The effect of phase cancellation on estimates of broadband ultrasound attenuation and backscatter coefficient in human calcaneus in vitro

Broadband ultrasound attenuation (BUA) is a clinically proven indicator of osteoporotic fracture risk. BUA measurements are typically performed in through- transmission with single-element phase sensitive (PS) receivers and therefore can be compromised by phase cancellation artifact. Phase-insensitive (PI) receivers suppress phase cancellation artifact. To study the effect of phase cancellation on BUA measurements, through-transmission measurements were performed on 16 human calcaneus samples in vitro using a two-dimensional receiver array that enabled PS and PI BUA estimation. The means plus or minus standard deviations for BUA measurements were 22.1 plusmn 15.8 dB/MHz (PS) and 17.6 plusmn 7.2 dB/MHz (PI), suggesting that, on the average, approximately 20% of PS BUA values in vitro can be attributed to phase cancellation artifact. Therefore, although cortical plates are often regarded as the primary source of phase cancellation artifact, the heterogeneity of cancellous bone in the calcaneal interior may also be a significant source. Backscatter coefficient estimates in human calcaneus that are based on PS attenuation compensation overestimate 1) average magnitude of backscatter coefficient at 500 kHz by a factor of about 1.6 plusmn 0.3 and 2) average exponent (n) of frequency dependence by about 0.34 plusmn 0.12 (where backscatter coefficient is fit to a power law form proportional to frequency to the nth power).     

The effect of phase cancellation on estimates of calcaneal broadband ultrasound attenuation in vivo

Broadband ultrasonic attenuation (BUA) is a clinically-accepted measurement for prediction of osteoporotic fracture risk. Typical clinical BUA measurements are performed with phase-sensitive receivers and, therefore, can be affected by phase cancellation. In order to separate the effects of conventional attenuation (absorption plus scattering) from phase cancellation, BUA was measured on phantoms with acrylic wedge phase aberrators and on 73 women using both phase sensitive (PS) and phase insensitive (PI) reception. A clinical bone sonometer with a two-dimensional (2-D) receiver array was used. PI BUA measurements on phantoms with acrylic wedge phase aberrators were found to be far more resistant to phase cancellation than PS BUA measurements. In data from 73 women, means and standard deviations for BUA measurements were 81.4 +/- 21.4 dB/MHz (PS) and 67.2 +/- 9.7 dB/MHz (PI). The magnitude of the discrepancy between PS BUA and PI BUA tended to increase with bone mineral density (BMD).     

Velocity dispersion of acoustic waves in cancellous bone

Measurement of ultrasonic attenuation and velocity in cancellous bone are being applied to aid diagnosis of women with high fracture risk due to osteoporosis. However, velocity dispersion in cancellous bone has received little attention up to now. The overall goal of this research was to characterize the velocity dispersion of human cancellous bone based on a spectral analysis of ultrasound transmitted through the bone specimens. We have followed a systematic approach, beginning with the investigation of a test material, moving on to the investigation of bone specimens. Particular attention is given to diffraction effect, a potential source of artifacts. Parametric images of phase velocity (measured at the center frequency of the pulse spectrum), slope of attenuation coefficient (dB/cm/MHz) and velocity dispersion were obtained by scanning 15 bone specimens. We have demonstrated that the diffraction effect is negligible in the useful frequency bandwidth, and that the ultrasonic parameters reflect intrinsic acoustic properties of bone tissue. The measured attenuation showed approximately linear behavior over the frequency range 200 to 600 kHz. Velocity dispersion of cancellous bone in the frequency range 200 to 600 kHz was unexpectedly found to be either negative or positive and not correlated with the slope of attenuation coefficient. There was a highly significant correlation between the slope of attenuation coefficient and phase velocity at the center frequency of the spectrum. This behavior contrasts with other biological or nonbiological materials where the local form of the Kramers-Kronig relationship provides accurate prediction of velocity dispersion from the experimental frequency dependent-attenuation for unbounded waves.     

