Remodelling of continuously distributed collagen fibres in soft connective tissues

Extracellular matrix remodelling plays an essential role in tissue engineering of load-bearing structures. The goal of this study is to model changes in collagen fibre content and orientation in soft connective tissues due to mechanical stimuli. A theory is presented describing the mechanical condition within the tissue and accounting for the effects of collagen fibre alignment and changes in fibre content. A fibre orientation tensor is defined to represent the continuous distribution of collagen fibre directions. A constitutive model is introduced to relate the fibre configuration to the macroscopic stress within the material. The constitutive model is extended with a structural parameter, the fibre volume fraction, to account for the amount of fibres present within the material. It is hypothesised that collagen fibre reorientation is induced by macroscopic deformations and the amount of collagen fibres is assumed to increase with the mean fibre stretch. The capabilities of the model are demonstrated by considering remodelling within a biaxially stretched cube. The model is then applied to analyse remodelling within a closed stented aortic heart valve. The computed preferred fibre orientation runs from commissure to commissure and resembles the fibre directions in the native aortic valve.     

Collagen's role in the cortical bone's behaviour: a numerical approach

Literature devoted to experimental measurements of the elastic properties of the human cortical bone gives us a relatively wide spectrum of values. This proves that the result depends on the bone itself and on the area from where the sample has been taken. Ultrasonic measurement, which is a fine technology, points out complex maps. The reason of this very strong heterogeneity is not completely explained. The present study is based on a numerical model of the human cortical bone, the SiNuPrOs model and aims to suggest an explanation. If one admits that mineral apposition occurs around collagen fibres, the spatial orientation of these fibres would have an important consequence on the elastic properties of the medium. On the basis of homogenisation theory allowing to compute all the components of the elasticity tensor, this study quantifies the main influence of this architectural orientation and its effect on the anisotropy of the cortical bone.     

Collagen's role in the cortical bone's behaviour: a numerical approach

Literature devoted to experimental measurements of the elastic properties of the human cortical bone gives us a relatively wide spectrum of values. This proves that the result depends on the bone itself and on the area from where the sample has been taken. Ultrasonic measurement, which is a fine technology, points out complex maps. The reason of this very strong heterogeneity is not completely explained. The present study is based on a numerical model of the human cortical bone, the SiNuPrOs model and aims to suggest an explanation. If one admits that mineral apposition occurs around collagen fibres, the spatial orientation of these fibres would have an important consequence on the elastic properties of the medium. On the basis of homogenisation theory allowing to compute all the components of the elasticity tensor, this study quantifies the main influence of this architectural orientation and its effect on the anisotropy of the cortical bone.     

Collagen fibre reorientation around a crack in biaxially stretched aortic media

The distribution and orientation of collagen fibres in unstretched and biaxially stretched pig aortic media have been determined by an X-ray diffraction technique in order to analyse the reorientation of collagen fibres in response to the presence of a notch in biaxially stretched samples. The results show that collagen fibres align themselves following the force trajectories. This results in preferential fibre orientation perpendicular to the advancing crack tip, in agreement with the theoretical predictions of stress concentration effect due to the presence of an elliptical notch in an elastic plate.     

A microstructurally based continuum model of cartilage viscoelasticity and permeability incorporating measured statistical fiber orientations

The remarkable mechanical properties of cartilage derive from an interplay of isotropically distributed, densely packed and negatively charged proteoglycans; a highly anisotropic and inhomogeneously oriented fiber network of collagens; and an interstitial electrolytic fluid. We propose a new 3D finite strain constitutive model capable of simultaneously addressing both solid (reinforcement) and fluid (permeability) dependence of the tissue’s mechanical response on the patient-specific collagen fiber network. To represent fiber reinforcement, we integrate the strain energies of single collagen fibers—weighted by an orientation distribution function (ODF) defined over a unit sphere—over the distributed fiber orientations in 3D. We define the anisotropic intrinsic permeability of the tissue with a structure tensor based again on the integration of the local ODF over all spatial fiber orientations. By design, our modeling formulation accepts structural data on patient-specific collagen fiber networks as determined via diffusion tensor MRI. We implement our new model in 3D large strain finite elements and study the distributions of interstitial fluid pressure, fluid pressure load support and shear stress within a cartilage sample under indentation. Results show that the fiber network dramatically increases interstitial fluid pressure and focuses it near the surface. Inhomogeneity in the tissue’s composition also increases fluid pressure and reduces shear stress in the solid. Finally, a biphasic neo-Hookean material model, as is available in commercial finite element codes, does not capture important features of the intra-tissue response, e.g., distributions of interstitial fluid pressure and principal shear stress.     

