Three-dimensional multi-field modelling of gastric arrhythmias and their effects on antral contractions.

The contraction activation of smooth muscle in the stomach wall (SW) is coordinated by slow electrical waves. The interstitial cells of Cajal (ICC), specialised pacemaker cells, initiate and propagate these slow waves. By establishing an electrically coupled network, each ICC adjusts its intrinsic pacing frequency to a single dominant frequency, to be a key aspect in modelling the electrophysiology of gastric tissue. In terms of modelling, additional fields associated with electrical activation, such as voltage-dependent calcium influx and the resulting deformation, have hardly been considered so far. Here we present a three-dimensional model of the electro-chemomechanical activation of gastric smooth muscle contractions. To reduce computational costs, an adaptive multi-scale discretisation strategy for the temporal resolution of the electric field is used. The model incorporates a biophysically based model of gastric ICC pacemaker activity that aims to simulate stable entrainment and physiological conduction velocities of the electrical slow waves. Together with the simulation of concomitant gastric contractions and the inclusion of a mechanical feedback mechanism, the model is used to study dysrhythmias of gastric slow waves induced by abnormal stretching of the antral SW. The model is able to predict the formation of stretch-induced gastric arrhythmias, such as the emergence of an ectopic pacemaker in the gastric antrum. The results show that the ectopic event is accompanied by smooth muscle contraction and, although it disrupts the normal propagation pattern of gastric slow electrical waves, it can also catalyse the process of handling indigestible materials that might otherwise injure the gastric SW.

On a three-dimensional model for the description of the passive characteristics of skeletal muscle tissue.

In this work, a three-dimensional model was developed to describe the passive mechanical behaviour of anisotropic skeletal muscle tissue. To validate the model, orientation-dependent axial ([Formula: see text], [Formula: see text], [Formula: see text]) and semi-confined compression experiments (mode I, II, III) were performed on soleus muscle tissue from rabbits. In the latter experiments, specimen deformation is prescribed in the loading direction and prevented in an additional spatial direction, fibre compression at [Formula: see text] (mode I), fibre elongation at [Formula: see text] (mode II) and a neutral state of the fibres at [Formula: see text] where their length is kept constant (mode III). Overall, the model can adequately describe the mechanical behaviour with a relatively small number of model parameters. The stiffest tissue response during orientation-dependent axial compression ([Formula: see text] kPa) occurs when the fibres are oriented perpendicular to the loading direction ([Formula: see text]) and are thus stretched during loading. Semi-confined compression experiments yielded the stiffest tissue ([Formula: see text] kPa) in mode II when the muscle fibres are stretched. The extensive data set collected in this study allows to study the different error measures depending on the deformation state or the combination of deformation states.

Correlating the microstructural architecture and macrostructural behaviour of the brain.

The computational simulation of pathological conditions and surgical procedures, for example the removal of cancerous tissue, can contribute crucially to the future of medicine. Especially for brain surgery, these methods can be important, as the ultra-soft tissue controls vital functions of the body. However, the microstructural interactions and their effects on macroscopic material properties remain incompletely understood. Therefore, we investigated the mechanical behaviour of brain tissue under three different deformation modes, axial tension, compression, and semi-confined compression, in different anatomical regions, and for varying axon orientation. In addition, we characterised the underlying microstructure in terms of myelin, cells, glial cells and neuron area fraction, and density. The correlation of these quantities with the material parameters of the anisotropic Ogden model reveals a decrease in shear modulus with increasing myelin area fraction. Strikingly, the tensile shear modulus correlates positively with cell and neuronal area fraction (Spearman's correlation coefficient of rs=0.40 and rs=0.33), whereas the compressive shear modulus decreases with increasing glial cell area (rs=-0.33). Our study finds that tissue non-linearity significantly depends on the myelin area fraction (rs=0.47), cell density (rs=0.41) and glial cell area (rs=0.49). Our results provide an important step towards understanding the micromechanical load transfer that leads to the non-linear macromechanical behaviour of the brain. STATEMENT OF SIGNIFICANCE: Within this article, we investigate the mechanical behaviour of brain tissue under three different deformation modes, in different anatomical regions, and for varying axon orientation. Further, we characterise the underlying microstructure in terms of various constituents. The correlation of these quantities with the material parameters of the anisotropic Ogden model reveals a decrease in shear modulus with increasing myelin area fraction. Strikingly, the tensile shear modulus correlates positively with cell and neuronal area fraction, whereas the compressive shear modulus decreases with increasing glial cell area. Our study finds that tissue non-linearity significantly depends on the myelin area fraction, cell density, and glial cell area. Our results provide an important step towards understanding the micromechanical load transfer that leads to the non-linear macromechanical behaviour of the brain.

