A numerical validation approach of a finite element muscle model using optical data

Aim of this work is to obtain a convenient data set for the validation of a recently developed three-dimensional constitutive muscle model. Therefore, an optical measurement technique is used to reconstruct a geometrical model of a rabbit soleus muscle. Thus, the muscle geometry and also the generated force characteristics are measured. The proposed numerical model is able to reproduce the experimental results in an adequate manner. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A posteriori control of modelling errors in linear elasticity

The concept of adaptive error control for finite element Galerkin discretizations has more recently been extended from the pure treatment of the discretization errors [1], [2] also to the control of modelling errors [4], [5]. These techniques can be employed for a rigorous justification of the local choice of the model out of a given hierarchy with increasing complexity. In the present paper the concept is exemplified by a hierarchy of linear-elastic models, consisting of a basic model with constant E modulus and an improved model with oscillating E modulus. Significant reduction of the computational complexity can be achieved by a proper choice of the model in different subdomains, automatically chosen by the error estimators. Several error indicators are investigated in the context of goal oriented error estimation. Their efficiency is compared by means of finite element simulations [3] of an elementary example. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A comparison of static optimization criteria for resolving the 3D muscle redundancy problem during human gait

In this paper, different approaches of static optimization for predicting muscle forces during human walking are investigated. In order to better reflect the true mechanics of the human body, a three-dimensional musculoskeletal model of a single leg is developed. The joint moments generated by muscles during walking are computed from inverse dynamics. The muscle force is estimated by different optimization criteria, each satisfying the moment constraints at all joints and the lower and upper muscle force constraints. Several polynomial and non-polynomial criteria frequently used in literature are studied. Then the results obtained from these calculations are compared with each other. This paper provides an overview of the effects of different optimization criteria on the 3D muscle force distribution problem during human walking. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nearness approximation space based on axiomatic fuzzy sets

The approximation space model was originally proposed by Pawlak (1982) [19]. It was Or?owska who first observed that approximation spaces serves as a formal counterpart of perception, or observation [16, §2, p. 8], in which approximations provide a means of approximating one set of objects with another set of objects using the indiscernibility relation. Topology has been used to enrich the original model of an approximation space as well as more recent models of generalized approximation spaces. In this paper, an extension of th e topology neighborhood based on AFS (Axiomatic Fuzzy Sets) theory is introduced, and some interesting properties are given. Furthermore, a new generalized approximation space model is established with two application examples, which can be used to deal with information tables with many category features and viewed as a multi-granulations form of nearness approximation space models.     

Bridging scales: An attempt to incorporate cellular responses within a three-dimensional FEM model of active muscle contraction

A mathematical model of the cellular responses of skeletal muscles has been integrated within a three-dimensional biomechanical Finite Element (FEM) model. The FEM model is based on a tri-cubic Hermite Finite Element discretisation of the governing equations of finite elasticity theory and a transversely isotropic constitutive law. To incorporate the cellular information, homogenised values of key physiological parameters, e.g. the pre- and post-power stroke concentration of crossbridge attachments, are computed at the Gauss points of the FEMintegration scheme. These values are then used to modify the stress tensor in such a way that it resembles the contractile response. The advantages of such an improved three-dimensional FEM model are far reaching. These models can be used, for example, to investigate and study local muscle contraction, muscle recruitment patterns, force generation, or fatigue response of skeletal muscles. As an illustrative example, one twitch of the tibialis anterior, in which 25% of the muscle fibres are excited by a nerve stimulus, is simulated. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An analytic approach for the analysis of rotations in fringe-balanced binary search trees

This paper presents an analytic approach to the construction cost of fringe-balanced binary search trees. In [7], Mahmoud used a bottom-up approach and an urn model of Pólya. The present method is top-down and uses differential equations and Hwang's quasi-power theorem to derive the asymptotic normality of the number of rotations needed to construct such afringe balanced search tree. We also obtain the exact expectation and variance with this method. Although Pólya's urn model is no longer needed, we also present an elegant analysis of it based on an operator calculus as in [4].This research was supported by the Austrian Research Society (FWF) under the project number P12599-MAT.     

A time dependent coupled system related to the tridimensional equations of a nematic liquid crystal

In this paper we prove some results about the existence, uniqueness and regularity of the solutions of a tridimensional variational approximated model for the Leslie's equations of an incompressible nematic liquid crystal (cf. [7]). This model was introduced in [1] where the bidimensional case is studied. Here we use the methods developed in [6], [4] and [8].     

