Collagen Fibres Orientation in the Bone Matrix around Dental Implants: Does the Implant's Thread Design Play a Role?

The aim of this study was to analyse the influence of different thread shapes of titanium dental implant on the bone collagen fibre orientation (BCFO) around loaded implants. Twenty titanium dental implants, divided for thread shapes in six groups (A-F) were analysed in the present study. All implants were immediately loaded and left in function for 6 months before retrieval. The parameters evaluated under scanning electron microscope were the thread width, thread depth, top radius of curvature, flank angle, and the inter-thread straight section. Two undecalcified histological sections were prepared from each implant. Birefringence analysis using circularly polarized light microscopy was used to quantitively measure BCFO. For groups A-F, respectively, transverse BCFO was 32.7%, 24.1%, 22.3%, 18.2%, 32.4%, and 21.2%, longitudinal BCFO was 28.2%, 14.5%, 44.9%, 33.1%, 37.7%, and 40.2%. The percentage differences between transverse and longitudinal orientation were 4.50% (A), 9.60% (B), -22.60% (C), -14.90% (D), -5.30% (E), and -19.00% (F). Following loading, the amount of transverse and longitudinal BCFO were significantly influenced by the thread shape. The greater flank angles and narrower inter-thread sections of the "V" shaped and "concave" shaped implant threads of groups A and B, respectively, promoted the predominance of transverse BCFO, compared to groups C-F (p < 0.05). A narrow inter-thread straight section promotes transverse BCFO, as do "V" shaped and "concave" shaped threads, which can thus be considered desirable design for implant threads.

Tensile Viscoelastic Properties of the Sclera after Glycosaminoglycan Depletion.

PURPOSE: Fibrillar collagen network and glycosaminoglycans (GAGs) are the primary components of extracellular matrix (ECM) of the sclera. The main goal of this study was to investigate the possible structural roles of GAGs in the scleral tensile properties as a function of preconditioning and displacement rate. METHODS: Four-step uniaxial stress-relaxation tests were used for characterizing the viscoelastic tensile response of the posterior porcine sclera with and without enzymatic GAG removal. The scleral strips were divided into different groups based on the displacement rate and the presence or absence of a preconditioning step in the loading protocol. The groups were (1) displacement rate of 0.2 mm/min without preconditioning, (2) displacement rate of 1 mm/min without preconditioning, (3) displacement rate of 0.2 mm/min with preconditioning, and (4) displacement rate of 1 mm/min with preconditioning. The peak stress, equilibrium stress, and the equilibrium elastic modulus were calculated for all specimens and compared against each other. RESULTS: Increasing the displacement rate from 0.2 mm/min to 1.0 mm/min was found to cause an insignificant change in the equilibrium stress and equilibrium elastic modulus of porcine scleral strips. Removal of GAGs resulted in an overall stiffer tensile behavior independent of the displacement rate in samples that were not preconditioned (P < .05). The behavior of preconditioned samples with and without GAG removal was not significantly different from each other. CONCLUSIONS: The experimental measurements of the present study showed that GAGs play an important role in the mechanical properties of the posterior porcine sclera. Furthermore, using a preconditioning step in the uniaxial testing protocol resulted in not being able to identify any significant difference in the tensile behavior of GAG depleted and normal scleral strips.

Nanoscale mechanisms in age-related hip-fractures.

Nanoscale mineralized collagen fibrils may be important determinants of whole-bone mechanical properties and contribute to the risk of age-related fractures. In a cross-sectional study nano- and tissue-level mechanics were compared across trabecular sections from the proximal femora of three groups (n = 10 each): ageing non-fractured donors (Controls); untreated fracture patients (Fx-Untreated); bisphosphonate-treated fracture patients (Fx-BisTreated). Collagen fibril, mineral and tissue mechanics were measured using synchrotron X-Ray diffraction of bone sections under load. Mechanical data were compared across groups, and tissue-level data were regressed against nano. Compared to controls fracture patients exhibited significantly lower critical tissue strain, max strain and normalized strength, with lower peak fibril and mineral strain. Bisphosphonate-treated exhibited the lowest properties. In all three groups, peak mineral strain coincided with maximum tissue strength (i.e. ultimate stress), whilst peak fibril strain occurred afterwards (i.e. higher tissue strain). Tissue strain and strength were positively and strongly correlated with peak fibril and mineral strains. Age-related fractures were associated with lower peak fibril and mineral strain irrespective of treatment. Indicating earlier mineral disengagement and the subsequent onset of fibril sliding is one of the key mechanisms leading to fracture. Treatments for fragility should target collagen-mineral interactions to restore nano-scale strain to that of healthy bone.

