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.     

Structure and orientation of collagen fibres in human mitral valve

The structure and distribution of collagen fibres in chordae tendineae, anterior leaflet and annulus fibrous of human mitral valve has been investigated using high and small angle X-ray diffraction. The molecular packing of collagen in native mitral valve components is very similar to that in native rat tail tendon. The distribution and orientation of collagen fibres in unstretched and stretched specimens has been deduced by the arcing of the high and small angle meridional reflections. Collagen fibres, which are aligned along the chordae tendineae, are preferentially distributed along the branchings of the chordae into the anterior leaflet and then course towards the annulus fibrous. However, in the anterior leaflet a considerable amount of collagen fibres are organized in a tridimensional isotropic network even after high deformation of the tissue.     

Collagen fibre orientation in the annulus fibrosus of intervertebral disc during bending and torsion measured by x-ray diffraction

X-ray diffraction has been used to measure the orientation of the collagen fibres in the ventral annulus fibrosus of intact L1/2 rabbit intervertebral disc during in vitro bending and torsion. Fibres are tilted with respect to the axis of the spine. As predicted by theory, fibre tilt decreases in those regions of the annulus which are stretched by bending but increases in the slackened regions. Good agreement with the quantitative predictions of bending theory was obtained in three of the six series of experiments, the predicted trend being found in all six. Tilt direction alternates in successive lamellae of the annulus. When discs were subjected to both clockwise and anticlockwise torsion of 5°, the two families of titled fibres reoriented in the expected directions.     

Multiphoton microscopy observations of 3D elastin and collagen fiber microstructure changes during pressurization in aortic media

Elastin and collagen fibers play important roles in the mechanical properties of aortic media. Because knowledge of local fiber structures is required for detailed analysis of blood vessel wall mechanics, we investigated 3D microstructures of elastin and collagen fibers in thoracic aortas and monitored changes during pressurization. Using multiphoton microscopy, autofluorescence images from elastin and second harmonic generation signals from collagen were acquired in media from rabbit thoracic aortas that were stretched biaxially to restore physiological dimensions. Both elastin and collagen fibers were observed in all longitudinal–circumferential plane images, whereas alternate bright and dark layers were observed along the radial direction and were recognized as elastic laminas (ELs) and smooth muscle-rich layers (SMLs), respectively. Elastin and collagen fibers are mainly oriented in the circumferential direction, and waviness of collagen fibers was significantly higher than that of elastin fibers. Collagen fibers were more undulated in longitudinal than in radial direction, whereas undulation of elastin fibers was equibiaxial. Changes in waviness of collagen fibers during pressurization were then evaluated using 2-dimensional fast Fourier transform in mouse aortas, and indices of waviness of collagen fibers decreased with increases in intraluminal pressure. These indices also showed that collagen fibers in SMLs became straight at lower intraluminal pressures than those in EL, indicating that SMLs stretched more than ELs. These results indicate that deformation of the aorta due to pressurization is complicated because of the heterogeneity of tissue layers and differences in elastic properties of ELs, SMLs, and surrounding collagen and elastin.     

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.     

Arrangement of microfibrils in collagen fibrils of tendons in the rat tail

Summary The microfibrillar arrangement in collagen fibrils of tendons in the tail of the rat was examined by electron microscopy and X-ray diffraction. Fresh and air-dried collagen fibers were examined in unstretched and stretched conditions. The results demonstrate that the microfibrils have a course parallel to the longitudinal axis of the collagen fibrils. The influence of stretching and hydration of the samples on the orientation of fibrils and microfibrils is also assessed.     

The modelling of fibre reorientation in soft tissue

In this paper, a hyperelastic and thermodynamically consistent model for soft tissue is developed that is able to describe the change of the initial orientation of the collagen fibres. Full numerical implementation is considered as well. The collagen architecture is assumed to reorient driven by a specific thermodynamical force. The anisotropy is described by a strain energy function, which is decomposed into a part related to the matrix and a part related to the fibres. The initial fibre orientation is defined by a structural tensor, while the current orientation is described by a time-dependent structural tensor, which results from the initial one by a rotational transformation. The rotation tensor is obtained via an integration process of a rate tensor, which depends on an adequately defined thermodynamical force. The integration is achieved via an exponential map algorithm, where it is shown that the rotation is necessarily a two-parametric one. Efficiency of the proposed formulation is demonstrated using some numerical examples.     

