at freq=78Hz mL/min 25 ISMBE, I.Avrahami, Afeka
26. 26. Acknowledgments• Prof. Mory Gharib, Caltech• Dr. Laurence Loumes, McGill University• Dr. Derek Rinderknecht• Dr. Anna Hickerson• Division of Materials Technology, NTU, Singapore• The Joseph Drown Foundation 26 ISMBE, I.Avrahami, Afeka
27. 27. References• Avrahami I. and Gharib M. (2008), "Computational Studies of Resonance Wave Pumping in Compliant Tubes”, Journal of Fluid mechanics, Vol. 608: 139-160.• Loumes, L., I. Avrahami and M. Gharib (2008), "Resonant pumping in a multilayer impedance pump." Physics of Fluids, Vol. 20(2)• Avrahami, I., L. Loumes and M. Gharib (2006). "Numerical investigation of the fluid and structure dynamics in models of impedance pump." Journal of Biomechanics 39: 438-400. 27 ISMBE, I.Avrahami, Afeka