Constitutive Laws and Failure Models for Compact Bones Subjected to Dynamic Loading

Many biological tissues, such as bones and ligaments, are fibrous. The geometrical structure of these tissues shows that they exhibit a similar hierarchy in their ultra- and macro-structures. The aim of this work is to develop a model to study the failure of fibrous structures subjected to dynamic loading. The important feature of this model is that it describes failure in terms of the loss of cohesion between fibres. We have developed a model based on the lamellar structure of compact bone with fibres oriented at 0, 45 and 90° to the longitudinal axis of the bone and have studied the influence of the model parameters on the failure process. Bone porosity and joint stress force at failure were found to be the most significant parameters. Using least square resolution, we deduced a phenomenological model of the lamellar structure. Finally, experimental results were found to be comparable with our numerical model.     

The Biomechanical Function of Periodontal Ligament Fibres in Orthodontic Tooth Movement

Orthodontic tooth movement occurs as a result of resorption and formation of the alveolar bone due to an applied load, but the stimulus responsible for triggering orthodontic tooth movement remains the subject of debate. It has been suggested that the periodontal ligament (PDL) plays a key role. However, the mechanical function of the PDL in orthodontic tooth movement is not well understood as most mechanical models of the PDL to date have ignored the fibrous structure of the PDL. In this study we use finite element (FE) analysis to investigate the strains in the alveolar bone due to occlusal and orthodontic loads when PDL is modelled as a fibrous structure as compared to modelling PDL as a layer of solid material. The results show that the tension-only nature of the fibres essentially suspends the tooth in the tooth socket and their inclusion in FE models makes a significant difference to both the magnitude and distribution of strains produced in the surrounding bone. The results indicate that the PDL fibres have a very important role in load transfer between the teeth and alveolar bone and should be considered in FE studies investigating the biomechanics of orthodontic tooth movement.     

The tensile properties and mode of fracture of elastoidin

The tensile properties and mode of fracture of elastoidin, a collagenous protein fibre from the fins of sharks, were compared with those of rat tail tendon fibres, considered to be a pure form of collagen. Elastoidin fibres were stronger than tendon in the dry state whereas the opposite was observed for fibres tested in the wet state. However, elastoidin was stiffer than tendon whether dry or wet. Scanning electron micrographs of the crosssections and fractured surfaces revealed that elastoidin fibres consisted of fibrils of varying diameter arranged in a lamellar fashion. From the nature of the fractured surfaces, it could be deduced that the primary failure mechanism for elastoidin was probably through a fissuring of the structure.     

A study of human root cementum surfaces as prepared for and examined in the scanning electron microscope

Summary The morphology of the cementum surface of human teeth was studied directly by scanning electron microscopy of 50 freeze-dried and 170 anorganic specimens. Extrinsic (Sharpey) fibres were found to occupy almost 100% of the surface in acellular cement, about 40% of the surface in cement with intrinsic fibres but no cells, and 15–40% in cellular cement, and averaged 6 m diameter. Some areas with no extrinsic fibres resembled adult lamellar bone. The mineral front of the intrinsic fibres generally was similar to forming and resting lamellar bone; that of the extrinsic fibres varied according to the activity of the surface, but was normal to the axis of the fibre, even where these entered the surface at a sharp angle. Resorption bays were either small and isolated, often seen in newly erupted teeth; or, more rarely, large and quite deep where excessive force must have occurred.This work has been supported by grants from the Medical Research Council and the Science Research Council.We would like to thank Mr. P. S. Reynolds and Mr. T. Brett for invaluable technical assistance and Mrs. J. Mills for secretarial assistance.     

Study of the stability of long-range-ordered lamellar structures for directed self-assembly lithography,performed using dissipative particle dynamics

We performed dissipative particle dynamics (DPD) simulations to obtain long-range-ordered lamellar structures for directed self-assembly lithography. The self-assembled structure of diblock copolymers (DBCs) depends on the length of the different blocks and the difference in their solubility parameters. In the DPD simulations, the DBCs were formed from coarse-grained particles, and the difference between the solubility parameters was represented by a repulsion parameter. We examined the phase separation morphology of the DBCs, which were confined using a trench model system. The repulsion parameter for the assembly of the lamellar structures from the DBC particles was chosen from six types of parameters. The orientation of the lamellar structure was controlled by the repulsion parameter that described the repulsion between the particles and the wall of the system. We changed the width of the trench, and examined the probability for the formation of the lamellar structure. The lamellar structure could not be obtained by increasing the width. To increase the probability, we placed a ridge at the centre of the bottom wall. It was found that the presence of the ridge increased the probability for the formation of the long-range-ordered lamellar structures.     