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.     

Phase transition in natural collagen]

The state of water protons and peptide chains in natural collagen was investigated by the method of nuclear magnetic resonance. The study of orientation and temperature dependence of collagen PMR spectra allows us to mage a conclusion about the considerable disorder of mutual orientation in the polypeptide chains at the temperature above -4 degrees C. Under these conditions it was observed that natural collagen was near to the liquid-crystal. The phasic transition at -4 degrees C was discovered, the latter was followed by an abrupt change of the character of water proton mobility and by the change of orientation of collagen fibres order. The thermal effect of transition was measured, the latter presents 18k/gr of the whole specimen.     

Myosin crossbridge orientation in demembranated muscle fibres studied by birefringence and X-ray diffraction measurements

Muscle contraction is generally thought to involve changes in the orientation of myosin crossbridges during their ATP-driven cyclical interaction with actin. We have investigated crossbridge orientation in equilibrium states of the crossbridge cycle in demembranated fibres of frog and rabbit muscle, using a novel combination of techniques: birefringence and X-ray diffraction. Muscle birefringence is sensitive to both crossbridge orientation and the transverse spacing of the contractile filament lattice. The latter was determined from the equatorial X-ray diffraction pattern, allowing accurate characterization of the orientation component of birefringence changes. We found that this component decreased when relaxed muscle fibres were put into rigor at rest length, and when either the ionic strength or temperature of relaxed fibres was lowered. In each case the birefringence decrease was accompanied by an increase in the intensity of the (1,1) equatorial X-ray reflection relative to that of the (1,0) reflection. When fibres that had been stretched largely to eliminate overlap between actin- and myosin-containing filaments were put into rigor, there was no change in the orientation component of the birefringence. When isolated myosin subfragment-1 was bound to these rigor fibres, the orientation component of the birefringence increased. The birefringence changes at rest length are likely to be due to changes in the orientation of myosin crossbridges, and in particular of the globular head region of the myosin molecules. In relaxed fibres from rabbit muscle, at 100 mM ionic strength, 15 degrees C, the long axis of the heads appears to be relatively well aligned with the filament axis. When fibres are put into rigor, or the temperature or ionic strength is lowered, the degree of alignment decreases and there is a transfer of crossbridge mass towards the actin-containing filaments.     

The effect of myosin light chain phosphorylation and Mg2+ on the conformation of myosin in thick filaments of glycerinated fibers of rabbit skeletal muscle

It has been shown by polarization microfluorimetry that phosphorylation of myosin light chain 2, in stretched single glycerinated fibers of rabbit skeletal muscle, results in changes in polarized fluorescence anisotropy of both the tryptophan residues of myosin molecules and the fluorescent label, N-iodoacetyl-N'-(5-sulfo-1-naphthyl)ethylenediamine, associated with the fast-reacting thiol group in myosin heads. These changes are also dependent on the presence or absence of Mg2+ in the medium: they are most pronounced in the presence of 5 mM MgCl2. It is assumed that both Mg2+ binding to myosin and phosphorylation of light chain 2 associated with myosin heads induce structural changes in myosin filaments of muscle fibres which are expressed as changes in the orientation of myosin heads and in the conformation of myosin rods.     

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.     

Ex-vivo observation of calcification process in chick tibia slice: Augmented calcification along collagen fiber orientation in specimens subjected to static stretch

Bone formation through matrix synthesis and calcification in response to mechanical loading is an essential process of the maturation in immature animals, although how mechanical loading applied to the tissue increases the calcification and improves mechanical properties, and which directions the calcification progresses within the tissue are largely unknown. To address these issues, we investigated the calcification of immature chick bone under static tensile stretch using a newly developed real-time observation bioreactor system. Bone slices perpendicular to the longitudinal axis obtained from the tibia in 2- to 4-day-old chick legs were cultured in the system mounted on a microscope, and their calcification was observed up to 24 h while they were stretched in the direction parallel to the slice. Increase in the calcified area, traveling distance and the direction of the calcification and collagen fiber orientation in the newly calcified region were analyzed. There was a significant increase in calcified area in the bone explant subjected to tensile strain over ∼3%, which corresponds to the threshold strain for collagen fibers showing alignment in the direction of stretch, indicating that the fiber alignment may enhance tissue calcification. The calcification progressed to a greater distance to the stretching direction in the presence of the loading. Moreover, collagen fiber orientation in the calcified area in the loaded samples was coincided with the progression angle of the calcification. These results clearly show that the application of static tensile strain enhanced tissue calcification, which progresses along collagen fibers aligned to the loading direction.     

