Regional differences in stomach stretch during organ filling and their implications on the mechanical stress response

As part of the digestive system, the stomach plays a crucial role in the health and well-being of an organism. It produces acids and performs contractions that initiate the digestive process and begin the break-up of ingested food. Therefore, its mechanical properties are of interest. This study includes a detailed investigation of strains in the porcine stomach wall during passive organ filling. In addition, the observed strains were applied to tissue samples subjected to biaxial tensile tests. The results show inhomogeneous strains during filling, which tend to be higher in the circumferential direction (antrum: 13.2%, corpus: 22.0%, fundus: 67.8%), compared to the longitudinal direction (antrum: 4.8%, corpus: 24.7%, fundus: 50.0%) at a maximum filling of 3500 ml. Consequently, the fundus region experienced the greatest strain. In the biaxial tensile experiments, the corpus region appeared to be the stiffest, reaching nominal stress values above 400 kPa in the circumferential direction, whereas the other regions only reached stress levels of below 50 kPa in both directions for the investigated stretch range. Our findings gain new insight into stomach mechanics and provide valuable data for the development and validation of computational stomach models.

Influence of muscle length on the three-dimensional architecture and aponeurosis dimensions of rabbit calf muscles

The function of a muscle is highly dependent on its architecture, which is characterized by the length, pennation, and curvature of the fascicles, and the geometry of the aponeuroses. During in vivo function, muscles regularly undergo changes in length, thereby altering their architecture. During passive muscle lengthening, fascicle length (FL) generally increases and the angle of fascicle pennation (FP) and the fascicle curvature (FC) decrease, while the aponeuroses increase in length but decrease in width. Muscles are differently structured, making their change during muscle lengthening complex and multifaceted. To obtain comprehensive data on architectural changes in muscles during passive length, the present study determined the three-dimensional fascicle geometry of rabbit M. gastrocnemius medialis (GM), M. gastrocnemius lateralis (GL), and M. plantaris (PLA). For this purpose, the left and right legs of three rabbits were histologically fixed at targeted ankle joint angles of 95° (short muscle length [SML]) and 60° (long muscle length [LML]), respectively, and the fascicles were tracked by manual three-dimensional digitization. In a second set of experiments, the GM aponeurosis dimensions of ten legs from five rabbits were determined at varying muscle lengths via optical marker tracking. The GM consisted of a uni-pennated compartment, whereas the GL and PLA contained multiple compartments of differently pennated fascicles. In the LML compared to the SML, the GM, GL, and PLA had on average a 41%, 29%, and 41% increased fascicle length, and a 30%, 25%, and 33% decrease in fascicle pennation and a 32%, 11%, and 35% decrease in fascicle curvature, respectively. Architectural properties were also differentiated among the different compartments of the PLA and GL, allowing for a more detailed description of their fascicle structure and changes. It was shown that the compartments change differently with muscle length. It was also shown that for each degree of ankle joint angle reduction, the proximal GM aponeurosis length increased by 0.11%, the aponeurosis width decreased by 0.22%, and the area was decreased by 0.20%. The data provided improve our understanding of muscles and can be used to develop and validate muscle models.

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.

Process Parameters and Geometry Effects on Piezoresistivity in Additively Manufactured Polymer Sensors

The current work experimentally determined how the initial resistance and gauge factor in additively manufactured piezoresistive sensors are affected by the material, design, and process parameters. This was achieved through the tensile testing of sensors manufactured with different infill angles, layer heights, and sensor thicknesses using two conductive polymer composites. Linear regression models were then used to analyze which of the input parameters had significant effects on the sensor properties and which interaction effects existed. The findings demonstrated that the initial resistance in both materials was strongly dependent on the sensor geometry, decreasing as the cross-sectional area was increased. The resistance was also significantly influenced by the layer height and the infill angle, with the best variants achieving a resistance that was, on average, 22.3% to 66.5% lower than less-favorable combinations, depending on the material. The gauge factor was most significantly affected by the infill angle and, depending on the material, by the layer height. Of particular interest was the finding that increasing in the infill angle resulted in an increase in the sensitivity that outweighed the associated increase in the initial resistance, thereby improving the gauge factor by 30.7% to 114.6%, depending on the material.