Lipoprotein charge and vascular lipid metabolism

The internal lipids were extracted from untreated hair without surface lipids. Liposomes were formed with the internal lipids at different hydration levels to determine the organization of these lipids and the influence of the water content on the lamellar structure of the hair fibres by X-ray Scattering (SAXS). Two structures of hair lipids were observed at 4.5 and approximately 9.0nm with a different behaviour as a function of water content: the largest bilayer being the one that showed a capacity to retain water inside its structure. SAXS was also applied directly to three samples: a packed swatch of hair fibres at 60% RH, fibres soaked in water and delipidized fibres. Only the lamella at 9.0nm was slightly affected by water content. Moreover, there was a small diminution in intensity probably due to a high permeability of wet fibres which could give rise to a disorder of the lipid structure. These two lamellar rearrangements are probably made up of lipids with a different and specific hydrophilic/hydrophobic balance.     

The biomaterial influences the ossification after sinus floor elevation using tissue-engineered bone grafts

Sinus floor elevation is the standard procedure that allows dental implant insertion in the atrophic posterior maxilla. Instead of autogenous bone, tissue-engineered bone grafts can be used, but clear comparative clinical studies also assessing the influence of the biomaterial are missing. In six patients, tissue-engineered bone grafts were used in eight sinus floor elevations. After culturing osteoblast-like cells from biopsies of the maxilla, they were seeded on scaffolds made either from demineralised bovine bone matrix (DBBM) or from solvent-dehydrated mineralised bone (SDBB), and grafted. In all patients primary wound healing was without complications, except for one patient in the SDBB group. After 12 months, implant insertion was possible only in the SDBB group; in the DBBM group, fibrous connective tissue was found in an attempt of implant insertion. After 5 months, implant placement was performed in one patient of each group. However, the two implants inserted in the DBBM group were lost after 6 weeks. Histology of the bone cores in the DBBM group at 5 months showed lamellar bone and osteoid, and at 12 months showed fibrous connective tissue. Inflammation and some resorption of the scaffold was found 5 months after SDBB grafting, and after 12 months cancellous bone formation encapsulating SDBB remnants were observed. These preliminary data suggest that the preparation method of the bovine bone matrix, in particular the mineral content, and therefore the mechanical stability may have some influence on the generation of new bone.     

Calcitonin gene-related peptide,substance P and GAP-43/B-50 immunoreactivity in the normal and arthrotic knee joint of the mouse

The aim of this study was to describe the normal distribution of calcitonin gene-related peptide (CGRP) and substance P (SP) containing fibres in the knee joint of the mouse and to obtain insight into the changes in innervation associated with degenerative processes in the joint. Arthrosis was induced by a single subpatellar intra-articular injection of bacterial collagenase. After decalcification in EDTA solutions, the CGRP and SP fibres were visualized by peroxidase-antiperoxidase pre-embedding immunocytochemistry for light microscopy. Control experiments on the mouse brain as a reference for the effect of EDTA on the immunostaining showed that the decalcification procedure with EDTA had not impaired the immunostaining. A rich innervation of thin varicose CGRP and SP immunoreactive fibres was found in most peri- and intra-articular tissue components. The periosteum, synovial tissues, the joint capsule and the intra-articular fat tissues were richly innervated. Less intense innervations were also found in the subchondral bone plates of the tibio-femoral joint and of the patella. Fibres were also found in the soft tissues between the patellar tendon and the femoral groove. No differences could be found between the location of CGRP and SP fibres with respect to the localization in the joint, but generally more CGRP fibres were found. The collagenase-induced osteoarthrosis was characterized by sclerosis of the subchondral bone, patellar dislocation, osteophyte formation, synovial proliferation and by severe cartilage abrasion, particularly on the medial side of the femoro-tibial joint. The overall distribution of CGRP and SP fibres was the same as in the control joints. However, major differences were found in all studied joints at specific locations around the cruciate ligaments, in the synovium around the patella, in the soft tissues lateral of the patella and in plica tissue between the patella and femoral groove. The CGRP and SP innervation was no longer detectable by immunolabelling with the antibodies. With a polyclonal antibody to the growth associated protein GAP-43/B-50, signs of degenerated axonal profiles were observed in these locations. At other peripheral locations, such as the muscles, the GAP-43/B-50 distribution was normal. In conclusion, the present study provides detailed information on the localization of CGRP and SP fibres, which may be involved in pain perception. Knowledge of the changes that occur during arthrosis may give more insight into the clinical symptoms.     

