Ultrasonic pulse waves in cancellous bone analyzed by finite-difference time-domain methods

The trabecular frame of cancellous bone has a high degree of porosity, anisotropy and inhomogeneity. The propagation of ultrasonic waves in cancellous bone is significantly affected by the trabecular structure. In this paper, two two-dimensional finite-difference time-domain (FDTD) methods, which were the popular viscoelastic FDTD method for a viscoelastic medium and Biot's FDTD method for a fluid-saturated porous medium, have been applied to numerically analyze the ultrasonic pulse waves propagating through bovine cancellous bone in the directions parallel and perpendicular to the trabecular alignment. The Biot's fast and slow longitudinal waves, which were identified in previous experiments for the propagation parallel to the trabecular orientation, could be analyzed using Biot's FDTD method rather than the viscoelastic FDTD method. For the single wave propagation in the perpendicular direction, on the other hand, the viscoelastic FDTD result was found to be in more good agreement with the experimental result.     

Quantitative visualization of a gas diffusion layer in a polymer electrolyte fuel cell using synchrotron X‐ray imaging techniques

A gas diffusion layer (GDL) in a polymer electrolyte fuel cell (PEFC) is quantitatively visualized using synchrotron X‐ray micro‐computed tomography. For three‐dimensional reconstruction, an adaptive threshold method is used. This method is compared with the conventional method, i.e. Otsu's method. Additionally, the spatial and temporal variations of the porosity distribution of the GDL under freeze‐and‐thaw cycles are investigated experimentally. The freeze‐and‐thaw cycles are established simply using a CRYO system and light source illumination, respectively. Structural defects are found to largely affect the porosity of the GDL. In addition, a cyclic porosity variation is observed in the GDL under freeze‐and‐thaw cycles. The heterogeneous porosity is irreversibly decreased with the progress of repetitive cycles.     

Proton magnetic resonance microimaging of human trabecular bone

Proton magnetic resonance (1H magnetic resonance imaging (MRI)) images of human trabecular bone were acquired and discussed for two samples with different porosity. Three-dimensional 3D Spin Echo (3D SE) and Multi-Slice Multi-Echo (MSME) pulse sequences were examined. A very high slice resolution of (38 microm)2 was achieved (MSME). The intensity histograms were found useful for the characterization of the bone porosity. A spatial distribution of the spin-spin relaxation time T2 was monitored with the MSME pulse program. The work demonstrates the great potential of the proton MRI technique in the study of the trabecular bone morphology.     

Phase velocity and normalized broadband ultrasonic attenuation in Polyacetal cuboid bone-mimicking phantoms

The variations of phase velocity and normalized broadband ultrasonic attenuation (nBUA) with porosity were investigated in Polyacetal cuboid bone-mimicking phantoms with circular cylindrical pores running normal to the surface along the three orthogonal axes. The frequency-dependent phase velocity and attenuation coefficient in the phantoms with porosities from 0% to 65.9% were measured from 0.65 to 1.10 MHz. The results showed that the phase velocity at 880 kHz decreased linearly with porosity, whereas the nBUA increased linearly with porosity. This study provides a useful insight into the relationships between ultrasonic properties and porosity in bone at porosities lower than 70%.     

Photon migration of Raman signal in bone as measured with spatially offset Raman spectroscopy

Spatially offset Raman spectroscopy (SORS) is currently being developed as an in vivo tool for bone disease detection, but to date, information about the interrogated volume as influenced by the light propagation and scattering characteristics of the bone matrix is still limited. This paper seeks to develop our general understanding of the sampling depths of SORS in bone specimens as a function of the applied spatial offset. Equine metacarpal bone was selected as a suitable specimen of compact cortical bone large enough to allow several thin slices (600 µm) to be cut from the dorsal surface. Photon migration at 830‐nm excitation was studied with five bone slices and a 380‐µm‐thin polytetrafluoroethylene (PTFE) slice placed consecutively between the layers. To optimize Raman signal recovery of the PTFE with increasing depth within the bone stack required a corresponding increase in spatial offset. For example, to sample effectively at 2.2‐mm depth within the bone required an optimal SORS offset of 7 mm. However, with a 7‐mm offset, the maximum accessible penetration depth from which the PTFE signal could be still recovered was 3.7 mm. These results provide essential basic information for developing SORS technology for medical diagnostics in general and optimizing sampling through bone tissue, permitting a better understanding of the relationship between the offset and depth of bone assessed, in particular. Potential applications include the detection of chemically specific markers for changes in bone matrix chemistry localized within the tissue and not present in healthy bone. © 2015 The Authors. Journal of Raman Spectroscopy published by John Wiley & Sons, Ltd.     

