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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.
Pelvic floor dysfunction (PFD) is characterized by the failure of the levator ani (LA) muscle to maintain the pelvic hiatus, resulting in the descent of the pelvic organs below the pubococcygeal line. This chapter adopts the modified Humphrey material model to consider the effect of the muscle fiber on passive stretching of the LA muscle. The deformation of the LA muscle subjected to intra-abdominal pressure during Valsalva maneuver is compared with the magnetic resonance imaging (MRI) examination of a nulliparous female. Numerical result shows that the fiber-based Humphrey model simulates the muscle behavior better than isotropic constitutive models. Greater posterior movement of the LA muscle widens the levator hiatus due to lack of support from the anococcygeal ligament and the perineal structure as a consequence of birth-related injury and aging. Old and multiparous females with uncontrolled urogenital and rectal hiatus tend to develop PFDs such as prolapse and incontinence.
Effectiveness of the edge-based smoothed finite element method applied to soft biological tissues
(2012)
Background/Aims: Common systems for the quantification of cellular contraction rely on animal-based models, complex experimental setups or indirect approaches. The herein presented CellDrum technology for testing mechanical tension of cellular monolayers and thin tissue constructs has the potential to scale-up mechanical testing towards medium-throughput analyses. Using hiPS-Cardiac Myocytes (hiPS-CMs) it represents a new perspective of drug testing and brings us closer to personalized drug medication. Methods: In the present study, monolayers of self-beating hiPS-CMs were grown on ultra-thin circular silicone membranes and deflect under the weight of the culture medium. Rhythmic contractions of the hiPS-CMs induced variations of the membrane deflection. The recorded contraction-relaxation-cycles were analyzed with respect to their amplitudes, durations, time integrals and frequencies. Besides unstimulated force and tensile stress, we investigated the effects of agonists and antagonists acting on Ca²⁺ channels (S-Bay K8644/verapamil) and Na⁺ channels (veratridine/lidocaine). Results: The measured data and simulations for pharmacologically unstimulated contraction resembled findings in native human heart tissue, while the pharmacological dose-response curves were highly accurate and consistent with reference data. Conclusion: We conclude that the combination of the CellDrum with hiPS-CMs offers a fast, facile and precise system for pharmacological, toxicological studies and offers new preclinical basic research potential.