A geometry model of the porcine stomach featuring mucosa and muscle layer thicknesses

The stomach is a vital organ responsible for food storage, digestion, and transport. Stomach diseases are of great economic and medical importance and require a large number of bariatric surgeries every year. To improve medical interventions, in silico modeling of the gastrointestinal tract has gained popularity in recent years to study stomach functioning. Because of the great structural and nutritional similarity between the porcine and human stomach, the porcine stomach is a suitable surrogate for the development and validation of gastric models. This study presents a realistic 3D geometry model of the porcine stomach based on a photogrammetric reconstruction of a real organ. Layer thicknesses of the stomach wall's mucosa and tunica muscularis were determined by more than 1900 manual measurements at different locations. Layer thickness distributions show mean mucosal and muscle thicknesses of 2.29 ± 0.45 mm and 2.83 ± 0.99 mm, respectively. In general, layer thicknesses increase from fundus (mucosa: 1.82 ± 0.19 mm, muscle layer: 2.59 ± 0.32 mm) to antrum (mucosa: 2.69 ± 0.31 mm, muscle layer: 3.73 ± 1.05 mm). The analysis of stomach asymmetry with respect to an idealized symmetrical stomach model, an approach often used in the literature, revealed volumetric deviations of 45%, 15%, and 92% for the antrum, corpus, and fundus, respectively. The present work also suggests an algorithm for the computation of longitudinal and circumferential directions at local points. These directions are useful for the implementation of material anisotropy. In addition, we present data on the passive pressure-volume relationship of the organ and perform an exemplary finite-element simulation, where we demonstrate the applicability of the model. We encourage others to utilize the geometry model featuring profound asymmetry for future model-based investigations on stomach functioning.

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.

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 r_s=0.40 and r_s=0.33), whereas the compressive shear modulus decreases with increasing glial cell area (r_s=-0.33). Our study finds that tissue non-linearity significantly depends on the myelin area fraction (r_s=0.47), cell density (r_s=0.41) and glial cell area (r_s=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.

On multiscale tension-compression asymmetry in skeletal muscle

Skeletal muscle tissue shows a clear asymmetry with regard to the passive stresses under tensile and compressive deformation, referred to as tension-compression asymmetry (TCA). The present study is the first one reporting on TCA at different length scales, associated with muscle tissue and muscle fibres, respectively. This allows for the first time the comparison of TCA between the tissue and one of its individual components, and thus to identify the length scale at which this phenomenon originates. Not only the passive stress-stretch characteristics were recorded, but also the volume changes during the axial tension and compression experiments. The study reveals clear differences in the characteristics of TCA between fibres and tissue. At tissue level TCA increases non-linearly with increasing deformation and the ratio of tensile to compressive stresses at the same magnitude of strain reaches a value of approximately 130 at 13.5% deformation. At fibre level instead it initially drops to a value of 6 and then rises again to a TCA of 14. At a deformation of 13.5%, the tensile stress is about 6 times higher. Thus, TCA is about 22 times more expressed at tissue than fibre scale. Moreover, the analysis of volume changes revealed little compressibility at tissue scale whereas at fibre level, especially under compressive stress, the volume decreases significantly. The data collected in this study suggests that the extracellular matrix has a distinct role in amplifying the TCA, and leads to more incompressible tissue behaviour. STATEMENT OF SIGNIFICANCE: This article analyses and compares for the first time the tension-compression asymmetry (TCA) displayed by skeletal muscle at tissue and fibre scale. In addition, the volume changes of tissue and fibre specimens with application of passive tensile and compressive loads are studied. The study identifies a key role of the extracellular matrix in establishing the mechanical response of skeletal muscle tissue: It contributes significantly to the passive stress, it is responsible for the major part of tissue-scale TCA and, most probably, prevents/balances the volume changes of muscle fibres during deformation. These new results thus shed light on the origin of TCA and provide new information to be used in microstructure-based approaches to model and simulate skeletal muscle tissue.

Surrogate-based Bayesian calibration of biomechanical models with isotropic material behavior

This work introduces a computational methodology to calibrate material models in biomechanical applications under uncertainty. We adopt a Bayesian approach, which estimates the probability distributions of hyperelastic material parameters, based on force-strain measurements. We approximate the parametric biomechanical model by combining a reduced order representation of the force response with a Polynomial Chaos expansion. The surrogate model allows to employ sampling-intensive Markov chain Monte Carlo methods and provides an efficient way to estimate (generalized) Sobol coefficients. We use a Sobol sensitivity analysis to assess the influence of material parameters and present an iterative procedure to quantify the accuracy of the surrogate model as additional uncertainty during Bayesian updating. The methodology is illustrated with three cases, tensile experiments on heat-induced whey protein gel, indentation experiments for oocytes and a manufactured example. Real experimental data are used for the calibration.

