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

1. Fluid and Structure Tango in
Biomedical Research
Idit Avrahami, Afeka
ISMBE, I.Avrahami, Afeka

2. Fluid-Structure Interaction (FSI)
The unknown motion of the structure
is a BC for the flow, and vice versa
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3. Fluid-Structure Interaction (FSI)
1. Separate the problem to:
– structural domain (S)
– fluid domain (F)
2. Solve each domain separately
3. The interactions occurs along the
interfaces
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ISMBE, I.Avrahami, Afeka

4. Governing Equations
For the fluid domain For the solid domain
∇⋅U = 0
DU && &
MU + CU + KU = R
ρ = −∇p + μ∇ 2 U
Dt
For moving boundaries
U = u f − ug
Interactions at the interfaces
Vf = Us
n ⋅ τ f = n ⋅ τs
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5. Numerical Methods
for solving the PDE
Meshing:
Divide each domain into elements
Discretization:
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
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6. Impedance Pump
based on resonance wave dynamics
Flexible graft Pincher
outflow Fluid
Impedance mismatch
(anastomosis)
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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
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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
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9. 9
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10. Resonance Wave Pumping
Channel
thickness
200 μm
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(Rinderknecht et al., 2005)
ISMBE, I.Avrahami, Afeka

11. Experimental Model
(Hickerson et al., 2005)
ISMBE, I.Avrahami, Afeka

12. Numerical Model
Full fixation Full fixation
Imposed harmonic Stress free
dY=dZ=0 dY=dZ=0
motion
Y Fluid-structure interface,
Contact surface no slip conditions
Z
Stress- Stress-
Axisymmetric
free BC free BC
BC
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13. Symmetric Excitation
=> no net flow
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14. Asymmetric Excitation
(Avrahami & Gharib,2008, JFM)
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15. Typical Transient Flow Rate
Positive outlet
flow rate
400
Instantaneous Flow The average
Bulk Flow
300
flow rate over a
Flow rate (cm /sec)
cycle in the
3
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)
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16. Effect of Excitation Point
(Rinderknecht, et al., 2005, JMM)
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17. Effect of Pinching Parameters
1.5
Numerical simulation 1.4
1.0
Non-dimensional flow rate
Experiments 1.2
Normalized 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)
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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
250
Flow rate (cm /sec)
Natural 0 . 0 0 0 8
Frequency
200
3
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. Active Bypass Graft
Using resonance wave pumping
Impedance
pump t
G ra f
y Stenosis
ar ter
nar y
Coro
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(Avrahami & Gharib, 2005, BMES)

20. The Numerical Model
Pincher
3D model based on
physiological geometry
Dacron
Graft
Artery
φ 2 mm Anastomosis
450
90% stenosis
(Avrahami & Gharib, 2005, BMES)
ISMBE, I.Avrahami, Afeka
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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 cm
FR (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)
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(Avrahami & Gharib, 2005, BMES)

22. Wall Shear Stress at the Anastomosis
without pump
with pump
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(Avrahami & Gharib, 2005, BMES)

23. Graft
Anastomosis
Toe Downstream
Artery
120 Graft
Anastomosis Toe
100 Downstream artery
Wall 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
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Time (sec)
ISMBE, I.Avrahami, Afeka

24. Additional Support Pump
pump
On Cavo-pulmonary Intra - Aortic support
connection support for Pump
Fontan procedure
(Loumes et al., 2008)
(Avrahami et al., 2006) 24
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25. Micro-Pump
for mixing and heat removal
Max Flow at freq=78Hz
mL/min
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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
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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.
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ISMBE, I.Avrahami, Afeka