Sensitivity analysis of ultrasonic guided waves propagating in trilayered bone models: a numerical study

The fundamental ultrasonic guided modes are consistently observed in long bones ex vivo and in vivo. However, the responses of ultrasonic guided waves to the changes of cortical thickness, cortical elastic parameters, and thickness of the overlying soft tissues are not comprehensively understood. This paper systematically presents a sensitivity analysis of leaky Lamb modes to the geometry and material characteristics of layered bone model by means of semi-analytical finite element modeling. The stratified bone model is consisted of a transversely isotropic cortex with an overlying soft tissue and underlying marrow. The study is important as it offers guidance to the parameter inversion process about the optimal selection of guided modes and regions of sensitivity for better inversion results.     

Phase velocity measurement of flexural waves in human tibia

A method is proposed to measure the phase velocities of the first mode of flexural waves in the human tibia. Keeping in mind the dispersive nature of flexural waves in beam-like bodies, a two point measurement method was developed which enables the calculation of the phase difference of the propagating wave between two observation points for a selected frequency range. The method for dispersion analysis was tested with synthetic and observed signals for a cylinder. This was done by comparison of observed radial acceleration on the surface of a PVC-cylinder with computed synthetic signals consisting only of first mode flexural waves. An in vivo study was performed with 43 subjects. The phase velocity measurements in human tibia show a good correlation with the bone mineral content estimated by means of the Cameron-Sorenson technique (Cameron and Sorenson, 1963). The bone mineral loss is reflected by decreasing phase velocities. This indicates that phase velocity measurements of flexural waves can be used for an estimation of bone mineral content in vivo.     

Accuracy of elastic property measurement in mandibular cortical bone is improved by using cylindrical specimens

Ultrasonic determination of elastic properties in human craniofacial cortical bone is problematic because of a lack of information about the principal material axes, and because the cortex is often thinner than in long bones. This study investigated solutions that permit reasonable determination of elastic properties in the human mandible. We tested whether ultrasonic velocities could be reliably measured in cylindrical samples of aluminum and mandibular bone, and the effects of reduced specimen thickness. Results indicted that (1) varying shape had minimal effects on ultrasonic velocities or derived elastic properties, and (2) ultrasonic velocities have relatively increased measurement error as propagation distances decreased. The increased error in velocity measurements of mandibular cortical specimens of less than 1.2 mm in thickness should be considered when assessing the reliability of single measurements.     

Non Destructive Characterization of Cortical Bone Micro-Damage by Nonlinear Resonant Ultrasound Spectroscopy

The objective of the study was to evaluate the ability of a nonlinear ultrasound technique, the so-called nonlinear resonant ultrasound spectroscopy (NRUS) technique, for detecting early microdamage accumulation in cortical bone induced by four-point bending fatigue. Small parallelepiped beam-shaped human cortical bone specimens were subjected to cyclic four-point bending fatigue in several steps. The specimens were prepared to control damage localization during four-point bending fatigue cycling and to unambiguously identify resonant modes for NRUS measurements. NRUS measurements were achieved to follow the evolution of the nonlinear hysteretic elastic behavior during fatigue-induced damage. After each fatigue step, a small number of specimens was removed from the protocol and set apart to quantitatively assess the microcrack number density and length using synchrotron radiation micro-computed tomography (SR-µCT). The results showed a significant effect of damage steps on the nonlinear hysteretic elastic behavior. No significant change in the overall length of microcracks was observed in damaged regions compared to the load-free control regions. Only an increased number of shortest microcracks, those in the lowest quartile, was noticed. This was suggestive of newly formed microcracks during the early phases of damage accumulation. The variation of nonlinear hysteretic elastic behavior was significantly correlated to the variation of the density of short microcracks. Our results suggest that the nonlinear hysteretic elastic behavior is sensitive to early bone microdamage. Therefore NRUS technique can be used to monitor fatigue microdamage progression in in vitro experiments.     

