Ultrasound (US) waves are mechanical vibrations that are applied to a material—bone tissue—in order to study its properties, that is, density, elasticity, and structure. In this study we evaluated in which way density and elasticity of the spongy bone influenced the transmission of 1.25 MHz US pulses. Twelve cylindrical specimens (diameter, 8 mm; height, 5 mm) excised from phalanxes of pig were decalcified with 0.5 M EDTA for different times (0, 2, and 5 days). During these periods, the samples underwent the following investigations: US transmission, density, and elasticity measurements. To assess the homogeneity of decalcification, the cross-sections of some samples were microradiographed. A detailed analysis of the US signal received was performed using velocity, Fourier analysis, and some parameters typical of signal processing technique. A good correlation was found between US velocity and density (r2 = 0.70); a lower correlation was found between velocity and elasticity (r2 = 0.59). If density and elasticity are considered simultaneously, the correlation with the US velocity improves significantly (r2 = 0.84). Fourier analysis enabled us to observe a shift of the main frequency toward lower values as the decalcification process advanced. We also observed that in the regressions weighted for density, US velocity correlated poorly with elasticity (r2 = 0.16), whereas signal processing parameters maintain a good correlation with elasticity (ultrasound peak amplitude [UPA], r2 = 0.48; slope, r2 = 0.62). In this study, it has been observed that when using a signal processing technique to analyze US pulses, it is possible to identify some parameters that are related in different ways to density and to elastic properties of bone. Our results show the potentiality of US technique to separate information on bone density and elasticity that X-ray-based densitometric methods do not provide.
INTEREST IN the study of bone tissue has grown considerably over the years in connection with the clinical problem of osteoporosis and its diagnosis. (1–4) Osteoporosis is a systemic disease of the skeleton, characterized by low bone mass and microarchitectural deterioration of bone tissue, leading to enhanced bone fragility and a consequent increase in fracture risk.(3) Formerly, dual-energy X-ray absorptiometry (DXA) occupied a leading place among the tools for diagnosing osteoporosis. The absorptiometric technique indeed is able to measure the bone mineral content (BMC), expressed in grams, of the bone segment analyzed, and the bone mineral density (BMD), expressed in grams per square centimeter, as surface density.(5) This measurement has been highly criticized because it does not represent a true bone density but rather an apparent bone density, which is dependent on mass thickness.(6) In fact, BMD is not a true physical density, because in the case of two layers of the same material with the same physical density but different thickness, the BMD measured by DXA is not equal but linearly proportional to the thickness of the two layers. However, bone tissue is not homogeneous and does not consist merely of calcium but has particular characteristics of anisotropy and is composed of both mineral and organic matrix.(7) The DXA technique is unable to provide information on these special characteristics of bone tissue that are, however, very important factors in determining the mechanical resistance of bone in the assessment of fracture risk.
Over the past decade, researchers have focused on the quantitative ultrasound (QUS) methods applied to bone tissue in the attempt to obtain information on the structure, the anisotropy, and the elastic properties of the tissue, which are important in determining the fracture risk associated with the study and diagnosis of osteoporosis. In particular, the velocity of US transmission, speed of sound (SoS), and attenuation (broadband US attenuation [BUA]), have been studied in order to investigate in vitro and in vivo cortical and trabecular bone tissue. (8–12) Although, as has been shown, there is a good and fairly high correlation of SoS and BUA with bone density (both physical density and BMD measured by DXA) and it also has been observed that SoS correlates with the mechanical properties of bone tissue, for example, the elastic modulus and the failure load. (13–23) It also has been remarked that BUA reflects some characteristics of bone structure—for example, porosity—and is influenced by the orientation and distribution of the trabeculae in cancellous bone.(15, 24, 25)
In a previous in vitro study on the bones of pig phalanxes, we showed that macroscopic morphological changes (structural modification) in bone tissue induce alterations in US transmission.(26) In the present study we aimed to investigate the influence exerted, the structure being unchanged, by modifications in density and mechanical properties of bone tissue on US transmission. To this end, we studied a group of samples of trabecular bone tissue taken from the epiphysis of pig phalanxes that were gradually decalcified. The aim of the study was to evaluate whether certain quantitative parameters linked to the morphological characteristics of the US signal may be associated with elastic properties of the material traversed, independently of its density and structure.
MATERIALS AND METHODS
Sample preparation and decalcification set-up
Twelve cylindrical samples of trabecular bone tissue were taken from the proximal epiphysis of the proximal phalanx (fourth digit) of the forelimb of healthy young pigs, 12 months of age and 120-150 kg in weight. Each sample measured 8 mm in diameter and 5 mm in thickness, and each was cut coaxial with the anteroposterior axis of the phalanx. All samples were defatted in a solution of 3% sodium hypochlorite for 24 h, and they were then decalcified for different periods of time (varying from sample to sample) up to a maximum of 7 days, as proposed by Shah et al.(27) Decalcification of the bone tissue was performed using a solution of 0.5 M of EDTA (pH 8.0) at room temperature.
