A Mathematical Model of Breast Tumor Progression Based on Immune Infiltration

Breast cancer is the most prominent type of cancer among women. Understanding the microenvironment of breast cancer and the interactions between cells and cytokines will lead to better treatment approaches for patients. In this study, we developed a data-driven mathematical model to investigate the dynamics of key cells and cytokines involved in breast cancer development. We used gene expression profiles of tumors to estimate the relative abundance of each immune cell and group patients based on their immune patterns. Dynamical results show the complex interplay between cells and molecules, and sensitivity analysis emphasizes the direct effects of macrophages and adipocytes on cancer cell growth. In addition, we observed the dual effect of IFN-γ role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eγ on cancer proliferation, either through direct inhibition of cancer cells or by increasing the cytotoxicity of CD8+ T-cells

Fracture mechanism simulation of inhomogeneous anisotropic rocks by extended finite element method

The vast majority of rock masses is anisotropic due to factors such as layering, unequal in-situ stresses, joint sets, and discontinuities. Meanwhile, given the frequently asymmetric distribution of pores, grain sizes or different mineralogical compounds in different locations, they are often classified as inhomogeneous materials. In such materials, stress intensity factors (SIFs) at the crack tip, which control the initiation of failure, strongly depend on mechanical properties of the material near that area. On the other hand, crack propagation trajectories highly depend on the orthotropic properties of the rock mass. In this study, the SIFs are calculated by means of anisotropic crack tip enrichments and an interaction integral are developed for inhomogeneous materials with the help of the extended finite element method (XFEM). We also use the T-stress within the crack tip fields to develop a new criterion to estimate the crack initiation angles and propagation in rock masses. To verify and validate the proposed approach, the results are compared with experimental test results and those reported in the literature. It is found that the ratio of elastic moduli, shear stiffnesses, and material orientation angles have a significant impact on the SIFs. However, the rate of change in material properties is found to have a moderate effect on these factors and a more pronounced effect on the failure force. The results highlight the potential of the proposed formulation in the estimation of SIFs and crack propagation paths in inhomogeneous anisotropic materials

From Architectured Materials to Large-Scale Additive Manufacturing

The classical material-by-design approach has been extensively perfected by materials scientists, while engineers have been optimising structures geometrically for centuries. The purpose of architectured materials is to build bridges across themicroscale ofmaterials and themacroscale of engineering structures, to put some geometry in the microstructure. This is a paradigm shift. Materials cannot be considered monolithic anymore. Any set of materials functions, even antagonistic ones, can be envisaged in the future. In this paper, we intend to demonstrate the pertinence of computation for developing architectured materials, and the not-so-incidental outcome which led us to developing large-scale additive manufacturing for architectural applications

Computational Homogenization of Architectured Materials

Architectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. The present chapter aims at providing such models, in the case of mechanical properties. As a matter of fact, one engineering challenge is to predict the effective properties of such materials; computational homogenization using finite element analysis is a powerful tool to do so. Homogenized behavior of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. Furthermore, computational homogenization is the basis for computational topology optimization which will give rise to the next generation of architectured materials. This chapter covers the computational homogenization of periodic architectured materials in elasticity and plasticity, as well as the homogenization and representativity of random architectured materials

Robust Topology Optimization of Skeletal Structures with Imperfect Structural Members

A topology optimization framework is proposed for robust design of skeletal structures with stochastically imperfect structural members. Imperfections are modeled as uncertain members\u27 out-of-straightness using curved frame elements in the form of predefined functions with random magnitudes throughout the structure. The stochastic perturbation method is used for propagating the imperfection uncertainty up to the structural response level, and the expected value of performance measure or constraint is used to form the stochastic topology optimization problem. Sensitivities are derived explicitly using the adjoint method and are used in conjunction with an efficient gradient-based optimizer in search for robust optimal topologies. Topological designs for three representative examples are investigated with the proposed algorithm and the resulting topologies are compared with the deterministic designs. It is observed that the new designs primarily feature load path diversification, which is pronounced with increasing level of uncertainty, and occasionally member thickening to mitigate the impact of the uncertainty in members\u27 out-of-straightness on structural performance

Robust Topology Optimization of Skeletal Structures with Imperfect Structural Members

A topology optimization framework is proposed for robust design of skeletal structures with stochastically imperfect structural members. Imperfections are modeled as uncertain members\u27 out-of-straightness using curved frame elements in the form of predefined functions with random magnitudes throughout the structure. The stochastic perturbation method is used for propagating the imperfection uncertainty up to the structural response level, and the expected value of performance measure or constraint is used to form the stochastic topology optimization problem. Sensitivities are derived explicitly using the adjoint method and are used in conjunction with an efficient gradient-based optimizer in search for robust optimal topologies. Topological designs for three representative examples are investigated with the proposed algorithm and the resulting topologies are compared with the deterministic designs. It is observed that the new designs primarily feature load path diversification, which is pronounced with increasing level of uncertainty, and occasionally member thickening to mitigate the impact of the uncertainty in members\u27 out-of-straightness on structural performance