The effect of cement creep and cement fatigue damage on the micromechanics of the cement–bone interface

The cement–bone interface provides fixation for the cement mantle within the bone. The cement–bone interface is affected by fatigue loading in terms of fatigue damage or microcracks and creep, both mostly in the cement. This study investigates how fatigue damage and cement creep separately affect the mechanical response of the cement–bone interface at various load levels in terms of plastic displacement and crack formation. Two FEA models were created, which were based on micro-computed tomography data of two physical cement–bone interface specimens. These models were subjected to tensile fatigue loads with four different magnitudes. Three deformation modes of the cement were considered: ‘only creep’, ‘only damage’ or ‘creep and damage’. The interfacial plastic deformation, the crack reduction as a result of creep and the interfacial stresses in the bone were monitored. The results demonstrate that, although some models failed early, the majority of plastic displacement was caused by fatigue damage, rather than cement creep. However, cement creep does decrease the crack formation in the cement up to 20%. Finally, while cement creep hardly influences the stress levels in the bone, fatigue damage of the cement considerably increases the stress levels in the bone. We conclude that at low load levels the plastic displacement is mainly caused by creep. At moderate to high load levels, however, the plastic displacement is dominated by fatigue damage and is hardly affected by creep, although creep reduced the number of cracks in moderate to high load region.     

Influence of phase angle between axial and torsional loadings on fatigue fractures of bone

Fatigue fractures of cortical bone involve combined axial-torsional loading yet it is unknown how the relationship between axial and torsional loadings affects the fatigue behavior of bone. In this study the effect of superimposing in-phase and out-of-phase torsional on axial loading on the fatigue behavior of bone was investigated by conducting in vitro tests involving 0 degrees and 90 degrees phase shift between cyclic torsional and axial loadings. Results obtained indicate that fatigue life, patterns of moduli loss, microcracking and modes of fractures are dependent on the phase angle between axial and torsional loadings. Specimens subjected to in-phase torsional on axial loading demonstrated greater mixed mode interaction, underwent proportionate stiffness losses in tension, compression, and torsion, and consequently had a shorter fatigue life. In contrast, specimens subjected to out-of-phase loading regime displayed a smaller contribution of mixed mode failure, underwent a disproportionately large stiffness loss in torsion, and had a longer fatigue life. Furthermore, increase in phase angle provided additional planes on which damage was diffused delaying the final failure. Change in phase angle, seen in vivo during a number of physiological activities including walking, running and sprinting, will therefore affect fatigue behavior and contribute to pathogenesis of fatigue fractures.     

An alternative ultrasonic method for measuring the elastic properties of cortical bone

We studied the elastic properties of bone to analyze its mechanical behavior. The basic principles of ultrasonic methods are now well established for varying isotropic media, particularly in the field of biomedical engineering. However, little progress has been made in its application to anisotropic materials. This is largely due to the complex nature of wave propagation in these media. In the present study, the theory of elastic waves is essential because it relates the elastic moduli of a material to the velocity of propagation of these waves along arbitrary directions in a solid. Transducers are generally placed in contact with the samples which are often cubes with parallel faces that are difficult to prepare. The ultrasonic method used here is original, a rough preparation of the bone is sufficient and the sample is rotated. Moreover, to analyze heterogeneity of the structure we measure velocities in different points on the sample. The aim of the present study was to determine in vitro the anisotropic elastic properties of cortical bones. For this purpose, our method allowed measurement of longitudinal and transverse velocities (C(L) and C(T)) in longitudinal (fiber direction) and the radial directions (orthogonal to the fiber direction) of compact bones. Young's modulus E and Poisson's ratio nu, were then deduced from the velocities measured considering the compact bone as transversely isotropic or orthotropic. The results are in line with those of other methods.     

