Validation and testing of 1D haemodynamics models
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1 Validation and testing of 1D haemodynamics models 6th Russian Workshop on Mathematical Models and Numerical Methods in Biomathematics 4-th International Workshop on the Multiscale Modeling and Methods in Biology and Medicine, 29.10.2014 Timur M. Gamilov 1,2,3 , Etienne Boileau 4 , , Sergey S. Simakov 1,2,3 , 1 Moscow Institute of Physics and Technology 2 MIPT Center for Human Physiology Studies e International Translational Medicine and Biomodelling Research te 4 Swansea University
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Validation and testing of 1D haemodynamics models. Timur M. Gamilov 1,2,3 , Etienne Boileau 4 , , Sergey S. Simakov 1,2,3 ,. 1 Moscow Institute of Physics and Technology 2 MIPT Center for Human Physiology Studies - PowerPoint PPT Presentation
Transcript of Validation and testing of 1D haemodynamics models
1
Validation and testing of 1D haemodynamics models
6th Russian Workshop on Mathematical Models and Numerical Methods in Biomathematics, 4-th International Workshop on the Multiscale Modeling and Methods in Biology and Medicine,
29.10.2014
Timur M. Gamilov1,2,3, Etienne Boileau4, ,Sergey S. Simakov1,2,3,
1 Moscow Institute of Physics and Technology2 MIPT Center for Human Physiology Studies
3 The International Translational Medicine and Biomodelling Research team4 Swansea University
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1D Haemodynamic Models
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Haemodynamic Models
3D models
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Haemodynamic Models
1D models3D models
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Enhanced External Counterpulsation (EECP)
1D Models
1 hour and more
whole body (legs - heart)
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1D Models
1D-3D coupling
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Blood flow circulation model
0
uAA
t x
2
2
u u P
t x
1) Mass balance
2) Momentum balance frf
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Blood flow circulation model
0
uAA
t x
2
2
u u P
t x
1) Mass balance
2) Momentum balance frf
8U
A
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Blood flow circulation model
0
uAA
t x
2
2
u u P
t x
1) Mass balance
2) Momentum balance
0
020
0
2,
16 ,,
A AA
u A A AA AAd
A A
frf
8U
A
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Blood flow circulation model
0
uAA
t x
2
2
u u P
t x
1) Mass balance
2) Momentum balance frf
Wall state ( )P P A
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Blood flow circulation model
0
uAA
t x
2
2
u u P
t x
1) Mass balance
2) Momentum balance frf
Wall state ( )P P APedley, Luo,
1998
Favorsky, Mukhin
0 0
m nA A
PA A
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Blood flow circulation model
0
uAA
t x
2
2
u u P
t x
1) Mass balance
2) Momentum balance frf
Wall state ( )P P A
2,extP A P t x c f A
0 0
0 0
exp 1 1,
ln ,
A A A Af A
A A A A
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Blood flow circulation model
0
uAA
t x
2
2
u u P
t x
1) Mass balance
2) Momentum balance frf
Wall state ( )P P A
3) Bifurcations
14
Blood flow circulation model
0
uAA
t x
2
2
u u P
t x
1) Mass balance
2) Momentum balance frf
Wall state ( )P P A
3) Bifurcations1 ,...,
0, 1,M
m mk k k k k k
k k k
Q Q u S
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Blood flow circulation model
0
uAA
t x
2
2
u u P
t x
1) Mass balance
2) Momentum balance frf
Wall state ( )P P A
3) Bifurcations1 ,...,
0, 1,M
m mk k k k k k
k k k
Q Q u S
,node mk k k kp p R Q
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Blood flow circulation model
0
uAA
t x
2
2
u u P
t x
1) Mass balance
2) Momentum balance frf
Wall state ( )P P A
3) Bifurcations1 ,...,
0, 1,M
m mk k k k k k
k k k
Q Q u S
,node mk k k kp p R Q
Compatibility conditions
