In situ estimation of tendon material properties: Differences between muscles of the feline hindlimb

Recent experiments to characterize the short-range stiffness (SRS)–force relationship in several cat hindlimb muscles suggested that the there are differences in the tendon elastic moduli across muscles [Cui, L., Perreault, E.J., Maas, H., Sandercock, T.G., 2008. Modeling short-range stiffness of feline lower hindlimb muscles. J. Biomech. 41 (9), 1945–1952.]. Those conclusions were inferred from whole muscle experiments and a computational model of SRS. The present study sought to directly measure tendon elasticity, the material property most relevant to SRS, during physiological loading to confirm the previous modeling results. Measurements were made from the medial gastrocnemius (MG), tibialis anterior (TA) and extensor digitorum longus (EDL) muscles during loading. For the latter, the model indicated a substantially different elastic modulus than for MG and TA. For each muscle, the stress–strain relationship of the external tendon was measured in situ during the loading phase of isometric contractions conducted at optimum length. Young's moduli were assessed at equal strain levels (1%, 2% and 3%), as well as at peak strain. The stress–strain relationship was significantly different between EDL and MG/TA, but not between MG and TA. EDL had a more apparent toe region (i.e., lower Young's modulus at 1% strain), followed by a more rapid increase in the slope of the stress–strain curve (i.e., higher Young's modulus at 2% and 3% strain). Young's modulus at peak strain also was significantly higher in EDL compared to MG/TA, whereas no significant difference was found between MG and TA. These results indicate that during natural loading, tendon Young's moduli can vary considerably across muscles. This creates challenges to estimating muscle behavior in biomechanical models for which direct measures of tendon properties are not available.     

Influence of asymmetric stiffness on the structural and aerodynamic response of synthetic vocal fold models

The influence of asymmetric vocal fold stiffness on voice production was evaluated using life-sized, self-oscillating vocal fold models with an idealized geometry based on the human vocal folds. The models were fabricated using flexible, materially-linear silicone compounds with Young's modulus values comparable to that of vocal fold tissue. The models included a two-layer design to simulate the vocal fold layered structure. The respective Young's moduli of elasticity of the “left” and “right” vocal fold models were varied to create asymmetric conditions. High-speed videokymography was used to measure maximum vocal fold excursion, vibration frequency, and left–right phase shift, all of which were significantly influenced by asymmetry. Onset pressure, a measure of vocal effort, increased with asymmetry. Particle image velocimetry (PIV) analysis showed significantly greater skewing of the glottal jet in the direction of the stiffer vocal fold model. Potential applications to various clinical conditions are mentioned, and suggestions for future related studies are presented.     

An investigation of dentinal fluid flow in dental pulp during food mastication: simulation of fluid–structure interaction

This study uses fluid–structure interaction (FSI) simulation to investigate the relationship between the dentinal fluid flow in the dental pulp of a tooth and the elastic modulus of masticated food particles and to investigate the effects of chewing rate on fluid flow in the dental pulp. Three-dimensional simulation models of a premolar tooth (enamel, dentine, pulp, periodontal ligament, cortical bone, and cancellous bone) and food particle were created. Food particles with elastic modulus of 2,000 and 10,000 MPa were used, respectively. The external displacement loading $(5\,\upmu \hbox {m})$ was gradually directed to the food particle surface for 1 and 0.1 s, respectively, to simulate the chewing of food particles. The displacement and stress on tooth structure and fluid flow in the dental pulp were selected as evaluation indices. The results show that masticating food with a high elastic modulus results in high stress and deformation in the tooth structure, causing faster dentinal fluid flow in the pulp in comparison with that obtained with soft food. In addition, fast chewing of hard food particles can induce faster fluid flow in the pulp, which may result in dental pain. FSI analysis is shown to be a useful tool for investigating dental biomechanics during food mastication. FSI simulation can be used to predict intrapulpal fluid flow in dental pulp; this information may provide the clinician with important concept in dental biomechanics during food mastication.     