The samples prepared for decalcification were inserted one by one in a plastic syringe (internal diameter, 9 mm) and the decalcifying solution was made to flow through the sample in the syringe by means of a peristaltic pump (speed, 20 ml/h) in a closed, isolated circuit. The part of the experimental setup including the syringe and the US probes was immersed in a water bath to enable measurement of US propagation during the decalcification process without having to reposition the sample. All measurements were made at room temperature (20°C). The water bath was added with a detergent in order to optimize the acoustic coupling of the different surfaces. The direction of propagation of the US pulses was kept fixed along a diameter of the circular base of the cylinder throughout the decalcification process. The samples were marked according to the US propagation direction, and labels were renewed every time the sample was removed from the syringe. Two reference signs also were made on the surface of the syringe to allow correct repositioning. Samples were kept fixed inside the syringe by the insertion of two thin rubber spacers. Two polyurethane masks that covered the external ring of the circular active zone of the probes have been used in order to minimize effects of diffraction; polyurethane was used because it highly absorbs and attenuates the US waves (Fig. 1).
All samples and solutions employed were degassed carefully in a vacuum pump for 24 h before being used in order to remove air bubbles within the samples; this procedure was used at the beginning of the experiment and after each mechanical test.
Measurements of weight, volume, and density
During decalcification, at pre-established intervals, samples were removed from the syringe and dried, and then measurements of density (ρ) were performed. Density was determined by calculating the ratio between weight of the dry sample and total volume of the cylindrical sample.
where r is the radius of the circle base of the cylinder, h is its height, and WB is the dry weight of the sample.
Samples were dried under vacuum for 24 h before mechanical tests. The samples were positioned between the compression plates. Plates were in contact with the convex surfaces of the specimen and were in the same position of the US probes so that the load was applied in the same direction of the US mechanical waves. An initial pressure load was applied to each sample by means of a compressed air pump connected with a 10KN load cell, and this was increased gradually (0.5-MPa steps) using pressures from 0.5-6 MPa. The specimens were always controlled after each mechanical test in order to verify the absence of permanent deformations caused by the compression. If a specimen was permanently deformed, it was not used for further analysis. The absolute deformation of the sample was measured for each pressure value applied, by means of a precision caliper. The relative deformation was calculated as the ratio between the absolute deformation (mm) of each sample and the length of the same unloaded sample (mm). This made it possible to visualize on the graph the curve of applied pressure (stress) versus the relative deformation (strain; Fig. 2). The curve always showed a particular characteristic zone above 2.5 MPa where it could be approximated with a straight line; the slope of the linear part of the curve produced represents the stiffness coefficient relative to the pre-established direction of the sample investigated.(13)
Measurements of US propagation
Measurement of US propagation was performed two times per day during the decalcification process. Four repeated acquisitions of the US signal received were recorded for each measurement. US measurements were performed using a DBM Sonic 1200 device (IGEA, Carpi Mo, Italy). This consists of two US transducers (1.25-MHz frequency and 12-mm diameter), one transmitter, and one receiver. The probes were kept at a fixed distance from one another during measurement and were not in contact with the syringe containing the sample. The pulse generated by the transmitting probe propagates across the sample and is detected by the receiving probe. The US vibration of the receiving probe is then translated into an electric signal that is displayed on the screen. The absolute values of the negative peaks are taken into consideration so that the entire signal appears on the screen as positive (rectified). The device also is connected to a PC for automatic storing of the entire US pulse and digitized so it can be used for further analysis (Fig. 3). The fastest part of the signal received propagates through the bone sample. For this reason, the study analyzed the parts of the signal that corresponded to propagation speeds above 1700 m/s, a velocity measured when only water was present in the syringe of the decalcifying circuit.
Once the part of the US signal to be analyzed was selected (velocity >1700 m/s), to prevent any artifact that might give false contribution to the frequency spectrum during fast Fourier transform (FFT), incomplete peaks, resulting from the cut-off procedure, were excluded. For Fourier analysis it was necessary(28) to return the digitized signal to its original form, that is, not rectified. The Fourier spectrum obtained by each signal was normalized with respect to the total area subtended by the spectrum itself. The selected US signal was then studied by signal pattern analysis techniques. Besides the velocity of the US, the following other electrical parameters of the US signal were considered, based on indications resulting from previous in vitro and clinical experiences and on the theory of signal processing (29–33) :
Velocity of propagation of the US pulse, SoS, calculated by considering as instant of arrival the point of maximum amplitude of the first peak, that is, the fast part of the signal that has been shown to travel through the center of the sample.(26) The values of velocity were calculated using the substitution method so as to calculate the velocity of US propagation only in the bone tissue. The formula used is
where VB is velocity in bone; VW is velocity in water; SB is bone thickness, that is, the diameter (8 mm) of the sample; and Δt is the difference of time measured in the presence and absence of the sample.
US peak amplitude (UPA), maximum amplitude of the US signal considered, measured in millivolts.
Energy contained in the signal, calculated as the integral below the signal.
Weighted slope (W_Slope), that is, the slope of the straight regression line passing through the maximum points of the signal peaks weighted on the correlation coefficient calculated for the regression considered.
