A stochastic Molecular Dynamics method for multiscale modeling of blood platelet phenomena
•
PIs : G.E. Karniadakis, P.D. Richardson, M.R. Maxey
• Collaborators : Harvard Medical School, Imperial College, Ben Gurion
•
Arterioles/venules 50 microns activated platelets
•
Platelet diameter is 2-4 µm
•
Normal platelet concentration in blood is 300,000/mm 3
•
Functions: activation, adhesion to injured walls, and other platelets
•Multiscale Simulation of Arterial Tree on TeraGrid

1
2
3
4

•Fibrinogen consists of three pairs of protein chains
•Prothrombin/thrombin activate fibrinogen
•Fibrinogen monomers create fibrin threads

dynamics (MD), and DPD in particular, a very effective simulation tool for biological flows.
• Couple DPD-MD at the molecular level (protein interactions, scales less than 10 nm), and DPD-continuum at the large scales (hybrid
3D/1D arterial tree model).
• Validate simulations of platelet aggregation against existing in-vivo and in-vitro experiments and quantify uncertainties.
• Study thrombous formation and migration in the circulatory system.
• Disseminate algorithmic framework for multiscale coupling and software to interested parties.
• Involve undergraduates in this research and introduce high-school students to computational science and cyber-infrastructure.

Dissipative Particle Dynamics (DPD) – Coarse-Grained MD
MD
•
Conservative
•
Dissipative
•
Random
DPD
•
Momentum-conserving
• Galilean-invariant
•
Off-lattice
• Soft-potentials
• Speed-up w.r.t. MD (N mol/DPD)
•1000 x N 8/3
; e.g. N=10: 500,000 times
• Drag coefficient
Periodic
F
• viscosity
Periodic

Intra-Polymer Forces – Combinations Of the Following:
• Lennard-Jones Repulsion
• Stiff (Fraenkel) / Hookean Spring
• Finitely-Extensible Non-linear Elastic (FENE) Spring

• Marko-Siggia WormLike Chain
Intra-Polymer Forces (continued)
Can be adjusted if M>2
(Underhill, Doyle 2004)
Stiff: Schlijper, Hoogerbrugge, Manke, 1995
Hookean + Lennard-Jones: Nikunen, Karttunen, Vattulainen, 2003
FENE: Chen, Phan-Thien, Fan, Khoo, 2004

R g

( M

1 )
0 .
50
R g

( M

1 )
0 .
59
Flory Formula
  d
3

2
Radius of Gyration for Polymer Chains
Linear, ideal
R g
2 
1
M i
M 

1
( R i

R cm
)
2
Excluded volume, real
100 beads
50 beads
5 beads
10 beads
20 beads

Mixing Soft-Hard Potentials
Motivation for 2 different time-steps (Δt,δt):
Symeonidis & Karniadakis, J. Comp. Phys., on line, 2006
Solvent
(soft repulsive)
Polymer
Lennard-Jones
(hard repulsive)
Forrest+Suter, (J. Chem. Phys., 1995) idea of pre-averaging - in the spirit of conservative forces in DPD solvent

DNA Dynamics: Shear Flow – Wormlike Chain
Sc ~ 35
Sc ~ 690
Sc ~ 2574
Sc ≈ 1.4 x Γ 2 k
B
T=0.2

FENE Chains in Poiseuille Flow
10 beads
H/2R g
=3.96
60 beads
H/2R g
=1.32
Center-of-Mass Distribution From Wall

Stochastic Model - First Simulation of Begent & Born Experiment
•
Thrombus growing on a blood vessel wall in vivo
•
Accumulation of platelets in a thrombus
• Exponential thrombus growth rate coefficients -- effects of pulsation (right)

•DPD simulations show exponential growth rate of thrombus
• RBCs increase diffusivity

•Effects of red blood cells (Experiment I, in vitro results)
•Deformation of cells (effect on aggregation rates)
•Model plasma adhesive proteins (vWf, fibrinogen, …)
•Simulate diffusion of chemicals (ADP, …)
•Validation against available experimental results
•Gorog’s hemostatometer (in-vitro)
•Begent & Born (in-vivo)

References on Dissipative Particle Dynamics
•E. Keaveny, I. Pivkin, M.R. Maxey and G.E. Karniadakis, “A comparative study between dissipative particle dynamics and molecular dynamics for simple- and complex-geometry flows”, J. Chemical Physics, vol. 123, p. 104107, 2005.
•I. Pivkin and G.E. Karniadakis, “A new method to impose no-slip boundary conditions in dissipative particle dynamics”, J. Computational Phys., vol. 207, pp. 114-128, 2005.
•V. Symeonidis, G.E. Karniadakis and B. Caswell, “A seamless approach to multiscale complex fluid simulation”,
Computing in Science & Engineering, pp. 39-46, May/June 2005.
•V. Symeonidis, G.E. Karniadakis and B. Caswell, “Dissipative particle dynamics simulations of polymer chains:
Scaling laws and shearing response compared to DNA experiments”, Phys. Rev. Lett., vol 95, 076001, 2005.
•V. Symeonidis & G.E. Karniadakis, “A family of time-staggered schemes for integrating hybrid DPD models for polymers: Algorithms and applications”, J. Computational Phys., available on line, 2006.
•I. Pivkin and G.E. Karniadakis, “Coarse-graining limits in open and wall-bounded DPD systems”, J. Chemical
Physics, vol 124, 184101, 2006.
•I. Pivkin and G.E. Karniadakis, “ Controlling density fluctuations in wall-bounded DPD systems, Phys. Rev. Lett., vol 96 (20), 206001, 2006