A Method for Material Parameter Determination for the Human Mandible Based on Simulation and Experiment

In cranio-maxillofacial surgery planning and implant design, it is important to know the elastic response of the mandible to load forces as they occur, e.g., in biting. The goal of the present study is to provide a method for a quantitative determination of material parameters for the human jaw bone, whose values can, e.g., be used to devise a prototype plastic model for the mandible. Non-destructive load experiments are performed on a cadaveric mandible using a specially designed test bed. The identical physiological situation is simulated in a computer program. The underlying mathematical model is based on a two component, linear elastic material law. The numerical realization of the model, difficult due to the complex geometry and morphology of the mandible, is via the finite element (FE) method. Combining the validated simulation with the results of the tests, an inverse problem for the determination of Young's modulus and the Poisson ratio of both cortical and cancellous bone can then be solved.     

Measurement of the circumferential mechanical properties of the umbilical vein: experimental and numerical analyses

Coronary artery disease is responsible for almost 30% of all deaths worldwide. The saphenous vein and umbilical vein (UV) are the most common veins using for treatment as a coronary artery bypass graft (CABG). The mechanical properties of UV belonging to its long-term patency for CABG are very important. However, there is a lack of knowledge on the linear elastic and nonlinear hyperelastic mechanical properties of the UV. In this study, three stress definitions (second Piola–Kichhoff stress, engineering stress and true stress) and four strain definitions (Almansi–Hamel strain, Green–St Venant strain, engineering strain and true strain) are used to determine the elastic modulus, maximum stress and strain of eight human UVs under circumferential loading. The nonlinear mechanical behaviour of the UV is computationally investigated using Mooney–Rivlin hyperelastic model. A numerical finite element analysis is also carried out to simulate the constitutive modelling versus its numerical results. The results show that the Almansi–Hamel strain definition overestimates the elastic modulus while Green–St Venant strain definition underestimates the elastic modulus at different stress definitions. The true stress–true strain definition, which gives more accurate measurements of the tissue's response using the instantaneous values, reveals the Young's modulus and maximum stress of 2.18 and 6.01 MPa, respectively. The Mooney–Rivlin material model is well represented by the nonlinear mechanical behaviour of the UV. The findings of this study could have implications not only for understanding the extension and rupture mechanism of UV but also for interventions and surgeries, including balloon angioplasty, bypass and stenting.     

MECHANICAL BEHAVIOR OF PLANT TISSUES AS INFERRED FROM THE THEORY OF PRESSURIZED CELLULAR SOLIDS

The mechanical behavior of plant tissues and its dependency on tissue geometry and turgor pressure are analytically dealt with in terms of the theory of cellular solids. A cellular solid is any material whose matter is distributed in the form of beamlike struts or complete “cell” walls. Therefore, its relative density is less than one and typically less than 0.3. Relative density is the ratio of the density of the cellular solid to the density of its constitutive (“cell wall”) material. Relative density depends upon cell shape and the density of cell wall material. It largely influences the mechanical behavior of cellular solids. Additional important parameters to mechanical behavior are the elastic modulus of “cell walls” and the magnitude of internal “cell” pressure. Analyses indicate that two “stiffening” agents operate in natural cellular solids (plant tissues): 1) cell wall infrastructure and 2) the hydrostatic influence of the protoplasm within each cellular compartment. The elastic modulus measured from a living tissue sample is the consequence of both agents. Therefore, the mechanical properties of living tissues are dependent upon the magnitude of turgor pressure. High turgor pressure places cell walls into axial tension, reduces the magnitude of cell wall deformations under an applied stress, and hence increases the apparent elastic modulus of the tissue. In the absence of turgid protoplasts or in the case of dead tissues, the cell wall infrastructure will respond as a linear elastic, nonlinear elastic, or “densifying” material (under compression) dependent upon the magnitude of externally applied stress. Accordingly, it is proposed that no single tangent (elastic) modulus from a stress-strain curve of a plant tissue is sufficient to characterize the material properties of a sample. It is also suggested that when a modulus is calculated that it be referred to as the tissue composite modulus to distinguish it from the elastic modulus of a noncellular solid material.     

