A stochastic Molecular Dynamics method for multiscale modeling of blood platelet phenomena...
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Transcript of A stochastic Molecular Dynamics method for multiscale modeling of blood platelet phenomena...
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