The architecture and spatial organization of the living human body as revealed by intratissular endoscopy - An osteopathic perspective.

This article presents an overview of research conducted by Dr Jean-Claude Guimberteau into the architecture and spatial organization of living matter and the relationship between the cells and the extracellular matrix. His research is discussed in the context of previous and current research into fascial anatomy. Andrew Taylor Still, the founder of Osteopathy, did not have access to modern research and yet his observations are proving to be surprisingly accurate in the light of recent findings. This article sets out to highlight the relevance of his insights from a purely anatomical perspective, and to draw parallels with a new way of thinking about the architecture of the living human body that is slowly emerging. Dr Guimberteau's research shows that a force applied to the surface of the skin is transmitted deep into living tissue via a continuous bodywide multifibrillar network. It also confirms the concept of the body as a dynamic functional unit, as proposed by A.T. Still. Still also proposed that structure and function are interrelated at all levels within the living human body. There is a growing body of research to support this. Intratissular endoscopy has highlighted the importance of the quality of the mobility and adaptability of the network of collagen and elastin fibers that structures the ECM in healthy living tissue. Factors such as abnormal stiffness of collagen fibers in the ECM are thought to have adverse effects on local tissue health.

Mapping the Young's modulus distribution of the human tympanic membrane by microindentation.

The human tympanic membrane (TM, or eardrum) is composed primarily of layers of collagen fibers oriented in the radial and circumferential directions, as well as epidermal and mucosal layers at the lateral and medial surfaces. The mechanical properties of the TM depend on the microstructures of the collagen fibers, which vary with location, resulting in a spatial variation of Young's modulus. In this study, the Young's modulus of the human TM is measured using microindentation. A 10 µm diameter spherical nanoindenter tip is used to indent the TM at different locations in the lateral and medial surfaces. Through a viscoelastic contact analysis, the steady state out-of-plane (through thickness) Young's modulus at a constant strain rate for the TM is determined from the uniaxial relaxation modulus. The measured spatial distribution of Young's modulus is reported for the entire TM pars tensa on both lateral and medial surfaces. The Young's modulus, for the four TM quadrants, is analyzed statistically using a normal quantile-quantile (Q-Q) plot. The obtained S-shaped curve indicates a bi-modal Gaussian distribution in the Q-Q plot. The spatial distribution of the Young's modulus is modeled by a bivariate Gaussian function in the polar coordinates over the entire TM on both the lateral and medial surfaces. It is shown that the anterior-superior quadrant has the smallest value of Young's modulus. Differences are observed in the spatial distribution of the Young's modulus for both the lateral and medial surfaces. For the medial surface, Young's modulus varies mainly along the radial direction following a small-large-small trend, emanating from the umbo. For the lateral surface, the modulus at the anterior-superior quadrant shows the smallest modulus; the modulus decreases gradually along the radial directions. The quantitative results presented in this paper will help improve future simulation models of the middle ear by using spatial dependence of Young's modulus over the entire TM.

The "central vein sign" in inflammatory demyelination: The role of fibrillar collagen type I.

Accumulating evidence corroborates the role of the "central vein sign" in the radiological diagnosis of multiple sclerosis (MS). Here, we report human magnetic resonance imaging (MRI) and corresponding pathological data that inflammation-dependent intracerebral remodeling of the vessel wall is directly associated with the prominence of intralesional veins on susceptibility-based MRI. In adult marmosets with experimental autoimmune encephalomyelitis, vessel-wall fibrosis was detected early in the demyelinating process, even in lesions <2 weeks old, though fibrosis was more evident after 6 weeks. Vascular remodeling consisted of both luminal enlargement and eccentric thickening of the perivascular space (fibrillar collagen type I deposition) and affected almost exclusively white matter, but not subpial cortical, lesions. The long-term effect of vessel remodeling in MS lesions is currently unknown, but it might potentially affect tissue repair. ANN NEUROL 2019;85:934-942.