Survival of cultured mammalian cells exposed to ultrasound

Summary The colony-forming ability of cultured mammalian cells exposed to monochromatic ultrasonic vibrations of different frequencies (0.1, 0.5, 1.0, 2.0, 3.3 MHz) was studied. The combined effect of x rays and 1.0-MHz ultrasonic waves on the survival of M3-1 cells was also investigated. Split-dose experiments showed that cells exposed to ultrasound are sensitized to a subsequent exposure. Almost twice as many cells survive a given ultrasonic dose when exposed in the M phase as when exposed in the S phase. A small amount of synergism between ultrasound and x rays has been observed. The extent of synergism depends on the experimental factors, and may be due to an interaction between nuclear damage caused by x rays and the damage to the cell membrane caused by ultrasound.Research supported by the U.S. Atomic Energy Commission and the National Aeronautics and Space Administration     

Emission of alfvén waves from a nonuniform MHD waveguide

The efficiency of the wave energy loss from a nonuniform MHD waveguide due to the conversion of the trapped magnetosonic waveguide modes into runaway Alfvén waves is estimated theoretically. It is shown that, if the waveguide parameters experience a jumplike change along the waveguide axis, the interaction between the waveguide modes and Alfvén waves occurs precisely at this “jump.” This effect is incorporated into the boundary conditions. A set of coupled integral equations with a singular kernel is derived in order to determine the transmission and reflection coefficients for the waveguide modes. The poles in the kernels of the integral operators correspond to the surface waves. When the jump in the waveguide parameters is small, analytic expressions for the frequency dependence of the transformation coefficients are obtained by using a model profile of the Alfvén velocity along the magnetic field. For the jump characterized by the small parameter value ε=0.3, the wave-amplitude transformation coefficient can amount to 5–10%. Under the phase synchronization condition (when the phase velocities of the waveguide modes on both sides of the jump are the same), the wave-energy transformation coefficient is much higher: it increases from a fraction of one percent to tens of percent. The transformation of fast magnetosonic waves into Alfvén waves is resonant in character, which ensures the frequency and wavelength filteringof the emitted Alfvén perturbations.     

A study of the efficacy of ultrasonic waves in removing biofilms

doi:10.1111/j.1741‐2358.2009.00325.x
A study of the efficacy of ultrasonic waves in removing biofilms Objective: The removal of adherent biofilms was assessed using ultrasonic waves in a non‐contact mode. Materials and Methods: In in vitro experiments, Streptococcus mutans (S. mutans) biofilms were exposed to ultrasonic waves at various frequencies (280 kHz, 1 MHz, or 2 MHz), duty ratios (0–90%), and exposure times (1–3 minutes), and the optimal conditions for biofilm removal were identified. Furthermore, the effect of adding a contrast medium, such as micro bubbles (Sonazoid^®), was examined. The spatial distribution and architecture of S. mutans biofilms before and after ultrasonic wave exposure were examined via scanning electron microscopy. The biofilm removal effect was also examined in in vivo experiments, using a custom‐made oral cleaning device. Results: When a 280 kHz probe was used, the biofilm‐removing effect increased significantly compared to 1 and 2 MHz probes; more than 80% of the adherent biofilm was removed with a duty cycle of 50–90% and a 3 minutes exposure time. The maximum biofilm‐removing effect was observed with a duty cycle of 80%. Furthermore, the addition of micro bubbles enhanced this biofilm‐removing effect. In in vivo experiments, moderate biofilm removal was observed when a 280 kHz probe was used for 5 minutes. Conclusions: This study demonstrated that ultrasonic wave exposure in a non‐contact mode effectively removed adherent biofilms composed of S. mutans in vitro.     

Mechanical wave propagation on nerve axons

The mechanical waves which may occur in or on a nerve axon are considered. It is shown that under rather general assumptions mechanical waves with phase velocities corresponding to nerve impulse propagation velocities belong to the natural modes of the axon membrane. This means that the mechanical disturbances which are connected with almost all models of nerve impulse propagation are readily supported by the axon, suggesting a possibility of interaction between electrical and mechanical events in the axon.     

