Force traction microscopy: An inverse problem with pointwise observations

Force Traction Microscopy is an inversion method that allows to obtain the stress field applied by a living cell on the environment on the basis of a pointwise knowledge of the displacement produced by the cell itself. This classical biophysical problem, usually addressed in terms of Green functions, can be alternatively tackled using a variational framework and then a finite elements discretization. In such a case, a variation of the error functional under suitable regularization is operated in view of its minimization. This setting naturally suggests the introduction of a new equation, based on the adjoint operator of the elasticity problem. In this paper we illustrate the rigorous theory of the two-dimensional and three dimensional problem, involving in the former case a distributed control and in the latter case a surface control. The pointwise observations require to exploit the theory of elasticity extended to forcing terms that are Borel measure

Behavior of cell aggregates under force-controlled compression

In this paper we study the mechanical behavior of multicellular aggregates under compressive loads and subsequent releases. Some analytical properties of the solution are discussed and numerical results are presented for a compressive test under constant force imposed on a cylindrical specimen. The case of a cycle of compressions at constant force and releases is also considered. We show that a steady state configuration able to bear the load is achieved. The analytical determination of the steady state value allows to obtain mechanical parameters of the cellular structure that are not estimable from creep tests at constant stres

a review of vasculogenesis models

Mechanical and chemical models of vasculogenesis are critically reviewed with an emphasis on their ability to predict experimentally measured quantities. Final remarks suggest a possibility to merge the capabilities of different models into a unified approach

ELEMENTARY MECHANICS OF THE MITRAL VALVE

We illustrate a bare-bones mathematical model that is able to account for the elementary mechanics of the mitral valve when the leaflets of the valve close under the systolic pressure. The mechanical model exploits the aspect ratio of the valve leaflets that are represented as inextensible rods, subject to the blood pressure, with one fixed endpoint (on the endocardium) and an attached wire anchored to the papillary muscle. Force and torque balance equations are obtained exploiting the principle of virtual work, where the first contact point between rods is identified by the Weierstrass-Erdmann condition of variational nature. The chordae tendineae are modeled as a force applied to the free endpoint of the flaps. Different possible boundary conditions are investigated at the mitral annulus, and, by an asymptotic analysis, we demonstrate that in the pressure regime of interest generic boundary conditions generate a tensional boundary layer. Conversely, a specific choice of the boundary condition inhibits the generation of high tensional gradients in a small layer

Properties of a New Group of Cosmic Nuclei: Results from the Alpha Magnetic Spectrometer on Sodium, Aluminum, and Nitrogen

We report the properties of sodium (Na) and aluminum (Al) cosmic rays in the rigidity range 2.15 GV to 3.0 TV based on 0.46 million sodium and 0.51 million aluminum nuclei collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. We found that Na and Al, together with nitrogen (N), belong to a distinct cosmic ray group. In this group, we observe that, similar to the N flux, both the Na flux and Al flux are well described by the sums of a primary cosmic ray component (proportional to the silicon flux) and a secondary cosmic ray component (proportional to the fluorine flux). The fraction of the primary component increases with rigidity for the N, Na, and Al fluxes and becomes dominant at the highest rigidities. The Na /Si and Al /Si abundance ratios at the source, 0.036 ±0.003 for Na /Si and 0.103 ±0.004 for Al /Si , are determined independent of cosmic ray propagation

Respostas a tecnologias de trigo nos anos de 1981 e 1982.

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Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications

Resorting to a multiphase modelling framework, tumours are described here as a mixture of tumour and host cells within a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental evidences, we propose to describe the interaction forces involving the extracellular matrix via some concepts coming from viscoplasticity. We then apply the model to the description of the growth of tumour cords and the formation of fibrosis

Modeling brain connectivity dynamics in functional Magnetic Resonance Imaging via Particle Filtering

Interest in the studying of functional connections in the brain has grown considerably in the last decades, as many studies have pointed out that alterations in the interaction among brain areas can play a role as markers of neurological diseases. Most studies in this field treat the brain network as a system of connections stationary in time, but dynamic features of brain connectivity can provide useful information, both on physiology and pathological conditions of the brain. In this paper, we propose the application of a computational methodology, named Particle Filter (PF), to study non-stationarities in brain connectivity in functional Magnetic Resonance Imaging (fMRI). The PF algorithm estimates time-varying hidden parameters of a first-order linear time-varying Vector Autoregressive model (VAR) through a Sequential Monte Carlo strategy. On simulated time series, the PF approach effectively detected and enabled to follow time-varying hidden parameters and it captured causal relationships among signals. The method was also applied to real fMRI data, acquired in presence of periodic tactile or visual stimulations, in different sessions. On these data, the PF estimates were consistent with current knowledge on brain functioning. Most importantly, the approach enabled to detect statistically significant modulations in the cause-effect relationship between brain areas, which correlated with the underlying visual stimulation pattern presented during the acquisition