Direct and inverse identification of constitutive parameters from the structure of soft tissues. Part 2: dispersed arrangement of collagen fibers.

This paper investigates on the relationship between the arrangement of collagen fibers within soft tissues and parameters of constitutive models. Starting from numerical experiments based on biaxial loading conditions, the study addresses both the direct (from structure to mechanics) and the inverse (from mechanics to structure) problems, solved introducing optimization problems for model calibration and regression analysis. A campaign of parametric analyses is conducted in order to consider fibers distributions with different main orientation and angular dispersion. Different anisotropic constitutive models are employed, accounting for fibers dispersion either with a generalized structural approach or with an increasing number of strain energy terms. Benchmark data sets, toward which constitutive models are fitted, are built by employing a multiscale description of fiber nonlinearities and accounting for fibers dispersion with an angular integration method. Results show how the optimal values of constitutive parameters obtained from model calibration vary as a function of fibers arrangement and testing protocol. Moreover, the fitting capabilities of constitutive models are discussed. A novel strategy for model calibration is also proposed, in order to obtain a robust accuracy with respect to different loading conditions starting from a low number of mechanical tests. Furthermore, novel results useful for the inverse determination of the mean angle and the variance of fibers distribution are obtained. Therefore, the study contributes: to better design procedures for model calibration; to account for mechanical alterations due to remodeling mechanisms; and to gain structural information in a nondestructive way.

Nano and micro biomechanical alterations of annulus fibrosus after in situ immobilization revealed by atomic force microscopy.

Annulus fibrosus is critical to bear loads and resist fluid flow in the intervertebral disc. However, the detailed biomechanical mechanism of annulus fibrosus under abnormal loading is still ambiguous, especially at the micro and nano scales. This study aims to characterize the alterations of modulus at the nano scale of individual collagen fibrils in annulus fibrosus after in-situ immobilization, and the corresponding micro-biomechanics of annulus fibrosus. An immobilization model was used on the rat tail with an external fixation device. The elastic modulus of annulus fibrosus at both the nano- and micro-scale was examined using atomic force microscopy after fixation for 4 and 8 weeks, respectively. The fibrils in inner layer showed an alteration in elastic modulus from 91.38 ± 20.19 MPa in the intact annulus fibrosus to 110.64 ± 15.58 MPa (p < 0.001) at the nano scale after immobilization for 8 weeks, while the corresponding modulus at the micro scale also underwent a change from 0.33 ± 0.04 MPa to 0.47 ± 0.04 MPa (p < 0.001). The fibril disorder after immobilization was observed by hematoxylin/eosin staining. The gene expression of annulus fibrosus was also measured by real-time reverse transcription-polymerase chain reaction, which showed the upregulation of collagen II (p = 0.003) after immobilization. The results indicated that the immobilization not only influenced the individual fibril at the nanoscale, but also the micro-biomechanical property of annulus fibrosus which is critical to define the cell response to surrounding biomechanical environment. These alterations may also lead to the change in the mechanical property of the whole disc and the load-bearing function. © 2018 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 9999:1-7, 2018.

Proline provides site-specific flexibility for in vivo collagen.

Fibrillar collagens have mechanical and biological roles, providing tissues with both tensile strength and cell binding sites which allow molecular interactions with cell-surface receptors such as integrins. A key question is: how do collagens allow tissue flexibility whilst maintaining well-defined ligand binding sites? Here we show that proline residues in collagen glycine-proline-hydroxyproline (Gly-Pro-Hyp) triplets provide local conformational flexibility, which in turn confers well-defined, low energy molecular compression-extension and bending, by employing two-dimensional 13C-13C correlation NMR spectroscopy on 13C-labelled intact ex vivo bone and in vitro osteoblast extracellular matrix. We also find that the positions of Gly-Pro-Hyp triplets are highly conserved between animal species, and are spatially clustered in the currently-accepted model of molecular ordering in collagen type I fibrils. We propose that the Gly-Pro-Hyp triplets in fibrillar collagens provide fibril "expansion joints" to maintain molecular ordering within the fibril, thereby preserving the structural integrity of ligand binding sites.

Collagen Fibril Assembly and Function.