Age-dependent mechanical and microstructural properties of the rabbit soleus muscle

During growth there are serious changes in the skeletal muscles to compensate for the changed requirements in terms of body weight and size. In this study, the age-dependent (between 21 and 100 days) mechanical and microstructural properties of rabbit soleus muscle tissue were investigated. For this purpose, morphological properties (animal mass, soleus muscle mass, tibial length) were measured at 5 different times during aging. On the other hand, fibre orientation-dependent axial and semi-confined compression experiments were realised. In addition, the essential components (muscle fibres, extracellular matrix, remaining components), dominating the microstructure of muscle tissue, were analysed. While the mechanical results show hardly any age-dependent differences, the morphological and microstructural results show clear age-dependent differences. All morphological parameters increase significantly (animal mass by 839.2%, muscle mass 1050.6%, tibial length 233.6%). In contrast, microstructural parameters change differently. The percentage of fibres (divided into slow-twitch (ST) and fast-twitch (FT) fibres) increases significantly (137.6%), while the proportions of the extracellular matrix and the remaining components (48.2% and 46.1%) decrease. At the same time, the cross-sectional area of the fibres increases significantly (697.9%). The totality of this age-dependent information provides a deeper understanding of age-related changes in muscle structure and function and may contribute to successful development and validation of growth models in the future. STATEMENT OF SIGNIFICANCE: This article reports the first comprehensive data set on age-dependent morphological (animal mass, soleus muscle mass, tibial length), mechanical (axial and semi-confined compression), and microstructural (muscle fibres, extracellular matrix, remaining components) properties of the rabbit soleus muscle. On the one hand, the results of this study contribute to the understanding of muscle mechanics and thus to understanding of load transfer mechanisms inside the muscle tissue during growth. On the other hand, these results are relevant to the fields of constitutive formulation of age-dependent muscle tissue.

On a phase-field approach to model fracture of small intestine walls

We address anisotropic elasticity and fracture in small intestine walls (SIWs) with both experimental and computational methods. Uniaxial tension experiments are performed on porcine SIW samples with varying alignments and quantify their nonlinear elastic anisotropic behavior. Fracture experiments on notched SIW strips reveal a high sensitivity of the crack propagation direction and the failure stress on the tissue orientation. From a modeling point of view, the observed anisotropic elastic response is studied with a continuum mechanical model stemming from a strain energy density with a neo-Hookean component and an anisotropic component with four families of fibers. Fracture is addressed with the phase-field approach, featuring two-fold anisotropy in the fracture toughness. Elastic and fracture model parameters are calibrated based on the experimental data, using the maximum and minimum limits of the experimental stress-stretch data set. A very good agreement between experimental data and computational results is obtained, the role of anisotropy being effectively captured by the proposed model in both the elastic and the fracture behavior. STATEMENT OF SIGNIFICANCE: This article reports a comprehensive experimental data set on the mechanical failure behavior of small intestinal tissue, and presents the corresponding protocols for preparing and testing the samples. On the one hand, the results of this study contribute to the understanding of small intestine mechanics and thus to understanding of load transfer mechanisms inside the tissue. On the other hand, these results are used as input for a phase-field modelling approach, presented in this article. The presented model can reproduce the mechanical failure behavior of the small intestine in an excellent way and is thus a promising tool for the future mechanical description of diseased small intestinal tissue.

Architectural model for muscle growth during maturation

Muscle architecture, which includes parameters like fascicle length, pennation angle, and physiological cross-sectional area, strongly influences skeletal muscles' mechanical properties. During maturation, the muscle architecture has to adapt to a growing organism. This study aimed to develop an architectural model capable of predicting the complete 3D fascicle architecture for primarily unipennate muscles of an arbitrary age, based on fascicle data for an initial age. For model development, we collected novel data on 3D muscle architecture of the rabbit (Oryctolagus cuniculus) M. plantaris of eight animals ranging in age from 29 to 106 days. Experimental results show that plantaris muscle belly length increases by 73%, whereas mean fascicle length and mean pennation angle increases by 39 and 14%, respectively. Those changes were incorporated into the model. In addition to the data collected for M. plantaris the predictions of the model were compared to existing literature data of rabbit M. soleus and M. gastrocnemius medialis. With an error of −1.0 ± 8.6% for relative differences in aponeurosis length, aponeurosis width, muscle height, and muscle mass, the model delivered good results matching interindividual differences. For future studies, the model could be utilized to generate realistic architectural data sets for simulation studies.

