1

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”

2

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

3

Global blood flow

4

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

5

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

6

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

7

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

8

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

9

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

11

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

12

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

13

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

14

Elasticity modelling

f S S

15

Elasticity modelling

,P T f n h

,P S P S x

16

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

17

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

18

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

30

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

33

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

42

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)

45

Motivation

46

Motivation

47

Motivation

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AVM

49

50

, 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

52

Velocity embolisation quality

53

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

54

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

55In collaboration with Lavrentyev Institute of Hydrodynamics RAS

56

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

58

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)

59

Thank You!

General outlines of this work are presented at http://dodo.inm.ras.ru/research/haemodynamics