Polyacrylamide Bead Sensors for in vivo Quantification of Cell-Scale Stress in Zebrafish Development

Mechanical stress exerted and experienced by cells during tissue morphogenesis and organ formation plays an important role in embryonic development. While techniques to quantify mechanical stresses in vitro are available, few methods exist for studying stresses in living organisms. Here, we describe and characterize cell-like polyacrylamide (PAAm) bead sensors with well-defined elastic properties and size for in vivo quantification of cell-scale stresses. The beads were injected into developing zebrafish embryos and their deformations were computationally analyzed to delineate spatio-temporal local acting stresses. With this computational analysis-based cell-scale stress sensing (COMPAX) we are able to detect pulsatile pressure propagation in the developing neural rod potentially originating from polarized midline cell divisions and continuous tissue flow. COMPAX is expected to provide novel spatio-temporal insight into developmental processes at the local tissue level and to facilitate quantitative investigation and a better understanding of morphogenetic processes.

Method for the quantification of rupture probability in soft collagenous tissues

A computational method is presented for the assessment of rupture probabilities in soft collagenous tissues. This may in particular be important for the quantitative analysis of medical diseases such as atherosclerotic arteries or abdominal aortic aneurysms, where an unidentified rupture has in most cases fatal consequences. The method is based on the numerical minimization and maximization of probabilities of failure, which arise from random input quantities, for example, tissue properties. Instead of assuming probability distributions for these quantities, which are typically unknown especially for soft collagenous tissues, only restricted knowledge of these distributions is taken into account. Given this limited statistical input data, the minimized/maximized probabilities represent optimal bounds on the rupture probability, which enable a quantitative estimation of potential risks of performing or not performing medical treatment. Although easily extendable to all kinds of mechanical rupture criteria, the approach presented here incorporates stretch-based and damage-based criteria. These are evaluated based on numerical simulations of loaded tissues, where continuum mechanical material formulations are considered, which capture the supra-physiological behavior of soft collagenous tissues. Numerical examples are provided demonstrating the applicability of the method in an overstretched atherosclerotic artery. Copyright © 2016 John Wiley & Sons, Ltd.

Simulation of discontinuous damage incorporating residual stresses in circumferentially overstretched atherosclerotic arteries

When a balloon-angioplasty is performed, the arterial wall is overstretched and thereby damaged, which leads to a stiffness reduction in the arterial layers. An anisotropic damage model able to reflect the main damage mechanisms in overstretched arterial walls is used in combination with a polyconvex hyperelastic stored energy function. Furthermore, a method for the incorporation of residual stresses present in the wall of unloaded configurations is applied. The energy describes the anisotropic hyperelastic behavior of arteries under physiological conditions. Due to the assumption that the rupture of cross-bridges between collageneous micro-fibrils is responsible for the damage inside arterial walls, the damage function is applied to that part of the energy only which is associated to the fiber elasticity. For the incorporation of the residual stresses into the simulation, we apply a method which consists of two simulation steps. Finally, a numerical simulation of the overstretching of a simplified atherosclerotic artery is performed taking into account residual stresses.