Influence of layer separation on the determination of stomach smooth muscle properties

Uniaxial tensile experiments are a standard method to determine the contractile properties of smooth muscles. Smooth muscle strips from organs of the urogenital and gastrointestinal tract contain multiple muscle layers with different muscle fiber orientations, which are frequently not separated for the experiments. During strip activation, these muscle fibers contract in deviant orientations from the force-measuring axis, affecting the biomechanical characteristics of the tissue strips. This study aimed to investigate the influence of muscle layer separation on the determination of smooth muscle properties. Smooth muscle strips, consisting of longitudinal and circumferential muscle layers (whole-muscle strips [WMS]), and smooth muscle strips, consisting of only the circumferential muscle layer (separated layer strips [SLS]), have been prepared from the fundus of the porcine stomach. Strips were mounted with muscle fibers of the circumferential layer inline with the force-measuring axis of the uniaxial testing setup. The force-length (FLR) and force-velocity relationships (FVR) were determined through a series of isometric and isotonic contractions, respectively. Muscle layer separation revealed no changes in the FLR. However, the SLS exhibited a higher maximal shortening velocity and a lower curvature factor than WMS. During WMS activation, the transversally oriented muscle fibers of the longitudinal layer shortened, resulting in a narrowing of this layer. Expecting volume constancy of muscle tissue, this narrowing leads to a lengthening of the longitudinal layer, which counteracted the shortening of the circumferential layer during isotonic contractions. Consequently, the shortening velocities of the WMS were decreased significantly. This effect was stronger at high shortening velocities.

Visco- and poroelastic contributions of the zona pellucida to the mechanical response of oocytes

Probing mechanical properties of cells has been identified as a means to infer information on their current state, e.g. with respect to diseases or differentiation. Oocytes have gained particular interest, since mechanical parameters are considered potential indicators of the success of in vitro fertilisation procedures. Established tests provide the structural response of the oocyte resulting from the material properties of the cell's components and their disposition. Based on dedicated experiments and numerical simulations, we here provide novel insights on the origin of this response. In particular, polarised light microscopy is used to characterise the anisotropy of the zona pellucida, the outermost layer of the oocyte composed of glycoproteins. This information is combined with data on volumetric changes and the force measured in relaxation/cyclic, compression/indentation experiments to calibrate a multi-phasic hyper-viscoelastic model through inverse finite element analysis. These simulations capture the oocyte's overall force response, the distinct volume changes observed in the zona pellucida, and the structural alterations interpreted as a realignment of the glycoproteins with applied load. The analysis reveals the presence of two distinct timescales, roughly separated by three orders of magnitude, and associated with a rapid outflow of fluid across the external boundaries and a long-term, progressive relaxation of the glycoproteins, respectively. The new results allow breaking the overall response down into the contributions from fluid transport and the mechanical properties of the zona pellucida and ooplasm. In addition to the gain in fundamental knowledge, the outcome of this study may therefore serve an improved interpretation of the data obtained with current methods for mechanical oocyte characterisation.

Direct measurement of the direction-dependent mechanical behaviour of skeletal muscle extracellular matrix

This paper reports the first comprehensive data set on the anisotropic mechanical properties of isolated endo- and perimysial extracellular matrix of skeletal muscle, and presents the corresponding protocols for preparing and testing the samples. In particular, decellularisation of porcine skeletal muscle is achieved with caustic soda solution, and mechanical parameters are defined based on compressive and tensile testing in order to identify the optimal treatment time such that muscle fibres are dissolved whereas the extracellular matrix remains largely intact and mechanically functional. At around 18 h, a time window was found and confirmed by histology, in which axial tensile experiments were performed to characterise the direction-dependent mechanical response of the extracellular matrix samples, and the effect of lateral pre-compression was studied. The typical, large variability in the experimental stress response could be largely reduced by varying a single scalar factor, which was attributed to the variation of the fraction of extracellular matrix within the tissue. While experimental results on the mechanical properties of intact muscle tissue and single muscle fibres are increasingly available in literature, there is a lack of information on the properties of the collagenous components of skeletal muscle. The present work aims at closing this gap and thus contributes to an improved understanding of the mechanics of skeletal muscle tissue and provides a missing piece of information for the development of corresponding constitutive and computational models.

Challenges of influencing cellular morphology by morphology engineering techniques and mechanical induced stress on filamentous pellet systems-A critical review

Filamentous microorganisms are main producers of organic acids, enzymes, and pharmaceutical agents such as antibiotics and other active pharmaceutical ingredients. With their complex cell morphology, ranging from dispersed mycelia to dense pellets, the cultivation is challenging. In recent years, various techniques for tailor-made cell morphologies of filamentous microorganisms have been developed to increase product formation and have been summarised under the term morphology engineering. These techniques, namely microparticle-enhanced cultivation, macroparticle-enhanced cultivation, and alteration of the osmolality of the culture medium by addition of inorganic salts, the salt-enhanced cultivation, are presented and discussed in this review. These techniques have already proven to be useful and now await further proof-of-concept. Furthermore, the mechanical behaviour of individual pellets is of special interest for a general understanding of pellet mechanics and the productivity of biotechnological processes with filamentous microorganisms. Correlating them with substrate uptake and finally with productivity would be a breakthrough not to be underestimated for the comprehensive characterisation of filamentous systems. So far, this research field is under-represented. First results on filamentous pellet mechanics are discussed and important future aspects, which the filamentous expert community should deal with, will be presented and critically discussed.