An approximation theorem of wong-zakai type for nonlinear stochastic partial differential equations

We present an extension of the Wong-Zakai approximation theorem for nonlinear 984 given by the Wiener process and a martingale. By approximating these disturbances we obtain in the limit equation the Ito correction term for the infinite dimensional case. Such form of the correction term connected with the Wiener process was proved in the author's papers [21] and [22], where the approximation theorem for semilinear stochastic evolution equations in Hilbert spaces was studied. Our model here is similar as the one considered by Pardoux [17]     

Modeling of a Pneumatic Hybrid Actuator using an Exponential Approach for Approximation of the Valve-Actuator Behaviour

The present paper describes a mathematical model for the control of a hybrid actuator consisting of a fluidic muscle and a linear pressure spring which is inflated by a proportional directional control valve in 3/3-way function. The device is applied for physical simulation of arbitrary force/displacement relationships. The mathematical model of the system fluidic muscle/valve consists of the approximation of the pressure time-history by an exponential function. The coefficients of the exponential function are identified from corresponding measurement and Least Squares minimization. The advantages of this approximation are that the differential equation for the pressure becomes simple and the computations more efficient. This makes the approach suitable for model-based control. The paper shows that with the proposed model sufficient accuracy can be achieved such as to have a good mathematical model for feedback linearization. For later use the device can be employed in fields of biomechanics as well as in general environments such as motion simulations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the well-posed coupling between free fluid and porous viscous flows

We present a well-posed model for the Stokes/Brinkman problem with a family of jump embedded boundary conditions (J.E.B.C.) on an immersed interface with weak regularity assumptions. It arises from a general framework recently proposed for fictitious domain problems. Our model is based on algebraic transmission conditions combining the stress and velocity jumps on the interface $\Sigma$ separating the fluid and porous domains. These conditions are well chosen to get the coercivity of the operator. Then, the general framework allows us to prove new results on the global solvability of some models with physically relevant stress or velocity jump boundary conditions for the momentum transport at a fluid–porous interface. The Stokes/Brinkman problem with Ochoa-Tapia and Whitaker (1995) [9], [10] interface conditions and the Stokes/Darcy problem with Beavers and Joseph (1967) [13] conditions are both proved to be well-posed, by an asymptotic analysis. Up to now, only the Stokes/Darcy problem with Saffman (1971) [15] approximate interface conditions with negligible tangential porous velocity was known to be well-posed.     

An improved solution to the replenishment policy for the EMQ model with rework and multiple shipments

Recently, Chiu et al. (2012) [1] present an alternative optimization procedure to derive the optimal replenishment lot size for an economic manufacturing quantity (EMQ) model with rework and multiple shipments. This inventory model was proposed by Chiu et al. (2011) [2]. Both papers do not consider the determining of the number of shipments. This paper determines both the optimal replenishment lot size and the optimal number of shipments jointly. The solution of this paper is better than the solutions of Chiu et al.  and .     

Investigation of an elastoplastic material model coupled to nonlocal damage in an implicit-gradient framework

In this work, an elastoplastic material model coupled to nonlocal damage is discussed which is based on an implicit gradient-enhanced approach. Combined nonlinear isotropic and kinematic hardening as well as continuum damage of Lemaitre-type are considered. The model is a direct nonlocal extension of a corresponding local model which was presented earlier (see e. g. [1], [2], [3]). Conclusions drawn from a numerical benchmark test performed in this study demonstrate that the nonlocal damage model is suitable to provide mesh-independent solutions in finite element simulations. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A partial model of NF with ZF

The theory New Foundations (NF) of Quine was introduced in [14]. This theory is finitely axiomatizable as it has been proved in [9]. A similar result is shown in [8] using a system called K. Particular subsystems of NF, inspired by [8] and [9], have models in ZF. Very little is known about subsystems of NF satisfying typical properties of ZF; for example in [11] it is shown that the existence of some sets which appear naturally in ZF is an axiom independent from NF (see also [12]). Here we discuss a model of subsystems of NF in which there is a set which is a model of ZF. MSC: 03E70.     

