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.

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

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A stochastic molecular dynamics method for multiscale modeling of blood platelet phenomena

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


Platelet aggregation

Interaction with

activated platelet,

injured vessel wall

Activation delay time,

chosen randomly

between 0.1 and 0.2 s

ACTIVATED

adhesive

PASSIVE

non-adhesive

TRIGGERED

non-adhesive

If not adhered after 5 s

- passive - triggered - activated

Platelet Aggregation

RBCs are treated as a continuum

Pivkin, Richardson & Karniadakis, PNAS, 103 (46), 2006


A stochastic molecular dynamics method for multiscale modeling of blood platelet phenomena

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


A stochastic molecular dynamics method for multiscale modeling of blood platelet phenomena

- passive - triggered - activated

Platelet Aggregation and RBCs

Model RBCs as rigid spheres of large diameter


A stochastic molecular dynamics method for multiscale modeling of blood platelet phenomena

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


Increase of aggregate growth for large aggregates

Increase of aggregate growthfor large aggregates

Black curves – platelets only

Red curves – platelets in the presence of large spheres


A stochastic molecular dynamics method for multiscale modeling of blood platelet phenomena

DPD

MD

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.,19:155-160, 1992


Conservative force

DPD

MD

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.


Dissipative and random forces

F1random

F1dissipative

V1

V2

F2dissipative

F2random

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


Solid objects in dpd

Solid Objects in DPD

Solid objects are modeled by collections of DPD particles.


Deformable rbcs

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


Biconcave and cup shapes

Biconcave and Cup Shapes

Deflating sphere to 65% of volume


Shear

Shear


Microchannel

Microchannel

Experiment by Stefano Guido,

Università di Napoli Federico II


A stochastic molecular dynamics method for multiscale modeling of blood platelet phenomena

RBCs


Open issues

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


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