A moving grid finite element method applied to a mechanobiochemical model for 3D cell migration

This work presents the development, analysis and numerical simulations of a biophysical model for 3D cell deformation and movement, which couples biochemical reactions and biomechanical forces. We propose a mechanobiochemical model which considers the actin filament network as a viscoelastic and contractile gel. The mechanical properties are modelled by a force balancing equation for the displacements, the pressure and contractile forces are driven by actin and myosin dynamics, and these are in turn modelled by a system of reaction-diffusion equations on a moving cell domain. The biophysical model consists of highly non-linear partial differential equations whose analytical solutions are intractable. To obtain approximate solutions to the model system, we employ the moving grid finite element method. The numerical results are supported by linear stability theoretical results close to bifurcation points during the early stages of cell migration. Numerical simulations exhibited show both simple and complex cell deformations in 3-dimensions that include cell expansion, cell protrusion and cell contraction. The computational framework presented here sets a strong foundation that allows to study more complex and experimentally driven reaction-kinetics involving actin, myosin and other molecular species that play an important role in cell movement and deformation

Description of olive morphological parameters by using open access software

Abstract Background The morphological analysis of olive leaves, fruits and endocarps may represent an efficient tool for the characterization and discrimination of cultivars and the establishment of relationships among them. In recent years, much attention has been focused on the application of molecular markers, due to their high diagnostic efficiency and independence from environmental and phenological variables. Results In this study, we present a semi-automatic methodology of detecting various morphological parameters. With the aid of computing and image analysis tools, we created semi-automatic algorithms applying intuitive mathematical descriptors that quantify many fruit, leaf and endocarp morphological features. In particular, we examined quantitative and qualitative characters such as size, shape, symmetry, contour roughness and presence of additional structures such as nipple, petiole, endocarp surface roughness, etc.. Conclusion We illustrate the performance and the applicability of our approach on Greek olive cultivars; on sets of images from fruits, leaves and endocarps. In addition, the proposed methodology was also applied for the description of other crop species morphologies such as tomato, grapevine and pear. This allows us to describe crop morphologies efficiently and robustly in a semi-automated way

MOESM1 of Description of olive morphological parameters by using open access software

Additional file 1. Morphological parameters extracted from the proposed methodology