Collagen fibrils are the major mechanical component in the extracellular matrix of a broad range of multicellular animals from echinoderms to vertebrates where they provide a stable framework for tissues. They form the key tension-resisting element of a complex fiber-composite system that has a tissue-specific hierarchical structure linked to mechanical demands. Remarkably, these tissues are self-maintaining and avoid fatigue failure over the lifetime of the animal. Collagen fibrils can assemble spontaneously from purified solutions of collagen molecules. In developing tissues, however, in addition to the intrinsic self-assembly properties, there is cellular machinery that regulates fibril nucleation, spatial orientation, and fibril size, according to the tissue and stage of development. The intricate mechanisms underlying the generation of a collagen fibril network of defined architecture and mechanical properties are now becoming apparent. Impairment of this system leads ultimately to mechanical failure or tissue fibrosis.

Impacts of maturation on the micromechanics of the meniscus extracellular matrix.

To elucidate how maturation impacts the structure and mechanics of meniscus extracellular matrix (ECM) at the length scale of collagen fibrils and fibers, we tested the micromechanical properties of fetal and adult bovine menisci via atomic force microscopy (AFM)-nanoindentation. For circumferential fibers, we detected significant increase in the effective indentation modulus, Eind, with age. Such impact is in agreement with the increase in collagen fibril diameter and alignment during maturation, and is more pronounced in the outer zone, where collagen fibrils are more aligned and packed. Meanwhile, maturation also markedly increases the Eind of radial tie fibers, but not those of intact surface or superficial layer. These results provide new insights into the effect of maturation on the assembly of meniscus ECM, and enable the design of new meniscus repair strategies by modulating local ECM structure and mechanical behaviors.

Severe disruption and disorganization of dermal collagen fibrils in early striae gravidarum.

BACKGROUND: Striae gravidarum (SG), or stretch marks of pregnancy, begin as erythematous streaks and mature into hypopigmented atrophic bands. OBJECTIVES: In order to investigate molecular alterations that may promote atrophy of SG, we investigated dermal type I collagen fibrils, which provide human skin with support. METHODS: We obtained skin samples of recently developed, erythematous abdominal SG from pregnant women. To examine the organization of collagen fibrils, second-harmonic generation imaging was performed using multiphoton microscopy. Immunostaining was used to determine protein expression and localization of type I procollagen, the precursor of type I collagen fibrils. Real-time polymerase chain reaction was used to determine gene expression levels. RESULTS: In control (hip) and stretched normal-appearing perilesional abdominal skin, dermal collagen fibrils were organized as tightly packed, interwoven bundles. In SG, collagen bundles appeared markedly separated, especially in the mid-to-deep dermis. In the spaces separating these bundles, loosely packed wavy collagen fibrils lacking organization as bundles were present. These disorganized fibrils persisted into the postpartum period and failed to form densely packed bundles. Numerous large fibroblasts displaying type I procollagen expression were in close proximity to the disorganized fibrils, suggesting that the fibrils are newly synthesized. Supporting this possibility, immunostaining and gene expression of type I procollagen were increased throughout the dermis of SG. CONCLUSIONS: Early SG display marked separation of collagen bundles and emergence of disorganized collagen fibrils that fail to form bundles. These alterations may reflect ineffective repair of collagen bundles disrupted by intense skin stretching. Persistent disruption of the collagenous extracellular matrix likely promotes formation and atrophy of SG.

Collagen organization regulates stretch-initiated pain-related neuronal signals in vitro: Implications for structure-function relationships in innervated ligaments.

Injury to the spinal facet capsule, an innervated ligament with heterogeneous collagen organization, produces pain. Although mechanical facet joint trauma activates embedded afferents, it is unclear if, and how, the varied extracellular microstructure of its ligament affects sensory transduction for pain from mechanical inputs. To investigate the effects of macroscopic deformations on afferents in collagen matrices with different organizations, an in vitro neuron-collagen construct (NCC) model was used. NCCs with either randomly organized or parallel aligned collagen fibers were used to mimic the varied microstructure in the facet capsular ligament. Embryonic rat dorsal root ganglia (DRG) were encapsulated in the NCCs; axonal outgrowth was uniform and in all directions in random NCCs, but parallel in aligned NCCs. NCCs underwent uniaxial stretch (0.25 ± 0.06 strain) corresponding to sub-failure facet capsule strains that induce pain. Macroscopic NCC mechanics were measured and axonal expression of phosphorylated extracellular signal-regulated kinase (pERK) and the neurotransmitter substance P (SP) was assayed at 1 day to assess neuronal activation and nociception. Stretch significantly upregulated pERK expression in both random and aligned gels (p < 0.001), with the increase in pERK being significantly higher (p = 0.013) in aligned than in random NCCs. That increase likely relates to the higher peak force (p = 0.025) and stronger axon alignment (p < 0.001) with stretch direction in the aligned NCCs. In contrast, SP expression was greater in stretched NCCs (p < 0.001) regardless of collagen organization. These findings suggest that collagen organization differentially modulates pain-related neuronal signaling and support structural heterogeneity of ligament tissue as mediating sensory function. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:770-777, 2018.

