A comparison of limited-stretch models of rubber elasticity

In this paper we describe various limited-stretch models of non-linear rubber elasticity, each dependent on only the first invariant of the left Cauchy-Green strain tensor and having only two independent material constants. The models are described as limited-stretch, or restricted elastic, because the strain energy and stress response become infinite at a finite value of the first invariant. These models describe well the limited stretch of the polymer chains of which rubber is composed. We discuss Gent's model which is the simplest limited-stretch model and agrees well with experiment. Various statistical models are then described: the one-chain, three-chain, four-chain and Arruda-Boyce eight-chain models, all of which involve the inverse Langevin function. A numerical comparison between the three-chain and eight-chain models is provided. Next, we compare various models which involve approximations to the inverse Langevin function with the exact inverse Langevin function of the eight-chain model. A new approximate model is proposed that is as simple as Cohen's original model but significantly more accurate. We show that effectively the eight-chain model may be regarded as a linear combination of the neo-Hookean and Gent models. Treloar's model is shown to have about half the percentage error of our new model but it is much more complicated. For completeness a modified Treloar model is introduced but this is only slightly more accurate than Treloar's original model. For the deformations of uniaxial tension, biaxial tension, pure shear and simple shear we compare the accuracy of these models, and that of Puso, with the eight-chain model by means of graphs and a table. Our approximations compare extremely well with models frequently used and described in the literature, having the smallest mean percentage error over most of the range of the argument

Digital dashboards visualizing public health data: a systematic review

IntroductionPublic health is not only threatened by diseases, pandemics, or epidemics. It is also challenged by deficits in the communication of health information. The current COVID-19 pandemic demonstrates that impressively. One way to deliver scientific data such as epidemiological findings and forecasts on disease spread are dashboards. Considering the current relevance of dashboards for public risk and crisis communication, this systematic review examines the state of research on dashboards in the context of public health risks and diseases.MethodNine electronic databases where searched for peer-reviewed journal articles and conference proceedings. Included articles (n = 65) were screened and assessed by three independent reviewers. Through a methodological informed differentiation between descriptive studies and user studies, the review also assessed the quality of included user studies (n = 18) by use of the Mixed Methods Appraisal Tool (MMAT).Results65 articles were assessed in regards to the public health issues addressed by the respective dashboards, as well as the data sources, functions and information visualizations employed by the different dashboards. Furthermore, the literature review sheds light on public health challenges and objectives and analyzes the extent to which user needs play a role in the development and evaluation of a dashboard. Overall, the literature review shows that studies that do not only describe the construction of a specific dashboard, but also evaluate its content in terms of different risk communication models or constructs (e.g., risk perception or health literacy) are comparatively rare. Furthermore, while some of the studies evaluate usability and corresponding metrics from the perspective of potential users, many of the studies are limited to a purely functionalistic evaluation of the dashboard by the respective development teams.ConclusionThe results suggest that applied research on public health intervention tools like dashboards would gain in complexity through a theory-based integration of user-specific risk information needs.Systematic review registrationhttps://www.crd.york.ac.uk/prospero/display_record.php?RecordID=200178, identifier: CRD42020200178

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 (pact) 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 (ppass) than the body. Moreover, the bladder exhibited greater ppass 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

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

The slings and arrows of communication on nanotechnology

According to numerous surveys the perceived risk of nanotechnology is low and most people feel that the benefits outweigh the risks. This article provides greater insight into risk perception and concludes that the positive attitude to nanotechnology is based not on knowledge but on hope and fascination. The perceived risk is low because of a lack of vivid and frightening images of possible hazards. If news flashes were to link nanotechnology to concrete hazards or actual harm to people, attitudes might suddenly change. Risk communication faces the problem of dealing with a public at large that has little or no knowledge about the technology. As it takes time and extensive additional research to develop appropriate communication strategies and disseminate them to the relevant institutions, this exercise should be started immediately

The Energy of Muscle Contraction. I. Tissue Force and Deformation During Fixed-End Contractions

During contraction the energy of muscle tissue increases due to energy from the hydrolysis of ATP. This energy is distributed across the tissue as strain-energy potentials in the contractile elements, strain-energy potential from the 3D deformation of the base-material tissue (containing cellular and extracellular matrix effects), energy related to changes in the muscle\u27s nearly incompressible volume and external work done at the muscle surface. Thus, energy is redistributed through the muscle\u27s tissue as it contracts, with only a component of this energy being used to do mechanical work and develop forces in the muscle\u27s longitudinal direction. Understanding how the strain-energy potentials are redistributed through the muscle tissue will help enlighten why the mechanical performance of whole muscle in its longitudinal direction does not match the performance that would be expected from the contractile elements alone. Here we demonstrate these physical effects using a 3D muscle model based on the finite element method. The tissue deformations within contracting muscle are large, and so the mechanics of contraction were explained using the principles of continuum mechanics for large deformations. We present simulations of a contracting medial gastrocnemius muscle, showing tissue deformations that mirror observations from magnetic resonance imaging. This paper tracks the redistribution of strain-energy potentials through the muscle tissue during fixed-end contractions, and shows how fibre shortening, pennation angle, transverse bulging and anisotropy in the stress and strain of the muscle tissue are all related to the interaction between the material properties of the muscle and the action of the contractile elements

Coupled Systems of Differential-Algebraic and Kinetic Equations with Application to the Mathematical Modelling of Muscle Tissue

We consider a coupled system composed of a linear differential-algebraic equation (DAE) and a linear large-scale system of ordinary differential equations where the latter stands for the dynamics of numerous identical particles. Replacing the discrete particles by a kinetic equation for a particle density, we obtain in the mean-field limit the new class of partially kinetic systems. We investigate the influence of constraints on the kinetic theory of those systems and present necessary adjustments. We adapt the mean-field limit to the DAE model and show that index reduction and the mean-field limit commute. As a main result, we prove Dobrushin's stability estimate for linear systems. The estimate implies convergence of the mean-field limit and provides a rigorous link between the particle dynamics and their kinetic description. Our research is inspired by mathematical models for muscle tissue where the macroscopic behaviour is governed by the equations of continuum mechanics, often discretised by the finite element method, and the microscopic muscle contraction process is described by Huxley's sliding filament theory. The latter represents a kinetic equation that characterises the state of the actin-myosin bindings in the muscle filaments. Linear partially kinetic systems are a simplified version of such models, with focus on the constraints.Comment: 32 pages, 18 figure

An Analysis of Scores of Prospective Biology Teachers on the Factors of MSLQ

Abstract. The factors of learning strategies and motivation as components of self-regulation are determined well in MSLQ (Motivated Strategies for Learning Questionnaire) scale. The scale includes 15 factors. But, these 15 factors are not appropriate for practical use. In this study, a survey research was conducted with 112 prospective biology teachers by using MSLQ to analyze the factors. One-way ANOVAs and Pearson Product-Moment Correlation Coefficients were used for analysis. The results of ANOVAs showed that there were no statistically significant differences between mean scores of the participants at different grade levels on scales of MSLQ. In addition, the "task value", the "self-efficacy" and the "help seeking" subfactors were found to be the most dominant sub-factors of the whole scale. In the article, results of the study and limitations will be discussed