A model of the structural and functional development of the normal human fetal left ventricle based on a global growth law

The purpose of this research is to study the growth of the normal human left ventricle (LV) during the fetal period from 14 to 40 weeks of gestation. A new constitutive law for the active myocardium describing the mechanical properties of the active muscle during the whole cardiac cycle has been proposed. The LV model is a thick-walled, incompressible, hyperelastic cylinder, with families of helicoidal fibers running on cylindrical surfaces [1]. Based on the works of Lin and Taber [2] done on the embryonic chick heart, we use for the human fetal heart a growth law in which the growth rate depends on the wall stresses. The parameters of the growth law are adapted to agree with sizes and volumes inferred from two dimensional ultrasound measurements performed on 18 human fetuses.Then calculations are performed to extrapolate the cardiac performance during normal growth of the fetal LV. The results presented support the idea that a growth law in which the growth rate depends linearly on the mean wall stresses averaged through the space and during whole cardiac cycle, is adapted to the normal human fetal LV development.     

A Model of the Structural and Functional Development of the Normal Human Fetal Left Ventricle Based on a Global Growth Law

The purpose of this research is to study the growth of the normal human left ventricle (LV) during the fetal period from 14 to 40 weeks of gestation. A new constitutive law for the active myocardium describing the mechanical properties of the active muscle during the whole cardiac cycle has been proposed. The LV model is a thick-walled, incompressible, hyperelastic cylinder, with families of helicoidal fibers running on cylindrical surfaces [1] . Based on the works of Lin and Taber [2] done on the embryonic chick heart, we use for the human fetal heart a growth law in which the growth rate depends on the wall stresses. The parameters of the growth law are adapted to agree with sizes and volumes inferred from two dimensional ultrasound measurements performed on 18 human fetuses. Then calculations are performed to extrapolate the cardiac performance during normal growth of the fetal LV. The results presented support the idea that a growth law in which the growth rate depends linearly on the mean wall stresses averaged through the space and during whole cardiac cycle, is adapted to the normal human fetal LV development.     

Study of stress concentration in the walls of the bovine coronary arterial branch

The intramural stress concentration in the arterial wall is studied at the bovine circumflex coronary arterial branch. The material properties, geometry, and strains in the arterial branch are determined from experiments. The stresses are determined using a finite element analysis. The arterial branch is modeled as two interesecting thin cylindrical shells incorporating local variations in the branch geometry, thickness, and material properties. The artery is considered orthotropic and loaded with an incremental pressure of 40 mmHg. The highest intramural stresses are found to be localized at the proximal and distal regions of the ostium and are not significantly affected by the elastic properties. The stresses are 3 to 4 times greater in the branch at the inner surface than in the straight segment. The strains are twice as large at the branch than in the straight segment. We speculate that this stress concentration could injure the artery and make the branch region susceptible to atherosclerosis.     

The relationship of voluntary running to fibre type composition, fibre area and capillary supply in rat soleus and plantaris muscles

Twenty 4-week-old Wistar rats exercised voluntarily in running wheels each day for 45 days. Fibre type composition, fibre cross-sectional area and the number of capillaries around a fibre of the slow-twitch soleus and fast-twitch plantaris muscles were examined and compared with animals which had no access to running wheels. The exercise group had a higher percentage of fast-twitch oxidative glycolytic (FOG) fibres and a lower percentage of fast-twitch glycolytic (FG) fibres in the deep portion of the plantaris muscle. The area of FOG fibres in the surface portion of the plantaris muscle was also greater in the exercise group. In the exercised animals, there was a positive relationship between the running distance and the area of FOG fibres in both the deep and surface portions of the plantaris muscle. In addition, the running distance correlated positively with the percentage of FOG fibres and negatively with that of FG fibres in the deep portion of the plantaris muscle. There were no relationships between the running distance and fibre type composition, or fibre area and capillary supply in the soleus muscle. These results suggested that the increase in the percentage and area of FOG fibres in the fast-twitch muscle was closely related to voluntary running.     

