On the thermodynamical admissibility of the triphasic theory of charged hydrated tissues

Modelling articular cartilage: the relative motion of two adjacent poroviscoelastic layers

In skeletal joints two layers of adjacent cartilage are often in relative motion. The individual cartilage layers are often modelled as a poroviscoelastic material. To model the relative motion, noting the separation of scales between the pore level and the macroscale, a homogenization based on multiple scale asymptotic analysis has been used in this study to derive a macroscale model for the relative translation of two poroviscoelastic layers separated by a very thin layer of fluid. In particular the fluid layer thickness is essentially zero at the macroscale so that the two poroviscoelastic layers are effectively in contact and their interaction is captured in the derived model via a set of interfacial conditions, including a generalization of the Beavers-Joseph condition at the interface between a viscous fluid and a porous medium. In the simplifying context of a uniform geometry, constant fixed charge density, a Newtonian interstitial fluid and a viscoelastic scaffold, modelled via finite deformation theory, we present preliminary simulations that may be used to highlight predictions for how oscillatory relative movement of cartilage under load influences the peak force the cartilage experiences and the extent of the associated deformations. In addition to highlighting such cartilage mechanics, the systematic derivation of the macroscale models will enable the study of how nanoscale cartilage physics, such as the swelling pressure induced by fixed charges, manifests in cartilage mechanics at much higher lengthscales.

Walking on water: revisiting the role of water in articular cartilage biomechanics in relation to tissue engineering and regenerative medicine

The importance, and the difficulty, of generating biosynthetic articular cartilage is widely recognized. Problems arise from obtaining sufficient stiffness, toughness and longevity in the material and integration of new material into existing cartilage and bone. Much work has been done on chondrocytes and tissue macromolecular components while water, which comprises the bulk of the tissue, is largely seen as a passive component; the ‘solid matrix’ is believed to be the main load-bearing element most of the time. Water is commonly seen as an inert filler whose restricted flow through the tissue is believed to be sufficient to generate the properties measured. We propose that this model should be turned on its head. Water comprises 70–80% of the matrix and has a bulk modulus considerably greater than that of cartilage. We suggest that the macromolecular components structure the water to support the loads applied. Here, we shall examine the structure and organization of the main macromolecules, collagen, aggrecan and hyaluronan, and explore how water interacts with their polyelectrolyte nature. This may inform the biosynthetic process by identifying starting points to enable developing tissue properties to guide the cells into producing the appropriate macromolecular composition and structure.

Dynamic viscoelastic characterisation of human osteochondral tissue: understanding the effect of the cartilage-bone interface

BACKGROUND

Despite it being known that subchondral bone affects the viscoelasticity of cartilage, there has been little research into the mechanical properties of osteochondral tissue as a whole system. This study aims to unearth new knowledge concerning the dynamic behaviour of human subchondral bone and how energy is transferred through the cartilage-bone interface.

METHODS

Dynamic mechanical analysis was used to determine the frequency-dependent (1-90 Hz) viscoelastic properties of the osteochondral unit (cartilage-bone system) as well as isolated cartilage and bone specimens extracted from human femoral heads obtained from patients undergoing total hip replacement surgery, with a mean age of 78 years (N = 5, n = 22). Bone mineral density (BMD) was also determined for samples using micro-computed tomography as a marker of tissue health.

RESULTS

Cartilage storage and loss moduli along with bone storage modulus were found to increase logarithmically (p < 0.05) with frequency. The mean cartilage storage modulus was 34.4 ± 3.35 MPa and loss modulus was 6.17 ± 0.48 MPa (mean ± standard deviation). In contrast, bone loss modulus decreased logarithmically between 1 and 90 Hz (p < 0.05). The storage stiffness of the cartilage-bone-core was found to be frequency-dependent with a mean value of 1016 ± 54.0 N.mm^- 1, while the loss stiffness was determined to be frequency-independent at 78.84 ± 2.48 N.mm^- 1. Notably, a statistically significant (p < 0.05) linear correlation was found between the total energy dissipated from the isolated cartilage specimens, and the BMD of the isolated bone specimens at all frequencies except at 90 Hz (p = 0.09).