Mechanical characterization of the bovine iris

Quantification of the mechanical properties of the iris is necessary to assess the clinical significance of passive iris deformation, which has been suggested as a mechanism for certain forms of glaucoma. Extension tests were performed on isolated bovine irises to determine the passive mechanical behavior of the iris and the contribution of each of its two constituent muscles, the sphincter iridis and the dilator pupillae, to the overall properties. Because of the shape of the iris and our desire to use intact tissue, a “loop” experiment was performed in which the iris was stretched by hooking the sample and pulling. A simple mathematical model was used to account for the geometry of the experiment and the progressive recruitment of tissue. Radial extension experiments on samples dissected from the iris were also performed. The iris was found to be anisotropic, elastic, and incompressible. The average azimuthal Young's modulus of the sphincter was found to be 340 kPa; the average azimuthal Young's modulus of the dilator was found to be 890 kPa, which was significantly higher (p<0.01). The radial Young's modulus of the dilator was found to be 9.6 kPa, much lower than the azimuthal value.     

An elastic rod model to evaluate effects of ionic concentration on equilibrium configuration of DNA in salt solution

As a coarse-gained model, a super-thin elastic rod subjected to interfacial interactions is used to investigate the condensation of DNA in a multivalent salt solution. The interfacial traction between the rod and the solution environment is determined in terms of the Young–Laplace equation. Kirchhoff’s theory of elastic rod is used to analyze the equilibrium configuration of a DNA chain under the action of the interfacial traction. Two models are established to characterize the change of the interfacial traction and elastic modulus of DNA with the ionic concentration of the salt solution, respectively. The influences of the ionic concentration on the equilibrium configuration of DNA are discussed. The results show that the condensation of DNA is mainly determined by competition between the interfacial energy and elastic strain energy of the DNA itself, and the interfacial traction is one of forces that drive DNA condensation. With the change of concentration, the DNA segments will undergo a series of alteration from the original configuration to the condensed configuration, and the spiral-shape appearing in the condensed configuration of DNA is independent of the original configuration.     

A mechanical model to compute elastic modulus of tissues for harmonic motion imaging

Numerous experimental and computational methods have been developed to estimate tissue elasticity. The existing testing techniques are generally classified into in vitro, invasive in vivo and non-invasive in vivo. For each experimental method, a computational scheme is accordingly proposed to calculate mechanical properties of soft biological tissues. Harmonic motion imaging (HMI) is a new technique that performs radio frequency (RF) signal tracking to estimate the localized oscillatory motion resulting from a radiation force produced by focused ultrasound. A mechanical model and computational scheme based on the superposition principle are developed in this paper to estimate the Young's modulus of a tissue mimicking phantom and bovine liver in vitro tissue from the harmonic displacement measured by HMI. The simulation results are verified by two groups of measurement data, and good agreement is shown in each comparison. Furthermore, an inverse function is observed to correlate the elastic modulus of uniform phantoms with amplitude of displacement measured in HMI. The computational scheme is also implemented to estimate 3D elastic modulus of bovine liver in vitro.     

