Smoothed finite element methods in simulation of active contraction of myocardial tissue samples.

In modelling and simulation of cardiac mechanics, tetrahedral meshes are often used due to the easy availability of efficient meshing algorithms. This is beneficial in particular when complex geometries such as cardiac structures are considered. The gold standard in simulating the cardiac cycle is to solve the mechanical balance equations with the finite element method (FEM). However, using linear shape functions in the FEM in combination with nearly-incompressible material models is known to produce overly stiff approximations, whereas higher order elements are computationally more expensive. To overcome these problems, smoothed finite element methods (S-FEMs) have been proposed by Liu and co-workers. So far, S-FEMs in 3D have been utilised only in simulations of passive mechanics. In the present work, different S-FEMs are for the first time used for simulation of an active cardiac contraction on three-dimensional myocardial tissue samples. Further, node-based S-FEM (NS-FEM), face-based S-FEM (FS-FEM) and selective FS/NS-FEM are for the first time implemented as user subroutine in the commercial software Abaqus. Our results confirm that all S-FEMs perform softer than linear FEM and volumetric locking is reduced. The FS/NS-FEM produces solutions with the relative error in maximum displacement and rotation being less than 5% with respect to the reference solution obtained by the quadratic FEM for all considered mesh sizes, although linear shape functions are used. We therefore conclude that in particular FS/NS-FEM is an efficient and accurate numerical method in the simulation of an active cardiac muscle contraction.

Transmural fibre orientations based on Laplace-Dirichlet-Rule-Based-Methods and their influence on human heart simulations.

It is well known that the orthotropic tissue structure decisively influences the mechanical and electrical properties of the heart. Numerous approaches to compute the orthotropic tissue structure in computational heart models have been developed in the past decades. In this study, we investigate to what extent different Laplace-Dirichlet-Rule-Based-Methods (LDRBMs) influence the local orthotropic tissue structure and thus the electromechanical behaviour of the subsequent cardiac simulation. In detail, we are utilising three Laplace-Dirichlet-Rule-Based-Methods and compare: (i) the local myofibre orientation; (ii) important global characteristics (ejection fraction, peak pressure, apex shortening, myocardial volume reduction, fractional wall thickening); (iii) local characteristics (active fibre stress, fibre strain). We observe that the orthotropic tissue structures for the three LDRBMs show significant differences in the local myofibre orientation. The global characteristics myocardial volume reduction and peak pressure are rather insensitive to a change in local myofibre orientation, while the ejection fraction is moderately influenced by the different LDRBMs. Moreover, the apical shortening and fractional wall thickening exhibit a sensitive behaviour to a change in the local myofibre orientation. The highest sensitivity can be observed for the local characteristics.

Comparison of stress and stress-strain approaches for the active contraction in a rat cardiac cycle model.

In the last decades, different strategies to model the active electromechanically coupled behaviour of the cardiac tissue were proposed in order to simulate electromechanics of the heart under healthy and pathological conditions. The main objective of this work is to compare two approaches for modelling the active contraction during the electromechanically coupled rat cardiac cycle -- the stress and the stress-strain approach. Firstly, a cylindrical benchmark is considered and secondly, for a generic model of a rat left ventricle, a simulation including the Windkessel model, excitation via Purkinje fibre network and mechano-electrical feedback is performed. The model is calibrated with experimental data for rats, partly from own measurements via cardiac ultrasound, partly from the literature. Further, possibilities to reach higher ejection fractions are discussed and considered for an exemplary rat left ventricle. Within each approach, we observe regionally different active stresses and fibre stretches. Moreover, the transmural active stress and fibre stretch distribution is influenced by the pressure load on the endocardial surface. The active stress approach is not sensitive to the fibre stretch and transmurally varying fibre stretch in the left ventricular domain is observed. The active stress-strain approach leads to transmurally more homogeneous fibre stretch at the end-systolic state.

The effect of subcutaneous injection of methylprednisolone acetate and lidocaine for refractory postherpetic neuralgia: a prospective, observational study.

BACKGROUND: Postherpetic neuralgia (PHN) is the most common and bearable complication of herpes zoster (HZ). This pain may have negative impact on the patient's all aspects of daily life and health-related quality of life (HRQOL). Despite numerous advances in treatment, many patients remain resistant to the current therapy options. It is the first time subcutaneous injection of methylprednisolone acetate and lidocaine has been used to treat refractory PHN. We report the results of this treatment evaluating pain relief and HRQOL improvement in this disorder. METHODS: A total of 43 patients with refractory PHN was enrolled in the observational study. All patients received daily subcutaneous injection of methylprednisolone acetate and lidocaine for 10 consecutive days. The severity of pain was assessed by using Visual Analog Scale (VAS), and 36-Item Short Form Survey (SF-36) was applied to evaluate HRQOL. Assessment of the pain and HRQOL was carried out at baseline and posttreatment at 4 weeks as well as 6 and 12 months. RESULTS: At baseline, all patients experienced severe PHN with average VAS scores of 8.44 ± 0.85 (minimum 7; maximum 10). At 4 weeks, 6 months, and 12 months after treatment, the pain had significantly decreased (P < .001), and all subjects showed significant improvement in all eight domains of HRQOL. No major adverse events associated with the subcutaneous injection were observed. CONCLUSIONS: Our results indicate that subcutaneous injection of methylprednisolone acetate and lidocaine can be an effective and safe treatment for PHN.

Towards the simulation of active cardiac mechanics using a smoothed finite element method.

In the last decades, various computational models have been developed to simulate cardiac electromechanics. The most common numerical tool is the finite element method (FEM). However, this method crucially depends on the mesh quality. For complex geometries such as cardiac structures, it is convenient to use tetrahedral discretisations which can be generated automatically. On the other hand, such automatic meshing with tetrahedrons together with large deformations often lead to elements distortion and volumetric locking. To overcome these difficulties, different smoothed finite element methods (S-FEMs) have been proposed in the recent years. They are known to be volumetric locking free, less sensitive to mesh distortion and so far have been used e.g. in simulation of passive cardiac mechanics. In this work, we extend for the first time node-based S-FEM (NS-FEM) towards active cardiac mechanics. Firstly, the sensitivity to mesh distortion is tested and compared to that of FEM. Secondly, an active contraction in circumferentially aligned fibre direction is modelled in the healthy and the infarcted case. We show, that the proposed method is more robust with respect to mesh distortion and computationally more efficient than standard FEM. Being furthermore free of volumetric locking problems makes S-FEM a promising alternative in modelling of active cardiac mechanics, respectively electromechanics.

Modelling of compressible and orthotropic surgical mesh implants based on optical deformation measurement.

There is a potential mismatch between surgical mesh implants for hernia repair of pelvic floor surgery and the host tissue because soft tissue is incompressible and meshes are compressible. Therefore, mesh and tissue may develop different stiffness over the range of deformation. In addition compressibility is related to a change of porosity of the mesh which may decrease during the deformation. Scar formation and the ingrowth of the mesh can be related to effective porosity which decreases discontinuously in uniaxial loading at a critical stretch when pore areas collapse and therefore the mesh becomes ineffective. Compressibility requires several non standard approaches which can be performed with high accuracy and local resolution by deformation measurement with digital image correlation (DIC). A compressible hyperelastic model is chosen and identified with biaxial deformation measurements. Also effective porosity of deformed meshes can be calculated on the basis of biaxial deformation. The proposed constitutive equation and the developed model of effective porosity are represented in form of principle stretch. Stretch can be measured with magnetic resonance imaging (MRI) visible meshes so that stress and effective porosity can be derived in vivo.