Biomechanical properties of murine TMJ articular disc and condyle cartilage via AFM-nanoindentation.

This study aims to quantify the biomechanical properties of murine temporomandibular joint (TMJ) articular disc and condyle cartilage using AFM-nanoindentation. For skeletally mature, 3-month old mice, the surface of condyle cartilage was found to be significantly stiffer (306±84kPa, mean±95% CI) than those of the superior (85±23kPa) and inferior (45±12kPa) sides of the articular disc. On the disc surface, significant heterogeneity was also detected across multiple anatomical sites, with the posterior end being the stiffest and central region being the softest. Using SEM, this study also found that the surfaces of disc are composed of anteroposteriorly oriented collagen fibers, which are sporadically covered by thinner random fibrils. Such fibrous nature results in both an F-D3/2 indentation response, which is a typical Hertzian response for soft continuum tissue under a spherical tip, and a linear F-D response, which is typical for fibrous tissues, further signifying the high degree of tissue heterogeneity. In comparison, the surface of condyle cartilage is dominated by thinner, randomly oriented collagen fibrils, leading to Hertzian-dominated indentation responses. As the first biomechanical study of murine TMJ, this work will provide a basis for future investigations of TMJ tissue development and osteoarthritis in various murine TMJ models.

The binding capacity of α1ß1-, α2ß1- and α10ß1-integrins depends on non-collagenous surface macromolecules rather than the collagens in cartilage fibrils.

Interactions of cells with supramolecular aggregates of the extracellular matrix (ECM) are mediated, in part, by cell surface receptors of the integrin family. These are important molecular components of cell surface-suprastructures regulating cellular activities in general. A subfamily of ß1-integrins with von Willebrand-factor A-like domains (I-domains) in their α-chains can bind to collagen molecules and, therefore, are considered as important cellular mechano-receptors. Here we show that chondrocytes strongly bind to cartilage collagens in the form of individual triple helical molecules but very weakly to fibrils formed by the same molecules. We also find that chondrocyte integrins α1ß1-, α2ß1- and α10ß1-integrins and their I-domains have the same characteristics. Nevertheless we find integrin binding to mechanically generated cartilage fibril fragments, which also comprise peripheral non-collagenous material. We conclude that cell adhesion results from binding of integrin-containing adhesion suprastructures to the non-collagenous fibril periphery but not to the collagenous fibril cores. The biological importance of the well-investigated recognition of collagen molecules by integrins is unknown. Possible scenarios may include fibrillogenesis, fibril degradation and/or phagocytosis, recruitment of cells to remodeling sites, or molecular signaling across cytoplasmic membranes. In these circumstances, collagen molecules may lack a fibrillar organization. However, other processes requiring robust biomechanical functions, such as fibril organization in tissues, cell division, adhesion, or migration, do not involve direct integrin-collagen interactions.

Organization of the dermal matrix impacts the biomechanical properties of skin.