Single-Cell Force Spectroscopy of Interaction of Lipopolysaccharides from <Emphasis Type="Italic">Yersinia pseudotuberculosis</Emphasis> and <Emphasis Type="Italic">Yersinia pestis</Emphasis> with J774 Macrophage Membrane Using Optical Tweezers

In order to investigate quantitatively the role of lipopolysaccharides (LPS) from outer bacterial membrane at the initial state of bacterium adhesion to a host cell membrane, a model system for single cell force spectroscopy was developed and used. The system comprised of an LPS-coated microsphere placed into optical trap and a J774 macrophage being approached the microsphere to initiate their binding and then moved back to rupture the bond. An “object shadow” phenomenon was discovered, manifested as large-scale variations of the signal of photodetector registering the trapped microsphere displacement, such variations emerging long before the actual interaction between the macrophage and microsphere. The theory and the measurements technique were developed for registration of the force required for detachment of bounded microsphere from the object investigated by means of optical tweezers under the “object shadow” conditions. Characteristic spectra of binding force between J774 macrophage and microspheres functionalized with various LPS, as well as LPS plus complementary antibodies preparations were obtained at the rate of detachment force application of 3–6 pN/s. Force spectrum characteristic of Yersinia pseudotuberculosis LPS possessing O-antigen had a maximum at ~14 pN with half-width of ~23 pN. The treatment of O-antigen with complementary antibodies resulted in transformation of this spectrum into a spectrum with maximum at ~10 pN and half-width of ~14 pN, being almost identical to the spectrum of Y. pestis LPS devoid of O-antigen, with a maximum at ~9 pN and half-width of ~13 pN. A possible mechanism of force spectra formation has been proposed under assumptions of nonspecific binding of O-antigen and probable receptor-type binding of LPS core region to the macrophage surface. The elastic modulus of macrophage envelope, as estimated using analysis of displacement of the contacting microsphere as an indenter, was ≈0.17 pN/nm.     

Elasticity of alveolar bone near dental implant-bone interfaces after one month's healing

Information is scarce about Young's modulus of healing bone surrounding an implant. The purpose of this preliminary study is to quantify elastic properties of pig alveolar bone that has healed for 1 month around titanium threaded dental implants, using the nanoindentation method. Two 2-year-old Sinclair miniswine were used for the study. Nanoindentation tests perpendicular to the bucco-lingual cross section were performed on harvested implant-bone blocks using the Hysitron TriboScope III. Nomarski differential interference contrast microscopy was used to identify pyramidal indentation measurements that were from bone. Reduced moduli, averaged for all anatomical regions, were found to start low (6.17 GPa) at the interface and gradually increase (slope=0.014) to a distance of 150 microm (7.89 GPa) from the implant surface, and then flatten to a slope of 0.001 from 150 to 1500 microm (10.13 GPa). Mean reduced modulus and its relationship to distance did not differ significantly by anatomic location (e.g., coronal, middle, and apical third; P>/=0.28 for all relevant tests) at 1 month after implantation.     

Ab initio predictions of structural and elastic properties of struvite: contribution to urinary stone research

In the present work, we carried out density functional calculations of struvite – the main component of the so-called infectious urinary stones – to study its structural and elastic properties. Using a local density approximation and a generalised gradient approximation, we calculated the equilibrium structural parameters and elastic constants C _ijkl . At present, there is no experimental data for these elastic constants C _ijkl for comparison. Besides the elastic constants, we also present the calculated macroscopic mechanical parameters, namely the bulk modulus (K), the shear modulus (G) and Young's modulus (E). The values of these moduli are found to be in good agreement with available experimental data. Our results imply that the mechanical stability of struvite is limited by the shear modulus, G. The study also explores the energy-band structure to understand the obtained values of the elastic constants.     

Quantitative investigation of calcimimetic R568 on beta cell adhesion and mechanics using AFM single-cell force spectroscopy

In this study we use a novel approach to quantitatively investigate mechanical and interfacial properties of clonal β-cells using AFM-Single Cell Force Spectroscopy (SCFS). MIN6 cells were incubated for 48 h with 0.5 mM Ca²⁺ ± the calcimimetic R568 (1 μM). AFM-SCFS adhesion and indentation experiments were performed by using modified tipless cantilevers. Hertz contact model was applied to analyse force–displacement (F–d) curves for determining elastic or Young’s modulus (E). Our results show CaSR-evoked increases in cell-to-cell adhesion parameters and E modulus of single cells, demonstrating that cytomechanics have profound effects on cell adhesion characterization.     

