A stochastic Molecular Dynamics method for multiscale

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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/mm3
• Functions activation, adhesion to injured walls,
  and other platelets

• Multiscale Simulation of Arterial Tree on TeraGrid

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Platelet and Fibrin Aggregation
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2
3
4
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Creation of Fibrin Threads

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

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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.

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Computational Methods

• Force Coupling Method (FCM) (continuum)
• Dissipative Particle Dynamics (DPD) (mesoscopic)
• Molecular Dynamics (LAMMPS)

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Dissipative Particle Dynamics (DPD)
Coarse-Grained MD

• Momentum-conserving
• Galilean-invariant
• Off-lattice
• Soft-potentials

DPD

• Conservative

• Speed-up w.r.t. MD (N mol/DPD)
• 1000 x N8/3 e.g. N10 500,000 times

• Dissipative

• Random

• Drag coefficient

• viscosity

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Intra-Polymer Forces Combinations Of the
Following

• Lennard-Jones Repulsion

• Stiff (Fraenkel) / Hookean Spring

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

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Intra-Polymer Forces (continued)

• Marko-Siggia WormLike Chain

Can be adjusted if Mgt2 (Underhill, Doyle 2004)
Stiff Schlijper, Hoogerbrugge, Manke,
1995 Hookean Lennard-Jones Nikunen, Karttunen,
Vattulainen, 2003 FENE Chen, Phan-Thien, Fan,
Khoo, 2004
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Radius of Gyration for Polymer Chains
Linear, ideal
Excluded volume, real
Flory Formula
100 beads
50 beads
20 beads
10 beads
5 beads
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Mixing Soft-Hard Potentials
Motivation for 2 different time-steps (?t,dt)
Symeonidis Karniadakis, J. Comp. Phys., on
line, 2006
Solvent (soft repulsive)
Polymer Lennard-Jones (hard repulsive)
ForrestSuter, (J. Chem. Phys., 1995) idea of
pre-averaging - in the spirit of conservative
forces in DPD solvent
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DNA Dynamics Shear Flow Wormlike Chain
Sc 35
Sc 690
Sc 2574
Sc 1.4 x G2
kBT0.2
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FENE Chains in Poiseuille Flow
10 beads H/2Rg3.96
60 beads H/2Rg1.32
Center-of-Mass Distribution From Wall
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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)

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Effects of Red Blood Cells

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

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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
• Gorogs hemostatometer (in-vitro)
• Begent Born (in-vivo)

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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