Stiffness Gradients Mimicking In Vivo Tissue Variation Regulate Mesenchymal Stem Cell Fate

Mesenchymal stem cell (MSC) differentiation is regulated in part by tissue stiffness, yet MSCs can often encounter stiffness gradients within tissues caused by pathological, e.g., myocardial infarction ∼8.7±1.5 kPa/mm, or normal tissue variation, e.g., myocardium ∼0.6±0.9 kPa/mm; since migration predominantly occurs through physiological rather than pathological gradients, it is not clear whether MSC differentiate or migrate first. MSCs cultured up to 21 days on a hydrogel containing a physiological gradient of 1.0±0.1 kPa/mm undergo directed migration, or durotaxis, up stiffness gradients rather than remain stationary. Temporal assessment of morphology and differentiation markers indicates that MSCs migrate to stiffer matrix and then differentiate into a more contractile myogenic phenotype. In those cells migrating from soft to stiff regions however, phenotype is not completely determined by the stiff hydrogel as some cells retain expression of a neural marker. These data may indicate that stiffness variation, not just stiffness alone, can be an important regulator of MSC behavior

On discontinuous strain fields in incompressible finite elastostatics

AbstractPiece-wise homogeneous three-dimensional deformations in incompressible materials in finite elasticity are considered. The emergence of discontinuous strain fields in incompressible materials is studied via singularity theory. Since the simplest singularities, including Maxwell’s sets, are the cusp singularities, cusp conditions for the total energy function of homogeneous deformations for incompressible materials in finite elasticity will be derived, compatible with strain jumping. The proposed method yields simple criteria for the study of discontinuous deformations in three-dimensional problems and for any homogeneous incompressible material. Furthermore the homogeneous stress tensor is also not restricted. Neither fictitious nor simplified constitutive relations are invoked. The theory is implemented in a simple shearing problem