Finite element models for hydrated soft biological tissue are numerous but often exhibit certain essential deficiencies concerning the reproduction of relevant mechanical and electro-chemical responses. As a matter of fact, singlephasic models can never predict the interstitial fluid flow or related effects like osmosis. Quite a few models have more than one constituent, but are often restricted to the small-strain domain, are not capable of capturing the intrinsic viscoelasticity of the solid skeleton, or do not account for a collagen fibre reinforcement. It is the goal of this contribution to overcome these drawbacks and to present a thermodynamically consistent model, which is formulated in a very general way in order to reproduce the behaviour of almost any charged hydrated tissue. Herein, the Theory of Porous Media (TPM) is applied in combination with polyconvex Ogden-type material laws describing the anisotropic and intrinsically viscoelastic behaviour of the solid matrix on the basis of a generalised Maxwell model. Moreover, other features like the deformation-dependent permeability, the possibility to include inhomogeneities like varying fibre alignment and behaviour, or osmotic effects based on the simplifying assumption of Lanir are also included. Finally, the human intervertebral disc is chosen as a representative for complex soft biological tissue behaviour. In this regard, two numerical examples will be presented with focus on the viscoelastic and osmotic capacity of the model.

Determining the internal dynamics of the human spine's biological structure is one essential step that allows enhanced understanding of spinal degeneration processes. The unavailability of internal load figures in other methods highlights the importance of the forward dynamics approach as the most powerful approach to examine the internal degeneration of spinal structures. Consequently, a forward dynamics full-body model of the human body with a detailed lumbar spine is introduced. The aim was to determine the internal dynamics and the contribution of different spinal structures to loading. The multi-body model consists of the lower extremities, two feet, shanks and thighs, the pelvis, five lumbar vertebrae, and a lumped upper body including the head and both arms. All segments are modelled as rigid bodies. 202 muscles (legs, back, abdomen) are included as Hill-type elements. 58 nonlinear force elements are included to represent all spinal ligaments. The lumbar intervertebral discs were modelled nonlinearly. As results, internal kinematics, muscle forces, and internal loads for each biological structure are presented. A comparison between the nonlinear (new, enhanced modelling approach) and linear (standard modelling approach, bushing) modelling approaches of the intervertebral disc is presented. The model is available to all researchers as ready-to-use C/C++ code within our in-house multi-body simulation code demoa with all relevant binaries included.

SUMMARYThis work investigates the possibilities of acceleration and approximation of multiscale systems using kernel methods. The key element is to learn the interface between the different scales using a fast surrogate for the microscale model, which is given by multivariate kernel expansions. The expansions are computed using statistically representative samples of input and output of the microscale model. We apply both support vector machines and a vectorial kernel greedy algorithm as learning methods. We demonstrate the applicability of the resulting surrogate models using two multiscale models from different engineering disciplines. We consider, first, a human spine model coupling a macroscale multibody system with a microscale intervertebral spine disc model and, second, a model for simulation of saturation overshoots in porous media involving nonclassical shock waves. Copyright © 2014 John Wiley & Sons, Ltd.

At present, there are two main numerical approaches that are frequently used to simulate the mechanical behaviour of the human spine. Researchers with a continuum-mechanical background often utilise the finite-element method (FEM), where the involved biological soft and hard tissues are modelled on a macroscopic (continuum) level. In contrast, groups associated with the science of human movement usually apply discrete multi-body systems (MBS). Herein, the bones are modelled as rigid bodies, which are connected by Hill-type muscles and non-linear rheological spring-dashpot models to represent tendons and cartilaginous connective tissue like intervertebral discs (IVD). A possibility to benefit from both numerical methods is to couple them and use each approach, where it is most appropriate. Herein, the basic idea is to utilise MBS in simulations of the overall body and apply the FEM only to selected regions of interest. In turn, the FEM is used as homogenisation tool, which delivers more accurate non-linear relationships describing the behaviour of the IVD in the multi-body dynamics model. The goal of this contribution is to present an approach to couple both numerical methods without the necessity to apply a gluing algorithm in the context of a co-simulation. Instead, several pre-computations of the intervertebral disc are performed offline to generate an approximation of the homogenised finite-element (FE) result. In particular, the discrete degrees of freedom (DOF) of the MBS, that is, three displacements and three rotations, are applied to the FE model of the IVD, and the resulting homogenised forces and moments are recorded. Moreover, a polynomial function is presented with the discrete DOF of the MBS as variables and the discrete forces an moments as function values. For the sake of a simple verification, the coupling method is applied to a simplified motion segment of the spine. Herein, two stiff cylindrical vertebrae with an interjacent homogeneous cylindrical IVD are examined under the restriction of purely elastic deformations in the sagittal plane.