X-ray investigation of the orientation of collagen fibres in aortic media layer under distending pressure

The structural organization of the collagen fibres in pig descending aortic media layer was studied by X-ray diffraction at various distending presusres. The degree of orientation of the collagen fibres along the circumference was evaluated. Furthermore, the variation of the mechanical behaviour of the aortic media layer was investigated as a function of the amount and distribution of collagen fibres in different portions along the artery. The results indicate that according to the model of Wolinsky and Glagov collagen is the effective structural component which bears most of the stressing forces while the elastic matrix distributes them uniformly.     

A model for saccular cerebral aneurysm growth by collagen fibre remodelling

The first structural model for saccular cerebral aneurysm growth is proposed. It is assumed that the development of the aneurysm is accompanied by a loss of the media, and that only collagen fibres provide load-bearing capacity to the aneurysm wall. The aneurysm is modelled as an axisymmetric multi-layered membrane, exposed to an inflation pressure. Each layer is characterized by an orientation angle, which changes between different layers. The collagen fibres and fibroblasts within a specific layer are perfectly aligned. The growth and the morphological changes of the aneurysm are accomplished by the turnover of collagen. Fibroblasts are responsible for collagen production, and the related deformations are assumed to govern the collagen production rate. There are four key parameters in the model: a normalized pressure, the number of layers in the wall, an exponent in the collagen mass production rate law, and the pre-stretch under which the collagen is deposited. The influence of the model parameters on the aneurysmal response is investigated, and a stability analysis is performed. The model is able to predict clinical observations and mechanical test results, for example, in terms of predicted aneurysm size, shape, wall stress and wall thickness.     

A structural constitutive model considering angular dispersion and waviness of collagen fibres of rabbit facial veins

Background  

Structural constitutive models of vascular wall integrate information on composition and structural arrangements of tissue. In blood vessels, collagen fibres are arranged in coiled and wavy bundles and the individual collagen fibres have a deviation from their mean orientation. A complete structural constitutive model for vascular wall should incorporate both waviness and orientational distribution of fibres. We have previously developed a model, for passive properties of vascular wall, which considers the waviness of collagen fibres. However, to our knowledge there is no structural model of vascular wall which integrates both these features.     

A computational model to describe the collagen orientation in statically cultured engineered tissues

Collagen provides cardiovascular tissues with the ability to withstand haemodynamic loads. A similar network is essential to obtain in tissue-engineered (TE) samples of the same nature. Yet, the mechanism of collagen orientation is not fully understood. Typically collagen remodelling is linked to mechanical loading. However, TE constructs also show an oriented collagen network when developed under static culture. Experiments under these conditions also indicate that the tissue gradually compacts due to contractile stresses developed in the α-actin fibres of the cells. Therefore, it is hypothesised that cellular contractile stresses are responsible for collagen orientation. A model describing the cellular α-actin turnover and the stresses developed by them is integrated in a structural constitutive model describing the mechanical behaviour of collagen fibres. Results show that the model can successfully capture the sample compaction, tissue stress generation and its heterogeneous collagen arrangement.     

Towards an analytical model of soft biological tissues

In the past years, soft-tissue modelling research has seen substantial developments, a significant part of which can be ascribed to the refinement of numerical techniques, such as Finite Element analysis. A large class of physico-mechanical properties can be effectively simulated and predictions can be made for a variety of phenomena. However, there is still much that can be conceptually explored by means of fundamental theoretical analysis. In the past few years, driven by our interest in articular cartilage mechanics, we have developed theoretical microstructural models for linear elasticity and permeability that accounted for the presence and arrangement of collagen fibres in cartilage. In this paper, we investigate analytically the non-linear elasticity of soft tissues with collagen fibres arranged according to a given distribution of orientation, a problem that, aside from the case of fibres aligned in a finite number of distinct directions, has been treated exclusively numerically in the literature. We show that, for the case of a tissue with complex fibre arrangement, such as articular cartilage, the theoretical framework commonly used leads to an integral expression of the elastic strain energy potential. The present model is a first attempt in the development of a unified analytical microstructural model for non-linear elasticity and permeability of hydrated, fibre-reinforced soft tissues.     