Mechanisms for attenuation in cancellous-bone-mimicking phantoms

Broadband ultrasound attenuation (BUA) in cancellous bone is useful for prediction of osteoporotic fracture risk, but its causes are not well understood. To investigate attenuation mechanisms, 9 cancellous-bone-mimicking phantoms containing nylon filaments (simulating bone trabeculae) embedded within soft-tissue-mimicking fluid (simulating marrow) were interrogated. The measurements of frequency-dependent attenuation coefficient had 3 separable components: 1) a linear (with frequency) component attributable to absorption in the soft-tissue-mimicking fluid, 2) a quasilinear (with frequency) component, which may include absorption in and longitudinal-shear mode conversion by the nylon filaments, and 3) a nonlinear (with frequency) component, which may be attributable to longitudinal-longitudinal scattering by the nylon filaments. The slope of total linear (with frequency) attenuation coefficient (sum of components #1 and #2) versus frequency was found to increase linearly with volume fraction, consistent with reported measurements on cancellous bone. Backscatter coefficient measurements in the 9 phantoms supported the claim that the nonlinear (with frequency) component of attenuation coefficient (component #3) was closely associated with longitudinal-longitudinal scattering. This work represents the first experimental separation of these 3 components of attenuation in cancellous bone-mimicking phantoms.     

Fatigue characterization of a polymer foam to use as a cancellous bone analog material in the assessment of orthopaedic devices

Analog materials are used as a substitute to cancellous bone for in vitro biomechanical tests due to their uniformity, consistency in properties and availability. To date, only the static material properties of these materials have been assessed, although they are often used in fatigue tests. Cancellous bone exhibits complex material behavior when subjected to fatigue loads, including modulus degradation, accumulation of permanent strain and increasing hysteresis. Analog materials should exhibit similar fatigue behavior to cancellous bone if they are to be used in cyclic loading tests. In our study, a polymer foam (commercial name HEREX C70.55) has been studied for its static and fatigue behavior and compared with that of cancellous bone. In compression, the foam exhibited qualitatively similar mechanical behavior, but the degree of modulus degradation and accumulation of permanent strain was lower than expected for cancellous bone. In general, the tensile properties of the foam were greater than found in compression, the opposite to the mechanical behavior of cancellous bone. The methodology employed here could form the basis of selecting suitable analog materials for cancellous bone in the future.     

The dependence of ultrasonic backscatter on trabecular thickness in human calcaneus: theoretical and experimental results

Trabecular thickness within cancellous bone is an important determinant of osteoporotic fracture risk. Noninvasive assessment of trabecular thickness potentially could yield useful diagnostic information. Faran's theory of elastic scattering from a cylindrical object immersed in a fluid has been used to predict the dependence of ultrasonic backscatter on trabecular thickness. The theory predicts that, in the range of morphological and material properties expected for trabecular bone, the backscatter coefficient at 500 kHz should be approximately proportional to trabecular thickness to the power of 2.9. Experimental measurements of backscatter coefficient were performed on 43 human calcaneus samples in vitro. Mean trabecular thicknesses on the 43 samples were assessed using micro computed tomography (CT). A power law fit to the data showed that the backscatter coefficient empirically varied as trabecular thickness to the 2.8 power. The 95% confidence interval for this exponent was 1.7 to 3.9. The square of the correlation coefficient for the linear regression to the log transformed data was 0.40. This suggests that 40% of variations in backscatter may be attributed to variations in trabecular thickness. These results reinforce previous studies that offered validation for the Faran cylinder model for prediction of scattering properties of cancellous bone, and provide added evidence for the potential diagnostic utility of the backscatter measurement.     

Recovery of parameters of cancellous bone by acoustic interrogation

The parameter recovery problem for cancellous bone by acoustic interrogation is investigated numerically. Biot’s equations coupled with boundary integral equations are used to model ultrasound propagation through a bone sample immersed in a water tank. The mathematical formulation for two-dimensional orthotropic bone is presented, but numerical results are only discussed in the isotropic case. The inversion procedure consists in minimizing some error on the pressure at measurement points located outside the bone sample. For this purpose, two different minimization algorithms are considered. A number of numerical tests are performed for a range of frequencies, which demonstrate the model’s ability to recover some bone parameters with satisfactory accuracy.     

