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/mm 3 Functions: activation, adhesion to injured walls, and other platelets activated platelets Arterioles/venules 50 microns

Platelet and Fibrin Aggregation

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 N 8/3 ; e.g. N=10: 500,000 times 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, 1995 Hookean + Lennard-Jones: Nikunen, Karttunen, Vattulainen, 2003 FENE: Chen, Phan-Thien, Fan, Khoo, 2004 Marko-Siggia WormLike Chain Can be adjusted if M>2 (Underhill, Doyle 2004)

Radius of Gyration for Polymer Chains Flory Formula Linear, ideal Excluded volume, real 100 beads 10 beads 20 beads 50 beads 5 beads

Mixing Soft-Hard Potentials Polymer Lennard-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 k B T=0.2 Sc ≈ 1.4 x Γ 2 Sc ~ 690

Center-of-Mass Distribution From Wall 60 beads H/2R g = beads H/2R g =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 , 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 , V. Symeonidis, G.E. Karniadakis and B. Caswell, “A seamless approach to multiscale complex fluid simulation”, Computing in Science & Engineering, pp , May/June 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, , 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, I. Pivkin and G.E. Karniadakis, “Coarse-graining limits in open and wall-bounded DPD systems”, J. Chemical Physics, vol 124, , I. Pivkin and G.E. Karniadakis, “ Controlling density fluctuations in wall-bounded DPD systems, Phys. Rev. Lett., vol 96 (20), , 2006