CONCLUSIONS

The viscoelastic properties of the cartilage-bone core were significantly different to the tissues in isolation (p < 0.05). Results from this study demonstrate that the functionality of these tissues arises because they operate as a unit. This is evidenced through the link between cartilage energy dissipated and bone BMD. The results may provide insights into the functionality of the osteochondral unit, which may offer further understanding of disease progression, such as osteoarthritis (OA). Furthermore, the results emphasise the importance of studying human tissue, as bovine models do not always display the same trends.

Finite element analysis of biological soft tissue surrounded by a deformable membrane that controls transmembrane flow

Background

Many biological soft tissues are hydrated porous hyperelastic materials, which consist of a complex solid skeleton with fine voids and fluid filling these voids. Mechanical interactions between the solid and the fluid in hydrated porous tissues have been analyzed by finite element methods (FEMs) in which the mixture theory was introduced in various ways. Although most of the tissues are surrounded by deformable membranes that control transmembrane flows, the boundaries of the tissues have been treated as rigid and/or freely permeable in these studies. The purpose of this study was to develop a method for the analysis of hydrated porous hyperelastic tissues surrounded by deformable membranes that control transmembrane flows.

Results

For this, we developed a new nonlinear finite element formulation of the mixture theory, where the nodal unknowns were the pore water pressure and solid displacement. This method allows the control of the fluid flow rate across the membrane using Neumann boundary condition. Using the method, we conducted a compression test of the hydrated porous hyperelastic tissue, which was surrounded by a flaccid impermeable membrane, and a part of the top surface of this tissue was pushed by a platen. The simulation results showed a stress relaxation phenomenon, resulting from the interaction between the elastic deformation of the tissue, pore water pressure gradient, and the movement of fluid. The results also showed that the fluid trapped by the impermeable membrane led to the swelling of the tissue around the platen.

Conclusions

These facts suggest that our new method can be effectively used for the analysis of a large deformation of hydrated porous hyperelastic material surrounded by a deformable membrane that controls transmembrane flow, and further investigations may allow more realistic analyses of the biological soft tissues, such as brain edema, brain trauma, the flow of blood and lymph in capillaries and pitting edema.

An overview of multiphase cartilage mechanical modelling and its role in understanding function and pathology

There is a long history of mathematical and computational modelling with the objective of understanding the mechanisms governing cartilage׳s remarkable mechanical performance. Nonetheless, despite sophisticated modelling development, simulations of cartilage have consistently lagged behind structural knowledge and thus the relationship between structure and function in cartilage is not fully understood. However, in the most recent generation of studies, there is an emerging confluence between our structural knowledge and the structure represented in cartilage modelling. This raises the prospect of further refinement in our understanding of cartilage function and also the initiation of an engineering-level understanding for how structural degradation and ageing relates to cartilage dysfunction and pathology, as well as informing the potential design of prospective interventions. Aimed at researchers entering the field of cartilage modelling, we thus review the basic principles of cartilage models, discussing the underlying physics and assumptions in relatively simple settings, whilst presenting the derivation of relatively parsimonious multiphase cartilage models consistent with our discussions. We proceed to consider modern developments that start aligning the structure captured in the models with observed complexities. This emphasises the challenges associated with constitutive relations, boundary conditions, parameter estimation and validation in cartilage modelling programmes. Consequently, we further detail how both experimental interrogations and modelling developments can be utilised to investigate and reduce such difficulties before summarising how cartilage modelling initiatives may improve our understanding of cartilage ageing, pathology and intervention.