Calcitonin gene-related peptide, substance P and GAP-43/B-50 immunoreactivity in the normal and arthrotic knee joint of the mouse.

The aim of this study was to describe the normal distribution of calcitonin gene-related peptide (CGRP) and substance P (SP) containing fibres in the knee joint of the mouse and to obtain insight into the changes in innervation associated with degenerative processes in the joint. Arthrosis was induced by a single subpatellar intra-articular injection of bacterial collagenase. After decalcification in EDTA solutions, the CGRP and SP fibres were visualized by peroxidase-antiperoxidase pre-embedding immunocytochemistry for light microscopy. Control experiments on the mouse brain as a reference for the effect of EDTA on the immunostaining showed that the decalcification procedure with EDTA had not impaired the immunostaining. A rich innervation of thin varicose CGRP and SP immunoreactive fibres was found in most peri- and intra-articular tissue components. The periosteum, synovial tissues, the joint capsule and the intra-articular fat tissues were richly innervated. Less intense innervations were also found in the subchondral bone plates of the tibio-femoral joint and of the patella. Fibres were also found in the soft tissues between the patellar tendon and the femoral groove. No differences could be found between the location of CGRP and SP fibres with respect to the localization in the joint, but generally more CGRP fibres were found. The collagenase-induced osteoarthrosis was characterized by sclerosis of the subchondral bone, patellar dislocation, osteophyte formation, synovial proliferation and by severe cartilage abrasion, particularly on the medial side of the femoro-tibial joint. The overall distribution of CGRP and SP fibres was the same as in the control joints. However, major differences were found in all studied joints at specific locations around the cruciate ligaments, in the synovium around the patella, in the soft tissues lateral of the patella and in plica tissue between the patella and femoral groove. The CGRP and SP innervation was no longer detectable by immunolabelling with the antibodies. With a polyclonal antibody to the growth associated protein GAP-43/B-50, signs of degenerated axonal profiles were observed in these locations. At other peripheral locations, such as the muscles, the GAP-43/B-50 distribution was normal. In conclusion, the present study provides detailed information on the localization of CGRP and SP fibres, which may be involved in pain perception. Knowledge of the changes that occur during arthrosis may give more insight into the clinical symptoms.     

Lamellar bone: structure-function relations.

The term "bone" refers to a family of materials that have complex hierarchically organized structures. These structures are primarily adapted to the variety of mechanical functions that bone fulfills. Here we review the structure-mechanical relations of one bone structural type, lamellar bone. This is the most abundant type in many mammals, including humans. A lamellar unit is composed of five sublayers. Each sublayer is an array of aligned mineralized collagen fibrils. The orientations of these arrays differ in each sublayer with respect to both collagen fibril axes and crystal layers, such that a complex rotated plywood-like structure is formed. Specific functions for lamellar bone, as opposed to the other bone types, could not be identified. It is therefore proposed that the lamellar structure is multifunctional-the "concrete" of the bone family of materials. Experimentally measured mechanical properties of lamellar bone demonstrate a clear-cut anisotropy with respect to the axis direction of long bones. A comparison of the elastic and ultimate properties of parallel arrays of lamellar units formed in primary bone with cylindrically shaped osteonal structures in secondary formed bone shows that most of the intrinsic mechanical properties are built into the lamellar structure. The major advantages of osteonal bone are its fracture properties. Mathematical modeling of the elastic properties based on the lamellar structure and using a rule-of-mixtures approach can closely simulate the measured mechanical properties, providing greater insight into the structure-mechanical relations of lamellar bone.     

