X-CAD: Optimizing CAD Models with Extended Finite Elements

We propose a novel generic shape optimization method for CAD models based on the eXtended Finite Element Method (XFEM). Our method works directly on the intersection between the model and a regular simulation grid, without the need to mesh or remesh, thus removing a bottleneck of classical shape optimization strategies. This is made possible by a novel hierarchical integration scheme that accurately integrates finite element quantities with sub-element precision. For optimization, we efficiently compute analytical shape derivatives of the entire framework, from model intersection to integration rule generation and XFEM simulation. Moreover, we describe a differentiable projection of shape parameters onto a constraint manifold spanned by user-specified shape preservation, consistency, and manufacturability constraints. We demonstrate the utility of our approach by optimizing mass distribution, strength-to-weight ratio, and inverse elastic shape design objectives directly on parameterized 3D CAD models

A Three-Dimensional Numerical Model of an Active Cell Cortex in the Viscous Limit

The cell cortex is a highly dynamic network of cytoskeletal filaments in which motor proteins induce active cortical stresses which in turn drive dynamic cellular processes such as cell motility, furrow formation or cytokinesis during cell division. Here, we develop a three-dimensional computational model of a cell cortex in the viscous limit including active cortical flows. Combining active gel and thin shell theory, we base our computational tool directly on the force balance equations for the velocity field on a discretized and arbitrarily deforming cortex. Since our method is based on the general force balance equations, it can easily be extended to more complex biological dependencies in terms of the constitutive laws or a dynamic coupling to a suspending fluid. We validate our algorithm by investigating the formation of a cleavage furrow on a biological cell immersed in a passive outer fluid, where we successfully compare our results to axi-symmetric simulations. We then apply our fully three-dimensional algorithm to fold formation and to study furrow formation under the influence of non-axisymmetric disturbances such as external shear. We report a reorientation mechanism by which the cell autonomously realigns its axis perpendicular to the furrow plane thus contributing to the robustness of cell division under realistic environmental conditions

A hyperelastic model for simulating cells in flow

In the emerging field of 3D bioprinting, cell damage due to large deformations is considered a main cause for cell death and loss of functionality inside the printed construct. Those deformations, in turn, strongly depend on the mechano-elastic response of the cell to the hydrodynamic stresses experienced during printing. In this work, we present a numerical model to simulate the deformation of biological cells in arbitrary three-dimensional flows. We consider cells as an elastic continuum according to the hyperelastic Mooney-Rivlin model. We then employ force calculations on a tetrahedralized volume mesh. To calibrate our model, we perform a series of FluidFM(R) compression experiments with REF52 cells demonstrating that all three parameters of the Mooney-Rivlin model are required for a good description of the experimental data at very large deformations up to 80%. In addition, we validate the model by comparing to previous AFM experiments on bovine endothelial cells and artificial hydrogel particles. To investigate cell deformation in flow, we incorporate our model into Lattice Boltzmann simulations via an Immersed-Boundary algorithm. In linear shear flows, our model shows excellent agreement with analytical calculations and previous simulation data.Comment: 15 pages, 9 figures, Supplementary information included. Unfortunately, the journal version misses an important contributor. The correct author list is the one given in this document. Biomech Model Mechanobiol (2020

Antimargination of microparticles and platelets in the vicinity of branching vessels

We investigate the margination of microparticles/platelets in blood flow through complex geometries typical for in vivo vessel networks: a vessel confluence and a bifurcation. Using 3D Lattice-Boltzmann simulations, we confirm that behind the confluence of two vessels a cell-free layer devoid of red blood cells develops in the channel center. Despite its small size of roughly one micrometer, this central cell-free layer persists for up to 100 $\mu$m after the confluence. Most importantly, we show from simulations that this layer also contains a significant amount of microparticles/platelets and validate this result by in vivo microscopy in mouce venules. At bifurcations, however, a similar effect does not appear and margination is largely unaffected by the geometry. This anti-margination towards the vessel center after a confluence may explain in vivo observations by Woldhuis et al. [Am. J. Physiol. 262, H1217 (1992)] where platelet concentrations near the vessel wall are seen to be much higher on the arteriolar side (containing bifurcations) than on the venular side (containing confluences) of the vascular system

Volume MLS ray casting

The method of Moving Least Squares (MLS) is a popular framework for reconstructing continuous functions from scattered data due to its rich mathematical properties and well-understood theoretical foundations. This paper applies MLS to volume rendering, providing a unified mathematical framework for ray casting of scalar data stored over regular as well as irregular grids. We use the MLS reconstruction to render smooth isosurfaces and to compute accurate derivatives for high-quality shading effects. We also present a novel, adaptive preintegration scheme to improve the efficiency of the ray casting algorithm by reducing the overall number of function evaluations, and an efficient implementation of our framework exploiting modern graphics hardware. The resulting system enables high-quality volume integration and shaded isosurface rendering for regular and irregular volume data

Optimal Design of Flexible-Link Mechanisms With Desired Load-Displacement Profiles

Robot mechanisms that exploit compliance can perform complex tasks under uncertainty using simple control strategies, but it remains difficult to design mechanisms with a desired embodied intelligence. In this paper, we propose an automated design technique that optimizes the desired load-displacement behavior of planar flexible-link mechanisms. To do so, we replace a subset of rigid with flexible links in an existing mechanism, and optimize their rest shape. We demonstrate the efficacy of our approach on a set of examples, including two fabricated prototypes, illustrating applications for grasping and locomotion tasks.ISSN:2377-376