An examination of tissue engineered scaffolds in a bioreactor

Replacement tissues, designed to fill in articular cartilage defects, should exhibit the same properties as the native material. The aim of this study is to foster the understanding of, firstly, the mechanical behavior of the material itself and, secondly, the influence of cultivation parameters on cell seeded implants as well as on cell migration into acellular implants. In this study, acellular cartilage replacement material is theoretically, numerically and experimentally investigated regarding its viscoelastic properties, where a phenomenological model for practical applications is developed. Furthermore, remodeling and cell migration are investigated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A hyperelastic biphasic fiber reinforced model for articular cartilage considering the distribution and orientation of collagen fibers

Articular cartilage is a multiphase material consisting of fluids and electrolytes, which is described with the Theory of Porous Media. The mechanical characteristics of articular cartilage are porosity, incompressible material behavior combined with transversely isotropic behavior for solid and fluid phases. There are two central points to model articular cartilage: the poro-viscosity of the porous matrix and the visco elasticity, and orientation of the collagen fibers. A numerical example is presented. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and numerical investigation of different types of articular cartilage replacement materials

The aim of the presented work is to characterize the mechanical properties of different types of articular cartilage replacement materials. For this propose an elastic-diffusion model is developed to identify the elastic and diffusion properties of the replacement materials. A set of unconfined compression tests were performed with several kinds of implants. By means of finite element simulation integrated with an user-defined material model, the material parameters were identified. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Biomechanical modelling of cellular articular cartilage replacement tissues

The aim of the present study is to investigate the strength and damping properties of cellular articular cartilage replacement material. For this purpose, a viscoelastic-diffusion model for the acellular water-saturated condensed collagen gel type I is proposed and validated experimentally. Moreover, a remodelling law for the cell seeded collagen gel is introduced. For an experimental study of the interaction between fibre growth and mechanical stimulation, bioreactors are developed and histological investigations are carried out. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Towards a Standardised Method for Visualisation of Stress Distribution at the Cartilage-Bone Interface

The degeneration of articular cartilage is one of the most common causes of pain and disability in middle-aged and older people. In this context, osteoarthritis is a well-known clinical syndrome related to cartilage degeneration. The degeneration of normal articular cartilage is not simply the result of aging and mechanical wear. Pathological loads may also increase the risk of degeneration of normal joints, and individuals who have an abnormal joint anatomy or inadequate muscle strength probably have a greater risk of degenerative joint disease. The goal of this contribution is to investigate the influence of cartilage degeneration on the stress pattern at the cartilage-bone interface. In this connection, articular cartilage is described as a highly anisotropic and heterogeneous charged biphasic solid-fluid aggregate in the framework of the Theory of Porous Media (TPM). After calibration of the model under physiological loading conditions, the results of a sensitivity analysis of the model parameters are presented. Realistic boundary conditions are applied on the cartilage surface of the femoral head obtained from multibody dynamics calculations. Use is made of the Hertzian contact theory for the contact pressure distribution. The applicability of a new rendition technique to visualise simulation results based on a standardised stereographic projection of the von Mises stresses along the curved cartilage-bone interface is introduced. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element modeling of finite deformable,biphasic biological tissues with transversely isotropic statistically distributed fibers: toward a practical solution

The distribution of collagen fibers across articular cartilage layers is statistical in nature. Based on the concepts proposed in previous models, we developed a methodology to include the statistically distributed fibers across the cartilage thickness in the commercial FE software COMSOL which avoids extensive routine programming. The model includes many properties that are observed in real cartilage: finite hyperelastic deformation, depth-dependent collagen fiber concentration, depth- and deformation-dependent permeability, and statistically distributed collagen fiber orientation distribution across the cartilage thickness. Numerical tests were performed using confined and unconfined compressions. The model predictions on the depth-dependent strain distributions across the cartilage layer are consistent with the experimental data in the literature.     

