Cell migration plays an essential role in cancer metastasis. In cancer invasion through confined spaces, cells must undergo extensive deformation, which is a capability related to their metastatic potentials. Here, we simulate the deformation of the cell and nucleus during invasion through a dense, physiological microenvironment by developing a phenomenological computational model. In our work, cells are attracted by a generic emitting source (e.g., a chemokine or stiffness signal), which is treated by using Green’s Fundamental solutions. We use an IMEX integration method where the linear parts and the nonlinear parts are treated by using an Euler backward scheme and an Euler forward method, respectively. We develop the numerical model for an obstacle-induced deformation in 2D or/and 3D. Considering the uncertainty in cell mobility, stochastic processes are incorporated and uncertainties in the input variables are evaluated using Monte Carlo simulations. This quantitative study aims at estimating the likelihood for invasion and the length of the time interval in which the cell invades the tissue through an obstacle. Subsequently, the two-dimensional cell deformation model is applied to simplified cancer metastasis processes to serve as a model for in vivo or in vitro biomedical experiments.Electronic supplementary materialThe online version of this article (10.1007/s10237-018-1036-5) contains supplementary material, which is available to authorized users.
Once I got the opportunity to go to Zambia to conduct field research and stay with the Lala people for several months, I discovered much to my delight that the kalimba — the lamellophone found there — took an important place in the musical culture of the Lala. THe richness and variety of the music and the open-heartedness of the musicians turned out to be a revelation to me. Moreover, it became clear that through the kalimba other aspects of the Lala society could be exposed.
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