## Objectives

The aim of the Summer School is to present a state of-the-art introduction to biomechanical modeling and computation at different length scales. The emphasis is on the nonlinear behavior embracing models of molecular dynamics, single filaments, network structures, the cytoskeleton and the nucleus. Multiscale models and continuum models for soft tissues including arteries, aortic valves, cartilage and the cornea will also be presented.

The Summer School will include lectures on single molecule and filament mechanics and on networkbased formulations with actin networks as an example including shear-driven visco- and poroelastic effects. Molecular dynamics models are introduced to demonstrate force-induced conformational changes that expose the vinculinbinding site under applied force along a realistic pulling direction; the molecular mechanics of actin binding proteins, i.e. alpha-actinin and filamin, is examined. Lectures introduce cellular mechanotransduction and provide an overview of cytoskeletal and nucleus models.

Basic equations of continuum mechanics (kinematics, stress, balance laws), constitutive laws for elastic materials (general principles and material symmetry) and the elasticity of fiber-reinforced solids are reviewed. Lectures introduce the mixture theory for tissues and cells. The concept of flow and deformation in soft hydrated tissues, a review of physical chemistry, solvent and solute transport in tissues and across cell membranes, and Donnan osmotic swelling of charged hydrated tissues are provided. Models for soft tissues with particular reference to the fibrous structure and the effect of fiber dispersion are presented. Particular applications are: arterial tissue, discussion of the extension and inflation of an artery, residual stresses and their effect on the mechanical response, balloon angioplasty, stenting, cerebral aneurysms and AAA including growth and remodeling; aortic valves including the dynamic behavior at the cell, tissue, and organ length scales; cartilage and the cornea.

## Audience

The Summer School is addressed to PhD students and postdoctoral researchers in mechanical and civil engineering, applied mathematics, (bio)physics, biomedical engineering, physiology and materials science interested in broadening their interests in the area of biomechanics, and more senior scientists and engineers (including some from relevant industries).

## Preliminary Suggested Readings

- G.A. Ateshian, C.T. Hung: The natural synovial joint: properties of cartilage. Proc of the Institution of Mechanical Engineers, J Eng Trib, 220:657-670, 2006. [pdf]
- G.A. Ateshian, K.D. Costa, C.T. Hung: A theoretical analysis of water transport through chondrocytes. Biomech Model Mechanobiol, 6:91-101, 2007. [pdf]
- E.U. Azeloglu, M.B. Albro, V.A. Thimmappa, G.A. Ateshian, K.D. Costa: Heterogeneous transmural proteoglycan distribution provides a mechanism for regulating residual stresses in the aorta. Am J Physiol Heart Circ Physiol, 294:H1197-1205, 2008. [pdf]
- G.A. Holzapfel, R.W. Ogden: Biomechanics of Soft Tissue in Cardiovascular Systems. Springer-Verlag, Wien, New York, 2003 (see the Chapters by the Editors). [pdf] [pdf]
- G.A. Holzapfel: Collagen in arterial walls: biomechanical aspects, in P. Fratzl (ed.): Collagen. Structure and Mechanics, Chapter 11, Springer-Verlag, Heidelberg, pp. 285-324, 2008. [pdf]
- M.R.K. Mofrad, R.D. Kamm (eds.): Cytoskeletal Mechanics: Models and Measurements. Cambridge University Press, 2006. [link]
- K.S. Kolahi, M.R.K. Mofrad: Molecular mechanics of filamin's rod domain. Biophys J, 94:1075-83, 2008. [pdf]
- M. Kroon, G.A. Holzapfel: Estimation of the distributions of anisotropic, elastic properties and wall stresses of saccular cerebral aneurysms by inverse analysis. Proc R Soc Lond A, 464:807-825, 2008. [pdf]
- J.S. Palmer, M.C. Boyce: Constitutive modeling of the stress-strain behavior of F-actin filament networks. Acta Biomater, 3:597-612, 2008. [pdf]
- R.W. Ogden: Elements of the theory of finite elasticity, in Y.B. Fu, R.W. Ogden (eds.): Nonlinear Elasticity: Theory and Applications. Cambridge University Press, pp. 1-57, 2001. [pdf]
- G. Sommer, T.C. Gasser, P. Regitnig, M. Auer, G.A. Holzapfel: Dissection of the human aortic media: an experimental study. J Biomech Eng, 130:021007, 2008. [pdf]
- E.J. Weinberg, M.R.K. Mofrad: Transient, three-dimensional, multiscale simulations of the human aortic valve. Cardiovasc Eng, 4:140-55, 2007. [pdf]