Modeling the onset and propagation of trabecular bone microdamage during low-cycle fatigue

Relatively small amounts of microdamage have been suggested to have a major effect on the mechanical properties of bone. A significant reduction in mechanical properties (e.g. modulus) can occur even before the appearance of microcracks. This study uses a novel non-linear microdamaging finite-element (FE) algorithm to simulate the low-cycle fatigue behavior of high-density trabecular bone. We aimed to investigate if diffuse microdamage accumulation and concomitant modulus reduction, without the need for complete trabecular strut fracture, may be an underlining mechanism for low-cycle fatigue failure (defined as a 30% reduction in apparent modulus). A microCT constructed FE model was subjected to a single cycle monotonic compression test, and constant and variable amplitude loading scenarios to study the initiation and accumulation of low-cycle fatigue microdamage. Microcrack initiation was simulated using four damage criteria: 30%, 40%, 50% and 60% reduction in bone element modulus (el-MR). Evaluation of structural (apparent) damage using the four different tissue level damage criteria resulted in specimen fatigue failure at 72, 316, 969 and 1518 cycles for the 30%, 40%, 50% and 60% el-MR models, respectively. Simulations based on the 50% el-MR model were consistent with previously published experimental findings. A strong, significant non-linear, power law relationship was found between cycles to failure (N) and effective strain (Deltasigma/E(0)): N=1.394x10(-25)(Deltasigma/E(0))(-12.17), r(2)=0.97, p<0.0001. The results suggest that microdamage and microcrack propagation, without the need for complete trabecular strut fracture, are mechanisms for high-density trabecular bone failure. Furthermore, the model is consistent with previous numerical fatigue simulations indicating that microdamage to a small number of trabeculae results in relatively large specimen modulus reductions and rapid failure.     

Experimental and probabilistic analysis of distal femoral periprosthetic fracture: a comparison of locking plate and intramedullary nail fixation. Part B: probabilistic investigation

The following is Part B of a two-part study. Part A evaluated, biomechanically, intramedullary (IM) nails versus locking plates for fixation of an extra-articular, metaphyseal wedge fracture in synthetic osteoporotic bone. Part B of this study introduces deterministic finite element (FE) models of each construct type in synthetic osteoporotic bone and investigates the probability of periprosthetic fracture of the locking plate compared with the retrograde IM nail using Monte Carlo simulation. Deterministic FE models of the fractured femur implanted with IM nail and locking plate, respectively, were developed and validated using experimental data presented in Part A of this study. The models were validated by comparing the load-displacement curve of the experimental data with the load-displacement curve of the FE simulation with a root-mean square error of less than 3?mm. The validated FE models were then modified by defining the cortical and cancellous bone modulus of elasticity as uncertain variables that could be assumed to vary randomly. Monte Carlo simulation was used to evaluate the probability of fracture (POF) of each fixation. The POF represents the cumulative probability that the predicted shear stresses in the cortical bone will exceed the expected shear strength of the cortical bone. This investigation provides information regarding the significance of post-operative damage accumulation on the POF of the implanted bones when the two fixations are used. The probabilistic analysis found the locking plate fixation to have a higher POF than the IM nail fixation under the applied loading conditions (locking plate 21.8% versus IM nail 0.019%).     

B超引导下乳腺肿块粗针穿刺诊断的分析（附120例报道）

目的：探讨B超引导下粗针穿刺在乳腺肿块诊断中的应用意义。方法：使用B超引导下粗针吸取穿刺对120例乳腺肿块进行穿刺活检,然后进行固定,脱水,染色,镜检,结合临床作出病理学诊断。结果：粗针穿刺诊断包括良性病变48例,非典型性导管上皮增生（ADH）32例,导管内癌12例,浸润性癌28例。与后续手术标本病理诊断比较得出确诊率,其中良性病变的诊断率为95．83％（46／48）,ADH的确诊率为75％（24／32）,导管内癌的确诊率为58．33％（7／12）,浸润性癌诊断率为92．86％（26／28）,其中导管内癌与浸润性导管癌和乳腺良性病变的确诊率有显著性差异,而ADH与浸润性导管癌和乳腺良性病变间的确诊率有差异,但本组数据没有统计学意义。结论：超声引导下粗针穿刺对乳腺浸润性癌和良性病变的诊断率较高,但对ADH和原位癌的确诊率较低,有待进一步改进。     