Blends and Nanocomposite Biomaterials for Articular Cartilage Tissue Engineering

This review provides a comprehensive assessment on polymer blends and nanocomposite systems for articular cartilage tissue engineering applications. Classification of various types of blends including natural/natural, synthetic/synthetic systems, their combination and nanocomposite biomaterials are studied. Additionally, an inclusive study on their characteristics, cell responses ability to mimic tissue and regenerate damaged articular cartilage with respect to have functionality and composition needed for native tissue, are also provided.

A review of the combination of experimental measurements and fibril-reinforced modeling for investigation of articular cartilage and chondrocyte response to loading

The function of articular cartilage depends on its structure and composition, sensitively impaired in disease (e.g. osteoarthritis, OA). Responses of chondrocytes to tissue loading are modulated by the structure. Altered cell responses as an effect of OA may regulate cartilage mechanotransduction and cell biosynthesis. To be able to evaluate cell responses and factors affecting the onset and progression of OA, local tissue and cell stresses and strains in cartilage need to be characterized. This is extremely challenging with the presently available experimental techniques and therefore computational modeling is required. Modern models of articular cartilage are inhomogeneous and anisotropic, and they include many aspects of the real tissue structure and composition. In this paper, we provide an overview of the computational applications that have been developed for modeling the mechanics of articular cartilage at the tissue and cellular level. We concentrate on the use of fibril-reinforced models of cartilage. Furthermore, we introduce practical considerations for modeling applications, including also experimental tests that can be combined with the modeling approach. At the end, we discuss the prospects for patient-specific models when aiming to use finite element modeling analysis and evaluation of articular cartilage function, cellular responses, failure points, OA progression, and rehabilitation.

Superficial collagen fibril modulus and pericellular fixed charge density modulate chondrocyte volumetric behaviour in early osteoarthritis

The aim of this study was to investigate if the experimentally detected altered chondrocyte volumetric behavior in early osteoarthritis can be explained by changes in the extracellular and pericellular matrix properties of cartilage. Based on our own experimental tests and the literature, the structural and mechanical parameters for normal and osteoarthritic cartilage were implemented into a multiscale fibril-reinforced poroelastic swelling model. Model simulations were compared with experimentally observed cell volume changes in mechanically loaded cartilage, obtained from anterior cruciate ligament transected rabbit knees. We found that the cell volume increased by 7% in the osteoarthritic cartilage model following mechanical loading of the tissue. In contrast, the cell volume decreased by 4% in normal cartilage model. These findings were consistent with the experimental results. Increased local transversal tissue strain due to the reduced collagen fibril stiffness accompanied with the reduced fixed charge density of the pericellular matrix could increase the cell volume up to 12%. These findings suggest that the increase in the cell volume in mechanically loaded osteoarthritic cartilage is primarily explained by the reduction in the pericellular fixed charge density, while the superficial collagen fibril stiffness is suggested to contribute secondarily to the cell volume behavior.

Multiscale mechanics of articular cartilage: potentials and challenges of coupling musculoskeletal, joint, and microscale computational models

Articular cartilage experiences significant mechanical loads during daily activities. Healthy cartilage provides the capacity for load bearing and regulates the mechanobiological processes for tissue development, maintenance, and repair. Experimental studies at multiple scales have provided a fundamental understanding of macroscopic mechanical function, evaluation of the micromechanical environment of chondrocytes, and the foundations for mechanobiological response. In addition, computational models of cartilage have offered a concise description of experimental data at many spatial levels under healthy and diseased conditions, and have served to generate hypotheses for the mechanical and biological function. Further, modeling and simulation provides a platform for predictive risk assessment, management of dysfunction, as well as a means to relate multiple spatial scales. Simulation-based investigation of cartilage comes with many challenges including both the computational burden and often insufficient availability of data for model development and validation. This review outlines recent modeling and simulation approaches to understand cartilage function from a mechanical systems perspective, and illustrates pathways to associate mechanics with biological function. Computational representations at single scales are provided from the body down to the microstructure, along with attempts to explore multiscale mechanisms of load sharing that dictate the mechanical environment of the cartilage and chondrocytes.