Visualization of Platelets in Small Blood Vessels

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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 Aggregation
RBCs are treated as a continuum
Pivkin, Richardson Karniadakis, PNAS, 103 (46),
2006
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Small Aggregates, no RBCs
The increase in volume of platelet aggregate is
plotted semi-logarithmically against time.
Effect of mean blood flow velocity on the growth
rate constant (s-1) of platelet aggregate.
Simulation results qualitatively agree with
experimental data from Begent and Born
Begent and Born, Nature, Vol. 227, No. 5261, pp.
926-930, 1970
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Platelet Aggregation and RBCs
Model RBCs as rigid spheres of large diameter
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Small aggregates, RBCs
The increase in volume of platelet aggregate is
plotted semi-logarithmically against time.
Effect of mean blood flow velocity on the growth
rate constant (s-1) of platelet aggregate.
Black curves platelets only Red curves
platelets in the presence of large spheres
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Increase of aggregate growthfor large aggregates
Black curves platelets only Red curves
platelets in the presence of large spheres
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Dissipative Particle Dynamics (DPD)

• Dissipative Particle Dynamics (DPD) was
  introduced by
• Hoogerbrugge and Koelman in 1992
• Particles interact through a simple pair-wise
  potential
• The DPD scheme consists of the calculation of the
  position and velocities of interacting particles
  over time. The time evolution of positions and
  velocities are given by

P.J. Hoogerbrugge and J.M.V.A. Koelman,
Europhys.Lett.,19155-160, 1992
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Conservative Force
From Forrest and Sutter, 1995
Soft potentials were obtained by averaging the
molecular field over the rapidly fluctuating
motions of atoms during short time intervals.
This approach leads to an effective potential
similar to one, used in DPD.
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Dissipative and Random Forces

• Dissipative (friction) force is reducing the
  relative velocity of the pair of particles
• Random force compensate for eliminated degrees
  of freedom
• Dissipative and random forces form DPD
  thermostat
• The magnitude of dissipative and random forces
  are defined by
• fluctuation dissipation theorem

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Solid Objects in DPD
Solid objects are modeled by collections of DPD
particles.
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Deformable RBCs
Membrane model J. Li et al., Biophys.J, 88
(2005)
bending and in-plane energies, constraints on
surface area and volume

• Coarse RBC model
• 500 DPD particles connected by links
• Average length of the link is about 500 nm

• RBCs are immersed into the DPD fluid
• The RBC particles interact with fluid particles
  through DPD potentials
• Temperature is controlled using DPD thermostat

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Biconcave and Cup Shapes
Deflating sphere to 65 of volume
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Shear
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Microchannel
Experiment by Stefano Guido, Università di
Napoli Federico II
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RBCs
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Open Issues

• Identify effective parameters for coarse RBC
  membrane
• Investigate dimensional consistency in DPD
• Validation with experiments, optical
  tweezers(MIT) or microchannel flow(MIT/Italy)
• Stress-free constraint