On the fibre composite material models of disc annulus--comparison of predicted stresses

An axisymmetric finite element model of a body-disc-body unit has been developed and used to study the relative effects of two distinct direction-dependent material representations of the disc annulus on the predicted state of stresses in the disc. The annulus fibrosus is modelled either as nonhomogeneous fibre reinforced composite or alternatively as homogeneous orthotropic with transverse isotropy. In order to have identical states of displacements and hence strains, the unknown properties of the latter model are chosen to be equivalent with those of the former. The fibre slopes of 20 degrees, 30 degrees, and 40 degrees are considered in this study. The stresses in the annulus matrix in the circumferential planes parallel to the fibre layers are predicted to be significantly different depending on the annulus model used. In the nonhomogeneous model, the fibre membranes while under tensile forces, in turn, apply compression to the annulus matrix and, hence, decrease the annulus normal stresses in the above planes. Had the membranes carried compressive forces, a reverse trend would have resulted. The foregoing relative differences are dependent on the fibre orientation, and the magnitude of the tensile forces carried by the fibre layers. The latter also depends, amongst others, on the orientation of the fibres, decreasing as the fibre slope increases from 20 degrees to 30 degrees and 40 degrees. On the basis of the annulus micro-structure and the relative mechanical functions of its components, namely the annulus bulk and the collagenous fibre layers, it appears that nonhomogeneous fibre reinforced composite model of the disc annulus is more realistic resulting in a more accurate computation of stresses in the annulus fibrosus.     

2D calculation method based on composite beam theory for the determination of local homogenised stiffnesses of long bones

A calculation method using the finite element technique is presented. Its main objective was to determine strains, stresses and more particularly stiffnesses in any cross section of a tibia, thus enabling the localisation of tibial torsion in vivo. Each tibial cross section was considered to be a non-uniform cross section of a composite beam with arbitrary orientation of fibres. The determination of stresses, strains and stiffnesses within a composite beam cross section has been defined by solving a variational problem. The validation of this method was performed on a tibial diaphysis of which each cross section was assumed to be the cross section of a composite beam made of orthotropic materials with orthotropic axes of any orientation with respect to the principal axis of the bone. The comparison of the results, from our model and that of a three-dimensional one, was performed on each nodal value (strains, stresses) of the meshed cross section as it was impossible to obtain local stiffnesses by experimentation. The good agreement between the results has validated our finite element program. Actually, this method has enabled to treat directly 2D geometric reconstructions from CT scan images with a good accuracy to determine locally the homogenised mechanical characteristics of human tibia in vivo, and particularly to quantify torsional tibial abnormalities of children without approximation of the shape of the cross section and by calculating the real moment of inertia J. The importance of the fibre orientation with regards to the stiffness values has been emphasised. This 2D method has also allowed to reduce CPU time of the 3D modelling and calculation.     

Hypothalamo-amygdaloid connections of cat's brain]

Under study were the afferent connections of the cat's amygdala nuclei with the hypothalamus (Nauta's method) in parallel with studying geometrical parameters of the afferent fibre endings in these nuclei by the Golgi method. It has been shown that the medial hypothalamus gives the beginning to a small amount of fibres running to the medial group of the amygdala nuclei; dissipated solitary fibres run to the large- and small-cellular parts of the basal nucleus. A considerable amount of fibres run from the lateral hypothalamus to the amygdala, mainly to the medial group of its nuclei and the anterior amygdalar area, only solitary fibres were followed in the basal nuclei. We failed to observe degenerated fibres from the medial preoptical area to the amygdale. The geometry of branches of these fibre systems in the amygdala nuclei was established: they all terminate as a compact but rarely branching brush.     

The number of satellite cells in slow and fast fibres from human vastus lateralis muscle

The aim of this investigation was to study the distribution of satellite cells in slow (type I fibres) and fast (type II fibres) fibres from human vastus lateralis muscle. This muscle is characterised by a mixed fibre type composition and is considered as the site of choice for biopsies in research work and for clinical diagnosis. Biopsy samples were obtained from five healthy young volunteers and a total of 1,747 type I fibres and 1,760 type II fibres were assessed. Satellite cells and fibre type composition were studied on serial muscle cross-sections stained with specific monoclonal antibodies. From a total of 218 satellite cells, 116 satellite cells were found in contact with type I fibres (53.6±8% of the satellite cells associated to type I fibres) and 102 satellite cells in contact with type II fibres (46.4±8% of the satellite cells associated to type II fibres). There was no significant difference (P=0.4) between the percentages of satellite cells in contact with type I and with type II fibres. Additionally, there was no relationship between the mean number of satellite cells per fibre and the mean cross-sectional area of muscle fibres. In conclusion, our results show that there is no fibre type-specific distribution of satellite cells in a human skeletal muscle with mixed fibre type composition.     

