Differentiable piecewise-Bézier surfaces on Riemannian manifolds

We generalize the notion of Bézier surfaces and surface splines to Riemannian manifolds. To this end we put forward and compare three possible alternative definitions of Bézier surfaces. We furthermore investigate how to achieve C0- and C1-continuity of Bézier surface splines. Unlike in Euclidean space and for one-dimensional Bézier splines on manifolds, C1-continuity cannot be ensured by simple conditions on the Bézier control points: it requires an adaptation of the Bézier spline evaluation scheme. Finally, we propose an algorithm to optimize the Bézier control points given a set of points to be interpolated by a Bézier surface spline. We show computational examples on the sphere, the special orthogonal group, and two Riemannian shape space

Differentiable piecewise-Bézier interpolation on Riemannian manifolds

We propose a generalization of classical Euclidean piecewise- B ezier surfaces to manifolds, and we use this generalization to compute a C1-surface interpolating a given set of manifold-valued data points associated to a regular 2D grid. We then propose an efficient algorithm to compute the control points defining the surface based on the Euclidean concept of natural C2-splines and show examples on different manifolds

Protection from septic peritonitis by rapid neutrophil recruitment through omental high endothelial venules

Acute peritonitis is a frequent medical condition that can trigger severe sepsis as a life-threatening complication. Neutrophils are first-responders in infection but recruitment mechanisms to the abdominal cavity remain poorly defined. Here, we demonstrate that high endothelial venules (HEVs) of the greater omentum constitute a main entry pathway in TNFα-, Escherichia coli (E. coli)- and caecal ligation and puncture-induced models of inflammation. Neutrophil transmigration across HEVs is faster than across conventional postcapillary venules and requires a unique set of adhesion receptors including peripheral node addressin, E-, L-selectin and Mac-1 but not P-selectin or LFA-1. Omental milky spots readily concentrate intra-abdominal E. coli where macrophages and recruited neutrophils collaborate in phagocytosis and killing. Inhibition of the omental neutrophil response exacerbates septic progression of peritonitis. This data identifies HEVs as a clinically relevant vascular recruitment site for neutrophils in acute peritonitis that is indispensable for host defence against early systemic bacterial spread and sepsis

Endothelial Basement Membrane Laminin 511 Contributes to Endothelial Junctional Tightness and Thereby Inhibits Leukocyte Transmigration

Endothelial basement membranes constitute barriers to extravasating leukocytes during inflammation, a process where laminin isoforms define sites of leukocyte exit; however, how this occurs is poorly understood. In addition to a direct effect on leukocyte transmigration, we show that laminin 511 affects endothelial barrier function by stabilizing VE-cadherin at junctions and downregulating expression of CD99L2, correlating with reduced neutrophil extravasation. Binding of endothelial cells to laminin 511, but not laminin 411 or non-endothelial laminin 111, enhanced transendothelial cell electrical resistance (TEER) and inhibited neutrophil transmigration. Data suggest that endothelial adhesion to laminin 511 via β1 and β3 integrins mediates RhoA-induced VE-cadherin localization to cell-cell borders, and while CD99L2 downregulation requires integrin β1, it is RhoA-independent. Our data demonstrate that molecular information provided by basement membrane laminin 511 affects leukocyte extravasation both directly and indirectly by modulating endothelial barrier properties