Engineering of pre‐vascularized urethral patch with muscle flaps and hypoxia‐activated hUCMSCs improves its therapeutic outcome

Tissue engineering has brought new hopes for urethral reconstruction. However, the absence of pre‐vascularization and the subsequent degradation of materials often lead to the failure of in vivo application. In this study, with the assistance of hypoxia‐activated human umbilical cord mesenchymal stem cells (hUCMSCs), pedicled muscle flaps were used as materials and pre‐incubated in ventral penile subcutaneous cavity of rabbit for 3 weeks to prepare a pre‐vascularized urethral construct. We found that small vessels and muscle fibres were scattered in the construct after 3 weeks' pre‐incubation. The construct presented a fibrous reticular structure, which was similar to that of the corpus spongiosum under microscope examination. The produced constructs were then used as a patch graft for reconstruction of the defective rabbit urethra (experimental group), natural muscular patch was used as control (control group). Twelve weeks after the reconstructive surgery, urethrography and urethroscope inspections showed wide calibres of the reconstructed urethra in the experimental group. Histopathological studies revealed that fibrous connective tissues and abundant muscle fibres constituted the main body of the patch‐grafted urethra. In contrast, in the control group, only adipose tissue was found in the stenosis‐reconstructed urethra, replacing the originally grafted muscular tissue. To our knowledge, this is the first report that successfully constructed a pre‐vascularized urethral construct by using hypoxia‐activated hUCMSC and pedicled muscle flaps. More importantly, the pre‐vascularized construct showed a good performance in urethral reconstruction when applied in vivo. The study provided a novel strategy for tissue engineering of pre‐vascularized urethral construct for the defective urethra, representing a further advancement in urethral reconstruction.     

Micro-computed tomography with iodine staining resolves the arrangement of muscle fibres

We illustrate here microCT images in which contrast between muscle and connective tissue has been achieved by means of staining with iodine. Enhancement is shown to be dependent on the concentration of iodine solution (I₂KI), time in solution and specimen size. Histological examination confirms that the arrangement of individual muscle fibres can be visualised on the enhanced microCT images, and that the iodine accumulates in the muscle fibres in preference to the surrounding connective tissues. We explore the application of this technique to describe the fibrous structure of skeletal muscle, and conclude that it has the potential to become a non-destructive and cost-effective method for investigating muscle fascicle architecture, particularly in comparative morphological studies.     

Lamellar Bone: Structure–Function Relations

The term “bone” refers to a family of materials that have complex hierarchically organized structures. These structures are primarily adapted to the variety of mechanical functions that bone fulfills. Here we review the structure–mechanical relations of one bone structural type, lamellar bone. This is the most abundant type in many mammals, including humans. A lamellar unit is composed of five sublayers. Each sublayer is an array of aligned mineralized collagen fibrils. The orientations of these arrays differ in each sublayer with respect to both collagen fibril axes and crystal layers, such that a complex rotated plywood-like structure is formed. Specific functions for lamellar bone, as opposed to the other bone types, could not be identified. It is therefore proposed that the lamellar structure is multifunctional—the “concrete” of the bone family of materials. Experimentally measured mechanical properties of lamellar bone demonstrate a clear-cut anisotropy with respect to the axis direction of long bones. A comparison of the elastic and ultimate properties of parallel arrays of lamellar units formed in primary bone with cylindrically shaped osteonal structures in secondary formed bone shows that most of the intrinsic mechanical properties are built into the lamellar structure. The major advantages of osteonal bone are its fracture properties. Mathematical modeling of the elastic properties based on the lamellar structure and using a rule-of-mixtures approach can closely simulate the measured mechanical properties, providing greater insight into the structure–mechanical relations of lamellar bone.     

A first estimation of prestress in so-called circularly fibered osteonic lamellae.

The existence and role of prestress in the various hierarchical structures of long bone are long standing questions. In this study, the prestress and associated strain that exist in a component of human bone microstructure, circularly fibered osteonic lamella, are estimated. Such estimates allow the formulation of hypotheses on prestress formation and lamellar stiffness. Dimensional measurements were obtained for eight fully calcified lamellae. These dimensions, before isolation from the surrounding alternate osteon and after strain relief by isolation and axial sectioning, furnish data upon which a geometric lamellar model is constructed. A material model is based on the most likely hypothesis as to lamellar structure. This geometric-material model allows estimation of the preexisting strain. The largest strains occur in shear circumferential-axial and normal axial strain directions, averaging 0.08 and 0.05, respectively. The geometric-material model expresses prestress in terms of as yet unknown elastic moduli. The average prestress magnitude is the largest in shear circumferential-axial direction, compensating for alternate osteon weakness in this direction. The estimated axial prestress confirms long hypothesized alternate osteon precompression, which impedes fractures of areas of collagen bundles transverse to the osteon axis at low stresses. The results of the model support the formulation of the following biological hypotheses: (a) lamellar prestress occurs at a supra-molecular level, namely through collagen bundles which are themselves likely to be prestressed; (b) collagen bundles oblique to the lamellar axis are responsible for shear prestress; (c) prestress ranges up to 0.11 GPa; and (d) the lamella is less stiff than alternate osteon.     