BACKGROUND: Human skin has the crucial roles of maintaining homeostasis and protecting against the external environment. Skin offers protection against mechanical trauma due to the reversible deformation of its structure; these biomechanical properties are amenable to dynamic testing using noninvasive devices. OBJECTIVES: To characterize the biomechanical properties of young, black African/African-Caribbean and white Northern European skin from different anatomical sites, and to relate underlying skin architecture to biomechanical function. METHODS: Using cutometry and ballistometry, the biomechanical properties of buttock and dorsal forearm skin were determined in black African/African-Caribbean (n = 18) and white Northern European (n = 20) individuals aged 18-30 years. Skin biopsies were obtained from a subset of the volunteers (black African/African-Caribbean, n = 5; white Northern European, n = 6) and processed for histological and immunohistochemical detection of the major elastic fibre components and fibrillar collagens. RESULTS: We have determined that healthy skin from young African and white Northern European individuals has similar biomechanical properties (F3): the skin is resilient (capable of returning to its original position following deformation, R1), exhibits minimal fatigue (R4) and is highly elastic (R2, R5 and R7). At the histological level, skin with these biomechanical properties is imbued with strong interdigitation of the rete ridges at the dermoepidermal junction (DEJ) and candelabra-like arrays of elastic fibres throughout the papillary dermis. Dramatic disruption to this highly organized arrangement of elastic fibres, effacement of the rete ridges and alterations to the alignment of the fibrillar collagens is apparent in the white Northern European forearm and coincides with a marked decline in biomechanical function. CONCLUSIONS: Maintenance of skin architecture - both epidermal morphology and elastic fibre arrangement - is essential for optimal skin biomechanical properties. Disruption to underlying skin architecture, as observed in the young white Northern European forearm, compromises biomechanical function.

Mechanical Characteristics of Bovine Glisson's Capsule as a Model Tissue for Soft Collagenous Membranes.

An extensive multiaxial experimental campaign on the monotonic, time- and history-dependent mechanical response of bovine Glisson's capsule (GC) is presented. Reproducible characteristics were observed such as J-shaped curves in uniaxial and biaxial configurations, large lateral contraction, cyclic tension softening, large tension relaxation, and moderate creep strain accumulation. The substantial influence of the reference state selection on the kinematic response and the tension versus stretch curves is demonstrated and discussed. The parameters of a large-strain viscoelastic constitutive model were determined based on the data of uniaxial tension relaxation experiments. The model is shown to well predict the uniaxial and biaxial viscoelastic responses in all other configurations. GC, the corresponding model, and the experimental protocols are proposed as a useful basis for future studies on the relation between microstructure and tissue functionality and on the factors influencing the mechanical response of soft collagenous membranes.

A Characteristic-Based Constitutive Law for Dispersed Fibers.

Biological tissues are typically constituted of dispersed fibers. Modeling the constitutive laws of such tissues remains a challenge. Direct integration over all fibers is considered to be accurate but requires very expensive numerical integration. A general structure tensor (GST) model was previously developed to bypass this costly numerical integration step, but there are concerns about the model's accuracy. Here we estimate the approximation error of the GST model. We further reveal that the GST model ignores strain energy induced by shearing motions. Subsequently, we propose a new characteristic-based constitutive law to better approximate the direct integration model. The new model is very cost-effective and closely approximates the "true" strain energy as calculated by the direct integration when stress-strain nonlinearity or fiber dispersion angle is small.

Can a continuous mineral foam explain the stiffening of aged bone tissue? A micromechanical approach to mineral fusion in musculoskeletal tissues.

UNLABELLED: Recent experimental data revealed a stiffening of aged cortical bone tissue, which could not be explained by common multiscale elastic material models. We explain this data by incorporating the role of mineral fusion via a new hierarchical modeling approach exploiting the asymptotic (periodic) homogenization (AH) technique for three-dimensional linear elastic composites. We quantify for the first time the stiffening that is obtained by considering a fused mineral structure in a softer matrix in comparison with a composite having non-fused cubic mineral inclusions. We integrate the AH approach in the Eshelby-based hierarchical mineralized turkey leg tendon model (Tiburtius et al 2014 Biomech. MODEL: Mechanobiol. 13 1003-23), which can be considered as a base for musculoskeletal mineralized tissue modeling. We model the finest scale compartments, i.e. the extrafibrillar space and the mineralized collagen fibril, by replacing the self-consistent scheme with our AH approach. This way, we perform a parametric analysis at increasing mineral volume fraction, by varying the amount of mineral that is fusing in the axial and transverse tissue directions in both compartments. Our effective stiffness results are in good agreement with those reported for aged human radius and support the argument that the axial stiffening in aged bone tissue is caused by the formation of a continuous mineral foam. Moreover, the proposed theoretical and computational approach supports the design of biomimetic materials which require an overall composite stiffening without increasing the amount of the reinforcing material.