Multiscale Modeling and Simulation - mapper-project.eu
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Multiscale Modeling and Simulation - mapper-project.eu
What (physical) principles must be satisfied during the transfer of information? ..... Substitute S with B if interactio
Multiscale Modeling and Simulation Alfons Hoekstra University of Amsterdam MAPPER Summerschool 2013 The Mapper project receives funding from the EC's Seventh Framework Programme (FP7/2007-2013) under grant agreement n° RI-261507.
Main contributors • • • •
Bastien Chopard – University of Geneva Jean-Luc Falcone – University of Geneva Eric Lorenz – University of Amsterdam Joris Borgdorf – University of Amsterdam
Special thanks to Pat Lawford, Rod Hose and Julian Gunn from Sheffield, UK
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What do we mean with ‘scale’?
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Nature is Multiscale • Natural processes are multiscale • 1 H2O molecule • A large collection of H2O molecules, forming H-bonds • A fluid called water, and, in solid form, ice.
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Multiscale models in Biomedicine Environment
Across Temporal scales
Population Organism Organ System
Organ Tissue Cell
Across dimensional scales
Molecule Atom H H C C H H
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What do we mean with ‘scale’? ‘typical’ length scale (level of organisation) quantum molecular macro-molecular sub-cellular cellular tissue organ organ system organism environment
‘typical’ time scale ‘fast’ ‘intermediate’ ‘slow’
In most multiscale studies we couple something ‘small and fast’ to something ‘large and slow’
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What is the size of the scales?
picture taken from:" Peter J. Hunter and Thomas K. Borg," Integration from Proteins to Organs, the Physiome Project," Nature Reviews Molecular Cell Biology, 4, 237-243, 2003"
10-9m
10-6m
10-3m
100m
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Example: drug eluting stent in a coronary artery • So, how do you figure out the scales? • First a few pictures to get going
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Coronary artery disease
Gross appearance!
Angiogram! 10
Balloon Angioplasty and Stent implantation
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What is Restenosis? Neointima Media Lumen Stent strut
Porcine coronary artery section 28 days post stenting displaying substantial neointima.
Human angiogram depicting restenosis six months postPCI.
c
Longitudinal section through stented artery showing variation in reaction along vessel length
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SMCs (WSS color scale)! Stent! Flow (Ribbons, color scale)!
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Drug concentration! coloring!
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Example: drug eluting stent in a coronary artery • So, how do you figure out the scales? • Your turn
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Length scales diameter of artery diameter of stent strut diameter of smooth muscle cells size of red blood cells
à à à à
1,5 mm 100 µm 20 µm 10 µm
subcellular ? length of artery ? curvature of artery ? thickness of artery wall ? others? 17
Time scales pulsatile flow à diffusion of drugs in artery wall à cell cycle of smooth muscle cells à
O(1 s) O(10 h) O(30 h)
transport time of cells in boundary layer ? cell signaling ? others ?
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Scale Separation Map!
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Multiscale Modelling
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Why multiscale models? • There is simply no hope to computationally track complex natural processes at their finest spatio-temporal scales. • Even with the ongoing (exponential) growth in computational power
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Minimal demand for multiscale methods cost of multiscale solver A model of the process that occurs in the artery after stenting.