A quantitative method to determine the orientation of collagen fibers in the dermis.

We have developed a quantitative microscopic method to determine changes in the orientation of collagen fibers in the dermis resulting from mechanical stress. The method is based on the use of picrosirius red-stained cryostat sections of piglet skin in which collagen fibers reflect light strongly when epipolarization microscopy is used. Digital images of sections were converted into binary images that were analyzed quantitatively on the basis of the length of the collagen fibers in the plane of the section as a measure for the orientation of the fibers. The length of the fibers was expressed in pixels and the mean length of the 10 longest fibers in the image was taken as the parameter for the orientation of the fibers. To test the procedure in an experimental setting, we used skin after 0 and 30 min of skin stretching. The orientation of the fibers in sections of control skin differed significantly from the orientation of fibers in sections of skin that was stretched mechanically for 30 min [76 +/- 15 (n=5) vs 132 +/- 36 (n=5)]. The method described here is a relatively simple way to determine (changes in) the orientation of individual collagen fibers in connective tissue and can also be applied for analysis of the orientation of any other structural element in tissues so long as a representative binary image can be created.     

A mathematical model of medial collateral ligament repair: migration,fibroblast proliferation and collagen formation

The partial rupture of ligament fibres leads to an injury known as grade 2 sprain. Wound healing after injury consists of four general stages: swelling, release of platelet-derived growth factor (PDGF), fibroblast migration and proliferation and collagen production. The aim of this paper is to present a mathematical model based on reaction–diffusion equations for describing the repair of the medial collateral ligament when it has suffered a grade 2 sprain. We have used the finite element method to solve the equations of this. The results have simulated the tissue swelling at the time of injury, predicted PDGF influence, the concentration of fibroblasts migrating towards the place of injury and reproduced the random orientation of immature collagen fibres. These results agree with experimental data reported by other authors. The model describes wound healing during the 9 days following such injury.     

A mathematical model of medial collateral ligament repair: migration, fibroblast proliferation and collagen formation

The partial rupture of ligament fibres leads to an injury known as grade 2 sprain. Wound healing after injury consists of four general stages: swelling, release of platelet-derived growth factor (PDGF), fibroblast migration and proliferation and collagen production. The aim of this paper is to present a mathematical model based on reaction-diffusion equations for describing the repair of the medial collateral ligament when it has suffered a grade 2 sprain. We have used the finite element method to solve the equations of this. The results have simulated the tissue swelling at the time of injury, predicted PDGF influence, the concentration of fibroblasts migrating towards the place of injury and reproduced the random orientation of immature collagen fibres. These results agree with experimental data reported by other authors. The model describes wound healing during the 9 days following such injury.     

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.     

Turbidimetric and morphological studies of type I collagen fibre self assembly in vitro and the influence of fibronectin

Collagen undergoes several stages of self assembly including turbidimetric lag, growth and plateau steps. The later stages of type I collagen self assembly were studied by turbidity—time measurements, low angle laser light scattering and by determination of the birefringence retardation of collagen fibres formed in vitro. These studies were conducted in the presence and absence of fibronectin to evaluate the effect of fibronectin on the kinetics and extent of type I collagen fibrillogenesis. The results of these studies indicate that the collagen fibres observed at the end of the lag phase appear to be identical to fibres seen in the growth phase of turbidity—time curves based on fibre diameter and birefringence retardation measurements. Birefringence retardation measurements suggest that the diffracting unit may be the collagen fibril and that the volume fraction of fibrils in fibres is about 0.95 using a model developed for a series of parallel ellipsoids. Morphological observations suggest that the distribution of fibre diameters formed in vitro during the growth phase is narrow and appears to be independent of time with only the mass of collagen in fibres increasing during the growth phase. During the growth phase, layers of parallel fibres are formed with alternating layers appearing almost orthogonal. In the presence of fibronectin the mechanism of fibre formation appeared unchanged. It was concluded that fibronectin appeared to modify the kinetics of self assembly by preventing collisions between collagen molecules.