Theoretical study of Beloussov’s hyper-restoration hypothesis for mechanical regulation of morphogenesis

Computational models were used to explore the idea that morphogenesis is regulated, in part, by feedback from mechanical stress according to Beloussov’s hyper-restoration (HR) hypothesis. According to this hypothesis, active tissue responses to stress perturbations tend to restore, but overshoot, the original (target) stress. To capture this behavior, the rate of growth or contraction is assumed to depend on the difference between the current and target stresses. Stress overshoot is obtained by letting the target stress change at a rate proportional to the same stress difference. The feasibility of the HR hypothesis is illustrated by models for stretching of epithelia, cylindrical bending of plates, invagination of cylindrical and spherical shells, and early amphibian development. In each case, an initial perturbation leads to an active mechanical response that changes the form of the tissue. The results show that some morphogenetic processes can be entirely self-driven by HR responses once they are initiated (possibly by genetic activity). Other processes, however, may require secondary mechanisms or perturbations to proceed to completion.     

3D finite element models of shoulder muscles for computing lines of actions and moment arms

Accurate representation of musculoskeletal geometry is needed to characterise the function of shoulder muscles. Previous models of shoulder muscles have represented muscle geometry as a collection of line segments, making it difficult to account for the large attachment areas, muscle–muscle interactions and complex muscle fibre trajectories typical of shoulder muscles. To better represent shoulder muscle geometry, we developed 3D finite element models of the deltoid and rotator cuff muscles and used the models to examine muscle function. Muscle fibre paths within the muscles were approximated, and moment arms were calculated for two motions: thoracohumeral abduction and internal/external rotation. We found that muscle fibre moment arms varied substantially across each muscle. For example, supraspinatus is considered a weak external rotator, but the 3D model of supraspinatus showed that the anterior fibres provide substantial internal rotation while the posterior fibres act as external rotators. Including the effects of large attachment regions and 3D mechanical interactions of muscle fibres constrains muscle motion, generates more realistic muscle paths and allows deeper analysis of shoulder muscle function.     

Effects of selected pectinolytic bacterial strains on water-retting of hemp and fibre properties

Aims:  To study the effect of selected bacterial strains on hemp water-retting and properties of retted fibre.
Methods and Results:  The trials were performed in laboratory tanks. The traditional water-retting process, without inoculum addition, was compared to a process modified by inoculating water tanks with two selected pectinolytic bacteria: the anaerobic strain Clostridium sp. L1/6 and the aerobic strain Bacillus sp. ROO40B. Six different incubation times were compared. Half the fibre obtained from each tank was combed. Micromorphological analyses were performed by scanning electron microscopy on uncombed and combed fibres. Moreover, organoleptic and chemical analyses of uncombed fibres were performed.
Conclusions:  The inoculum , besides speeding up the process, significantly improved the fibre quality. The fibre was not damaged by mechanical hackling, thanks to the good retting level obtained by the addition of selected strains, differently to what happened with the traditionally retted fibre. The best fibre quality was obtained after 3–4 days of retting with the addition of the bacterial inoculum .
Significance and Impact of the Study:  Retting is the major limitation to an efficient production of high-quality hemp fibres. The water-retting process and fibre quality were substantially improved by simultaneously inoculating water tanks with two selected pectinolytic strains.     