An enamel-like tissue,osteodermine, on the osteoderms of a fossil anguid (Glyptosaurinae) lizard

The Glyptosaurinae, a fossil clade of anguid lizards, have robust osteoderms, with a granular ornamentation consisting of tubercles. In this study, the structural and histological features of these osteoderms are described in order to reconstruct their developmental pattern and further document the possible homology that could exist between vertebrate integumentary skeletons. Glyptosaurine osteoderms display a diploe architecture and an unusually complex structure that includes four tissue types: an intensely remodeled core of woven-fibered bone, a thick basal layer of lamellar bone, a peripheral ring exhibiting histological features intermediate between these two tissues and containing dense bundles of long Sharpey fibers, and a superficial layer made of a monorefringent, acellular and highly mineralized material, different from bone, and comparable in many respects to hypermineralized tissues such as ganoine, enameloids and enamel. We call this tissue osteodermine. The growth pattern of glyptosaurine osteoderms is likely to have involved first metaplasia, at an early developmental stage, then appositional growth due to osteoblast activity. The superficial layer that is well developed at the tubercle level must have resulted from epidermal and dermal contributions, a conclusion that would support previous hypotheses on the role of epidermal-dermal interactions in the formation of squamate osteoderms.     

Experimental evaluation of ceramic calcium phosphate as a substitute for bone grafts.

Tricalcium phosphate (Synthos) is a bioceramic material which can be carved with a scalpel and wired into place as a bone graft would be. The process of bone replacement of the prosthesis begins with an ingrowth of cellular loose connective tissue, which is replaced later by dense connective tissue. Around the periphery of this dense fibrous connective tissue, osteoid tissue becomes evident and on later specimens this mixture seems to be converted to bone--which at first is in the form of spicules but later takes on the characteristics of lamellar bone (with tricalcium phosphate particles seen within its lacunae). The progressive replacement occurs in a circumferential pattern, but most heavily at the bone-prosthesis interface. Although the periosteum is beneficial, we do not feel that the major source of bone formation is as the soft tissue or subperiosteal area. The replacement of the tricalcium phosphate prosthesis is slower than we originally thought, or than reported by others. We have noted pockets of tricalcium phosphate, incompletely replaced, in dogs up to 18 months after implantation. We believe this may be related to the larger sized prostheses we used (2 x 2 cm blocks) with, therefore, longer distances that the ingrowth and calcification had to traverse.     

A micromechanical model to predict damage and failure in biological tissues. Application to the ligament-to-bone attachment in the human knee joint

Computational models are developed in injury biomechanics to assess lesions in biological tissues based on mechanical measurements. The linear mechanics of fracture theory (LMFT) is a common approach to establish injuries based on thresholds (such as force or strain thresholds) which are straightforward to implement and computationally efficient. However, LMFT does not apply to non-linear heterogeneous materials and does not have the ability to predict failure onset. This paper proposes the cohesive zone model theory (CZMT) as an alternative. CZMT focuses on the development of behaviour laws for crack initiation and propagation at an interface that apply within a fibrous material or at the interface between materials. With the view of evaluating CZMT for biological tissues, the model developed by Raous et al. [1999. A consistent model coupling adhesion, friction and unilateral contact. Comput. Methods Appl. Mech. Eng., 177, 383–399] was applied to the ligament-to-bone interface in the human knee joint. This model accounts for adhesion, friction and damage at the interface and provides a smooth transition from total adhesion to complete failure through the intensity of adhesion variable. A 2D finite element model was developed to mimic previous experiments, and the model parameters were determined using a dichotomy method. The model showed good results by its ability to predict damage. The extension to a 3D geometry, with an inverse problem approach, is, however, required to better estimate the model parameters values. Although it is computationally costly, CZMT supplements the improvements achieved in microimaging techniques to support the development of micro/macro approaches in biomechanical modelling.