Location- and layer-dependent biomechanical and microstructural characterisation of the porcine urinary bladder wall

The knowledge of the mechanical properties of the urinary bladder wall helps to explain its storage and micturition functions in health and disease studies; however, these properties largely remain unknown, especially with regard to its layer-specific characteristics and microstructure. Consequently, this study entails the assessment of the layer-specific differences in the mechanical properties and microstructure of the bladder wall, especially during loading. Accordingly, ninety-two (n=92) samples of porcine urinary bladder walls were mechanically and histologically analysed. Generally, the bladder wall and different tissue layers exhibit a non-linear stress-stretch relationship. In this study, the load transfer mechanisms were not only associated with the wavy structure of muscular and mucosal layers, but also with the entire bladder wall microstructure. Contextually, an interplay between the mucosal and muscular layers could be identified. Therefore, depending on the region and direction, the mucosal layer exhibited a stiffer mechanical response to equi-biaxial loading than that offered by the muscular layer when deformed to stretch levels higher than λ=1.6 to λ=2.2. For smaller stretches, the mucosal layer evinces no significant mechanical reaction, while the muscular layer bears the load. Owing to the orientation of its muscle fibres, the muscular layer shows an increased degree of anisotropy compared to the mucosal layer. Furthermore, the general incompressibility assumption is analysed for different layers by measuring the change in thickness during loading, which indicated a small volume loss.

3D finite element models from serial section histology of skeletal muscle tissue - The role of micro-architecture on mechanical behaviour

In this contribution we create three-dimensional (3D) finite element models from a series of histological sections of porcine skeletal muscle tissue. Image registration is performed on the stained sections by affinely aligning them using auxiliary markers, followed by image segmentation to determine muscle fibres and the extracellular matrix in each section, with particular regard to the continuity of the fibres through the stack. With this information, 3D virtual tissue samples are reconstructed, discretised, and associated with appropriate non-linear elastic anisotropic material models. While the gross anatomy is directly obtained from the images, the local directions of anisotropy were determined by the use of an analogy with steady state diffusion. The influence of the number of histological sections considered for reconstruction on the numerically simulated mechanical response of the virtual tissue samples is then studied. The results show that muscle tissue is fairly heterogeneous along the fascicles, and that transverse isotropy is inadequate in describing their material symmetry at the typical length scale of a fascicle. Numerical simulations of different load cases suggest that ignoring the undulations of fibres and their non-uniform cross-sections only moderately affects the passive response of the tissue in tensile and compressive modes, but can become crucial when predicting the response to generic loads and activation.

Mechano-geometrical skeletal muscle fibre characterisation under cyclic and relaxation loading

In the present work, mechano-geometrical characterisations of skeletal muscle fibres in two different deformation states, namely, axial tension and axial compression, were realised. In both cases, cyclic and relaxation tests were performed. Additionally, the changes in the volume of the fibres during deformation were recorded to obtain more detailed information about the muscle fibre load transfer mechanisms. To the best of the authors' knowledge, the present experimental investigation of the mechanical and geometrical characteristics of muscle fibres provides a novel comprehensive data set that can be used to obtain a better understanding of muscle fibre load transfer mechanisms and to construct meaningful models. In the present study, it is shown that muscle fibres exhibit incompressibility (5% volume decrease at maximum deformation) under tension and that this feature is more pronounced under compression loading (37% volume decrease at maximum deformation). These findings are particularly interesting and lead to a further understanding of load transfer mechanisms and to the development of new modelling strategies.

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.

Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model

Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (P i ), are then used-among other reactants, such as creatine phosphate-to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term "exhaustion" for force reduction (fatigue) that is caused by combined P i and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-P i dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit M. gastrocnemius and M. plantaris were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue.

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.