Development of a numerical cancellous bone model for finite-difference time-domain simulations of ultrasound propagation

The trabecular frame in cancellous bone has numerous porous spaces of various sizes and shapes. Their continual arrangement changes with position in the bone. Assuming that the complicated pore space is the aggregation of spherical pores, in this study, the trabecular structure was analyzed using a three-dimensional (3-D) X-ray microcomputed tomography (muCT) image. Analysis involved a 3-D cancellous bone model developed for numerical simulations of ultrasound propagation. In this model, the trabecular structure was simplified by regularly arranging spherical pores in a solid bone. Using a viscoelastic, finite-difference, time-domain (FDTD) method with the simplified cancellous bone model, ultrasound pulse waveforms propagating through cancellous bone were simulated in two cases of the propagations parallel and perpendicular to the main trabecular orientation. The porosity dependences of the propagation properties, attenuation, and propagation speed were derived from the simulated waveforms. Comparisons with simulated results using the realistic cancellous bone model reconstructed from a 3-D muCT image, assisted to further validate this simplified model.     

Combination of 3D MRI and connectivity analysis in structural evaluation of cancellous bone in rat proximal femur

Three dimensional (3-D) magnetic resonance (MR) microimaging combined with connectivity analysis was tested in the study of the structure of cancellous bone. MR microimaging was performed in vitro with an average resolution of 20*20*35 m. A 3-D connectivity analysis was used to model the trabecular bone as a network consisting of nodes and struts. Size distribution curves of these two structural elements and the interconnectivity of nodes was used to estimate the cancellous structure.The analysis suggested the occurrence of two simultaneous network structures in cancellous bone differed by the size of details. The degradative effect of ostcopenia is found to be slightly different in these two subsystems. Interconnectivity is seen to increase with the size of a node and the expected loss of connectivity due to ostcopenia is observed.The method described offers a new way in the topological estimation of interconnected medium. © 2001 Kluwer Academic Publishers     

Propagation of ultrasonic waves through demineralized cancellous bone

Ultrasonic velocity is determined in a number of bovine cancellous (spongy) bone samples by using a double-probe-through-transmission ultrasonic pulse technique. The ultrasonic velocity, total mineral content, bone density, and solid volume fraction of the specimen were determined. The relation between fast velocity and each of the other parameters was examined to explore the best correlation using linear, logarithmic, power, and exponential relationships. There is a strong positive relationship between ultrasonic velocity and each of the other parameters. The exponential model fits the data better than the linear model, logarithmic model, and power model. Biot's theory also is used to predict the velocity of ultrasound in the demineralized bone. It is shown that the transmission of ultrasonic pulses in the cancellous bone samples can be adequately described using Biot's theory. The different parameters occurring in the Biot theory have been measured independently, and the calculation has been compared with measured velocity of water-saturated bone samples. The correlation coefficients for regression analysis between the experimental velocities and those predicted by Biot's theory are greater than 0.86.     

Finite element modelling—predictor of implant survival?

The cancellous bone stresses surrounding proximal femoral prostheses were investigated using the finite element method and the results correlated with clinical subsidence data for similar implant configurations. The finite element study has shown that press-fit prostheses generate significantly higher cancellous bone stresses than bonded (cemented and HA coated) prostheses. The cancellous bone stresses surrounding press-fit implants are sensitive to the coefficient of friction, with up to a 60% decrease observed when the coefficient of friction was increased from 0 to 0.4. Resecting the femoral neck generally increased the cancellous bone stresses however varying the thickness of the cement mantle had little or no effect. Good correlation was found between the finite element results and the clinically measured subsidence data. Implant configurations generating higher cancellous bone stresses were those which subsided the most. This observation suggests that it may be possible to use the initial cancellous bone stresses to predict the likelihood of migration and hence late aseptic loosening.     

Model-based estimation of quantitative ultrasound variables at the proximal femur

To improve the prediction of the osteoporotic fracture risk at the proximal femur we are developing a scanner for quantitative ultrasound (QUS) measurements at this site. Due to multipath transmission in this complex shaped bone, conventional signal processing techniques developed for QUS measurements at peripheral sites frequently fail. Therefore, we propose a model-based estimation of the QUS variables and analyze the performance of the new algorithm. Applying the proposed method to QUS scans of excised proximal femurs increased the fraction of evaluable signals from approx. 60% (using conventional algorithms) to 97%. The correlation of the standard QUS variables broadband ultrasound attenuation (BUA) and speed of sound (SOS) with the established variable bone mineral density (BMD) reported in previous studies is maintained (BUA/BMD: r² = 0.69; SOS/BMD: r²⁼ 0.71; SOS+BUA/BMD: r² = 0.88). Additionally, different wave types could be clearly detected and characterized in the trochanteric region. The ability to separate superimposed signals with this approach opens up further diagnostic potential for evaluating waves of different sound paths and wave types through bone tissue.     

