The term “immersed boundary method” was first used in reference to a method developed by Peskin (1972) to simulate cardiac mechanics and associated blood flow. The distinguishing feature of this method was that the entire simulation was carried out on a Cartesian grid, which did not conform to the geometry of the heart, and a novel procedure was formulated for imposing the effect of the immersed boundary (IB) on the flow. Since Peskin introduced this method, numerous modifications and refinements have been proposed and a number of variants of this approach now exist. In addition, there is another class of methods, usually referred to as “Cartesian grid methods,” which were originally developed for simulating inviscid flows with complex embedded solid boundaries on Cartesian grids (Berger & Aftosmis 1998, Clarke et al. 1986, Zeeuw & Powell 1991). These methods have been extended to simulate unsteady viscous flows (Udaykumar et al. 1996, Ye et al. 1999) and thus have capabilities similar to those of IB methods. In this review, we use the term immersed boundary (IB) method to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries. Furthermore, this review focuses mainly on IB methods for flows with immersed solid boundaries. Application of these and related methods to problems with liquid-liquid and liquid-gas boundaries was covered in previous reviews by Anderson et al. (1998) and Scardovelli & Zaleski (1999). Consider the simulation of flow past a solid body shown in Figure 1a. The conventional approach to this would employ structured or unstructured grids that conform to the body. Generating these grids proceeds in two sequential steps. First, a surface grid covering the boundaries b is generated. This is then used as a boundary condition to generate a grid in the volume f occupied by the fluid. If a finite-difference method is employed on a structured grid, then the differential form of the governing equations is transformed to a curvilinear coordinate system aligned with the grid lines (Ferziger & Peric 1996). Because the grid conforms to the surface of the body, the transformed equations can then be discretized in the

/pdf/immersed-boundary-methods-4id27kda4o.pdf

Immersed boundary methods

Additive manufacturing (AM) alias 3D printing translates computer-aided design (CAD) virtual 3D models into physical objects. By digital slicing of CAD, 3D scan, or tomography data, AM builds objects layer by layer without the need for molds or machining. AM enables decentralized fabrication of customized objects on demand by exploiting digital information storage and retrieval via the Internet. The ongoing transition from rapid prototyping to rapid manufacturing prompts new challenges for mechanical engineers and materials scientists alike. Because polymers are by far the most utilized class of materials for AM, this Review focuses on polymer processing and the development of polymers and advanced polymer systems specifically for AM. AM techniques covered include vat photopolymerization (stereolithography), powder bed fusion (SLS), material and binder jetting (inkjet and aerosol 3D printing), sheet lamination (LOM), extrusion (FDM, 3D dispensing, 3D fiber deposition, and 3D plotting), and 3D bioprinting....

Polymers for 3D Printing and Customized Additive Manufacturing

A coated implantable medical device 10 includes a structure 12 adapted for introduction into the vascular system, esophagus, trachea, colon, biliary tract, or urinary tract; at least one layer 18 of a bioactive material positioned over the structure 12; and at least one porous layer 20 positioned over the bioactive material layer 18. Preferably, the structure 12 is a coronary stent, and the bioactive material is at least one of heparin, dexamethasone or a dexamethasone derivative. The device 10 includes layers 18 and 22 of heparin and dexamethasone, the layer 22 of dexamethasone being positioned above the layer 18 of heparin. The layers of bioactive material also can be individual materials or a combination of different materials. Unexpectedly, the more soluble heparin markedly promotes the release of the less soluble dexamethasone above it. The porous layer 20 is composed of a polymer applied by vapor or plasma deposition and provides a controlled release of the bioactive material. It is particularly preferred that the polymer is a polyimide, parylene or a parylene derivative, which is deposited without solvents, heat or catalysts, merely by condensation of a monomer vapor.

Coated implantable medical device

A polymer-based, paclitaxel-eluting stent in patients with coronary artery disease☆

Light- and ink-based three-dimensional (3D) printing methods allow the rapid design and fabrication of materials without the need for expensive tooling, dies or lithographic masks. They have led to an era of manufacturing in which computers can control the fabrication of soft matter that has tunable mechanical, electrical and other functional properties. The expanding range of printable materials, coupled with the ability to programmably control their composition and architecture across various length scales, is driving innovation in myriad applications. This is illustrated by examples of biologically inspired composites, shape-morphing systems, soft sensors and robotics that only additive manufacturing can produce.