Wave propagation characteristics in long bones to diagnose osteoporosis

A mathematical model of stress wave propagation in bone is developed assuming a long bone to be a thick-walled, long cylindrical shell filled with a fluid. The calculated phase and group velocities in adult human femurs were found to be a function of the wave number and they were different for population groups of above and below 55 yr of age. The velocities were also sex dependent, being different for males and females of the same age group. Diagnostic methods based on the measurement of wave propagation characteristics may potentially be used to measure the structural changes in long bones due to osteoporosis.     

Xylanase mass transfer studies in aqueous two-phase systems using spray and sieve plate columns

Aqueous two-phase systems (ATPSs) have long been used for biomolecule partitioning; these systems offer the possibility of using continuous or semicontinuous extraction processes. They require relatively simple equipment like spray or sieve plate columns that can be adapted for use in ATPSs. The aim of this work was to study the semicontinuous extraction of a model enzyme, xylanase, in spray and sieve plate columns, since, unlike centrifugal contactors, the cost of construction and maintenance of this equipment is low and it is easy to operate. For the spray column, the dispersed phase hold-up and overall mass transfer coefficients K(D) a were evaluated for different column heights and for different superficial velocities of the dispersed phase (light phase). Results indicated that an increase in superficial velocity in the range of 0-0.18 mm/s of the dispersed phase had a positive effect on K(D) a and on hold-up in all column heights studied, 75, 161 and 246 mm. For the same superficial velocity of the dispersed phase, the larger the hold-up was, the shorter the column. For the sieve plate column, the effects of the superficial velocity of the dispersed phase and the number of plates were also studied. Results showed that the K(D) a and hold-up increased with an increase in both parameters. The selectivity of separation of xylanase and BSA (model contaminant) was very high, since 60% of the enzyme was extracted in the light phase, whereas no significant amount of BSA was extracted. The possibility of using the sieve plate column in continuous operation for enzyme extraction was studied because previous work had only addressed the semicontinuous extraction of enzyme. The residence time distribution of the PEG phase using different superficial velocities of the salt phase was studied in continuous operation. The time required to reach the steady state was 40 min, and 70% of the xylanase was recovered. It was found that the Modified Power Spline software was well adjusted to the experimental results.     

Numerical Simulation of Bone Plate with Fatigue Crack and Investigation of Attraction Hole for Retarding Crack Growth

Premature fracture of the bone plate caused by fatigue crack is the main failure mode in treating femoral shaft fracture. In order to improve the durability of the plate, this study proposed a crack attraction hole (CAH) to retard the crack propagation based on the fracture mechanics. In this paper, a numerical model of the femoral fracture internal fixation system was constructed, in which the femur was developed using a validated simplified model. First, the fatigue crack initiation location was defined at the stress concentration through static analysis. Next, with the joint simulation method of Franc3D and ABAQUS, the fatigue crack path in the bone plate was predicted. Meanwhile, the Paris parameters of Ti-6Al-4V obtained through experiments were encoded into Franc3D to calculate the crack propagation life. Finally, we considered the influence of CAH designs with different relative vertical distances (2.0, 3.0, and 4.0 mm) and diameters (1.5, 2.0, and 2.5 mm) on the crack propagation path and life of the bone plate. Additionally, the effects of all CAH configurations on the biomechanical performance of the bone plate fixation system were evaluated. The results indicated that the fatigue crack growth path in the bone plate is comparable to a straight line, and the crack growth rate significantly increases when the crack tip reaches the outer boundary of the plate. The findings suggest that the addition of CAH in the bone plate will lead to the deflection of the crack path and increase the fatigue life. Equally important, the improvement of the fatigue life was positively correlated with the diameter of CAH and negatively correlated with the relative vertical distance. In addition, the biomechanical properties of the bone plate system were slightly affected by CAH, substantiating the feasibility of this method. Finally, the comparative analysis verified that a CAH with a relative vertical distance of 3 mm and a diameter of 2 mm exhibited superior improvement in the comprehensive performance on the bone plate.     