Poro-viscoelastic behaviour of the zona pellucida: Impact of three-dimensional modelling on material characterisation.

The development of objective biomarkers for the qualitative assessment of oocytes prior to in-vitro fertilisation procedures is crucial, and in this respect the mechanical response of cells has already emerged as a promising and valid measure. The test setups derived from this conceptual approach usually induce complex, partly asymmetric deformation states, so that the process of material parameter identification can only be realised via three-dimensional, mathematical models. In the present study, a three-dimensional model for oocytes is proposed and implemented in the form of the finite element method. In particular, the contribution of each cellular component to the overall mechanical response is considered by including an anisotropic poro-, viscoelastic approach for the zona pellucida and an incompressible neo-Hookean material for the ooplasm. The model is calibrated and validated using experiments on porcine oocytes under plate-plate compression and indentation during quasi-static cyclic and relaxation tests. In addition to investigating the influence of glycoprotein orientation on the shape and extent of deformation, the applicability of the model to identify mechanical properties is demonstrated and discussed in relation to real, complex testing devices.

On a coupled electro-chemomechanical model of gastric smooth muscle contraction.

The stomach is a central organ in the gastrointestinal tract that performs a variety of functions, in which the spatio-temporal organisation of active smooth muscle contraction in the stomach wall (SW) is highly regulated. In the present study, a three-dimensional model of the gastric smooth muscle contraction is presented, including the mechanical contribution of the mucosal and muscular layer of the SW. Layer-specific and direction-dependent model parameters for the active and passive stress-stretch characteristics of the SW were determined experimentally using porcine smooth muscle strips. The electrical activation of the smooth muscle cells (SMC) due to the pacemaker activity of the interstitial cells of Cajal (ICC) is modelled by using FitzHugh-Nagumo-type equations, which simulate the typical ICC and SMC slow wave behaviour. The calcium dynamic in the SMC depends on the SMC membrane potential via a gaussian function, while the chemo-mechanical coupling in the SMC is modelled via an extended Hai-Murphy model. This cascade is coupled with an additional mechano-electrical feedback-mechanism, taking into account the mechanical response of the ICC and SMC due to stretch of the SW. In this way the relaxation responses of the fundus to accommodate incoming food, as well as the typical peristaltic contraction waves in the antrum for mixing and transport of the chyme, have been well replicated in simulations performed at the whole organ level. STATEMENT OF SIGNIFICANCE: In this article, a novel three-dimensional electro-chemomechanical model of the gastric smooth muscle contraction is presented. The propagating waves of electrical membrane potential in the network ofinterstitial cells of Cajal (ICC) and smooth muscle cells (SMC) lead to a global pattern of change in the calciumdynamics inside the SMC. Taking additionally into account the mechanical response of the ICC and SMC due to stretch of the stomach wall, also referred to as mechanical feedback-mechanism, the result is a complex spatio-temporal regulation of the active contraction and relaxation of the gastric smooth muscle tissue. Being a firstapproach, in future view such a three-dimensional model can give an insight into the complexload transferring system of the stomach wall, as well as into the electro-chemomechanicalcoupling process underlying smooth muscle contraction in health and disease.

Biomechanical and microstructural characterisation of the porcine stomach wall: Location- and layer-dependent investigations.

