11

Transport phenomena and structure formation at micro/nanometerscale in

biomedicine and material science Daniel Vizman, West University of Timisoara, Faculty of Physics Victor Sofonea, Center for Fundamental and Advanced Technical

Research, Romanian Academy – Timisoara Branch Titus Beu, Babes-Bolyai University, Faculty of Physics, Cluj- Napoca Adrian Neagu, “Victor Babes” University of Medicine and Pharmacy,

Timisoara

22

MOLECULARLEVEL (~10-9m)

MESOSCALE (10-6m)

MACROSCALE(>10-3m)

ParticlePosition momentum,

interaction forces

Distribution functionBoltzmann Equation

Challenge: Multiscale simulation Challenge: Multiscale simulation

Continuum media mechanics mass, momentum, energy

equations

•Monte Carlo•Molecular Dynamics

•Lattice Boltzmann•Phase Field

•Finite Element•Finite Volume

33

MONTE CARLO SIMULATIONSMONTE CARLO SIMULATIONSMONTE CARLO SIMULATIONSMONTE CARLO SIMULATIONS

The biological tissue is represented on a cubic lattice. Cell rearrangements are obtained by random sampling.

Probability of acceptance

Monte Carlo simulations yield energetically favourable tissue conformations by minimizing the total energy of adhesion.

UNIVERSITATEA DE MEDICINĂ ŞI FARMACIE “VICTOR BABEŞ” TIMIŞOARA,

CENTRUL DE MODELARE A SISTEMELOR BIOLOGICE ŞI ANALIZA DATELOR

(CMSBAD)

UNIVERSITATEA DE MEDICINĂ ŞI FARMACIE “VICTOR BABEŞ” TIMIŞOARA,

CENTRUL DE MODELARE A SISTEMELOR BIOLOGICE ŞI ANALIZA DATELOR

(CMSBAD)

1P 0 if E

)exp( TEEP otherwise

ET = effective measure of cell motility.

44

EXAMPLEEXAMPLEEXAMPLEEXAMPLE

Spontaneous emergence of tubular structures:

TE7.001

Aggregate:

•200 m diameter

•Rint/Rext = 0.8

•2060 cells

•2109 nodes occupied by gel

TE5.102

TE3.012

0 Type

1 Type

2 Type

Neagu A. et al. Phys. Rev. Lett. 95:178104-1– 4.

20 000 MCS 100 000 MCS

55

Ion channels – proteins that control the passage of ions (Na+, K+ etc) across cell membranes

Molecular dynamics – solving Newton’s law for all particles

The electrolyte – 1M NaCl solution: 600 H2O molecules, 8 Na+ and 8 Cl-

Water – rigid molecules:• Site-site intermolecular potential TIP4P• Rigid-body dynamics – rotation about CM – quaternions

Periodic boundary conditions

Coulomb interactions – Ewald sum technique with lattice-based charge distribution and Fast Fourier Transform – increases speed substantially

Titus Beu, University ”Babeş-Bolyai”, Faculty of PhysicsTitus Beu, University ”Babeş-Bolyai”, Faculty of PhysicsTitus Beu, University ”Babeş-Bolyai”, Faculty of PhysicsTitus Beu, University ”Babeş-Bolyai”, Faculty of Physics

Molecular Dynamics Simulation of biological ion channels

66

Titus Beu, University ”Babeş-Bolyai”, Faculty of PhysicsTitus Beu, University ”Babeş-Bolyai”, Faculty of PhysicsTitus Beu, University ”Babeş-Bolyai”, Faculty of PhysicsTitus Beu, University ”Babeş-Bolyai”, Faculty of Physics

The model membrane channel

similar to nicotine acetycloline receptor 388 interaction sites: charges (-0.5e, -0.35e, +0.35e, +0.5e, neutral)

+ Lennard-Jones interactions

11 20-atom rings11 20-atom rings

relative rotation 9relative rotation 9°°

77

SNAPSHOSNAPSHOTT

88

Phase space discretized Boltzmann equations with BGK approximation

Equilibrium distribution functions

Boltzmann equation:

)],(),([ 1 )],( [1 ),(e),( teqift

if

ift

iTBkt

if

it

ift

xxxueFxx

the force term

relaxation time

collisionsttftf

mt

),( ),(

vr,vr,Fv vr

F

22422

2)(2

1 cc

iciniw

eqif

uuueue

Center for Fundamental and Advanced Technical Research Romanian Academy – Timisora Branch,

Center for Fundamental and Advanced Technical Research Romanian Academy – Timisora Branch,

Lattice Boltzmann method

99

Approach: development of appropiate numerical schemes; implementation of diffuse reflection boundary conditions; parallel computing

thermal transpiration

Center for Fundamental and Advanced Technical Research Romanian Academy – Timisora Branch,

Center for Fundamental and Advanced Technical Research Romanian Academy – Timisora Branch,

Objective: investigation of two - dimensional, non - isothermal fluid flow phenomena in micro – electro – mechanical systems (MEMS)

1010

pressure-driven

Flow

Rarefaction effects in micro-channels

Velocity slip and temperature jump in Couette flow

Center for Fundamental and Advanced Technical Research Romanian Academy – Timisora Branch,

Center for Fundamental and Advanced Technical Research Romanian Academy – Timisora Branch,

1111

forward

Process paramete

rs

e.g. geometry, heating power

Crystalproperties

defined by application,

e.g. LED, Laser diode

Growthcondition

s

e.g. temperature T and stress vm

distribution

T(x,y,t,t) vm

Formation of crystal defects

b

desired (doping),

undesired (e.g. dislocation)

inverse

goal: understanding of relation between crystal properties and the conditions (parameters) of the crystal growth process

Faculty of Physics, West University of Timisoara Faculty of Physics, West University of Timisoara

1212

global 3D

Global 3D-modeling is very expensive.

2D axi-symmetricproblem: 3D-phenomena

partial 3DSTHAMAS3D – developed in collaboration with Fraunhofer Institute, Erlangen, Germany

Reduction of the complexity

• by using symmetry effects (e.g. axi-symmetric) • simplification of geometry (partial model)

Faculty of Physics, West University of Timisoara Faculty of Physics, West University of Timisoara

Development of Simulation Programs for Crystal Growth

1313

0.1

1

10

100

1000

10000

100000

1000000

Perfo

rman

ce [G

Flop

/s]

N=1

N=500

Sum

N=10

1 TFlop/s

1 PFlop/s

ASCI

Earth Simulator

Challenges in Computational Power Challenges in Computational Power

•Computing speeds advances (uni- and multi-processor systems), Grid Computing• Systems Software•Applications Advances (parallel & grid computing)•Algorithms advances (parallel &grid computing, numeric and non-numeric techniques: dynamic meshing, data assimilation)

NANOSIM – cluster at West University of Timisoara, Faculty of Physics

1414

Conclusions Conclusions

•Challenge is to integrate what is happening on the atomic level with the mesoscopic and macroscopic classical level. Collaboration between scientists ‘working at every level’ is strongly necessary

•Theoretical and computational skills can be learned by training, meaningful applications is achieved only with experience. User friendly software should be developed.

•Grids and Service Oriented Architectures are necessary (worldwide networks of interconnected computers that behave as a single entity) to increase computational power

•Local hardware infrastructure development necessary

•While computational experiment is much less expensive than real experiment it is necessary to develop an application oriented computational culture and community

1515

Acknowledgements Acknowledgements

The authors would like to acknowledge the Romanian Ministry of Education and Research for the financial

assistance under CEEX 11/2005