Quantification of guided mode propagation in fractured long bones

Guided modes propagation in intact, fractured and healing long bone has drawn significant research interests. However, mode quantifications for the direct comparison are still necessary to address. The aim of the study is to analyze the mode interaction with a notch-fracture in the long bone and find quantitative ultrasound parameters sensitive to depth and width variation of the fracture. We analyzed the impacts of the partially and completely diaphyseal osteotomy on fundamental guided modes propagation using the two-dimension finite-difference time-domain (2D-FDTD) simulations. The long bones were built as three layer models by a cortical plate embedded between overlying soft tissue and inner-coated marrow. Narrowband low-frequency sinusoids (100 kHz) were employed to only excite two fundamental guided modes. The mode amplitude variations were investigated as functions of the gap-breakage width and depth. It is found that the transverse fractures have strong influences on the anti-symmetric mode A0 transmission and reflection, whereas amplitudes of the symmetric mode S0 are not sensitive to the fracture degree. The quantitative results consistently indicate that reflection energy and transmission coefficients of the S0 and A0 modes can be used to quantify the mode interaction in the fractured long bone and further to evaluate long bone fracture status. Future study is needed to investigate the physical experiments on realistic fractured long bone and to insure that the proposed ultrasound parameters can be used to quantitatively evaluate the long bone fracture in clinical application.     

High-speed spectroscopic imaging for cancellous bone marrow R(2)* mapping and lipid quantification

In this work an interleaved multiple-gradient-echo chemical shift imaging (IMGE-CSI) technique was designed, implemented and evaluated at 1.5 and 4T for high-resolution lipid quantification and R(2)* measurement in-vivo. The method is analogous to echo planar CSI but utilizes conventional gradient echoes, exploiting the principle of spectroscopic bandwidth extension by interleaving temporally offset gradient-echo trains. It is shown that IMGE-CSI is able to measure true fat volume fraction in oil/water mixtures with high accuracy, not possible with Dixon-type methods which approximate the spectrum as consisting of only two spectral components. Correlation of the CSI- derived volume fractions with volumetry afforded r(2) > 0.99 with a slope of 0.98. The method is shown to be able to quantify regional variations in bone marrow composition in vivo with a spatial resolution of 2.5 x 2.5 x 5 mm(3.) R(2)* was obtained by multi-line spectral curve fitting. For the measurement of R(2)* in cancellous bone marrow the method is shown to agree well with time-domain fitting techniques but is superior in instances where the marrow has both hematopoietic and fatty constituents. Finally, excellent inter-scan reproducibility (1% coefficient of variation for global means and medians) was achieved, yielding r(2) = 0.98 of the test-retest correlation for three scans in four test subjects. In conclusion, IMGE-CSI is found to enable highly accurate lipid quantification and measurement of cancellous bone marrow R(2)* at spatial resolutions and scan times typical of standard clinical protocols.     

空间频率域超声背散射参量用于骨质状况的评价*

在超声背散射骨质评价中,不同测量感兴趣区域(ROI)的超声背散射信号会有波动,致使诊断准确度降低。该文目的是研究超声背散射信号随测量区域的变化规律。采用空间扫描方法离体测量了35块骨样本,将超声背散射参数从空间域变换到空间频率域。结果表明,超声背散射参数的主要空间频率成分集中于低频部分;空间频率域超声背散射参量最大值(MASF)与骨矿密度等参数具有中高度显著相关性(R2=0.45~0.83,p0.001);空间频率域超声背散射参量衰减系数(AC)也与松质骨密度及结构特征有显著相关性(R2=0.41~0.72,p0.001)。研究表明空间频率域变换方法有助于明确超声背散射信号随测量ROI的变化规律,空间频率域的超声背散射相关新参量评价松质骨状况具有可行性。     

Measurement technique for depth profiling in time-domain low-coherence interferometer

A measurement technique for depth profiling in a time-domain low-coherence interferometer has been proposed. The spatial variation of the optical path caused by a diffraction grating in the Littrow configuration produces a white-light interferogram. A one-dimensional charge-coupled device (1D-CCD) detector is used to measure the undersampled white-light interferogram. The position of the reflective boundary is calculated from the rate of phase change with spatial frequency, which is based on the sub-Nyquist sampling of the white-light interferogram in the frequency domain.     

