血小板血栓生成過程のマルチスケール・マルチフィジックス解析

杉山 和靖 (理化学研究所・情報基盤センター)

課題ID: hp120238

Blood clot in vessel① Bleed ② Platelet aggregation ③ Coagulation

(fibrinous network)

④ Vessel repair ⑤ Fibrolytic activity ⑥ Recanalization

http://www.hit-1.net/mimizu2/kesen.htm

→ A major role is the arrest of bleeding (hemostasis)

Thrombus simulator

exaggerated platelet aggregation→ vessel occlusion→ myocardial and cerebral infarctions

Thrombus

fluid-structure/membrane interaction, ligand-receptor interactionbiochemical reaction, ...

In the present study: the primary stage (platelet aggregation)

*Gaehtgens et al. (1980) Blood Cells, 6, 799.・multiphase flow nature・nolinearity in geometry

Feasibility of blood flow simulations

・arteriole ～100μm diameter・Red Blood Cell (RBC): 8μm diameter, 2μm thickness・platelet: 2μm diameter・grid size: O(0.1μm)

length scales

x O(103)→ O(109) degree of freedom

in 3DphenomenaRBC and platelet motions, blood rheology

challenging issueto treat a large number of soft dispersed bodiesin massively parallel computing

Blood flow(continuum dynamics)

Ligand-Receptor bond(stochastic)

Molecular interaction(molecular dynamics)

Simulation approach (multi-scale/multi-physics)

GPIbα-vWF・bond formation/breakage・elastic force

0, | | (( ) ,) ( )s s sm t p P τv σ qv nv v

211 2 2

2 (II 1)I I

,

I tr( ) 2, II {(tr( )

III 1

tr( )} 1.

s ss s

s sss

s s s s

W W

τ B P

B B B B

in-plane stress strain energy function

surface left Cauchy-Green deformation

surface projection, ,

,

Ts s s R

B P G P G F P FP I nn

Fluid-Structure/Membrane Interaction (on a fixed mesh)

shear tension

12

{( ) ( )} ,, .

s b R

R R

E

q P κ P Pκ n n

・ Sugiyama, Ii et al. (2011) J. Comput . Phys., 230, 596.・Ii, Gong et al. (2012) Comm. Comput. Phys., 12, 544.

2 ,G σ D BCauchy 's stress tensor

s

( ) 0, ( ) 0,t t s s v v

( ) ,

( ) ,

Tt

Tt s s s s

B v B L B B L

G v G L G G L

structure/membrane kinematics (on a fixed mesh)

( ) ,Tt R R R v n L n

, , .| | | |s s

B P G P n κ

VOFs

left Cauchy-Green deformation tensor, surface strain

reference frame curvature

T L v

Typical result of blood flow simulations

including RBCs and plateletsvessel diameter: 104μmHt = 20%

3,072x640x640 mesh4800 nodes

1 exp( )

1 exp( )

formation

breakageRandom numbers[0,1] ( , : )

f f f

r

f

r

r

r

P k

P k

t R

t RR R

20

0

20

0

( )( ) exp2

( )( ) ex (p2

)

f f ts

r

b

r p tsb

llk l kk T

lk l lkk T

0( )p lf l Luo et al. (2007) Blood, 109, 603.

Stochastic model with energetic elasticity

4

10 0

10 [N/m], 0.9 [N/m]

60 [nm], 3 [s ]

s

r

tp p

l k

Ligand-Receptor bond model

Eyring (1935) J. Chem. Phys., 3, 107.Bell (1978) Science, 200, 618.Dembo (1988) Proc. R. Soc. Lond. B, 234, 55.Hammer & Apte (1992) Biophys. J., 63, 35.Shiozaki et al. (2012) J. Biomech. Sci. Eng.,7, 275.

forward reaction rate

reverse reaction rateFox et al. (1988) J. Biol. Chem., 263, 4882.Arya et al. (2005) Biophys. J., 88, 4391.Kim et al. (2010) Nature, 466, 992.

Constants for the model

formation

breakage

Development of adhesion force and platelet motion

Platelet adhesion in channel flowwithout RBCs

with RBCs

・ platelet: undergoing a hydrodynamic lift force

・ RBCs： inducing a wall-normal fluctuation・ platelet: getting a chance to adhere to the wall

temporal change in the number of GPIbα-vWF bonds

Platelet adhesion in stenosed blood vesselvessel diameter: up to 40μmup to 128 nodes

SummaryComputational models for Fluid-Structure/Membrane Interaction and platelet adhesion• Shear dependent adhesion and rolling behaviors• Spanwise motion induced by randomly formed bond• Flow fluctuation-induced adhesion (w/ RBCs)

Future works• Further development for massively parallel computing• Comparison with flow chamber experiment

(~100m channel height)