The mechanical properties of the stomach wall help to explain its function of storing, mixing, and emptying in health and disease. However, much remains unknown about its mechanical properties, especially regarding regional heterogeneities and wall microstructure. Consequently, the present study aimed to assess regional differences in the mechanical properties and microstructure of the stomach wall. In general, the stomach wall and the different tissue layers exhibited a nonlinear stress-stretch relationship. Regional differences were found in the mechanical response and the microstructure. The highest stresses of the entire stomach wall in longitudinal direction were found in the corpus (201.5 kPa), where food is ground followed by the antrum (73.1 kPa) and the fundus (26.6 kPa). In contrast, the maximum stresses in circumferential direction were 39.7 kPa, 26.2 kPa, and 15.7 kPa for the antrum, fundus, and corpus, respectively. Independent of the fibre orientation and with respect to the biaxial loading direction, partially clear anisotropic responses were detected in the intact wall and the muscular layer. In contrast, the innermost mucosal layer featured isotropic mechanical characteristics. Pronounced layers of circumferential and longitudinal muscle fibres were found in the fundus only, whereas corpus and antrum contained almost exclusively circumferential orientated muscle fibres. This specific stomach structure mirrors functional differences in the fundus as well as corpus and antrum. Within this study, the load transfer mechanisms, connected with these wavy layers but also in total with the stomach wall's microstructure, are discussed. STATEMENT OF SIGNIFICANCE: This article examines for the first time the layer-specific mechanical and histological properties of the stomach wall attending to the location of the sample. Moreover, both mechanical behaviour and microstructure were explicitly match identifying the heterogeneous characteristics of the stomach. On the one hand, the results of this study contribute to the understanding of stomach mechanics and thus to their functional understanding of stomach motility. On the other hand, they are relevant to the fields of constitutive formulation of stomach tissue, whole stomach mechanics, and stomach-derived scaffolds i.e., tissue-engineering grafts.

On a three-dimensional constitutive model for history effects in skeletal muscles.

An exceptional property of skeletal muscles that distinguishes them from other soft tissues is their ability to contract by generating active forces, which in turn are initiated by an electrochemical trigger. Some of these so-called active material properties are generally characterised using isometric contraction experiments at various muscle lengths. In this context, experimental observations revealed that unlike the widespread assumption in muscle modelling, reaction forces indeed depend on so-called history effects, which can be classified into force enhancement and force depression. For the experimental settings of force enhancement, two subsequent isometric contractions are interrupted by an isokinetic extension. The isometric reaction force is increased after the isokinetic extension with respect to a reference measurement, while in the case of force depression, isokinetic shortening is responsible for forces below a certain isometric reference measurement. Most theoretical investigations of force enhancement and force depression use one-dimensional models to simulate the force response considering muscle deformation to be homogeneous. In contrast, the aim of the present study is to analyse history effects in skeletal muscle tissue using a three-dimensional geometry model of the whole muscle-tendon unit. Therefore, a purely phenomenological approach is presented. The model is implemented in the finite element framework to analyse history effects for the boundary value problem of the entire three-dimensional muscle-tendon geometry. The constitutive model shows good agreement with the experimental data. Furthermore, the simulations reveal information about the inhomogeneous stretch distributions within the muscle tissues.

Three-dimensional mechano-electrochemical model for smooth muscle contraction of the urinary bladder.

The urinary bladder is a central organ of vertebrates and imposes, based on its extreme deformation (volume changes up to several 100%), special requirements on the overall bladder tissue. However, studies focusing on three-dimensional modelling of bladder deformation and bladder function during micturition are rare. Based on three fields, namely, the membrane potential, calcium concentration, and placement, a mechano-electrochemical-coupled, three-dimensional model describing the contractile behaviour of urinary bladder smooth muscle is presented using a strain energy function. The strain energy functions for the different layers of the bladder wall are additively decomposed into a passive part comprising elastin, the extracellular matrix (ECM), and collagen and an active electrochemical-driven part comprising the contraction of smooth muscle cells (SMC). While the two-variable FitzHugh-Nagumo-type membrane model (FitzHugh, 1961; Nagumo et al., 1962) has been used to describe the membrane potential characteristics, the four-state, cross-bridge model of Hai and Murphy (1988) is implemented into the finite element method for the quantification of the calcium phase. Appropriate model parameters were determined experimentally using 40 tissue strips isolated from porcine bladders. Characteristic orientation-dependent passive and active stress-stretch relationships were identified for muscle strips, including the entire bladder wall structure and those featuring the isolated muscle layer only. Active experiments on the smooth muscle layers revealed higher stresses in the longitudinal (28.9kPa) direction than in the transversal (22.7kPa) one. Additionally, three-dimensional deformation characteristics were recorded from single muscle strips to qualitatively confirm the strip simulations. Three-dimensional simulations at the tissue strip level and the organ level were performed to analyse the interaction among the electrical action potential, calcium distribution, chemical degree of activation, and equivalent von Mises stress.