Microstructural Modeling and Multiscale Mechanical Properties Analysis of Cancellous Bone

This paper is devoted to the microstructure geometric modeling and mechanical properties computation of cancellous bone. The microstructure of the cancellous bone determines its mechanical properties and a precise geometric modeling of this structure is important to predict the material properties. Based on the microscopic observation, a new microstructural unit cell model is established by introducing the Schwarz surface in this paper. And this model is very close to the real microstructure and satisfies the main biological characteristics of cancellous bone. By using the unit cell model, the multiscale analysis method is newly applied to predict the mechanical properties of cancellous bone. The effective stiffness parameters are calculated by the up-scaling multi-scale analysis. And the distribution of microscopic stress in cancellous bone is determined through the down-scaling procedure. In addition, the effect of porosity on the stiffness parameters is also investigated. The predictive mechanical properties are in good agreement with the available experimental results, which verifies the applicability of the proposed unit cell model and the validness of the multiscale analysis method to predict the mechanical properties of cancellous bone.     

The static and cyclic strength of a bone–cement bond

Four-point bending static and fatigue tests were carried out on bone–cement bonds. The effects of the pressurization and the washing of the bone joint face on the bond strength were investigated. The results are summarized as follows. When the bond surface of cancellous bone is washed prior to the application of the bone cement, both the static and fatigue strengths of the bond are increased relative to the corresponding properties of unwashed bone–cement bonds. From observations of bone–cement interfaces as well as the fracture surfaces of bone–cement specimens, it has been determined that bone cement was able to infiltrate into fine holes present in washed cancellous bone. However, such infiltration occurred to a much lesser degree in the case of unwashed cancellous bone. Increasing the molding pressure during the time of cement application to the bone from 39200 to 117600 Pa had a beneficial effect on the bending strength and fatigue properties, particularly in the case of washed bone cement specimens. An increase in molding pressure also resulted in a reduction in the amount of scatter in test results.     

Cancellous bone from porous T{i}6Al4V by multiple coating technique

A highly porous T{i}6Al4V with interconnected porous structure has been developed in our previous study. By using a so-called “Multiple coating” technique, the porous T{i}6Al4V can be tailored to resemble cancellous bone in terms of porous structure and mechanical properties. A thin layer of T{i}6Al4V slurry was coated on the struts of base porous T{i}6Al4V to improve the pore structure. After two additional coating, pore sizes ranged from 100 μm to 700 μm, and the porosity was decreased from ∼90% to ∼ 75%, while the compressive strength was increased from 10.3 ± 3.3 MPa to 59.4 ± 20.3 MPa and the Young's modulus increased from 0.8 ± 0.3 GPa to 1.8 ± 0.3 GPa. The pore size and porosity are similar to that of cancellous bone, meanwhile the compressive strength is higher than that of cancellous bone, and the Young's modulus is between that of cancellous bone and cortical bone. Porosity, pore size and mechanical properties can be controlled by the parameters in such multiple coating processes. Therefore the porous T{i}6Al4V with the characteristics of cancellous bone is expected to be a promising biomaterial for biomedical applications. Author to whom all correspondence should be addressed.     

