Thesis (Doctoral)--Universität Bonn, 1990. / Includes bibliographical references.

Thesis (Doctoral)--Ruhr-Universität Bochum, [1991] / Includes bibliographical references.

Thesis (PH. D.)--Cornell University. / Reprinted from the American Journal of Mathematics, vol. XXIX, no. 4.

Thesis (Ph. D.)--Lehigh University, 2006. / Includes vita. Includes bibliographical references (leaves 72-76).

Abstract Not Provided. / Thesis / Master of Science (MSc)

Indispensable to all modes of migration used during single cell metastasis, cytoplasmic protrusions are pivotal in surveying cells local surroundings which ultimately initiates migration of the cell body. Cancer cell migration is fairly well studied with the traditional focus on protrusion driven cell body displacement, while less is known on the role of protrusions in sensing cellular microenvironments. Here, we present a suspended and aligned fiber platform capable of high spatio-temporal imaging of protrusions capable of sensing fiber curvature contrasts independent of cell migration. By varying the diameter of suspended fibers, we are able to maintain cell migration along low curvature-large diameter (2μm) fibers, while solely allowing cells to sense, initiate, and mature protrusions on orthogonally deposited high curvature-low diameter (~100, 200 and 600 nm) fibers. Using highly aggressive breast MDA-MB-231 and brain glioblastoma DBTRG-05MG model systems, we find that MDA-MB-231 protrusion maturation dynamics are more sensitive to changes in fiber curvature and fibronectin ligand coating concentration compared to DBTRG-05MG. Furthermore, we find that vimentin intermediate filaments localize within 70% of mature protrusions, which normally form on larger diameter fibers. Additionally, protrusion lengths fluctuate continuously until the protrusion is either terminated or stabilized, and occasionally protrusions are observed to shed cytoplasmic fragments. Through manipulation of curvature contrasts, we demonstrate single protrusive hierarchical decomposition and coordination in zeroth (main), first and second order branches. The fiber curvature platform presented here uniquely allows cancer cells to sense nanofiber curvature contrasts, thus providing new mechanistic insights in protrusion initiation, maturation, and hierarchical coordination. / Master of Science

In recent decades science has become an increasingly multidisciplinary field in which the lines that used to divide starkly different fields have blurred or disappeared completely. This work is a compendium of different angles focused at exploring disease progression of cancer biology through the perspective of mechanical engineering. We explore cancer through a holistic approach considering mechanistic, physical, genetic biology, biochemical, and immune cells to explore how the interplay with fiber networks can expand our understanding. We explored the physical interplay with biological processes of fibroblastic cells and show how these are critically regulated by forces that alter their ability to coil depends on fiber curvature and adhesion strength; thus, showing how cellular processes are driven by the balances of mechanical forces. Conversely, not all cell types are driven by the same factors, where we report that the structural features of migratory DCs enable them to be less influenced by the differences in fiber diameters, contrasting drastically what we previously reported on the other cell lines. Finally developing a novel composite nanofiber platform, we reported how some cancer cells are mechanistically influenced by the architecture of a substrate and thus resulting in completely different migratory responses that we have associated with key regulatory genes and responding completely differently when in the presence of clinically relevant molecular therapies. Overall, we investigated cancer biology through stiffness gradients, geometric influence through biophysics on myoblasts, and immune cell migration forces as a strong indicator of cell behavior. / Master of Science / Biology has historically been studied through chemistry and genetics, an approach that has produced incredible scientific discoveries such as vaccines and various therapies. Similarly, mechanical engineering has taken us to corners of the world that we never thought possible through the creation of machines, vehicles and the creation of new metal alloys. This research work is part of an emergent field of collaborative science which is paving the way to new ideas and the development of compound fields such as mechanobiology. Here we investigate how cells migrate through small rope-like environments that imitate the same fibers our cells can encounter in the body. We control the thickness, the arrangement, the orientation and the strength of these ropes to investigate how cells react to these environments, thus reporting on the new behaviors cells adopts in these conditions as well as their potential medical implications. Overall, we have developed new methods of studying cancer and other types of cells by tackling new questions using a mechanical perspective.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / O objetivo desta dissertaÃÃo à apresentar uma demonstraÃÃo para uma desigualdade pontual, denominada conjectura da curvatura escalar normal, a qual à vÃlida para subvariedades n-dimensionais, Mn, imersas isometricamente em formas espaciais Nn+m(c) de curvatura seccional constante c. / In this work we present a proof of the Normal Scalar Curvature Conjecture for submanifolds Mn, isometrically immersed into space forms Nn+m(c) of constant sectional curvature c.

This thesis consists of two parts. In the first part, we study certain Ricci flow invariant nonnegative curvature conditions as given by B. Wilking. We begin by proving that any such nonnegative curvature implies nonnegative isotropic curvature in the Riemannian case and nonnegative orthogonal bisectional curvature in the K¨ahler case. For any closed AdSO(n,C) invariant subset S so(n, C) we consider the notion of positive curvature on S, which we call positive S- curvature. We show that the class of all such subsets can be naturally divided into two subclasses: The first subclass consists of those sets S for which the following holds: If two Riemannian manifolds have positive S- curvature then their connected sum also admits a Riemannian metric of positive S- curvature. The other subclass consists of those sets for which the normalized Ricci flow on a closed Riemannian manifold with positive S-curvature converges to a metric of constant positive sectional curvature. In the second part of the thesis, we study the behavior of Ricci flow for a manifold having positive S - curvature, where S is in the first subclass. More specifically, we study the Ricci flow for a special class of metrics on Sp+1 x S1 , p ≥ 4, which have positive isotropic curvature.

<p dir="ltr">In composites manufacturing, predicting the shape change in parts is vital for making sure part dimensions are properly compensated. Different factors in the manufacturing process, such as the temperature change throughout a thermoset cure cycle, can influence shape change. The compensation process becomes more difficult for geometries with double curvature, as interactions between the two radii of curvature can reduce the effectiveness of applying methodologies for single curvature geometries. Additionally, using finite element analysis (FEA) to predict shape change can be costly and time-consuming depending on part geometry.</p><p dir="ltr">This thesis studies an approach for predicting the shape change of a symmetric thermoset laminate with a double-curved L-angle section in its geometry. Specifically, the conservation of Gaussian curvature is applied to predict shape change. The geometry studied in this thesis can be broken down and analyzed as a segment of a torus, which is attached on one end by a cylinder and on the other end by a curved flange. Varying the length of the cylinder and flange sections, the effectiveness of Gauss’s theorem is determined for the different part geometries, with developed formulas compared against finite element simulations and experimental measurements.</p><p dir="ltr">By approximating torus segments with certain geometric criteria as cylinders, linear elasticity equations for a cylinder undergoing free thermal strain can be solved and the change in the larger arc length in the double-curved geometry is predicted after deformation. The integral form of Gauss’ theorem is then applied to determine the deformed angle of the larger arc, from which geometric relations can be applied to extract the deformed radius. Abaqus is used first to study the torus segment on its own, and then to see the effects of the cylinder and flange segments on the overall geometry. Experimental measurements are also used as a comparison.</p><p dir="ltr">Generally, the formula derived using Gauss’ theorem predicts shape change very well for the torus segment on its own. When cylinder and flange segments are included in the geometry, an empirical correction factor can be introduced to account for geometrically induced stiffening effects. Future developments and next steps in this research are discussed.</p>