Interfacial Susceptibilities in Nanoplasmonics via Inversion of Fresnel Coefficients

The reflection coefficients of a nanoparticle film are driven to a large extent by perpendicular and parallel interfacial susceptibilities that have the meaning of “dielectric thicknesses” which combine the actual geometry of the film and its dielectric properties. The direct determination of these parameters faces the long-standing issue of the derivation of complex optical constants from Fresnel coefficients via a unique spectroscopic measurement. The present work sets up an iterative algorithm based on inversion of the reflection coefficients recorded in the UV–visible range for two polarization states s and p and Kramers–Kronig (KK) analysis. To calculate the KK integrals over a limited energy window, the strategy was to complement measurements by spectra calculated in the framework of the spheroidal dipole approximation. The algorithm has been successfully tested on synthetic data of differential reflectivity for supported truncated spheres. These were chosen to span different dielectric behaviors, involving (a) for the particles, metals whose optical response is dominated by plasmonic excitations with a noticeable Drude behavior (Ag and Au) and (b) for the substrate, either nonabsorbing wide bandgap (alumina) or semiconducting (zincite and titania) oxides. Unlike the thin plate model, the approach was proven to apply to “dielectric thicknesses” of several tens of nanometres in cases in which, even for geometric sizes of the order of the nanometer, the classical long-wavelength dielectric approximation fails because of strong plasmon resonances. Therefore, the disentanglement of dielectric behaviors along the parallel and perpendicular directions simplifies the understanding on the interface polarization process by removing substrate contribution. The present work that deals with plasmonics in nanoparticles can be easily generalized to different morphologies as well as to other combinations of Fresnel coefficients.     

Mechanical changes in the rat right ventricle with decellularization

The stiffness, anisotropy, and heterogeneity of freshly dissected (control) and perfusion-decellularized rat right ventricles were compared using an anisotropic inverse mechanics method. Cruciform tissue samples were speckled and then tested under a series of different biaxial loading configurations with simultaneous force measurement on all four arms and displacement mapping via image correlation. Based on the displacement and force data, the sample was segmented into piecewise homogeneous partitions. Tissue stiffness and anisotropy were characterized for each partition using a large-deformation extension of the general linear elastic model. The perfusion-decellularized tissue had significantly higher stiffness than the control, suggesting that the cellular contribution to stiffness, at least under the conditions used, was relatively small. Neither anisotropy nor heterogeneity (measured by the partition standard deviation of the modulus and anisotropy) varied significantly between control and decellularized samples. We thus conclude that although decellularization produces quantitative differences in modulus, decellularized tissue can provide a useful model of the native tissue extracellular matrix. Further, the large-deformation inverse method presented herein can be used to characterize complex soft tissue behaviors.     

Comparison of single-phase isotropic elastic and fibril-reinforced poroelastic models for indentation of rabbit articular cartilage

Classically, single-phase isotropic elastic (IE) model has been used for in situ or in vivo indentation analysis of articular cartilage. The model significantly simplifies cartilage structure and properties. In this study, we apply a fibril-reinforced poroelastic (FRPE) model for indentation to extract more detailed information on cartilage properties. Specifically, we compare the information from short-term (instantaneous) and long-term (equilibrium) indentations, as described here by IE and FRPE models. Femoral and tibial cartilage from rabbit (age 0–18 months) knees (n=14) were tested using a plane-ended indenter (diameter=0.544 mm). Stepwise creep tests were conducted to equilibrium. Single-phase IE solution for indentation was used to derive instantaneous modulus and equilibrium (Young's) modulus for the samples. The classical and modified Hayes’ solutions were used to derive values for the indentation moduli. In the FRPE model, the indentation behavior was sample-specifically described with three material parameters, i.e. fibril network modulus, non-fibrillar matrix modulus and permeability. The instantaneous and fibril network modulus, and the equilibrium Young's modulus and non-fibrillar matrix modulus showed significant (p<0.01) linear correlations of R²=0.516 and 0.940, respectively (Hayes’ solution) and R²=0.531 and 0.960, respectively (the modified Hayes’ solution). No significant correlations were found between the non-fibrillar matrix modulus and instantaneous moduli or between the fibril network modulus and the equilibrium moduli. These results indicate that the instantaneous indentation modulus (IE model) provides information on tensile stiffness of collagen fibrils in cartilage while the equilibrium modulus (IE model) is a significant measure for stiffness of PG matrix. Thereby, this study highlights the feasibility of a simple indentation analysis.     

