Stability analysis of injection molding flows

We numerically investigate the stability problem of the injection molding process. It was indicated by Bulters and Schepens Bulters and Schepens 2000 that surface defects of injection molded products may be attributed to a flow instability near the free surface during the filling stage of the mold. We examine the stability of this flow using the extended Pom–Pom constitutive equations. The model allows for controlling the degree of strain hardening of the fluids without affecting the shear behavior considerably. To study the linear stability characteristics of the injection molding process we use a transient finite element algorithm that is able to efficiently handle time dependent viscoelastic flow problems and includes a free surface description to take perturbations of the computational domain into account. It is shown that the fountain flow, which is a model flow for the injection molding process, is subject to a viscoelastic instability. If the various rheologies are compared, we observe that the onset of unstable flow can be delayed by increasing the degree of strain hardening of the fluid by increasing the number of arms in the Pom–Pom model. The most unstable disturbance which is obtained after exponential growth is a swirling flow near the fountain flow surface which is consistent with the experimental findings. © 2004 The Society of Rheology. DOI: 10.1122/1.1753276 I

Quantification of the Temporal Evolution of Collagen Orientation in Mechanically Conditioned Engineered Cardiovascular Tissues

Load-bearing soft tissues predominantly consist of collagen and exhibit anisotropic, non-linear visco-elastic behavior, coupled to the organization of the collagen fibers. Mimicking native mechanical behavior forms a major goal in cardiovascular tissue engineering. Engineered tissues often lack properly organized collagen and consequently do not meet in vivo mechanical demands. To improve collagen architecture and mechanical properties, mechanical stimulation of the tissue during in vitro tissue growth is crucial. This study describes the evolution of collagen fiber orientation with culture time in engineered tissue constructs in response to mechanical loading. To achieve this, a novel technique for the quantification of collagen fiber orientation is used, based on 3D vital imaging using multiphoton microscopy combined with image analysis. The engineered tissue constructs consisted of cell-seeded biodegradable rectangular scaffolds, which were either constrained or intermittently strained in longitudinal direction. Collagen fiber orientation analyses revealed that mechanical loading induced collagen alignment. The alignment shifted from oblique at the surface of the construct towards parallel to the straining direction in deeper tissue layers. Most importantly, intermittent straining improved and accelerated the alignment of the collagen fibers, as compared to constraining the constructs. Both the method and the results are relevant to create and monitor load-bearing tissues with an organized anisotropic collagen network

La trigonometría como herramienta para medir nuestro entorno

En esta experiencia de aula se presenta el trabajo de un grupo de estudiantes de grado décimo que realizaron una actividad en la clase de trigonometría en la que aplicaron conceptos trigonométricos para calcular las medidas de las instalaciones de la institución educativa a la cual pertenecen. El objetivo es mostrar un ejemplo de cómo se puede generar un ambiente de aprendizaje en el que los estudiantes puedan elaborar significados de objetos matemáticos como lo son las razones trigonométricas mediante una labor que permita la aplicación fundamental de la trigonometría realizando mediciones indirectas

Effect of Strain Magnitude on the Tissue Properties of Engineered Cardiovascular Constructs

Mechanical loading is a powerful regulator of tissue properties in engineered cardiovascular tissues. To ultimately regulate the biochemical processes, it is essential to quantify the effect of mechanical loading on the properties of engineered cardiovascular constructs. In this study the Flexercell FX-4000T (Flexcell Int. Corp., USA) straining system was modified to simultaneously apply various strain magnitudes to individual samples during one experiment. In addition, porous polyglycolic acid (PGA) scaffolds, coated with poly-4-hydroxybutyrate (P4HB), were partially embedded in a silicone layer to allow long-term uniaxial cyclic mechanical straining of cardiovascular engineered constructs. The constructs were subjected to two different strain magnitudes and showed differences in biochemical properties, mechanical properties and organization of the microstructure compared to the unstrained constructs. The results suggest that when the tissues are exposed to prolonged mechanical stimulation, the production of collagen with a higher fraction of crosslinks is induced. However, straining with a large strain magnitude resulted in a negative effect on the mechanical properties of the tissue. In addition, dynamic straining induced a different alignment of cells and collagen in the superficial layers compared to the deeper layers of the construct. The presented model system can be used to systematically optimize culture protocols for engineered cardiovascular tissues