First investigation of the collagen D-band ultrastructure in fossilized vertebrate integument

The ultrastructure of dermal fibres of a 200Myr thunniform ichthyosaur, Ichthyosaurus, specifically the 67nm axial repeat D-banding of the fibrils, which characterizes collagen, is presented for the first time by means of scanning electron microscopy (SEM) analysis. The fragment of material investigated is part of previously described fossilized skin comprising an architecture of layers of oppositely oriented fibre bundles. The wider implication, as indicated by the extraordinary quality of preservation, is the robustness of the collagen molecule at the ultrastructural level, which presumably contributed to its survival during the initial processes of decomposition prior to mineralization. Investigation of the elemental composition of the sample by SEM-energy dispersive X-ray spectroscopy indicates that calcite and phosphate played important roles in the rapid mineralization and fine replication of the collagen fibres and fibrils. The exceedingly small sample used in the investigation and high level of information achieved indicate the potential for minimal damage to prized museum specimens; for example, ultrastructural investigations by SEM may be used to help resolve highly contentious questions, for example, 'protofeathers' in the Chinese dinosaurs.     

A synchrotron radiation X-ray diffraction study of the crystallinity of tendon fibres

The equatorial diffraction pattern of tendon collagen fibres was measured during short successive exposures at different lengths using a double focusing X-ray synchrotron radiation camera with film and with an area detector. Similarly, patterns from thin fibres from premature rats were recorded. The patterns unambiguously illustrate the relationship between fibre crystallinity and the age of the animal. Further, the results indicate that in the initial part of the linear region of the stiffness-versus-length curve, the collagen fibres are characterized by a quasihexagonal arrangement of collagen molecules, whereas at the end of this region, the molecular arrangement becomes hexagonal.     

On the anisotropy and inhomogeneity of permeability in articular cartilage

Articular cartilage is known to be anisotropic and inhomogeneous because of its microstructure. In particular, its elastic properties are influenced by the arrangement of the collagen fibres, which are orthogonal to the bone-cartilage interface in the deep zone, randomly oriented in the middle zone, and parallel to the surface in the superficial zone. In past studies, cartilage permeability has been related directly to the orientation of the glycosaminoglycan chains attached to the proteoglycans which constitute the tissue matrix. These studies predicted permeability to be isotropic in the undeformed configuration, and anisotropic under compression. They neglected tissue anisotropy caused by the collagen network. However, magnetic resonance studies suggest that fluid flow is "directed" by collagen fibres in biological tissues. Therefore, the aim of this study was to express the permeability of cartilage accounting for the microstructural anisotropy and inhomogeneity caused by the collagen fibres. Permeability is predicted to be anisotropic and inhomogeneous, independent of the state of strain, which is consistent with the morphology of the tissue. Looking at the local anisotropy of permeability, we may infer that the arrangement of the collagen fibre network plays an important role in directing fluid flow to optimise tissue functioning.     

Structural and mechanistic insights into collagen degradation by a bacterial collagenolytic serine protease in the subtilisin family

A number of proteases in the subtilisin family derived from environmental or pathogenic microorganisms have been reported to be collagenolytic serine proteases. However, their collagen degradation mechanisms remain unclear. Here, the degradation mechanism of type I collagen fibres by the S8 collagenolytic protease MCP‐01, from Pseudoalteromonas sp. SM9913, was studied. Atomic force microscopy observation and biochemical analysis confirmed that MCP‐01 progressively released single fibrils from collagen fibres and released collagen monomers from fibrils mainly by hydrolysing proteoglycans and telopeptides in the collagen fibres. Structural and mutational analyses indicated that an enlarged substrate‐binding pocket, mainly composed of loops 7, 9 and 11, is necessary for collagen recognition and that the acidic and aromatic residues on these loops form a negatively charged, hydrophobic environment for collagen binding. MCP‐01 displayed a non‐strict preference for peptide bonds with Pro or basic residues at the P1 site and/or Gly at the P1’ site in collagen. His211 is a key residue for the P1‐basic‐residue preference of MCP‐01. Our study gives structural and mechanistic insights into collagen degradation of the S8 collagenolytic protease, which is helpful in developing therapeutics for diseases with S8 collagenolytic proteases as pathogenic factors and in studying environmental organic nitrogen degradation mechanisms.     