A Microscopic model for a cell-seeded material

The aim of the present paper is to account for the growth of fiber which is observed in a cell-seeded material stimulated in a bioreactor. For this purpose, the change of mass is considered in the balance laws, and the deformation energy is assumed to be a function of varying mass and the Helmholtz free-energy. Fiber growth at the microscopic level causes a macroscopic change of the material's mechanical properties. The study is a first approach towards a micromechanical model accounting for remodelling in cartilage replacement materials. In so doing, constitutive equations for renewable soft tissues are proposed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anisotropic viscohyperelastic behavior of intervertebral discs: Modeling and experimental validation

Biomechanical investigations of human cartilage, especially intervertebral discs (IVDs), have greatly helped to improve people's health over the last several decades. The study of the underlying biomechanical characteristics of cartilage tissues is a key issue to understand its physiological function and degeneration or damage behavior. The aim of this investigation is to describe the biomechnical behavior of healthy sheep IVDs under various loading conditions. Experimental and cartilage histological data, including fiber orientation, are used to develop a viscohyperelastic material model, which allowed us to numerically study the mechanical behavior of IVDs, consisting of a cartilaginous, fiber-reinforced ring surrounding a highly hydrated, gelatinous core. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fractional-order elastic models of cartilage: A multi-scale approach

The objective of this research is to develop new quantitative methods to describe the elastic properties (e.g., shear modulus, viscosity) of biological tissues such as cartilage. Cartilage is a connective tissue that provides the lining for most of the joints in the body. Tissue histology of cartilage reveals a multi-scale architecture that spans a wide range from individual collagen and proteoglycan molecules to families of twisted macromolecular fibers and fibrils, and finally to a network of cells and extracellular matrix that form layers in the connective tissue. The principal cells in cartilage are chondrocytes that function at the microscopic scale by creating nano-scale networks of proteins whose biomechanical properties are ultimately expressed at the macroscopic scale in the tissue’s viscoelasticity. The challenge for the bioengineer is to develop multi-scale modeling tools that predict the three-dimensional macro-scale mechanical performance of cartilage from micro-scale models. Magnetic resonance imaging (MRI) and MR elastography (MRE) provide a basis for developing such models based on the nondestructive biomechanical assessment of cartilage in vitro and in vivo. This approach, for example, uses MRI to visualize developing proto-cartilage structure, MRE to characterize the shear modulus of such structures, and fractional calculus to describe the dynamic behavior. Such models can be extended using hysteresis modeling to account for the non-linear nature of the tissue. These techniques extend the existing computational methods to predict stiffness and strength, to assess short versus long term load response, and to measure static versus dynamic response to mechanical loads over a wide range of frequencies (50–1500 Hz). In the future, such methods can perhaps be used to help identify early changes in regenerative connective tissue at the microscopic scale and to enable more effective diagnostic monitoring of the onset of disease.     

Modelling of Swelling Phenomena in Charged Hydrated Porous Media

Biological tissues like articular cartilage and geomaterials like clay have a multicomponent microstructure. The charged solid is saturated by a viscous fluid, which itself is composed of several components: the liquid solvent and the dissolved ions, namely, water, anions and cations. These charged multiphase materials exhibit a swelling behaviour under varying chemical conditions. The model describing such materials combines electrochemical and mechanical effects like osmosis and electrostatics within a macroscopic formulation. Starting from the Theory of Porous Media (TPM), a four component model is presented, wherein all constituents are materially incompressible and mass exchanges are excluded. This isothermal model leads to a set of equations which consists of three primary variables: the solid displacement u _S, the pore‐pressure p and the molar ion concentration c_m, since the ion concentrations always depend on each other because of the electroneutrality condition. For the numerical treatment, the weak formulations of governing equations are implemented in the FE tool PANDAS, wherein Taylor‐Hood elements are used for the spatial discretization. Finally, a simulation of a 3‐d swelling experiment is shown. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A viscoelastic-diffusion model for cartilage replacement material

In order to predict deformations and internal stresses of articular cartilage replacement material, two viscoelastic diffusion models are proposed in the present study. Also, the remodeling effect of the material seeded with human cells is verified experimentally. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of a biphasic and a multicomponent model describing viscoelastic swelling phenomena

Biological soft tissues like articular cartilage and their artificial replacement hydrogel have a multicomponent microstructure, consisting of a charged viscoelastic solid matrix saturated by a fluid, which is composed of the liquid solvent and the dissolved anions and cations. Such charged multiphasic materials exhibit a swelling behaviour under varying chemical conditions. These materials are best described by a macroscopic approach like the Theory of Porous Media (TPM). Starting from this point, a standard two-phase model is extended by dividing the fluid into the above mentioned components. Therein, the chemical relations describing the behaviour of the ions and their interaction with the other mixture constituents are incorporated. The resulting model covers mechanical as well as osmotic and electrostatic effects. For numerical and simplicity reasons, it is possible to describe the swelling phenomena by a simplified biphasic model, where the ions as a third degree of freedom and their time-dependent diffusion are neglected. Furthermore, the viscoelastic solid matrix can be replaced by an elastic material. Note that using the multicomponent model generally results in numerical problems, since the boundary conditions depend on the internal fixed charge density. It is shown that this problem can be solved by including the boundary conditions into the weak formulation. Finally, to compare the different behaviour of the above mentioned models by means of an swelling example, they are implemented into the FE tool PANDAS using stable Taylor-Hood elements for the spatial discretization. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cellular articular cartilage replacement tissues: Modeling and analysis

