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Computational haemodynamics for clinical applications
Sergey Simakov
Moscow Institute of Physics and Technology
Moscow, INM, 16.04.2014
The British Council Reseacher Links Workshop“Mathematical and Computational Modelling in
Cardiovascular Problems”
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Review
Global blood flowClosed 1D modelElasticity modelingPhysiological reactions: gravity,
autoregulation
ApplicationsSport: stride frequency optimizationVascular surgery: stenosis treatment, cava
filtersEnhanced external counterpulsation (EECP)Arterio-venous malformation (AVM)
Patient specific fittingMulti-touch sensor panel1D core graph reconstruction
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Global blood flow
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Global blood flow
0
uSS
t x
02
020
0
2,
16 ... ,,2
S SP S Su u
u S SSS St x Sd
S S
1) Mass balance
2) Momentum balance
1 ,...,
0, 1M
m mk k k k
k k k
u S
, , 0,node mk k k m k k k k k kp S x p R u S x L
3) Boundary conditions at junctions
3.1
3.2
Compatibility conditions along outgoing characteristics
3.31 1 1 1n n n n
k k k ku S 2 1N equations
2 1N equations
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Boundary conditions at junctions
,k k kV S u
,k k kg
1
k k
kk
k k
u SF
A PV u
S
0ki k kiW A E
k kk
V Fg
t x
k k kki ki ki ki k
dV V VW W W g
dt t x
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Boundary conditions at junctions
k k kki ki ki ki k
dV V VW W W g
dt t x
0 00 0
0 0
( 1) exp 1 ,
( 1) ,
i k kk k k k
ki k k
ik k k k
S Su c S S
S S
u c S S
0 00 0
0 0
1exp 1 ,( 1) ,
, ( 1) ,
ikk k k k
k kki
ik k k k
Sc S S S
S SW
c S S S
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Boundary conditions at junctions
1, , , , 1
,2 ,2 ,2
1,1 ,1 ,2 ,11 1 1
,1 ,1 ,1
n n n nk M k M k M k MM M M
k k k kk
n n n nk k k k
k k k kk
V V V VW W g
h
V V V VW W g
h
1 1, , , 1 , , 1 ,
1 1,1 ,1,2 ,1,2 ,1
n n n nk M k M M k M M k M
n n n nk k k k
S u
S u
,k k kV S u
,k k kg
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Boundary conditions at junctions
1 1 1 1 11 1 1 1 1 1 1
1 1 1 1 12 2 2 2 2 2 21
1 1 1 1 1
( )... ...
n n n n n
n n n n nn
n n n n nN N N N N N N
S S P S
S S P SD
S S P S
F S R 0
1 1 1 1 1
, , , , , [1, ]N N N N N
j ii k ij ki j j k k
j i j i k i k ik j k j
D R R R i j k N
R R
N equations
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Heart model
Isovolumetric contraction (0.08 s), Ejection (0.293 с), Isovolumetric relaxation (0.067 с), Filling (0.56 с)
2
2( ) ( ), 1...4j j j ext
j j j jj
d V dV VI r p t P t j
dt dt c
ijij j i
ij
Q p pr
1 51 51 14 14
2 62 23 23
3 37 37 23 23
4 48 14 14
V Q Q
V Q Q
V Q Q
V Q Q
Mass conservation
Volume averaged chamber motion Left
auricle
Left ventricle
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Boundary conditions at heart junctions
Arteries:
Veins:
,0 ,0 , , 5,1 , 6,2
i ij k ki i
k k ijij
p t p Su t S t Q t i j
r
, , , , 3,7 , 4,8
j jk k ij j
k k k k ijij
p S p tu t L S t L Q t i j
r
Discretisation of compatibility conditions
1 1 1 1n n n nk k k ku S
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Next step with 1D
51 37( , )y V Q Q
51 37 5 7, ,Q Q s s
5,7max
i i
new old
is s
5 7,s s
5 7, ,y A t y B s s
1.
2.
3.
4.
5.
6.
Boundary conditions at heart junctions
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Elasticity modeling
4) Vessel wall elasticity
Pedley, Luo, 1998
Modelling
0 0
0 0
exp 1 1,
ln ,
S S S Sf S
S S S S
2,extP S P t x c f S Analytic approximation
f S S
Toro, Muller
Favorsky, Mukhin. SosninKholodov
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Elasticity modeling
T
,f Ts
* * *
*
, ,
0,
T R R
R
1) Tension in deformable fiber
2) Density of elasticity force
3) Tansmural pressure
for collagen fibers
* 1R
* 1R for the others
,p f n h
Peskin, Rosar 2001
X
s
Will be reported later today by V.Salamatova
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Elasticity modelling
f S S
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Elasticity modelling
,P T f n h
,P S P S x
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Physiological reactions: gravity
Ориентация сосуда
g
g cosk k
4) Right part of momentum balance: gravity
2
216 ...