A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: continuum basis,computational aspects and applications

Cartilage is a multi-phase material composed of fluid and electrolytes (68–85% by wet weight), proteoglycans (5–10% by wet weight), chondrocytes, collagen fibres and other glycoproteins. The solid phase constitutes an isotropic proteoglycan gel and a fibre network of predominantly type II collagen, which provides tensile strength and mechanical stiffness. The same two components control diffusion of the fluid phase, e.g. as visualised by diffusion tensor MRI: (i) the proteoglycan gel (giving a baseline isotropic diffusivity) and (ii) the highly anisotropic collagenous fibre network. We propose a new constitutive model and finite element implementation that focus on the essential load-bearing morphology: an incompressible, poroelastic solid matrix reinforced by an inhomogeneous, dispersed fibre fabric, which is saturated with an incompressible fluid residing in strain-dependent pores of the collagen–proteoglycan solid matrix. The inhomogeneous, dispersed fibre fabric of the solid further influences the fluid permeability, as well as an intrafibrillar portion that cannot be ‘squeezed out’ from the tissue. Using representative numerical examples on the mechanical response of cartilage, we reproduce several features that have been demonstrated experimentally in the cartilage mechanics literature.     

Structural evidence for insertion of collagen fibres to smooth muscle cells in the carotid arterial system of the giraffe (Giraffa camelopardalis)

Summary Previous anatomical studies have failed to resolve the question relating to whether or not collagen fibres, like elastic fibres, are attached to smooth muscle cells in the arterial wall. The current ultrastructural study demonstrates the insertion of collagen fibres to the sarcolemmal dark areas in the smooth muscle cells of the carotid arterial system of the giraffe. It is concluded, therefore, that this morphological linkage between collagen and smooth muscle cells may facilitate transmission of the force of contraction between the cells and to the surrounding connective tissue framework since the myofilaments appear to be spatially placed in series with the extracellular collagen fibres at the sarcolemmal dark areas.Presented as part of Ph.D. thesis to the University of Nairobi     

Effect of collagen fibre orientation on intervertebral disc torsion mechanics

The intervertebral disc is a complex fibro-cartilaginous material, consisting of a pressurized nucleus pulposus surrounded by the annulus fibrosus, which has an angle-ply structure. Disc injury and degeneration are noted by significant changes in tissue structure and function, which significantly alters stress distribution and disc joint stiffness. Differences in fibre orientation are thought to contribute to changes in disc torsion mechanics. Therefore, the objective of this study was to evaluate the effect of collagen fibre orientation on internal disc mechanics under compression combined with axial rotation. We developed and validated a finite element model (FEM) to delineate changes in disc mechanics due to fibre orientation from differences in material properties. FEM simulations were performed with fibres oriented at \(\pm 30^{\circ }\) throughout the disc (uniform by region and fibre layer). The initial model was validated by published experimental results for two load conditions, including \(0.48\,\hbox {MPa}\) axial compression and \(10\,\hbox {Nm}\) axial rotation. Once validated, fibre orientation was rotated by \(4^{\circ }\) or \(8^{\circ }\) towards the horizontal plane, resulting in a decrease in disc joint torsional stiffness. Furthermore, we observed that axial rotation caused a sinusoidal change in disc height and radial bulge, which may be beneficial for nutrient transport. In conclusion, including anatomically relevant fibre angles in disc joint FEMs is important for understanding stress distribution throughout the disc and will be important for understanding potential causes for disc injury. Future models will include regional differences in fibre orientation to better represent the fibre architecture of the native disc.