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Blood flow circulation model
0
uAA
t x
2
2
u u P
t x
1) Mass balance
2) Momentum balance frf
Wall state ( )P P A
3) Bifurcations1 ,...,
0, 1,M
m mk k k k k k
k k k
Q Q u S
, , 0,node mk k m k k k k kp t x p t R Q x L
Compatibility conditions
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Blood flow circulation model
0
uAA
t x
2
2
u u P
t x
1) Mass balance
2) Momentum balance frf
Wall state ( )P P A
3) Bifurcations
4) Numerical method
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Validation and testing
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Gaussian pulse
Straight long vessel
Left boundary
Right boundary - no reflection
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Gaussian pulse
Discontinuous Galerkin
22 ( )
0 ( )
fr
fr
Uf dashed
Af solid
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Gaussian pulse
Locally Conservative Galerkin
22 ( )
0 ( )
fr
fr
Uf dashed
Af solid
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Gaussian pulse
22 ( )
0 ( )
fr
fr
Uf dashed
Af solid
Discontinuous Galerkin
Locally Conservative Galerkin
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Gaussian pulse
0 ;frf
Grid Characteristic 1st order
Grid Characteristic 2nd order
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Gaussian pulse
22 ;fr
Uf
A
Grid Characteristic 1st order
Grid Characteristic 2nd order
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Gaussian pulse
0 ;frf
Grid Characteristic 1st order
Grid Characteristic 2nd order
2 ,P A c f A
0 0
0 0
exp 1 1,
ln ,
A A A Af A
A A A A
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Gaussian pulse. Amplitude
0 ;frf
Grid Characteristic 2nd order(exponent)
Grid Characteristic 2nd order(sqrt)
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Gaussian pulse. Distance traveled
Grid Characteristic 2nd order(exponent)
Grid Characteristic 2nd order(sqrt)
Discontinuous Galerkin(sqrt)
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Shock formation in a strait vessel
~ 0.4 s; 2 m(GC 1st order,Exponent wall state)
Mathematical analysis of the quasilinear eects in a hyperbolicmodel blood ow through compliant axi-symmetric vessels Suncica Canic and Eun Heui KimMath. Meth. Appl. Sci. 2003; 26:1161–1186 (DOI: 10.1002/mma.407)
~ 0.478 s; 2.95 m (theory)
~ 0.57 s; 3.3 m (two-step Lax–Wendroff)
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AutoregulationEd VanBavel, Jos P.M. Wesselman, Jos A.E. Spaan Myogenic, Activation and Calcium Sensitivity of Cannulated Rat Mesenteric Small Arteries.Circulation Research,1998
Rat artery
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AutoregulationEd VanBavel, Jos P.M. Wesselman, Jos A.E. Spaan Myogenic, Activation and Calcium Sensitivity of Cannulated Rat Mesenteric Small Arteries.Circulation Research,1998
Rat artery
2
0
exp 1 1S
P cS
Wall state adaptation:
tT T
newPoldP12
new new
old old
c P
c P
(only arteries)
Heart cycle
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Autoregulation
Leg artery
time
Cross-section
No autoregulation
With autoregulation
Ed VanBavel, Jos P.M. Wesselman, Jos A.E. Spaan Myogenic, Activation and Calcium Sensitivity of Cannulated Rat Mesenteric Small Arteries.Circulation Research,1998
Rat artery
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\Silicon-tube model
Inlet: Q=Q(t) Outlets: RoutP P
QR
Koen S. Matthys, Jordi Alastruey, Joaquim Peiro, et. al., 2007
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\Thoracic aorta (15)
0 0.2 0.4 0.6 0.87
8
9
10
11
12
13
14
15
16
GCExp
Q,
ml/s
Time, s
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
Time, s
P, k
Pa
Exp
GC
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Right carotid (3)
GC 1st DG
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Discussion
Variety of 1d models
Different methods, wall state equations, etc.
Toro, Muller
