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Edge-based and face-based smoothed finite element methods (ES-FEM and FS-FEM, respectively) are modified versions of the finite element method allowing to achieve more accurate results and to reduce sensitivity to mesh distortion, at least for linear elements. These properties make the two methods very attractive. However, their implementation in a standard finite element code is nontrivial because it requires heavy and extensive modifications to the code architecture. In this article, we present an element-based formulation of ES-FEM and FS-FEM methods allowing to implement the two methods in a standard finite element code with no modifications to its architecture. Moreover, the element-based formulation permits to easily manage any type of element, especially in 3D models where, to the best of the authors' knowledge, only tetrahedral elements are used in FS-FEM applications found in the literature. Shape functions for non-simplex 3D elements are proposed in order to apply FS-FEM to any standard finite element.
In this work, the effect of low air relative humidity on the operation of a polymer electrolyte membrane fuel cell is investigated. An innovative method through performing in situ electrochemical impedance spectroscopy is utilised to quantify the effect of inlet air relative humidity at the cathode side on internal ionic resistances and output voltage of the fuel cell. In addition, algorithms are developed to analyse the electrochemical characteristics of the fuel cell. For the specific fuel cell stack used in this study, the membrane resistance drops by over 39 % and the cathode side charge transfer resistance decreases by 23 % after increasing the humidity from 30 % to 85 %, while the results of static operation also show an increase of ∼2.2 % in the voltage output after increasing the relative humidity from 30 % to 85 %. In dynamic operation, visible drying effects occur at < 50 % relative humidity, whereby the increase of the air side stoichiometry increases the drying effects. Furthermore, other parameters, such as hydrogen humidification, internal stack structure, and operating parameters like stoichiometry, pressure, and temperature affect the overall water balance. Therefore, the optimal humidification range must be determined by considering all these parameters to maximise the fuel cell performance and durability. The results of this study are used to develop a health management system to ensure sufficient humidification by continuously monitoring the fuel cell polarisation data and electrochemical impedance spectroscopy indicators.
Purpose:
MRI plays a leading diagnostic role in assessing the musculoskeletal (MSK) system and is well established for most questions at clinically used field strengths (up to 3 T). However, there are still limitations in imaging early stages of cartilage degeneration, very fine tendons and ligaments, or in locating nerve lesions, for example. 7 T MRI of the knee has already received increasing attention in the current published literature, but there is a strong need to develop new radiofrequency (RF) coils to assess more regions of the MSK system. In this work, an eight-channel transmit/receive RF array was built as a multipurpose coil for imaging some of the thus far neglected regions. An extensive coil characterization protocol and first in vivo results of the human wrist, shoulder, elbow, knee, and ankle imaged at 7 T will be presented.
Methods:
Eight surface loop coils with a dimension ofurn:x-wiley:00942405:media:mp7176:mp7176-math-0001 were machined from FR4 circuit board material. To facilitate easy positioning, two coil clusters, each with four loop elements, were combined to one RF transmit/receive array. An overlapped and shifted arrangement of the coil elements was chosen to reduce the mutual inductance between neighboring coils. A phantom made of body-simulating liquid was used for tuning and matching on the bench. Afterward, the S-parameters were verified on a human wrist, elbow, and shoulder. For safety validation, a detailed compliance test was performed including full wave simulations of the RF field distribution and the corresponding specific absorption rate (SAR) for all joints. In vivo images of four volunteers were assessed with gradient echo and spin echo sequences modified to obtain optimal image contrast, full anatomic coverage, and the highest spatial resolution within a reasonable acquisition time. The performance of the RF coil was additionally evaluated by in vivo B1 mapping.
Results:
A comparison of B1 per unit power, flip angle distribution, and anatomic images showed a fairly homogeneous excitation for the smaller joints (elbow, wrist, and ankle), while for the larger joints, the shoulder and especially the knee, B1 inhomogeneities and limited penetration depth were more pronounced. However, the greater part of the shoulder joint could be imaged.In vivo images rendered very fine anatomic details such as fascicles of the median nerve and the branching of the nerve bundles. High-resolution images of cartilage, labrum, and tendons could be acquired. Additionally, turbo spin echo (TSE) and inversion recovery sequences performed very well.
Conclusions:
This study demonstrates that the concept of two four-channel transmit/receive RF arrays can be used as a multipurpose coil for high-resolutionin vivo MR imaging of the musculoskeletal system at 7 T. Not only gradient echo but also typical clinical and SAR-intensive sequences such as STIR and TSE performed well. Imaging of small structures and peripheral nerves could in particular benefit from this technique.