Long-term studies reveal that mechanical stimulation causes growth and remodeling phenomena within biological tissues. The main aim of this research is to fully understand and control these phenomena. For accomplishing that, two steps are considered: first, we determine a suitable numerical model based on different approaches by a comparative study using experimental validations, and second, investigate the mechanical properties of the tissue specimens after a remodeling process. We start with the first step by choosing a convenient model that mimics the biotissue for running the numerical simulations in the second step. There are different models available that determine the mechanical properties of soft replacement tissues seeded with human chondrocytes in modern medical applications. It is our objective to achieve a common methodology of theory and experiments that allows the determination of the mechanical properties of the native material. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Contact problem for a thin elastic layer with variable thickness: Application to sensitivity analysis of articular contact mechanics

In the framework of the recently developed asymptotic models for tibio-femoral contact incorporating frictionless elliptical contact interaction between thin elastic, viscoelastic, or biphasic cartilage layers, we apply an asymptotic modeling approach for analytical evaluating the sensitivity of crucial parameters in joint contact mechanics due to small variations in the thicknesses of the contacting cartilage layers. The four term asymptotic expansion for the normal displacement at the contact surface is explicitly derived, which recovers the corresponding solution obtained previously for the 2D case in the compressible case. It was found that to minimize the influence of the cartilage thickness non-uniformity on the force–displacement relationship, the effective thicknesses of articular layers should be determined from a special optimization criterion.     

Analysis of modified Reynolds equation using the wavelet‐multigrid scheme

The combined study of effects of surface roughness and poroelasticity on the squeeze film behavior of bearings in general and that of synovial joints in particular are presented. The modified form of Reynolds equation, which incorporates the randomized roughness structure as well as elastic nature of articular cartilage, is derived. Christensen stochastic theory describing roughness structure of cartilage surfaces is used by assuming the roughness asperity heights to be small compared to the film thickness. A recently developed wavelet‐multigrid method is used for the solution of Reynolds equation. The method has the greatest advantage of minimizing the errors using wavelet transforms in obtaining accurate solution, as grid size tends to zero. Based on the results obtained, the influence of roughness and elasticity on bearing characteristics are discussed in some detail. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007     

A micro-sphere-based remodelling formulation for anisotropic biological tissues

Soft biological tissues possess a pronounced composite-type multi-scale structure together with strongly anisotropic mechanical properties. A fibre-like network structure is characteristic for this kind of materials. If the tissue is exposed to mechanical loading, the initially possibly unstructured collagen fibre network tends to reorient with the local dominant stretch direction – it adapts according to the particular loading conditions. In general, biological tissues exhibit changes in mass, also denoted as growth, and internal structure, which is commonly referred to as remodelling. In this regard, an anisotropic micromechanically motivated model that incorporates such time-dependent remodelling effects will be discussed in this contribution. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient parallel simulation of biphasic materials in biomechanics

Biphasic materials are widely used for the modelling and the numerical simulation of articular cartilage within joints. In combination with contact, the numerical solution of the arising discrete systems is a demanding task, in particular for realistic geometries. We consider the stability and efficiency of different multilevel approaches for the numerical solution of the resulting non–smooth systems. Moreover, multilevel methods are derived which allow for the efficient numerical simulation of biphasic materials in contact. Numerical examples on problem specific geometries in three space dimensions are given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evolution of the Fiber Density in Biological Tissues

An important challenge in the field of biomechanics is to understand and to model the properties of fibrous tissues. We consider a matrix-fiber composite for which the matrix microstructure and its mechanical properties are taken to be constant. The initial fiber distribution is assumed to be unstructured and the mechanical properties of the fibers evolve during deformation. Further we assume that the fiber creation rate is constant while the fiber degeneration is stretch-dependent. In particular, this study investigates the change of the fiber orientation density when a sudden simple shear is applied to the material. The fiber orientation density depends on the current deformation, the history of the deformation, and the deformation state of the fibers at the time of their creation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)