A stochastic Molecular Dynamics method for multiscale modeling of blood platelet phenomena Multiscale Simulation of Arterial Tree on TeraGrid PIs: G.E.

A stochastic Molecular Dynamics method for multiscale

modeling of blood platelet phenomena

•Multiscale Simulation of Arterial Tree on TeraGrid

•PIs: G.E. Karniadakis, P.D. Richardson, M.R. Maxey

•Collaborators: Harvard Medical School, Imperial College, Ben Gurion

•Platelet diameter is 2-4 µm

•Normal platelet concentration in blood is 300,000/mm3

•Functions: activation, adhesion to injured walls, and other platelets

activated platelets

•Arterioles/venules 50 microns

Platelet and Fibrin Aggregation1 2

3 4

Creation of Fibrin Threads

•Fibrinogen consists of three pairs of protein chains

•Prothrombin/thrombin activate fibrinogen

•Fibrinogen monomers create fibrin threads

Objectives

• Develop new algorithms that will make coarse-grained molecular 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.

Computational Methods• Force Coupling

Method (FCM) (continuum)

• Dissipative Particle Dynamics (DPD) (mesoscopic)

• Molecular Dynamics (LAMMPS)

MD DPD

Dissipative Particle Dynamics (DPD) – Coarse-Grained MD

•Momentum-conserving

•Galilean-invariant

•Off-lattice

•Soft-potentials

•Conservative

•Dissipative

•Random

•Speed-up w.r.t. MD (N mol/DPD)

•1000 x N8/3; e.g. N=10: 500,000 times

Periodic

Periodic

Periodic

Periodic

F

•Drag coefficient

•viscosity

Intra-Polymer Forces – Combinations Of the Following:

• Stiff (Fraenkel) / Hookean Spring

• Lennard-Jones Repulsion

• Finitely-Extensible Non-linear Elastic (FENE) Spring

Intra-Polymer Forces (continued)

Stiff: Schlijper, Hoogerbrugge, Manke, 1995Hookean + Lennard-Jones: Nikunen, Karttunen, Vattulainen, 2003FENE: Chen, Phan-Thien, Fan, Khoo, 2004

• Marko-Siggia WormLike Chain

Can be adjusted if M>2(Underhill, Doyle 2004)

M

icmig RR

MR

1

22 )(1

Radius of Gyration for Polymer Chains

59.0)1( MRg

50.0)1( MRg

Flory Formula

2

3

d

Linear, ideal

Excluded volume, real

100 beads

10 beads

20 beads

50 beads

5 beads

Mixing Soft-Hard Potentials

PolymerLennard-Jones

(hard repulsive)

Solvent(soft repulsive)

Motivation for 2 different time-steps (Δt,δt): Symeonidis & Karniadakis, J. Comp. Phys., on line, 2006

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 ~ 2574

Sc ~ 35

kBT=0.2

Sc ≈ 1.4 x Γ2

Sc ~ 690

Center-of-Mass Distribution From Wall

60 beadsH/2Rg=1.32

10 beadsH/2Rg=3.96

FENE Chains in Poiseuille Flow

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)

Effects of Red Blood Cells

•DPD simulations show exponential growth rate of thrombus

• RBCs increase diffusivity

Future Plans

•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