Matrix stiffness that is sensed by a cell or measured by a purely physical probe reflects the intrinsic elasticity of the matrix and also how thick or thin the matrix is. Here, mesenchymal stem cells (MSCs) and their nuclei spread in response to thickness-corrected matrix microelasticity, with increases in nuclear tension and nuclear stiffness resulting from increases in myosin-II and lamin-A,C...

BACKGROUND Reports of adhesions in cells growing in 3D vary widely-from nonexistent to very large and elongated-and are often in apparent conflict, due largely to our minimal understanding of the underlying mechanisms that determine 3D cell phenotype. We address this problem directly by systematically identifying mechanisms that determine adhesion in 3D matrices and, from our observations, deve...

In this paper, we present an adaptive approach for simulating elastic deformation of homogeneous and inhomogeneous objects based on continuum mechanics. In typical adaptive simulation approaches, the deforming elastic object is usually subdivided to form a tree structure on the fly. However, they are not directly applicable for inhomogeneous elastic deformation, since the elasticity matrix, whi...

Mineralized collagen fibrils have been usually analyzed like a two-phase composite material where crystals are considered as platelets that constitute the reinforcement phase. Different models have been used to describe the elastic behavior of the material. In this work, it is shown that when Halpin-Tsai equations are applied to estimate elastic constants from typical constituent properties, no...

Hierarchical matrices provide a technique to efficiently compute and store explicit approximations to the inverses of stiffness matrices computed in the discretization of partial differential equations. In a previous paper, Le Borne [2003], it was shown how standard H-matrices must be modified in order to obtain good approximations in the case of a convection dominant equation with a constant c...

Hierarchical matrices provide a data-sparse way to approximate fully populated matrices. In this paper we exploit H-matrix techniques to approximate the LU -decompositions of stiffness matrices as they appear in (finite element or finite difference) discretizations of convectiondominated elliptic partial differential equations. These sparse H-matrix approximations may then be used as preconditi...