Quasi-Newton Methods for Topology Optimization Using a Level-Set Method

The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for solving PDE-constrained topology optimization problems. Our approach is based on and extends the popular solution algorithm of Amstutz and Andr\"a (A new algorithm for topology optimization using a level-set method, Journal of Computational Physics, 216, 2006). To do so, we introduce a new perspective on the commonly used evolution equation for the level-set method, which allows us to derive our quasi-Newton methods for topology optimization. We investigate the performance of the proposed methods numerically for the following examples: Inverse topology optimization problems constrained by linear and semilinear elliptic Poisson problems, compliance minimization in linear elasticity, and the optimization of fluids in Navier-Stokes flow, where we compare them to current state-of-the-art methods. Our results show that the proposed solution algorithms significantly outperform the other considered methods: They require substantially less iterations to find a optimizer while demanding only slightly more resources per iteration. This shows that our proposed methods are highly attractive solution methods in the field of topology optimization

Fractalkine Induces the Expression of Intercellular Adhesion Molecule-1 on CD4+ T-lymphocytes: implications for the immunopathogenesis of Multiple Sclerosis

Fractalkine (CX3CL1) is a chemokine that has been shown to play roles in lymphocyte chemotaxis, inflammation, and neuroprotection in central nervous system (CNS) diseases. Here we examined roles for CX3CL1 in CD4+ T-cell chemotaxis mediated via their upregulation of adhesion molecule expression as well as secretion of inflammatory cytokines involved in the pathogenesis of relapsing remitting multiple sclerosis (RRMS). We found that CX3CL1 concentrations are elevated in the cerebrospinal fluid (CSF) of RRMS patients, and that CX3CL1 increases mRNA expression of IFN-γ and TNF-α, and protein secretion of IFN-γ by CD4+ T-cells derived from RRMS patients but not those derived from healthy controls (HCs). We also show that blood-derived CD4+T-cells express increased surface levels of CX3CL1 receptor (CX3CR1) and intercellular adhesion molecule (ICAM)-1 in RRMS patients in comparison to HCs. Furthermore, the percentage of CX3CR1+ICAM-1+CD4+ T-cells are increased in the CSF of untreated RRMS patients in comparison to their peripheral blood samples, and CD4+ T-cells which migrate in-vitro toward a CX3CL1 gradient express higher levels of ICAM-1 than CD4+ T-cells that do not migrate. Furthermore, we demonstrated that CX3CL1 upregulates ICAM-1 expression on the surface of RRMS patient-derived but not HC derived CD4+ T-cells. Lastly, we show that CX3CL1 stimulates ICAM-1 expression on myelin-antigen-specific CD4+ T-cell lines derived from RRMS and healthy donors. These results indicate that CX3CL1 may preferentially recruit CX3CR1+ICAM-1+CD4+ T-cells into the CNS during RRMS development, and may activate CD4+ T-cells to express higher levels of ICAM-1, as well as the proinflammatory cytokines IFN-γ and TNF-α.Doctor of Philosoph

A Novel Deflation Approach for Topology Optimization and Application for Optimization of Bipolar Plates of Electrolysis Cells

Topology optimization problems usually feature multiple local minimizers. To guarantee convergence to local minimizers that perform best globally or to find local solutions that are desirable for practical applications due to easy manufacturability or aesthetic designs, it is important to compute multiple local minimizers of topology optimization problems. Existing methods typically rely on Newton-type solvers during the optimization process, which makes them unsuitable for sensitivity-based topology optimization. In this paper, we introduce a novel deflation approach to systematically find multiple local minimizers of general topology optimization problems. The approach is based on a penalization of previously found local solutions in the objective. We validate our approach on the so-called two-pipes five-holes example. Finally, we introduce a model for the topology optimization of bipolar plates of hydrogen electrolysis cells and demonstrate that our deflation approach enables the discovery of novel designs for such plates

Computing Multiple Local Minimizers for the Topology Optimization of Bipolar Plates in Electrolysis Cells

In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We use the Borvall-Petersson model to describe the fluid flow and derive a criterion for a uniform flow distribution in the bipolar plate. Furthermore, we introduce a novel deflation approach to compute multiple local minimizers of topology optimization problems. The approach is based on a penalty method that discourages convergence towards previously found solutions. Finally, we demonstrate this technique on the topology optimization for bipolar plates and show that multiple distinct local solutions can be found

Topology Optimization for Uniform Flow Distribution in Electrolysis Cells

In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We present a model for the bipolar plate using the Stokes equation with an additional drag term, which models the influence of fluid and solid regions. Furthermore, we derive a criterion for a uniform flow distribution in the bipolar plate. To obtain shapes that are well-manufacturable, we introduce a novel smoothing technique for the fluid velocity. Finally, we present some numerical results and investigate the influence of the smoothing on the obtained shapes

Axonal Ensheathment and Intercellular Barrier Formation in Drosophila

Glial cells are critical players in every major aspect of nervous system development, function, and disease. Other than their traditional supportive role, glial cells perform a variety of important functions such as myelination, synapse formation and plasticity, and establishment of blood–brain and blood–nerve barriers in the nervous system. Recent studies highlight the striking functional similarities between Drosophila and vertebrate glia. In both systems, glial cells play an essential role in neural ensheathment thereby isolating the nervous system and help to create a local ionic microenvironment for conduction of nerve impulses. Here, we review the anatomical aspects and the molecular players that underlie ensheathment during different stages of nervous system development in Drosophila and how these processes lead to the organization of neuroglial junctions. We also discuss some key aspects of the invertebrate axonal ensheathment and junctional organization with that of vertebrate myelination and axon–glial interactions. Finally, we highlight the importance of intercellular junctions in barrier formation in various cellular contexts in Drosophila. We speculate that unraveling the genetic and molecular mechanisms of ensheathment across species might provide key insights into human myelin-related disorders and help in designing therapeutic interventions

A Laminin G-EGF-Laminin G Module in Neurexin IV Is Essential for the Apico-Lateral Localization of Contactin and Organization of Septate Junctions

Septate junctions (SJs) display a unique ultrastructural morphology with ladder-like electron densities that are conserved through evolution. Genetic and molecular analyses have identified a highly conserved core complex of SJ proteins consisting of three cell adhesion molecules Neurexin IV, Contactin, and Neuroglian, which interact with the cytoskeletal FERM domain protein Coracle. How these individual proteins interact to form the septal arrays that create the paracellular barrier is poorly understood. Here, we show that point mutations that map to specific domains of neurexin IV lead to formation of fewer septae and disorganization of SJs. Consistent with these observations, our in vivo domain deletion analyses identified the first Laminin G-EGF-Laminin G module in the extracellular region of Neurexin IV as necessary for the localization of and association with Contactin. Neurexin IV protein that is devoid of its cytoplasmic region is able to create septae, but fails to form a full complement of SJs. These data provide the first in vivo evidence that specific domains in Neurexin IV are required for protein-protein interactions and organization of SJs. Given the molecular conservation of SJ proteins across species, our studies may provide insights into how vertebrate axo-glial SJs are organized in myelinated axons

Über eine Klasse polynomialer Scharen selbstadjungierter Operatoren im Hilbertraum

HEK293A cells expressing either mouse MOG (mMOG) or rat MOG (rMOG) C terminally tagged with EGFP. (DOCX 2792 kb