A model for cell migration in non-isotropic fibrin networks with an application to pancreatic tumor islets
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Cell migration, known as an orchestrated movement of cells, is crucially important for wound healing, tumor growth, immune response as well as other biomedical processes. This paper presents a cell-based model to describe cell migration in non-isotropic fibrin networks around pancreatic tumor islets. This migration is determined by the mechanical strain energy density as well as cytokines-driven chemotaxis. Cell displacement is modeled by solving a large system of ordinary stochastic differential equations where the stochastic parts result from random walk. The stochastic differential equations are solved by the use of the classical Euler–Maruyama method. In this paper, the influence of anisotropic stromal extracellular matrix in pancreatic tumor islets on T-lymphocytes migration in different immune systems is investigated. As a result, tumor peripheral stromal extracellular matrix impedes the immune response of T-lymphocytes through changing direction of their migration.Keywords:
Pancreatic Islets
In this paper, we discuss five parameters that indicate the inhomogeneity of a stack of parallel isotropic layers. We show that, in certain situations, they provide further insight into the intrinsic inhomogeneity of a Backus medium, as compared to the Thomsen parameters. Additionally, we show that the Backus average of isotropic layers is isotropic if and only if $\gamma=0$. This is in contrast to parameters $\delta$ and $\epsilon$, whose zero values do not imply isotropy.
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Isotropy is a fundamental property of a diffuse sound field. Although several studies have proposed an isotropy indicator to quantify the extent of the isotropy of a sound field, what is not yet very clear is how to interpret the quantified isotropy using these indicators. This study aims to contribute to the understanding of the isotropy by (i) modifying an existing isotropy indicator based on the spherical harmonic expansion and (ii) presenting isotropic sound field model composed of a finite number of plane waves. Theoretical and numerical investigations show that a limited-degree isotropy can be established by using the isotropy indicator and the isotropic sound field model.
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Despite the tailorability of laminated fiber composites, the tendency has been to use lay-ups that more closely approximate an isotropic material. These so-called quasi-isotropic lay-ups are used so the structure or component fabricated from them can withstand loads oriented in many directions or perhaps accommodate an unexpected loading. Since there is so much literature associated with predicting the static and dynamic response of isotropic beams, plates, and shells, particularly in table look-up format, the question arises as to the applicability of these tabulated results to members made from quasi-isotropic composite materials. The purposes of this paper are: (1) to indicate the degree of isotropy exhibited by a certain quasi-isotropic sandwich construction, (2) to verify that standard isotropic strength-of-materials formulas can be used to predict the response of these quasi-isotropic components for certain loadings, and (3) to present numerical data for a particular material system. It is felt that even though the results are presented for a sandwich construction, they can be extended to quasi-isotropic lay-ups in general.
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Isotropy is an important index of performance evaluation for a six-dimensional force sensor,and the isotropic performance analysis is a key problem in the structural design of Stewart platform-based force sensor.In order to achieve the best isotropy performance,the static mathematical model of Stewart platform-based force sensor is built by using screw theory,and the isotropy indices of the sensor are studied systematically.By using the mathmatical analysis method,the performance analysis of the forward and backward isotropy is presented.The analytic expressions of the key structural parameters are derived when both forward force and torque isotropy are satisfied.It is proved to be impossible to realize the backward force and torque isotropy simultaneously,and the restrictive relationships of the four isotropy indices are obtained.By compromising all the four isotropy indices and solving the extreme of the comprehensive performance objective function,the best comprehensive isotropy index of Stewart platform-based force sensor is achieved and the corresponding analytic expressions of the key structural parameters are obtained.The results of the theoretical deduction are important to the performance evaluation and structure design of the six-dimensional force sensor.
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Eukaryotic cells actively respond to variations in ligand density and stiffness of their extracellular matrix (ECM). This cell-ECM relationship plays an important role in regulating cell migration, wound healing, tumor invasion and metastasis. A better understanding of these mechanosenstive responses requires more rigorous models of the relationships between ECM biophysical properties, mechanotransductive signals, assembly of contractile and adhesive structures, and cell migration.
Matrix (chemical analysis)
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In this paper, we discuss five parameters that indicate the inhomogeneity of a stack of parallel isotropic layers. We show that, in certain situations, they provide further insight into the intrinsic inhomogeneity of a Backus medium, as compared to the Thomsen parameters. Additionally, we show that the Backus average of isotropic layers is isotropic if and only if $\gamma=0$. This is in contrast to parameters $\delta$ and $\epsilon$, whose zero values do not imply isotropy.
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The study of isotropy of mechanical properties of cellular structures was carried out. The studied objects are based on triply periodic minimal surfaces (“Schwarz primitive”) with various cell size parameter t. The mechanical loading was applied with different loading directions. It was shown, that triply periodic minimal surface (TPMS)-based materials have high isotropy of mechanical properties.
Mechanical design
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Uniform circular arrays are popular in direction finding applications because they show to be isotropic, i.e. they exhibit the same accuracy (in terms of the Cramer-Rao bound) at all possible planar look directions. We prove that this is not absolutely true if the constituent sensors are not isotropic. For instance, we specify how the anisotropic sensors should be directed and how many are needed in order to ensure an isotropic behavior of the array. We study, in more details, the performance of arrays of cardioid sensors, including anisotropic arrays of cardioid sensors.
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Stewart platform
Spatial configuration
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