Parental care as a differential game: A dynamic extension of the Houston–Davies game

An interpretation of the conflict between male and female parents during the process of caring for their common offspring by means of Game Theory was given in Houston and Davies. [A.I. Houston, N.B. Davies, The evolution of cooperation and life history in the dunnock Prunella modularis, in: R.M. Sibly, R.H. Smith (Eds.), Behavioral Ecology, Blackwell Scientific Publications, 1985, pp. 471–487]. Mathematically, this model represents a static game with continuous strategy sets. Recently, this model was reconsidered in a dynamic discrete time framework which also included state dependencies [J.M. McNamara et al., A dynamic game-theoretic model of parental care, J. Theor. Biol. 205 (2000) 605–623]. In this article, we give an interpretation of the parental care conflict in continuous time by means of a differential game with state dependent strategies.     

Structural model of thorax and abdomen for respiratory mechanics

This paper describes a structural model of the human rib cage and abdomen that incorporates many geometrical and functional features important to the understanding of respiratory mechanics. The rib cage, diaphragm, abdominal wall and lungs are characterized by nonlinear stress-strain characteristics that depend on muscle activity. The positions, volumes, forces and pressures for each set of initial conditions are found by determining mechanical equilibrium. Many such determinations allow predictions for large displacements. The model predicts passive respiratory system behavior and the action of individual respiratory muscles that are qualitatively consistent with physiological data. Respiratory mechanics includes both pulmonary mechanics and mechanics of the chest wall by which we mean the mechanics of the thorax, the abdomen and the diaphragm. The geometrical complexity of the chest wall and its associated muscles of respiration makes rigorous analysis of the mechanics of the respiratory system difficult. This paper describes a structural model of the respiratory system with two degrees of freedom of motion that has been useful for understanding the actions of respiratory muscles. The model was initially developed to test the hypothesis of Goldman and Mead[1] that the diaphragm, contracting by itself, can expand the abdomen and rib cage in the same way as passive inflation of the respiratory system. The model's predictions suggest that coordinated activity of rib cage musculature and diaphragm are required to expand the respiratory system in this way.     

A ternary phase bi-scale FE-model for diffusion-driven dendritic alloy solidification processes

It is of high interest to describe alloy solidification processes with numerical simulations. In order to predict the material behavior as precisely as possible, a ternary phase, bi-scale numerical model will be presented. This paper is based on a coupled thermo-mechanical, two-phase, two-scale finite element model developed by Moj et al. [2], where the theory of porous media (TPM) [1] has been used. Finite plasticity extended by secondary power-law creep is utilized to describe the solid phase and linear visco-elasticity with Darcy's law of permeability for the liquid phase, respectively. Here, the microscopic, temperature-driven phase transition approach is replaced by the diffusion-driven 0D model according to Wang and Beckermann [3]. The decisive material properties during solidification are captured by phenomenological formulations for dendritic growth and solute diffusion processes. A columnar as well as an equiaxial solidification example will be shown to demonstrate the principal performance of the presented model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Designing an optimal connected nature reserve

We consider a landscape divided into elementary cells, each of these cells containing some species to be protected. We search to select a set of cells to form a natural reserve in order to protect all the species present in the landscape. A species is considered protected if it is present in a certain number of cells of the reserve. There is an important spatial constraint concerning the set of selected cells: a species must be able to go from any cell to any cell without leaving the reserve. An integer linear programming model was proposed by Önal and Briers [2] for this reserve selection problem, but the size of the problems which can be handled by this model is limited: several hours of computation are required for solving instances with hundred of cells and hundred of species. Having proposed an improvement of this model which reduces appreciably the computation time, we propose another integer linear programming model, easy to carry out, which allows to obtain, in a few seconds of computation, optimal or near-optimal solutions for instances with hundred of cells and hundred of species. However, the computation time becomes prohibitive for instances with more than 200 cells and 100 species. But, this approach can be particularly useful to solve the problem, in an approximate way, by aggregation of cells as proposed by Önal and Briers [2].     

Elastic Properties of Muscle Tissue: Comparison of an Inverse Finite Element Approach and Homogeneous Deformation

Parameters of material models are commonly identified by fitting predicted stress-stretch relations to experimentally derived ones, assuming homogeneous deformation. This approach has been compared with an inverse finite element strategy, where an FE model of the actual measurement set-up is created to obtain stress-stretch data. Compressive tests of skeletal muscle tissue have been conducted for different fiber orientations, with a stereo camera system capturing the geometry of the sample. The material exhibited an exponential increase in stiffness with increasing stretch, with large differences related to the fiber orientation; this behavior is described well by a model for arterial layers. Assuming homogeneous deformation led to significantly different stress-stretch curves indicating that this assumption is unrealistic in this case. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)