A genetic model of dental reduction through the probable mutation effect

A simulation approach is used in order to elucidate the nature of the hypothesized “probable mutation effect” as it applies to dental reduction in man. Computer-generated simulations of the accumulation of mutations in a human gene pool show the results of the proposed model under the influence of various parameters, as well as illustrating the nature of such genetic change through time. This approach supports a polygenic model of the probable mutation effect as a viable hypothesis for an explanation of the dental reduction which has occurred in some human populations over the last 40,000 years.     

Effect of microstructure upon elastic behaviour of human tooth enamel

Tooth enamel is the stiffest tissue in the human body with a well-organized microstructure. Developmental diseases, such as enamel hypomineralisation, have been reported to cause marked reduction in the elastic modulus of enamel and consequently impair dental function. We produce evidence, using site-specific transmission electron microscopy (TEM), of difference in microstructure between sound and hypomineralised enamel. Built upon that, we develop a mechanical model to explore the relationship of the elastic modulus of the mineral–protein composite structure of enamel with the thickness of protein layers and the direction of mechanical loading. We conclude that when subject to complex mechanical loading conditions, sound enamel exhibits consistently high stiffness, which is essential for dental function. A marked decrease in stiffness of hypomineralised enamel is caused primarily by an increase in the thickness of protein layers between apatite crystals and to a lesser extent by an increase in the effective crystal orientation angle.     

Load transfer along the bone–dental implant interface

In this paper the variation of normal and shear stresses along a path defined on the bone–dental implant interface is investigated. In particular, the effects of implant diameter, collar length and slope, body length, and the effects of four different types of external threads on the interfacial stress distribution are studied. The geometry of the bone is digitized from a CT scan of a mandibular incisor and the surrounding bone. The bone and the implant are assumed to be perfectly bonded. The finite element method with 2D plane strain assumption is used to compute interfacial stresses. Highest continuous interfacial stresses are encountered in the region where the implant collar engages the cortical region, and near the apex of the implant in the subcortical region. Stress concentrations in the interfacial stresses occur near the geometric discontinuities on the implant contour, and jumps in stress values occur where the elastic modulus of the bone transitions between the cortical and trabecular bone values. Among the six contour parameters, the slope and the length of the implant collar, and the implant diameter influence the interfacial stress levels the most, and the effects of changing these parameters are significantly noticed only in the cortical bone (alveolar ridge) area. External threads cause significant stress concentrations in interfacial stresses in otherwise smoothly varying regions. This work shows that the presence of external threads could cause significant variations in both normal and shear stresses along the bone–implant interface, but not reduction in shear stress as previously thought.     

The Effect of Coumarin on Young's Modulus in Sunflower Stems and Maize Roots and on Water Permeability in Potato Parenchyma

By means of the resonance frequency method Young's, modulus has been determined after coumarin treatment of growing segments of etiolated sunflower hypocotyl segments and in maize roots. Coumarin caused a decrease in Young's modulus in both shoot and root tissue. The response was very rapid; in sunflower hypocotyls the decrease in elastic modulus appeared 3 min after application of coumarin. The effects produced by coumarin were similar to those found by auxin. Coumarin increased the rate of water efflux out of potato parenchyma by about 20%. The increase in water permeability was evident within 3 min.