Efficient isogeometric thin shell formulations for soft biological materials

This paper presents three different constitutive approaches to model thin rotation-free shells based on the Kirchhoff-Love hypothesis. One approach is based on numerical integration through the shell thickness while the other two approaches do not need any numerical integration and so they are computationally more efficient. The formulation is designed for large deformations and allows for geometrical and material nonlinearities, which makes it very suitable for the modeling of soft tissues. Furthermore, six different isotropic and anisotropic material models, which are commonly used to model soft biological materials, are examined for the three proposed constitutive approaches. Following an isogeometric approach, NURBS-based finite elements are used for the discretization of the shell surface. Several numerical examples are investigated to demonstrate the capabilities of the formulation. Those include the contact simulation during balloon angioplasty.Comment: Typos are removed. Remark 3.4 is added. Eq. (18) in the previous version is removed. Thus, the equations get renumbered. Example 5.5 is updated. Minor typos in Eqs. (17), (80), (145) and (146), are corrected. They do not affect the result

A finite membrane element formulation for surfactants

Surfactants play an important role in various physiological and biomechanical applications. An example is the respiratory system, where pulmonary surfactants facilitate the breathing and reduce the possibility of airway blocking by lowering the surface tension when the lung volume decreases during exhalation. This function is due to the dynamic surface tension of pulmonary surfactants, which depends on the concentration of surfactants spread on the liquid layer lining the interior surface of the airways and alveoli. Here, a finite membrane element formulation for liquids is introduced that allows for the dynamics of concentration-dependent surface tension, as is the particular case for pulmonary surfactants. A straightforward approach is suggested to model the contact line between liquid drops/menisci and planar solid substrates, which allows the presented framework to be easily used for drop shape analysis. It is further shown how line tension can be taken into account. Following an isogeometric approach, NURBS-based finite elements are used for the discretization of the membrane surface. The capabilities of the presented computational model is demonstrated by different numerical examples - such as the simulation of liquid films, constrained and unconstrained sessile drops, pendant drops and liquid bridges - and the results are compared with experimental data.Comment: Some typos are removed. Eqs. 13 and 105 are modified. Eqs. 64 and 73 are added; thus, the rest of equations is renumbered. All the numerical experiments are repeated. The example of Sec. 6.3 is slightly modifie

A New Amplification Regime for Traveling Wave Tubes with Third Order Modal Degeneracy

Engineering of the eigenmode dispersion of slow-wave structures (SWSs) to achieve desired modal characteristics, is an effective approach to enhance the performance of high power traveling wave tube (TWT) amplifiers or oscillators. We investigate here for the first time a new synchronization regime in TWTs based on SWSs operating near a third order degeneracy condition in their dispersion. This special three-eigenmode synchronization is associated with a stationary inflection point (SIP) that is manifested by the coalescence of three Floquet-Bloch eigenmodes in the SWS. We demonstrate the special features of "cold" (without electron beam) periodic SWSs with SIP modeled as coupled transmission lines (CTLs) and investigate resonances of SWSs of finite length. We also show that by tuning parameters of a periodic SWS one can achieve an SIP with nearly ideal flat dispersion relationship with zero group velocity or a slightly slanted one with a very small (positive or negative) group velocity leading to different operating schemes. When the SIP structure is synchronized with the electron beam potential benefits for amplification include (i) gain enhancement, (ii) gain-bandwidth product improvement, and (iii) higher power efficiency, when compared to conventional Pierce-like TWTs. The proposed theory paves the way for a new approach for potential improvements in gain, power efficiency and gain-bandwidth product in high power microwave amplifiers.Comment: 15 pages, 11 figure

Atypical patterns of spinal segment degeneration in patients with abdominal aortic aneurysms

PURPOSE Abdominal aortic aneurysms (AAAs) affect the vascular perfusion of the lumbar spine. The treatment of AAAs with endovascular aortic aneurysm repair (EVAR) completely occludes the direct vascular supply to the lumbar spine. We hypothesized that patients with AAA who undergo EVAR show a different pattern of spinal degeneration than individuals without AAA. METHODS In this retrospective institutional review board-approved study, 100 randomly selected patients with AAA who underwent EVAR with computed tomography (CT) scans between 2005 and 2017 were compared with age- and gender-matched controls without AAA. In addition, long-term follow-up CT images (> 6 months before EVAR, at the time of EVAR, and > 12 months after EVAR) of the patients were analysed to compare the progression of degeneration from before to after EVAR. Degeneration scores, lumbar levels with the most severe degeneration, and lumbar levels with progressive degeneration were analysed in all CT images. Fisher's exact test, Wilcoxon signed-rank test, and Mann-Whitney U test were performed for statistical analyses. RESULTS Compared with the control group (n = 94), the most severe degeneration was more commonly detected in the mid-lumbar area in the patient group (n = 100, p = 0.016), with significantly more endplate erosions being detected in the lumbar spine (p = 0.015). However, EVAR did not result in significant additional acceleration of the degenerative process in the long-term follow-up analysis (n = 51). CONCLUSION AAA is associated with atypical, more cranially located spinal degradation, particularly in the mid-lumbar segments; however, EVAR does not seem to additionally accelerate the degenerative process. This observation underlines the importance of disc and endplate vascularization in the pathomechanism of spinal degeneration. LEVEL OF EVIDENCE I Diagnostic: individual cross-sectional studies with consistently applied reference standard and blinding