Printing soft matter in three dimensions

Multi-material stereolithography

Magnetic resonance velocimetry (MRV) is a non-invasive technique capable of measuring the three-component mean velocity field in complex three-dimensional geometries with either steady or periodic boundary conditions. The technique is based on the phenomenon of nuclear magnetic resonance (NMR) and works in conventional magnetic resonance imaging (MRI) magnets used for clinical imaging. Velocities can be measured along single lines, in planes, or in full 3D volumes with sub-millimeter resolution. No optical access or flow markers are required so measurements can be obtained in clear or opaque MR compatible flow models and fluids. Because of its versatility and the widespread availability of MRI scanners, MRV is seeing increasing application in both biological and engineering flows. MRV measurements typically image the hydrogen protons in liquid flows due to the relatively high intrinsic signal-to-noise ratio (SNR). Nonetheless, lower SNR applications such as fluorine gas flows are beginning to appear in the literature. MRV can be used in laminar and turbulent flows, single and multiphase flows, and even non-isothermal flows. In addition to measuring mean velocity, MRI techniques can measure turbulent velocities, diffusion coefficients and tensors, and temperature. This review surveys recent developments in MRI measurement techniques primarily in turbulent liquid and gas flows. A general description of MRV provides background for a discussion of its accuracy and limitations. Techniques for decreasing scan time such as parallel imaging and partial k-space sampling are discussed. MRV applications are reviewed in the areas of physiology, biology, and engineering. Included are measurements of arterial blood flow and gas flow in human lungs. Featured engineering applications include the scanning of turbulent flows in complex geometries for CFD validation, the rapid iterative design of complex internal flow passages, velocity and phase composition measurements in multiphase flows, and the scanning of flows through porous media. Temperature measurements using MR thermometry are discussed. Finally, post-processing methods are covered to demonstrate the utility of MRV data for calculating relative pressure fields and wall shear stresses.

Magnetic resonance velocimetry: applications of magnetic resonance imaging in the measurement of fluid motion

To characterize gradient field nonuniformity and its effect on velocity encoding in phase contrast (PC) MRI, a generalized model that describes this phenomenon and enables the accurate reconstruction of velocities is presented. In addition to considerable geometric distortions, inhomogeneous gradient fields can introduce deviations from the nominal gradient strength and orientation, and therefore spatially-dependent first gradient moments. Resulting errors in the measured phase shifts used for velocity encoding can therefore cause significant deviations in velocity quantification. The true magnitude and direction of the underlying velocities can be recovered from the phase difference images by a generalized PC velocity reconstruction, which requires the acquisition of full three-directional velocity information. The generalized reconstruction of velocities is applied using a matrix formalism that includes relative gradient field deviations derived from a theoretical model of local gradient field nonuniformity. In addition, an approximate solution for the correction of one-directional velocity encoding is given. Depending on the spatial location of the velocity measurements, errors in velocity magnitude can be as high as 60%, while errors in the velocity encoding direction can be up to 45 degrees. Results of phantom measurements demonstrate that effects of gradient field nonuniformity on PC-MRI can be corrected with the proposed method.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/mrm.10582

Generalized reconstruction of phase contrast MRI: analysis and correction of the effect of gradient field distortions.

A stent based drug delivery system. A biological agent of interest is entrapped within a matrix, which is loaded into channels on the surface of a stent. The matrix allows for release, usually sustained release, of the entrapped agent. The stent and matrix is sheathed with a covalently bound gel. In one embodiment of the invention, the stent is used to deliver therapeutic agents to a patient, providing the advantage of efficient delivery and sustained release of an agent at a localized site. In another embodiment of the invention, the drug delivery system is used for testing and comparison of candidate drugs in an in vivo setting.

Drug delivery platform

An adaptation of a medical magnetic resonance imaging system to the noninvasive measurement of three-component mean velocity fields in complex turbulent engineering flows is described. The aim of this paper is to evaluate the capabilities of the technique with respect to its accuracy, time efficiency and applicability as a design tool for complex turbulent internal geometries. The technique, called 4D magnetic resonance velocimetry (4D-MRV), is used to measure the mean flow in fully developed low-Reynolds number turbulent pipe flow, Re=6400 based on bulk mean velocity and diameter, and in a model of a gas turbine blade internal cooling geometry with four serpentine passages, Re=10,000 and 15,000 based on bulk mean velocity and hydraulic diameter. 4D-MRV is capable of completing full-field measurements in three-dimensional volumes with sizes on the order of the magnet bore diameter in less than one hour. Such measurements can include over 2 million independent mean velocity vectors. Velocities measured in round pipe flow agreed with previous experimental results to within 10%. In the turbulent cooling passage flow, the average flow rates calculated from the 4D-MRV velocity profiles agreed with ultrasonic flowmeter measurements to within 7%. The measurements lend excellent qualitative insight into flow structures even in the highly complex 180° bends. Accurate quantitative measurements were obtained throughout the Re=10,000 flow and in the Re=15,000 flow except in the most complex regions, areas just downstream of high-speed bends, where velocities and velocity fluctuations exceeded MRV capabilities for the chosen set of scan parameters. General guidelines for choosing scanning parameters and suggestions for future development are presented.

Christopher J. Elkins

Papers

Multi-material stereolithography

Magnetic resonance velocimetry: applications of magnetic resonance imaging in the measurement of fluid motion

Generalized reconstruction of phase contrast MRI: analysis and correction of the effect of gradient field distortions.

Drug delivery platform

4D Magnetic resonance velocimetry for mean velocity measurements in complex turbulent flows