Growth of human tumor cells as three-dimensional (3D) multicellular spheroids modifies their invasive properties. Here we study the differences in the biological features of MCF-7, a human breast cancer cell line, and its multidrug resistant variant (MDR-MCF-7) cultured as spheroids or as monolayers. Three-dimensional culture decreased the proliferative rate of both cell lines, reduced the drug sensitivity of MCF-7 cells and did not affect the resistance of MDR-MCF-7 cells. Transmission electron microscopic studies and intercellular junctions labeling showed that MCF-7 spheroids had a junctional system involving E-cadherin, tight-junctions and desmosomes. In MDR-MCF-7 cell spheroids, cell cohesion was mostly due to membrane interdigitations. MDR-MCF-7 cells, but not their parental counterpart, displayed a higher invasive potential when cultured as spheroids, as shown in the Boyden chamber assay. 3D-induced invasiveness was correlated with serine protease and plasminogen activator (PA) secretion. MCF-7 cells did not show any tendency to invade, whatever the mode of culture. These results show that 3D-cultures as spheroids distinctively altered structural features of parental and MDR-MCF-7 cells. In MCF-7 cells, 3D-culture increased cell-cell contacts and drug resistance; in MDR-MCF-7 cells, it induced invasive properties.

Metamodeling, the science of modeling functions observed at a finite number of points, benefits from all auxiliary information it can account for. Function gradients are a common auxiliary information and are useful for predicting functions with locally changing behaviors. This article is a review of the main metamodels that use function gradients in addition to function values. The goal of the article is to give the reader both an overview of the principles involved in gradientenhanced metamodels while also providing insightful formulations. The following metamodels have gradient-enhanced versions in the literature and are reviewed here: classical, weighted and moving least squares, Shepard weighting functions, and the kernel-based methods that are radial basis functions, kriging and support vector machines. The methods are set in a common framework of linear combinations between a priori chosen functions and coefficients that depend on the observations. The characteristics common to all kernel-based approaches are underlined. A new ν-GSVR metamodel which uses gradients is given. Numerical comparisons of the metamodels are carried out for approximating analytical test functions. The experiments are replicable, as they are performed with an opensource available toolbox. The results indicate that there is a trade-off between the better computing time of least squares methods and the larger versatility of kernelbased approaches.

No abstract

In the course of designing structural assemblies, performing a full optimization is very expensive in terms of computation time. In order or reduce this cost, we propose a multilevel model optimization approach. This paper lays the foundations of this strategy by presenting a method for constructing an approximation of an objective function. This approach consists in coupling a multiparametric mechanical strategy based on the LATIN method with a gradientbased metamodel called a cokriging metamodel. The main difficulty is to build an accurate approximation while keeping the computation cost low. Following an introduction to multiparametric and cokriging strategies, the performance of kriging and cokriging models is studied using one-and two-dimensional analytical functions; then, the performance of metamodels built from mechanical responses provided by the multiparametric strategy is analyzed based on two mechanical test examples.

This paper deals with the building of a gradient-based metamodel using a dedicated strategy for solving structural assemblies problems. This work is the first part of a two-levels global optimization strategy. The general objective is to reduce computation costs; here, we focus on the costs which are associated with the generation of the metamodel. Our goal is achieved through the introduction of two main elements: what we call a "multiparametric strategy" based on the LATIN method, which reduces the computation costs when the parameters vary, and the use of a cokriging metamodel taking gradients into account. Several examples illustrate the efficiency of these two elements.

This work uses Multi-Material Topology Optimization (MMTO) to maximize the average torque of a 3-phase Permanent Magnet Synchronous Machine (PMSM). Eight materials are considered in the stator: air, soft magnetic steel, three electric phases, and their three returns. To address the challenge of designing a 3-phase PMSM stator, a generalized density-based framework is used. The proposed methodology places the prescribed material candidates on the vertices of a convex polytope, interpolates material properties using Wachspress shape functions, and defines Cartesian coordinates inside polytopes as design variables. A rational function is used as penalization to ensure convergence towards meaningful structures, without the use of a filtering process. The influences of different polytopes and penalization parameters are investigated. The results indicate that a hexagonal-based diamond polytope is a better choice than the classical orthogonal domains for this MMTO problem. In addition, the proposed methodology yields high-performance designs for 3-phase PMSM stators by implementing a continuation method on the electric load angle.

This paper deals with a multilevel model optimization strategy for structural assemblies. Two levels are introduced: the full mechanical model and a metamodel. The general objective is to reduce computation costs; here, we focus on the costs which are associated with the generation of the metamodel. Our goal is achieved through the introduction of two main elements: what we call a "multiparametric strategy" based on the LATIN method, which reduces the computation costs when the parameters vary, and the use of a cokriging metamodel taking gradients into account. Several examples illustrate the efficiency of these two elements.

This paper investigates the optimization of iron distribution in the rotor of a permanent magnet synchronous machine. The objective is to maximize the average torque for fixed permanent magnets positions, stator, and current feedings. To do so, a density-based algorithm is used with the adjoint variable method to compute sensitivities. It returns nonsymmetric geometries, which are related to the interactions between magnets and winding fluxes, as well as the machine operating mode (motor or generator for a given rotation direction). For a given single working point, we obtain asymmetric topologies that outperform the optimized symmetric design, while the symmetric rotor topology is more multifunctional.