Development of a new synthetic bone graft

A process for the replication of bovine cancellous bone in synthetic bioceramic materials for use as artificial bone graft substitutes is described. The process detailed here may be easily implemented to allow production of large numbers of blocks of material, even on a laboratory scale. The graft material has a pore morphology and interconnectivity identical with that of the original cancellous bone used as a starting material. Strength of the material is adequate, and at lower porosity levels it meets the FDA requirements for coralline materials for spinal applications. The synthetic graft is also shown to have excellent fluid-retention characteristics, making it a potential carrier for morphogenic agents such as solutions of bone morphogenic protein. © 1998 Kluwer Academic Publishers/p>     

Mechanical properties of open-cell foam synthetic thoracic vertebrae

This study presents comprehensive morphological and mechanical properties (static, dynamic) of open-cell rigid foams (Pacific Research Laboratories Inc. Vashon, WA) and a synthetic vertebral body derived from each of the foams. Synthetic vertebrae were comprised of a cylindrical open-cell foam core enclosed by a fiberglass resin cortex. The open-cell rigid foam was shown to have similar morphology and porosity as human vertebral cancellous bone, and exhibited a crush or fracture consolidation band typical of open-celled materials and cancellous bone. However, the foam material density was 40% lower than natural cancellous bone resulting in a lower compressive apparent strength and apparent modulus in comparison to human bone. During cyclic, mean compression fatigue tests, the synthetic vertebrae exhibited an initial apparent modulus, progressive modulus reduction, strain accumulation and S-N curve behaviour similar to human and animal vertebral cancellous bone. Synthetic open-cell foam vertebrae offer researchers an alternative to human vertebral bone for static and dynamic biomechanical experiments, including studies examining the effects of cement injection. Presented, in part, at the XXth Congress of the International Society of Biomechanics and 29th Annual Meeting of the American Society of Biomechanics, Cleveland, OH, July 31-August 5, 2005     

Effect of heat treatment on bioactivity and mechanical properties of PDMS-modified CaO-SiO2-TiO2 hybrids via sol-gel process

Crack- and pore-free transparent monolithic disks of polydimethylsiloxane (PDMS)- modified CaO-SiO₂-TiO₂ hybrids were obtained by hydrolysis and polycondensation of PDMS, tetraethoxysilane, tetraisopropyltitanate and calcium nitrate. The product as-dried at 60 °C formed an apatite on its surface in a simulated body fluid (SBF) within only one day, indicating its high bioactivity. The apatite-forming ability decreased slightly by a heat treatment below 250 °C. The bending strength of the product was about 11 MPa, independent of the heat treatment. This average strength value is comparable to that of the human cancellous bone. Young's modulus of the products increased from 100 to 500 MPa with increasing heat treatment temperature from 60 to 250 °C, but its values were within the range of those of the human cancellous bone. The strain at failure of the products decreased with increasing heat treatment temperature. Failure strains went down to the magnitudes exhibited by the human cancellous bone, when the products were heat treated in the temperature range from 150 to 250 °C. Thus, highly bioactive hybrids with mechanical properties analogous to those of the human cancellous bone were obtained. This new kind of bioactive hybrid may be useful as a bone-repairing material. © 2001 Kluwer Academic Publishers     

评价松质骨状况的一种背散射频谱方法

采用超声背散射信号的质心偏移量来评价松质骨,并对牛胫骨和人体跟骨中背散射信号的质心偏移量与松质骨表观密度的关系,以及人体跟骨松质骨中背散射信号频谱质心位置与年龄的关系进行了分析讨论。分析结果表明,随松质骨表观密度的增大,背散射信号频谱的质心向低频方向移动;随年龄的增大,质心位置越接近于发射超声的中心频率。根据超声背散射信号质心偏移量的大小,可用于评价松质骨健康状况。     

The structure and mechanics of bone

The four levels of hierarchy considered in this review are the nanoscale (the mineralised collagen fibre and the extrafibrillar mineral), the microscale (the structure as visible under the microscope), the mesoscale (particularly the relationship between cancellous and cortical bone) and the whole bone scale. The explosion of papers at the nanoscale precludes any settling on one best model. At the microscale the inadequacies of linear elastic fracture mechanics, the importance of R-curves for understanding what is happening to cracks in bone, and the effect of different histological types are emphasised. At the mesoscale the question of whether cancellous bone is anything but compact bone with a lot of holes in it, and the question of whether cancellous bone obeys Wolff’s ‘law’ is discussed. The problem of not damaging bone when examining it with X-rays is mentioned (though not solved). At the whole bone level the relative roles of genetics and the external forces and the question of the way in which bones are loaded, in bending or compression, is raised, and the question of size effects, long underestimated or ignored by the bone community, is discussed. Finally, the question of why there are hierarchies at all in bone is addressed