A finite element model of the human left ventricular systole

Local wall stress is the pivotal determinant of the heart muscle's systolic function. Under in vivo conditions, however, such stresses cannot be measured systematically and quantitatively. In contrast, imaging techniques based on magnetic resonance (MR) allow the determination of the deformation pattern of the left ventricle (LV) in vivo with high accuracy. The question arises to what extent deformation measurements are significant and might provide a possibility for future diagnostic purposes. The contractile forces cause deformation of LV myocardial tissue in terms of wall thickening, longitudinal shortening, twisting rotation and radial constriction. The myocardium is thereby understood to act as a densely interlaced mesh. Yet, whole cycle image sequences display a distribution of wall strains as function of space and time heralding a significant amount of inhomogeneity even under healthy conditions. We made similar observations previously by direct measurement of local contractile activity. The major reasons for these inhomogeneities derive from regional deviations of the ventricular walls from an ideal spheroidal shape along with marked disparities in focal fibre orientation. In response to a lack of diagnostic tools able to measure wall stress in clinical routine, this communication is aimed at an analysis and functional interpretation of the deformation pattern of an exemplary human heart at end-systole. To this end, the finite element (FE) method was used to simulate the three-dimensional deformations of the left ventricular myocardium due to contractile fibre forces at end-systole. The anisotropy associated with the fibre structure of the myocardial tissue was included in the form of a fibre orientation vector field which was reconstructed from the measured fibre trajectories in a post mortem human heart. Contraction was modelled by an additive second Piola-Kirchhoff active stress tensor. As a first conclusion, it became evident that longitudinal fibre forces, cross-fibre forces and shear along with systolic fibre rearrangement have to be taken into account for a useful modelling of systolic deformation. Second, a realistic geometry and fibre architecture lead to typical and substantially inhomogeneous deformation patterns as they are recorded in real hearts. We therefore, expect that the measurement of systolic deformation might provide useful diagnostic information.     

Structure,composition and mechanical properties of the silk fibres of the egg case of the Joro spider, <Emphasis Type="Italic">Nephila clavata</Emphasis> (Araneae,Nephilidae)

The silk egg case and orb web of spiders are elaborate structures that are assembled from a number of components. We analysed the structure, the amino acid and fibre compositions, and the tensile properties of the silk fibres of the egg case of Nephila clavata. SEM shows that the outer and inner covers of the egg case consist of thick, medium and thin silk fibres. The silk fibres of the outer cover of the egg case are probably produced by the major and minor ampullate glands. The silk fibres of the inner cover of the egg case from cylindrical glands appears to be distinct from the silk fibres of the major ampullate glands based on their micro-morphology, mole percent amino acid composition and types, and tensile behaviour and properties. Collectively, our investigations show that N. clavata uses silk fibres from relatively few glands in varying combinations to achieve different physical and chemical properties (e.g., color, diameter, morphology and amino acid composition) and functional and mechanical properties in the different layers of the egg case.     

Stress transfer in collagen fibrils reinforcing connective tissues: effects of collagen fibril slenderness and relative stiffness

Unlike engineering fibre composite materials which comprise of fibres that are uniform cylindrical in shape, collagen fibrils reinforcing the proteoglycan-rich (PG) gel in the extra-cellular matrices (ECMs) of connective tissues are taper-ended (paraboloidal in shape). In an earlier paper we have discussed how taper of a fibril leads to an axial stress up-take which differs from that of a uniform cylindrical fibre and implications for fibril fracture. The present paper focuses on the influence of fibre aspect ratio, q (slenderness), and Young's modulus (stiffness), relative to that of the gel phase, E(R), on the magnitude of the axial tensile stresses generated within a fibril and wider implications on failure at tissue level. Fibre composite models were evaluated using finite element (FE) and mathematical analyses. When the applied force is low, there is elastic stress transfer between the PG gel and a fibril. FE modelling shows that the stress in a fibril increases with E(R) and q. At higher applied forces, there is plastic stress transfer. Mathematical modelling predicts that the stress in a fibril increases linearly with q. For small q values, fibrils may be regarded as fillers with little ability to provide tensile reinforcement. Large q values lead to high stress in a fibril. Such high stresses are beneficial provided they do not exceed the fracture stress of collagen. Modulus difference regulates the strain energy release density, u, for interfacial rupture; large E(R) not only leads to high stress in a fibril but also insures against interfacial rupture by raising the value of u.     

Finite element modeling of banded structures in Bombyx mori silk fibres.

Transmission electron microscopy studies have shown curved bands of contrast in degummed Bombyx mori fibres. This contrast implies a molecular difference between the light and dark bands, which in turn implies a periodic variation in mechanical properties along the fibre axis. Finite element modeling was used to compare the mechanical behaviour of fibres with various banded geometries. Lateral, longitudinal and diagonal lamellae were compared with V-shaped and parabolic cupped lamellae. The simulation results from the lamellar models were compared to laminar composite theory. The cupped parabolic and V-shaped geometrics both showed a redistribution of the axial stresses from the centre toward the edge of the fibre. This redistribution allowed for a substantial increase in the toughness compared to simple lateral lamella as well as a moderate increase in the initial modulus without a significant change in the yield strength.     