偏振干涉成像光谱仪中偏振化方向对调制度的影响

论述了自行研制的偏振干涉臧像光谱仪的原理,分析了其分光机理和成像原理;实在 重就起偏器、分析器的偏振化方向对干涉图调制度的影响进行了分析和计算,推导了偏振化方向偏离理想方向时调制度偏角的变化关系,给出和讨论了调制度随偏 角变化的空间曲面以及最大调制离（Ｖ＝１）和最小调制度（Ｖ＝０）时偏振器偏振化方向的空间取向。     

Effect of porosity on effective diagonal stiffness coefficients (cii) and elastic anisotropy of cortical bone at 1 MHz: a finite-difference time domain study

Finite-difference time domain (FDTD) numerical simulations coupled to real experimental data were used to investigate the propagation of 1 MHz pure bulk wave propagation through models of cortical bone microstructures. Bone microstructures were reconstructed from three-dimensional high resolution synchrotron radiation microcomputed tomography (SR-muCT) data sets. Because the bone matrix elastic properties were incompletely documented, several assumptions were made. Four built-in bone matrix models characterized by four different anisotropy ratios but the same Poisson's ratios were tested. Combining them with the reconstructed microstructures in the FDTD computations, effective stiffness coefficients were derived from simulated bulk-wave velocity measurements. For all the models, all the effective compression and shear bulk wave velocities were found to decrease when porosity increases. However, the trend was weaker in the axial direction compared to the transverse directions, contributing to the increase of the effective anisotropy. On the other hand, it was shown that the initial Poisson's ratio value may substantially affect the variations of the effective stiffness coefficients. The present study can be used to elaborate sophisticated macroscopic computational bone models incorporating realistic CT-based macroscopic bone structures and effective elastic properties derived from muCT-based FDTD simulations including the cortical porosity effect.     

Ultrasound propagation in trabecular bone: A numerical study of the influence of microcracks

The accumulation of microdamage in trabecular bone tissue is suspected of being a predictive indicator of osteoporosis diagnosis. To quantify this microdamage, the Dynamic AcoustoElastic Testing (DAET) method measures the Time Of Flight (TOF) and amplitude variations of transmitted ultrasound (US) pulses, while the bone sample is submitted to a low frequency sinusoidal hydrostatic pressure (opening/closing of microcracks). However, DAET is both sensitive to viscoelastic properties changes and microcracks density. To verify the microcracks density contribution on DAET results, a numerical approach is proposed. Multliple configurations of microdamaged trabecular bone-tissue-like mesh have been simulated. A 2D pseudo-spectral time domain numerical model was then developed to simulate linear wave propagation in heterogeneous solids. The influence of the microcracks number and orientation on the US TOF was particularly investigated. Results are discussed and compared with experimental data obtained from DAET measurements in trabecular bone samples.     

Experimental study of the porosity of loose stacks of stiff cylindrical fibres: Influence of the aspect ratio of fibres

The aim of this work is to study the porosity of three-dimensional and two-dimensional packing of stiff cylindrical fibres according to their aspect ratio. First, we have carried out an experimental study of the porosity for 3D and 2D packing. In this last case, the elementary representative surfaces have been determined. Then, an attempt of interpretation of the porosity variations for 2D stacks has been realized on the basis of the excluded volume theory and a variation law has been proposed. To conclude, we have studied the relevance of a simplified packing model based on a single geometry of the defects. Received 12 April 1999 and Received in final form 4 August 1999     

Prediction of backscatter coefficient in trabecular bones using a numerical model of three-dimensional microstructure

A model of ultrasonic backscattering for cancellous bone saturated by water is proposed. This model assumes that scattering is caused by the solid trabeculae and describes the cancellous bone as a weak scattering medium. The backscatter coefficient is related to the spatial Fourier transform of bone microarchitecture and to the density and compressibility fluctuations between the solid trabeculae and the saturating fluid. The computations of the model make use of three-dimensional numerical images of bone microarchitecture, obtained by tomographic reconstructions with a 10 microm spatial resolution. With this model, the predictions of the frequency dependence and of the magnitude of the backscatter coefficient are reasonably accurate. The theoretical predictions are compared to experimental data obtained on 19 specimens. An accuracy error of approximately 1 dB was found (difference between the averaged experimental values and theoretical predictions). One limit of the model may come from inaccurate values of trabecular bone characteristics needed for the computations (density and longitudinal velocity), which are yet to be precisely determined for human trabecular bone. However, the model is only slightly sensitive to variations of bone material properties. It was found that an accuracy error of 2.2 dB at maximum resulted from inaccurate a priori values of bone material properties. A computation of the elastic mean free path in the medium suggests that multiple scattering plays a minor role in the working frequency bandwidth (0.4-1.2 MHz). It follows from these results that a weak scattering medium model may be appropriate to describe scattering from trabecular bone.     