2
Su u Pu
t x Sd
- space orientationk kg
( )k k t
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2
0
exp 1 1S
P cS
Wall elasticity adaptation
T T
newPoldP
Physiological reactions: autoregulation
12
new new
old old
c P
c P
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Physiological reactions: gravity and autoregulation
S
S
Head
Leg
AuotregulationCollapsible tube
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Physiological reactions: gravity and autoregulation
1Ed VanBavel, Jos P.M. Wesselman, Jos A.E. Spaan Myogenic, Activation and Calcium Sensitivity of Cannulated Rat Mesenteric Small Arteries. Circ. Research,1998
Rat artery response to static pressure load1
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Patient specific fitting
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Patient specific fitting
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Patient specific fitting: multi-touch sensor panel
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Patient specific fitting: multi-touch sensor panel
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Patient specific fitting
Normal Plaque Plaque with bypass
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1D Core grpah reconstruction
Reported yesterday by Yu. Ivanov
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Sport: stride frequency
optimization
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Skeletal-muscle pumping
max
2
2sin 12muscular k
s
PP t T
Wall state: muscularP S P S P
Venous valves in the leg
( , ), 0, max
, 0friction
friction friction
f s u uF A f
A u
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Кров
оток
ч
ерез
но
ги
Skeletal-muscle pumping
Right shin
Left shin
Right thigh
Left thigh
Pressure
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Skeletal-muscle pumping
Ven
ous
pre
ssur
e in
the
leg
Time
«Human Physiology» Schmidt, Thews
Simulations
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Height, cm
Str
ide
fre
que
ncy
Skeletal-muscle pumping
SSSSSSSSSSSSSSSSSS
SimulationsCompetition data
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Vascular surgery: stenosis
treatment
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Vascular surgery: atherosclerosis treatment
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Vascular surgery: atherosclerosis treatment
0
100
200
300
400
cm/s
3 4 12 5 7 9
Peak blood velocity before treatment
measured simulated
`
0
100
200
300
400
cm/s
3 4 12 5 7 9
Peak blood velocity after treatment
measured simulated
Patient-specific MRI and Doppler ultrasound data thanks to I.M. Sechenov First Moscow State Medical University (Ph.Kopylov, A.Tagiltsev)
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Vascular surgery: endovascular
implants
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Endovascular implants: cava filters
1D netwrok – placement, throbmus capturing, dissolving3D local blood flow – filter structure opotimisation
3D elasticity – pressure-area relationship, critical stress assesment
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Endovascular implants: cava filters
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1D global netwrok
1D global netwrok
3D flow
Multiscale (1D-3D)
Will be reported later today by T. Dobroserdova
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Enhanced External
Counterpulsation (EECP)
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Motivation
• Ischemia
• Arterial Hypertension
• Cardiovascular insufficiency
Indications
Effect
• Non-invasive increased
collateral perfusion
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EECP optimization: structural model
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EECP procedure
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A
B
C
EECP model
Wall state equation
2
0
exp 1 1 add
SP c P
S
:addP
Cardiac cycle
0 1
systole diastole
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EECP optimization
Terminal coronary arteryPressure averaged over cardiac cycle (kPa)
Continuous pulsations (standard procedure)
1 sec pulsation + 1 sec pause
10 sec pulsations + 10 sec pause
10 sec pulsations + 100 sec pause
Will be reported later today by T. Gamilov
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Arterio-Venous Malformation
treatment (AVM)
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Motivation
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Motivation
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Motivation
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AVM
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, 53,54R ref
i i
P refi
P Pe i
P
, 53,54R refi i
U refi
U Ue i
U
Pressure embolisation quality
Velocity embolisation quality
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Pressure embolisation quality
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Velocity embolisation quality
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ArteriesBefore surgery
BeforeAfter
12
3
4
5
6
7
2 4 6 8
2
4
6
8
12
34
5 6
7
20 40 60 80 100 120 140
10
20
30
40
50
60
70
V-P
Q-E
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1
234
2 0 4 0 6 0 8 0 1 0 0 1 2 0
2 0
4 0
6 0
1
23
4
1 2 3 4 5 6
1
2
3
4
5
6
ArteriesAfter
surgery
BeforeAfter
V-P
Q-E
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55In collaboration with Lavrentyev Institute of Hydrodynamics RAS
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Discussion
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•Fast patient-specific vascular network
skeletonization
•Reference geometry and patient-specific
fitting
•Fast simulations with automatic or semi-
automatic decision making process
Current problems
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Acknowledgements
Kholodov A.S.Kholodov A.S., , RAS corresponding memberRAS corresponding member(MIPT, Institute of computer-aided design RAS)(MIPT, Institute of computer-aided design RAS)Vassilevski Yu.V. Vassilevski Yu.V. D.Sc. D.Sc. (Institute of numerical mathematics (Institute of numerical mathematics RAS, MIPT)RAS, MIPT)Chupakhin A.P. Chupakhin A.P. D.Sc. D.Sc. (Lavrentyev Institute of Hydrodynamics (Lavrentyev Institute of Hydrodynamics RAS, NSU)RAS, NSU)Mynbaev O.A. MD (New European Surgical Academy, MIPT) Mynbaev O.A. MD (New European Surgical Academy, MIPT) Rezvan V.V. MD (N.V.Sklifosovsky Research Institute of Rezvan V.V. MD (N.V.Sklifosovsky Research Institute of Emergency Medicine)Emergency Medicine)Kopylov Ph.Yu. MD (1st Moscow State Medical University)Kopylov Ph.Yu. MD (1st Moscow State Medical University)
Salamatova V. (MIPT), Dobroserdova T.Salamatova V. (MIPT), Dobroserdova T. ( (INM, MSUINM, MSU), ), Gamilov Gamilov T.T. ( (MIPTMIPT), ), Khe A. (LIH, NSU), Cherevko A. (LYH, NSU), Ivanov Khe A. (LIH, NSU), Cherevko A. (LYH, NSU), Ivanov Yu.Yu. ( (INM, MSUINM, MSU), ), Kramarenko V.Kramarenko V. (MIPT(MIPT)), Gorodnova N. (MIPT), , Gorodnova N. (MIPT), Golov A. (MIPT), Pryamonosov R. (MSU), Zavodaev P. (MIPT)Golov A. (MIPT), Pryamonosov R. (MSU), Zavodaev P. (MIPT)
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Thank You!
General outlines of this work are presented at http://dodo.inm.ras.ru/research/haemodynamics