A finite element model of the human left ventricular systole

Local wall stress is the pivotal determinant of the heart muscle's systolic function. Under in vivo conditions, however, such stresses cannot be measured systematically and quantitatively. In contrast, imaging techniques based on magnetic resonance (MR) allow the determination of the deformation pattern of the left ventricle (LV) in vivo with high accuracy. The question arises to what extent deformation measurements are significant and might provide a possibility for future diagnostic purposes.

The contractile forces cause deformation of LV myocardial tissue in terms of wall thickening, longitudinal shortening, twisting rotation and radial constriction. The myocardium is thereby understood to act as a densely interlaced mesh. Yet, whole cycle image sequences display a distribution of wall strains as function of space and time heralding a significant amount of inhomogeneity even under healthy conditions. We made similar observations previously by direct measurement of local contractile activity. The major reasons for these inhomogeneities derive from regional deviations of the ventricular walls from an ideal spheroidal shape along with marked disparities in focal fibre orientation.

In response to a lack of diagnostic tools able to measure wall stress in clinical routine, this communication is aimed at an analysis and functional interpretation of the deformation pattern of an exemplary human heart at end-systole. To this end, the finite element (FE) method was used to simulate the three-dimensional deformations of the left ventricular myocardium due to contractile fibre forces at end-systole. The anisotropy associated with the fibre structure of the myocardial tissue was included in the form of a fibre orientation vector field which was reconstructed from the measured fibre trajectories in a post mortem human heart. Contraction was modelled by an additive second Piola–Kirchhoff active stress tensor.

As a first conclusion, it became evident that longitudinal fibre forces, cross-fibre forces and shear along with systolic fibre rearrangement have to be taken into account for a useful modelling of systolic deformation. Second, a realistic geometry and fibre architecture lead to typical and substantially inhomogeneous deformation patterns as they are recorded in real hearts. We therefore, expect that the measurement of systolic deformation might provide useful diagnostic information.     

Plywood‐like shell microstructures in hyoliths from the middle Cambrian (Drumian) Gowers Formation,Georgina Basin,Australia

Hyoliths are a group of Palaeozoic fossils with calcareous shells whose affinities remain controversial. As their shells were originally aragonitic, their fossils are usually coarsely recrystallized, and few data on their microstructure are available. We report hyoliths from the middle Cambrian (Drumian, Floran) Gowers Formation of the eastern Georgina Basin, Queensland. These are preserved as phosphatic internal moulds, often with the inner layers of the shell also partly replaced by phosphate. Microstructural details preserved by this early diagenetic phosphatization show that these hyolith conchs were originally composed of fibrous crystallites, c. 0.5 μm wide, parallel to one another and to the inner surface of the shell. In several species, the fibres are arranged in a plywood‐like structure composed of multiple lamellae with a different fibre orientation in each lamella: often they are transversely oriented (relative to the long axis of the conch) in the inner part of the wall and longitudinally oriented in the outer part. Opercula also show a microstructure of parallel fibres. The lamello‐fibrillar microstructure we report from hyoliths is reminiscent of microstructures of many Cambrian molluscs; that this microstructure is found in both conchs and opercula suggests that these structures are serial homologues of one another, and in this respect they resemble brachiopod valves. As with many other biological plywoods, the hyolith shell probably records self‐organization in a liquid‐crystal‐like organic matrix. This provided a straightforward way to construct a material that could resist stresses from different directions, offering an effective defence against predators.     

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.     

A unique cross section through the skin of the dinosaur Psittacosaurus from China showing a complex fibre architecture

This paper reports on a unique preservation of soft tissues in the ventrolateral region of the plant-eating dinosaur Psittacosaurus from the Jehol biota of China. The preservation is of a deep cross section through the dermis, which includes multiple layers of collagenous fibres in excess of 25, among the highest recorded in vertebrates, with a further 15 more layers (poorly preserved) estimated for the entire height of the section. Also, for the first time in a dinosaur two fibre layers parallel to the skin surface are preserved deep within the dermis at the base of the cross section. These fibre layers comprise regularly disposed fibres arranged in left- and right-handed geodesic helices, matching the pattern at the surface and reasonably inferred for the entire section. As noted from the studies on modern-day animals, this fibre structure plays a critical part in the stresses and strains the skin may be subjected to and is ideally suited to providing support and protection. Psittacosaurus gives a remarkable, unprecedented understanding of the dinosaur skin.