Molecular scale

RBC aggregationNon-Newtonianblood model

Cell–ECM interaction

Computational angioplastystent surgery modelingGay, Zhang, and Liu

Vascular atherogenesis andgrowth of intimal hyperplasiaS.Liu, NWU

Leftatrium

Leftventricle

Rightatrium

Rightventricle

?-actinin

Vinculin

Cappingprotein

Fibronectin

Actinfilament

Paxillin

Integrin)

talin

Self-organizationof microtubules,Surrey et al.

10–3 m 10–6 m

Subcellularscale

Organic scale

Biofiberstructures

Actin filamentsG.Schatz, NWU

Hughes et al.,Texas-AustinLiuetal., NWU

Focal adhesioncomplex

10–1 m 10–9 m10–7–10–8 m

Vessel scale Cellular scale

50 nm

Plate 1 Modeling of biological processes using multiscale techniques. Middle image in thesecond column is reproduced from Liu (1998) with permission from Elsevier. Reprinted fromAtherosclerosis, 140(2), Liu S. Q., Prevention of focal intimal hyperplasia in rat vein graftsby using a tissue engineering approach, 365–377, 1998, with permission from Elsevier.

Plate 2 Deposition of an amorphous carbon film (green atoms) on top of a diamondsubstrate (red atoms).

(a) (b)

Plate 3 Initial conditions for two-dimensional wave propagation example. Contours ofdisplacement magnitude shown. A later snapshot of wave propagation from the MD regioninto the continuum region. Contours of displacement magnitude shown. Reproduced fromPark et al. (2005c) with permission from Taylor & Francis.

Plate 4 Snapshots of FEM deformation as a response to MD crack propagation. Reprintedfrom Journal of Computational Physics, 207(2), Park et al., Three-dimensional bridgingscale analysis of dynamic fracture, 588–609, 2005, with permission from Elsevier.

Plate 5 Submicro scale mechanism of failure between two microscale voids. High stressbetween the voids leads to debonding of submicro scale particles, and eventual void linkage.

Plate 6 Snap-shots of the localization-induced debonding process. Reprinted from Com-puter Methods in Applied Mechanics and Engineering, 193, Hao et al., Multi-scale con-stitutive model and computational framework for the design of ultra-high strength, hightoughness steels, 1865–1908, 2004, with permission from Elsevier.

Plate 7 Ductile fracture simulator. Reprinted from Computer Methods in Applied Mechan-ics and Engineering, 193, Hao et al., Multi-scale constitutive model and computationalframework for the design of ultra-high strength, high toughness steels, 1865–1908, 2004,with permission from Elsevier.

Plate 8 Homogenized continuum modeling of crack propagation and healing in the BSSSMA composite.

Plate 9 Fiber–matrix debonding in the SMA composite on the course of a fracture–healingcycle. Seen on the middle and bottom snapshots of this simulation, voids are formed inbetween the spherical parts of the reinforcing inclusion and the matrix material.

(a) Heart model immersed in fluid mesh (b) Aortic valve

Plate 10 The Heart model (Liu et al. 2004b).

(a) 3D RBC Model (b) RBC Cross-Section (c) RBC Mesh

Plate 11 Three-dimensional finite element mesh of a single RBC model. Reproducedwith permission from Liu Y et al., International Journal for Numerical Methods in Fluids,published by John Wiley and Sons Ltd, 2004.

Plate 12 Simulation of the assembly of CNTs between semicircular electrodes by theapplication of an AC field. Three processes of assembly, namely, the transport, attractionand alignment of the nanotubes are shown.