Investigating the passive mechanical behaviour of skeletal muscle fibres: Micromechanical experiments and Bayesian hierarchical modelling

Characterisation of the skeletal muscle's passive properties is a challenging task since its structure is dominated by a highly complex and hierarchical arrangement of fibrous components at different scales. The present work focuses on the micromechanical characterisation of skeletal muscle fibres, which consist of myofibrils, by realising three different deformation states, namely, axial tension, axial compression, and transversal compression. To the best of the authors' knowledge, the present study provides a novel comprehensive data set representing of different deformation states. These data allow for a better understanding of muscle fibre load transfer mechanisms and can be used for meaningful modelling approaches. As the present study shows, axial tension and compression experiments reveal a strong tension-compression asymmetry at fibre level. In comparison to the tissue level, this asymmetric behaviour is more pronounced at the fibre scale, elucidating the load transfer mechanism in muscle tissue and aiding in the development of future modelling strategies. Further, a Bayesian hierarchical modelling approach was used to consider the experimental fluctuations in a parameter identification scheme, leading to more comprehensive parameter distributions that reflect the entire observed experimental uncertainty. STATEMENT OF SIGNIFICANCE: This article examines for the first time the mechanical properties of skeletal muscle fibres under axial tension, axial compression, and transversal compression, leading to a highly comprehensive data set. Moreover, a Bayesian hierarchical modelling concept is presented to identify model parameters in a broad way. The results of the deformation states allow a new and comprehensive understanding of muscle fibres' load transfer mechanisms; one example is the effect of tension-compression asymmetry. On the one hand, the results of this study contribute to the understanding of muscle mechanics and thus to the muscle's functional understanding during daily activity. On the other hand, they are relevant in the fields of skeletal muscle multiscale, constitutive modelling.

Locational and Directional Dependencies of Smooth Muscle Properties in Pig Urinary Bladder

The urinary bladder is a distensible hollow muscular organ, which allows huge changes in size during absorption, storage and micturition. Pathological alterations of biomechanical properties can lead to bladder dysfunction and loss in quality of life. To understand and treat bladder diseases, the mechanisms of the healthy urinary bladder need to be determined. Thus, a series of studies focused on the detrusor muscle, a layer of urinary bladder made of smooth muscle fibers arranged in longitudinal and circumferential orientation. However, little is known about whether its active muscle properties differ depending on location and direction. This study aimed to investigate the porcine bladder for heterogeneous (six different locations) and anisotropic (longitudinal vs. circumferential) contractile properties including the force-length-(FLR) and force-velocity-relationship (FVR). Therefore, smooth muscle tissue strips with longitudinal and circumferential direction have been prepared from different bladder locations (apex dorsal, apex ventral, body dorsal, body ventral, trigone dorsal, trigone ventral). FLR and FVR have been determined by a series of isometric and isotonic contractions. Additionally, histological analyses were conducted to determine smooth muscle content and fiber orientation. Mechanical and histological examinations were carried out on 94 and 36 samples, respectively. The results showed that maximum active stress (p_act ) of the bladder strips was higher in the longitudinal compared to the circumferential direction. This is in line with our histological investigation showing a higher smooth muscle content in the bladder strips in the longitudinal direction. However, normalization of maximum strip force by the cross-sectional area (CSA) of smooth muscle fibers yielded similar smooth muscle maximum stresses (165.4 ± 29.6 kPa), independent of strip direction. Active muscle properties (FLR, FVR) showed no locational differences. The trigone exhibited higher passive stress (p_pass ) than the body. Moreover, the bladder exhibited greater p_pass in the longitudinal than circumferential direction which might be attributed to its microstructure (more longitudinal arrangement of muscle fibers). This study provides a valuable dataset for the development of constitutive computational models of the healthy urinary bladder. These models are relevant from a medical standpoint, as they contribute to the basic understanding of the function of the bladder in health and disease.

Porcine Stomach Smooth Muscle Force Depends on History-Effects

The stomach serves as food reservoir, mixing organ and absorption area for certain substances, while continually varying its position and size. Large dimensional changes during ingestion and gastric emptying of the stomach are associated with large changes in smooth muscle length. These length changes might induce history-effects, namely force depression (FD) following active muscle shortening and force enhancement (FE) following active muscle stretch. Both effects have impact on the force generating capacity of the stomach, and thus functional relevance. However, less is known about history-effects and active smooth muscle properties of stomach smooth muscle. Thus, the aim of this study was to investigate biomechanical muscle properties as force-length and force-velocity relations (FVR) of porcine stomach smooth muscle strips, extended by the analysis of history-effects on smooth muscle force. Therefore, in total n = 54 tissue strips were dissected in longitudinal direction from the ventral fundus of porcine stomachs. Different isometric, isotonic, and isokinetic contraction protocols were performed during electrical muscle stimulation. Cross-sectional areas (CSA) of smooth muscles were determined from cryo-histological sections stained with Picrosirius Red. Results revealed that maximum smooth muscle tension was 10.4 ± 2.6 N/cm². Maximum shortening velocity (V_max) and curvature factor (curv) of the FVR were 0.04 ± 0.01 [optimum muscle length/s] and 0.36 ± 0.15, respectively. The findings of the present study demonstrated significant (P < 0.05) FD [up to 32% maximum muscle force (F_im)] and FE (up to 16% F_im) of gastric muscle tissue, respectively. The FE- and FD-values increased with increasing ramp amplitude. This outstanding muscle behavior is not accounted for in existing models so far and strongly supports the idea of a holistic reflection of distinct stomach structure and function. For the first time this study provides a comprehensive set of stomach smooth muscle parameters including classic biomechanical muscle properties and history-dependent effects, offering the possibility for the development and validation of computational stomach models. Furthermore, this data set facilitates novel insights in gastric motility and contraction behavior based on the re-evaluation of existing contractile mechanisms. That will likely help to understand physiological functions or dysfunctions in terms of gastric accommodation and emptying.