Studies by imaging TOF-SIMS of bone mineralization on porous titanium implants after 1 week in bone

Anodic oxidation was used to grow porous layers on titanium discs. Six different oxidation procedures were used producing six different surfaces. The implants were inserted in rat bone (tibia) for 7 days. After implant retrieval, mineralization (hydroxyapatite formation) on the implant surfaces was investigated using time-of-flight secondary ion mass spectrometry (TOF-SIMS). Bone tissue around the implants was sectioned and stained. The amount of bone in close apposition to the implant was calculated. The porosity showed great variation between the surfaces. Hydroxyapatite was detected on all surfaces. A slight positive correlation between porosity and mineralization was found, although the most porous surface was not the best mineralized one. Bone had formed around all implants after 7 days. The bone-to-metal contact for the porous implants did not differ significantly from the non-porous control. Porosity is known to influence cellular events. The results indicate that porosity could have an initial, positive influence on bone integration of implants, by stimulating the mineralization process. The methods used were found to be suitable tools for investigation of initial healing around implants in bone.     

Acoustic wave propagation in two-phase heterogeneous porous media

The propagation of an acoustic wave through two-phase porous media with spatial variation in porosity is studied. The evolutionary wave equation is derived, and the propagation of an acoustic wave is numerically analyzed in application to marine sediments with various physical parameters.     

Abrasive wear under multiscratching of polystyrene + single-walled carbon nanotube nanocomposites. Effect of sliding direction and modification by ionic liquid

Single-walled carbon nanotubes (NTs) and single-walled carbon nanotubes modified (NTms) by the room-temperature ionic liquid (IL) 1-octyl, 3-methylimidazolium tetrafluoroborate ([OMIM]BF₄) were added in a 1 wt.% to polystyrene (PS) and processed by compression or injection moulding to obtain PS + NT and PS + NTm, respectively. Friction coefficients and abrasive wear from penetration depth, residual depth and viscoelastic recovery were determined under multiple scratching. The effect of the moulding process, the additives and the sliding direction was studied. Compression moulded PS shows a transition to more severe damage after a critical number of successive passes. Addition of NTs or NTms to compression moulded PS induces a strain hardening effect and reduces friction, residual depth and viscoelastic recovery. Strain hardening is also observed in injection moulded PS with sliding in the longitudinal and random directions, but not in the transverse direction. The scratch resistance of PS + NTm depends on sliding direction. The lowest friction coefficient and residual depth values, and the highest viscoelastic recovery were found for injection moulded PS + NTm, in the sliding direction parallel to injection flow. Mechanisms of surface damage are discussed upon scanning electron microscopy (SEM), focused ion beam-field emission scanning electron microscopy (FIB-FESEM), 3D surface topography, surface roughness and profilometry observations.     

Analysis of two colliding fractionally damped spherical shells in modelling blunt human head impacts

The collision of two elastic or viscoelastic spherical shells is investigated as a model for the dynamic response of a human head impacted by another head or by some spherical object. Determination of the impact force that is actually being transmitted to bone will require the model for the shock interaction of the impactor and human head. This model is indended to be used in simulating crash scenarios in frontal impacts, and provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. It is assumed that the viscoelastic features of the shells are exhibited only in the contact domain, while the remaining parts retain their elastic properties. In this case, the contact spot is assumed to be a plane disk with constant radius, and the viscoelastic features of the shells are described by the fractional derivative standard linear solid model. In the case under consideration, the governing differential equations are solved analytically by the Laplace transform technique. It is shown that the fractional parameter of the fractional derivative model plays very important role, since its variation allows one to take into account the age-related changes in the mechanical properties of bone.     

Radon in groundwater of eastern Doon valley, Outer Himalaya

The radon content in water may serve as a useful tracer for several geohydrological processes. The hydrodynamic factor, presence of radium in host rocks, as well as the soil porosity and permeability control its concentration in groundwater. In order to understand the factors that control the occurrence of radon in groundwater of Doon valley in Outer Himalaya, a total of 34 groundwater samples were collected from handpumps and tubewells covering three hydrogeological units/areas in the eastern part of Doon valley. Radon variation in tubewells and handpumps varies from 25.4±1.8 to 92.5±3.4 Bq/l with an average of 53.5±2.6 Bq/l. A significant positive correlation between radon concentration and depth of the wells was observed in the Doiwala–Dudhli and Jolleygrant areas suggesting that radon concentration increases with drilling depth in areas consisting of sediments of younger Doon gravels, whereas samples of the Ganga catchment show negative correlation. The high radon levels at shallower depths in the Ganga catchment (consisting of fluvial terraces of Ganga basin) indicate uranium-rich sediments at shallower depth.