Microdamage Caused by Fatigue Loading in Human Cancellous Bone: Relationship to Reductions in Bone Biomechanical Performance

Vertebral fractures associated with osteoporosis are often the result of tissue damage accumulated over time. Microscopic tissue damage (microdamage) generated in vivo is believed to be a mechanically relevant aspect of bone quality that may contribute to fracture risk. Although the presence of microdamage in bone tissue has been documented, the relationship between loading, microdamage accumulation and mechanical failure is not well understood. The aim of the current study was to determine how microdamage accumulates in human vertebral cancellous bone subjected to cyclic fatigue loading. Cancellous bone cores (n = 32) from the third lumbar vertebra of 16 donors (10 male, 6 female, age 76±8.8, mean ± SD) were subjected to compressive cyclic loading at σ/E₀ = 0.0035 (where σ is stress and E₀ is the initial Young’s modulus). Cyclic loading was suspended before failure at one of seven different amounts of loading and specimens were stained for microdamage using lead uranyl acetate. Damage volume fraction (DV/BV) varied from 0.8±0.5% (no loading) to 3.4±2.1% (fatigue-loaded to complete failure) and was linearly related to the reductions in Young’s modulus caused by fatigue loading (r² = 0.60, p<0.01). The relationship between reductions in Young’s modulus and proportion of fatigue life was nonlinear and suggests that most microdamage generation occurs late in fatigue loading, during the tertiary phase. Our results indicate that human vertebral cancellous bone tissue with a DV/BV of 1.5% is expected to have, on average, a Young’s modulus 31% lower than the same tissue without microdamage and is able to withstand 92% fewer cycles before failure than the same tissue without microdamage. Hence, even small amounts of microscopic tissue damage in human vertebral cancellous bone may have large effects on subsequent biomechanical performance.     

Near-terminal creep damage does not substantially influence fatigue life under physiological loading

Cortical bone specimens were damaged using repeated blocks of tensile creep loading until a near-terminal amount of creep damage was generated (corresponding to a reduction in elastic modulus of 15%). One group of cortical bone specimens was submitted to the near-terminal damage protocol and subsequently underwent fatigue loading in tension with a maximum strain of 2000 με (Damage Fatigue, n=5). A second group was submitted to cyclic fatigue loading but was not pre-damaged (Control Fatigue, n=5). All but one specimen (a damaged specimen) reached run-out (10 million cycles, 7.7 days). No significant differences in microscopic cracks or other tissue damage were observed between the two groups or between either group and additional, completely unloaded specimens. Our results suggest that damage in cortical bone allograft that is not obvious or associated with a stress riser may not substantially affect its fatigue life under physiologic loading.     

Asymmetric long-wavelength surface modes of isotropic plasma waveguides

A theoretical study is made of the dispersion properties of electromagnetic surface waves with arbitrary azimuthal mode numbers and a small axial wavenumber in cylindrical isotropic waveguides partially filled with plasma. The plasma is assumed to be cold and radially inhomogeneous, and the problem is solved in the hydrodynamic approximation. The eigenfrequency of the waves is investigated as a function of the plasma parameters, the width and the permittivity of the dielectric gap between the metal waveguide wall and the plasma column, the axial wavenumber, and the azimuthal mode number. It is shown that the axial phase velocities of asymmetric surface modes are higher than the speed of light in a dielectric and that the surface modes do not propagate in a waveguide with a vanishingly small width of the dielectric gap. The theory developed is employed in practice in the calculation of the electrodynamic model of a gas discharges maintained by asymmetric long-wavelength surface modes. The power absorbed by the gas-discharge plasma in the regimes of Ohmic damping and resonant damping is calculated, and the plasma produced during the discharge is shown to be azimuthally homogeneous.