Intermuscular pressure between synergistic muscles correlates with muscle force

The purpose of the study was to examine the relationship between muscle force generated during isometric contractions (i.e. at a constant muscle–tendon unit length) and the intermuscular (between adjacent muscles) pressure in synergistic muscles. Therefore, the pressure at the contact area of the gastrocnemius and plantaris muscle was measured synchronously to the force of the whole calf musculature in the rabbit species Oryctolagus cuniculus. Similar results were obtained when using a conductive pressure sensor, or a fibre-optic pressure transducer connected to a water-filled balloon. Both methods revealed a strong linear relationship between force and pressure in the ascending limb of the force-length relationship. The shape of the measured force–time and pressure–time traces was almost identical for each contraction (r=0.97). Intermuscular pressure ranged between 100 and 700 mbar (70,000 Pa) for forces up to 287 N. These pressures are similar to previous (intramuscular) recordings within skeletal muscles of different vertebrate species. Furthermore, our results suggest that the rise in intermuscular pressure during contraction may reduce the force production in muscle packages (compartments).

Three-Dimensional Muscle Architecture and Comprehensive Dynamic Properties of Rabbit Gastrocnemius, Plantaris and Soleus: Input for Simulation Studies

The vastly increasing number of neuro-muscular simulation studies (with increasing numbers of muscles used per simulation) is in sharp contrast to a narrow database of necessary muscle parameters. Simulation results depend heavily on rough parameter estimates often obtained by scaling of one muscle parameter set. However, in vivo muscles differ in their individual properties and architecture. Here we provide a comprehensive dataset of dynamic (n = 6 per muscle) and geometric (three-dimensional architecture, n = 3 per muscle) muscle properties of the rabbit calf muscles gastrocnemius, plantaris, and soleus. For completeness we provide the dynamic muscle properties for further important shank muscles (flexor digitorum longus, extensor digitorum longus, and tibialis anterior; n = 1 per muscle). Maximum shortening velocity (normalized to optimal fiber length) of the gastrocnemius is about twice that of soleus, while plantaris showed an intermediate value. The force-velocity relation is similar for gastrocnemius and plantaris but is much more bent for the soleus. Although the muscles vary greatly in their three-dimensional architecture their mean pennation angle and normalized force-length relationships are almost similar. Forces of the muscles were enhanced in the isometric phase following stretching and were depressed following shortening compared to the corresponding isometric forces. While the enhancement was independent of the ramp velocity, the depression was inversely related to the ramp velocity. The lowest effect strength for soleus supports the idea that these effects adapt to muscle function. The careful acquisition of typical dynamical parameters (e.g. force-length and force-velocity relations, force elongation relations of passive components), enhancement and depression effects, and 3D muscle architecture of calf muscles provides valuable comprehensive datasets for e.g. simulations with neuro-muscular models, development of more realistic muscle models, or simulation of muscle packages.

On the anisotropy of skeletal muscle tissue under compression

This paper deals with the role of the muscle fibres and extracellular matrix (ECM) components when muscle tissue is subjected to compressive loads. To this end, dissected tissue samples were tested in compression modes which induced states of fibres in compression (I), in tension (II) or at constant length (III), respectively. A comparison of the stress responses indicated that the tissue behaviour is significantly different for these modes, including differences between the modes (I) and (III). This contradicts the paradigm of many constitutive models that the stress response can be decomposed into an isotropic part relating to the ECM and an anisotropic fibre part the contribution of which can be neglected under compression. Conversely, the results provide experimental evidence that there is an anisotropic contribution of the fibre direction to the compressive stress. Interpreting these results in terms of recent microscopical studies, potential connections between the observed behaviour and the structure of muscle ECM are established.