Remodelling of the angular collagen fiber distribution in cardiovascular tissues

Understanding collagen fiber remodelling is desired to optimize the mechanical conditioning protocols in tissue-engineering of load-bearing cardiovascular structures. Mathematical models offer strong possibilities to gain insight into the mechanisms and mechanical stimuli involved in these remodelling processes. In this study, a framework is proposed to investigate remodelling of angular collagen fiber distribution in cardiovascular tissues. A structurally based model for collagenous cardiovascular tissues is extended with remodelling laws for the collagen architecture, and the model is subsequently applied to the arterial wall and aortic valve. For the arterial wall, the model predicts the presence of two helically arranged families of collagen fibers. A branching, diverging hammock-type fiber architecture is predicted for the aortic valve. It is expected that the proposed model may be of great potential for the design of improved tissue engineering protocols and may give further insight into the pathophysiology of cardiovascular diseases

Collagen Matrix Remodeling in Stented Pulmonary Arteries after Transapical Heart Valve Replacement

The use of valved stents for minimally invasive replacement of semilunar heart valves is expected to change the extracellular matrix and mechanical function of the native artery and may thus impair long-term functionality of the implant. Here we investigate the impact of the stent on matrix remodeling of the pulmonary artery in a sheep model, focusing on matrix composition and collagen (re)orientation of the host tissue. Ovine native pulmonary arteries were harvested 8 (n = 2), 16 (n = 4) and 24 (n = 2) weeks after transapical implantation of self-expandable stented heart valves. Second harmonic generation (SHG) microscopy was used to assess the collagen (re)orientation of fresh tissue samples. The collagen and elastin content was quantified using biochemical assays. SHG microscopy revealed regional differences in collagen organization in all explants. In the adventitial layer of the arterial wall far distal to the stent (considered as the control tissue), we observed wavy collagen fibers oriented in the circumferential direction. These circumferential fibers were more straightened in the adventitial layer located behind the stent. On the luminal side of the wall behind the stent, collagen fibers were aligned along the stent struts and randomly oriented between the struts. Immediately distal to the stent, however, fibers on both the luminal and the adventitial side of the wall were oriented in the axial direction, demonstrating the stent impact on the collagen structure of surrounding arterial tissues. Collagen orientation patterns did not change with implantation time, and biochemical analyses showed no changes in the trend of collagen and elastin content with implantation time or location of the vascular wall. We hypothesize that the collagen fibers on the adventitial side of the arterial wall and behind the stent straighten in response to the arterial stretch caused by oversizing of the stent. However, the collagen organization on the luminal side suggests that stent-induced remodeling is dominated by contact guidance

Influence of osmotic pressure changes on the opening of existing cracks in 2 intervertebral disc models

An experimental hydrogel model and a numerical mixture model were used to investigate why the disc herniates while osmotic pressure is decreasing. To investigate the influence of decreasing osmotic pressure on the opening of cracks in the disc. In the degeneration process, the disc changes structure (i.e., cracks occur, and osmotic pressure decreases). Disc herniation typically develops when hydration declines, but, on the other hand, it is said that the anulus of a highly hydrated disc has a high risk of rupture. We hypothesized that disc herniation is preceded by the opening of cracks as a result of decreasing osmotic pressure. The osmotic pressure was changed in hydrogel samples with a crack, which was visualized with a confocal laser scanning microscope (Zeiss, Göttingen, Germany). A 2-dimensional finite element mixture model simulated a decrease in osmotic pressure around a crack in a swelling material. Experiments and simulations show that a decrease in osmotic pressure results in the opening of cracks. The simulations show high effective stress concentrations around the crack tip, while the overall stress level decreases, indicating an increased risk of crack growth. Decreasing osmotic pressure in a degenerating intervertebral disc enhances the opening of existing cracks, despite the concomitant decrease in anular stresse