Determination of three-dimensional muscle architectures: validation of the DTI-based fiber tractography method by manual digitization

In the last decade, diffusion tensor imaging (DTI) has been used increasingly to investigate three-dimensional (3D) muscle architectures. So far there is no study that has proved the validity of this method to determine fascicle lengths and pennation angles within a whole muscle. To verify the DTI method, fascicle lengths of m. soleus as well as their pennation angles have been measured using two different methods. First, the 3D muscle architecture was analyzed in vivo applying the DTI method with subsequent deterministic fiber tractography. In a second step, the muscle architecture of the same muscle was analyzed using a standard manual digitization system (MicroScribe MLX). Comparing both methods, we found differences for the median pennation angles (P < 0.001) but not for the median fascicle lengths (P = 0.216). Despite the statistical results, we conclude that the DTI method is appropriate to determine the global fiber orientation. The difference in median pennation angles determined with both methods is only about 1.2° (median pennation angle of MicroScribe: 9.7°; DTI: 8.5°) and probably has no practical relevance for muscle simulation studies. Determining fascicle lengths requires additional restriction and further development of the DTI method.

On a staggered iFEM approach to account for friction in compression testing of soft materials

An inverse finite element method (iFEM) to estimate material parameters from compression tests of soft materials is presented, where alginate hydrogel was used as a phantom material. The method applies if the boundary conditions at the loaded surfaces are not ideal, i.e. neither free of friction nor fully constrained, as it may be the case in most realistic testing set-ups. Assuming a linear friction law, the friction coefficient μ was considered unknown and estimated in a first step by minimising the difference between the contours of the sample, obtained by optical measurements, and the simulated shape. Force-displacement data were used in a second step to determine the parameters of the constitutive law. Staggering these two steps, both friction and material parameters were identified by optimisation. Skipping the first step and predefining μ instead, a unique parameter set could only be clearly identified if the deviations of the contours were considered in addition to the deviations in the force-displacement data. Finally, forward FEM calculations with differently shaped specimens were used to verify the goodness of the obtained parameter sets.

Modelling mechanical characteristics of microbial biofilms by network theory

In this contribution, we present a constitutive model to describe the mechanical behaviour of microbial biofilms based on classical approaches in the continuum theory of polymer networks. Although the model is particularly developed for the well-studied biofilms formed by mucoid Pseudomonas aeruginosa strains, it could easily be adapted to other biofilms. The basic assumption behind the model is that the network of extracellular polymeric substances can be described as a superposition of worm-like chain networks, each connected by transient junctions of a certain lifetime. Several models that were applied to biofilms previously are included in the presented approach as special cases, and for small shear strains, the governing equations are those of four parallel Maxwell elements. Rheological data given in the literature are very adequately captured by the proposed model, and the simulated response for a series of compression tests at large strains is in good qualitative agreement with reported experimental behavior.

Stretching skeletal muscle: chronic muscle lengthening through sarcomerogenesis

Skeletal muscle responds to passive overstretch through sarcomerogenesis, the creation and serial deposition of new sarcomere units. Sarcomerogenesis is critical to muscle function: It gradually re-positions the muscle back into its optimal operating regime. Animal models of immobilization, limb lengthening, and tendon transfer have provided significant insight into muscle adaptation in vivo. Yet, to date, there is no mathematical model that allows us to predict how skeletal muscle adapts to mechanical stretch in silico. Here we propose a novel mechanistic model for chronic longitudinal muscle growth in response to passive mechanical stretch. We characterize growth through a single scalar-valued internal variable, the serial sarcomere number. Sarcomerogenesis, the evolution of this variable, is driven by the elastic mechanical stretch. To analyze realistic three-dimensional muscle geometries, we embed our model into a nonlinear finite element framework. In a chronic limb lengthening study with a muscle stretch of 1.14, the model predicts an acute sarcomere lengthening from 3.09m to 3.51m, and a chronic gradual return to the initial sarcomere length within two weeks. Compared to the experiment, the acute model error was 0.00% by design of the model; the chronic model error was 2.13%, which lies within the rage of the experimental standard deviation. Our model explains, from a mechanistic point of view, why gradual multi-step muscle lengthening is less invasive than single-step lengthening. It also explains regional variations in sarcomere length, shorter close to and longer away from the muscle-tendon interface. Once calibrated with a richer data set, our model may help surgeons to prevent muscle overstretch and make informed decisions about optimal stretch increments, stretch timing, and stretch amplitudes. We anticipate our study to open new avenues in orthopedic and reconstructive surgery and enhance treatment for patients with ill proportioned limbs, tendon lengthening, tendon transfer, tendon tear, and chronically retracted muscles.