Amplitude of the first peak (UPA first peak), expressed in millivolts.
To improve the measurement precision, each of these values was calculated for each of the four acquisitions recorded and the mean value was considered in the analysis. To compare changes of the parameters among different samples, the percent variations referred to the first measured value have been calculated for each selected specimen. Concerning the velocity measurements, the percentage variations have been calculated on the dynamic range, taking as minimum velocity value the one measured when the syringe didn't contain the bone sample (1700 m/s).
To verify that the decalcification process was actually occurring homogeneously throughout the specimens and that it was dependent on EDTA elution length, microradiographs were taken on four specimens, each decalcified for different times. These were fixed in metacrylate and from each cylinder a 100-μm section was cut in the two major directions. All the sections thus obtained were microradiographed (Micro-X-ray; Italstructure, Como, Italy).(26) To verify the decalcification homogeneity, we analyzed the X-ray images digitized using the software Image Pro Plus (Media Cybernetics, Inc., Silver Spring, MD, U.S.A.). We studied the distribution of the intensity of the trabeculae (gray scale) in the space as compared with the background. By tracing two lines in perpendicular directions, we could obtain an intensity scan for each point along these lines. Plotting these data on a graph in which the y axis was represented by the intensity and the x axis was represented by the sorted sequence of the points on the line, we could evidence eventual intensity trends toward a specific direction using linear regression analysis.
All statistical analyses were performed with the Statistical Packages for Social Sciences (SPSS, Inc., Chicago, IL, U.S.A.) software. To study the associations among all the variables, bivariate linear regression analysis was used and the correlation coefficients (R2) were calculated. In addition, to determine the degree of correlation between two variables independently of a third variable, the partial correlation coefficients were calculated. Polynomial correlation analyses also were carried out between pairs of variables, determining the correct polynomial degree on the basis of log-transformed relationship analysis of the data. However, polynomial degrees higher than a third were not used. To determine if the polynomial fit used yielded significant improvement to the model, the level of significance for the T value, calculated for the coefficient relative to the highest degree to which the variable is elevated in the model, was used. Linear multivariate analysis also was used. To assess whether a variable improves the model, we calculated the p value for the contribution of each variable in the multivariate regression.
For all the correlation coefficients obtained from the linear and polynomial uni- and multivariate models, the statistical significance of the model was calculated according to the χ2 method.(34)
During the decalcification process, the positioning of the sample within the decalcifying circuit was controlled after each session of weight, volume, and mechanical measurements. No inhomogeneity was found in the intensity of the trabeculae in all the directions (Fig. 4A). The removal of calcium from the specimen was homogeneous. No difference was found in the distribution of the gray scale intensity of the trabeculae in the radiographic images taken at different times of decalcification ( Figs. 4A and 4B). Figure 4C shows how the mean gray scale intensity decreased over decalcification time.
Throughout the decalcification process measurements of US propagation were performed at a distance of 12 h from one another. Figure 5 shows the normalized mean percentage variations of SoS in time for all the samples that underwent the process up to the fifth day of decalcification; the error bars represent the mean SDs calculated on all the samples. Also recorded were measurements of density, weight, and stiffness coefficient, at pre-established instants during the decalcification time (at time T0 before decalcification, T1 after 2 days of decalcification, and T2 after 5 days of decalcification; Fig. 6).
The linear correlation coefficients between density, stiffness coefficient, and SoS were calculated for all the samples and reported in Table 1. The best correlations are between SoS and density (R2 = 0.67). In this first analysis of the data, it was remarked that using polynomial regressions—as is suggested anyway by theory—instead of linear regressions, the correlation coefficients obtained are significantly higher. It was noted that the regression coefficient R2 increased from 0.58 to 0.72 (p < 0.05) in the correlation between density and stiffness coefficient and from 0.67 to 0.71 (p < 0.05) in the correlation between density and SoS when polynomial fits were used ( Figs. 7A and 7B).
Table Table 1.. Correlation Coefficients R2 Among Density, Stiffness, and US Parameters
To evaluate the reciprocal incidence of SoS and stiffness coefficient, excluding the effect of the density, the linear correlation between the parameters weighted on the density was calculated. Analysis of the partial correlation thus obtained, it can be observed that SoS and stiffness coefficient are only marginally significantly correlated (R2 = 0.16; p = 0.05). Then partial correlation coefficient, weighted for stiffness coefficient, has been calculated between SoS and density; even without the effect of stiffness coefficient, SoS remains significantly related to density (R2 = 0.31; p < 0.005).
Finally, we evaluated the relative weight of density and stiffness coefficient combined together in models for SoS variations. Now, applying the multivariate linear model, we observed that when density and stiffness coefficient are combined together, the correlation with the SoS significantly increases with respect to the univariate linear models (R2 = 0.72; p < 0.05). The T values and their relative significance for density and stiffness coefficient are, respectively, T = 3.23 and p < 0.005 and T = 2.072 and p < 0.05. But if we combine mathematically the two variables in the form of the bar wave equation (V=√E/ρ), where E is the stiffness coefficient, ρ is the density value, and V is the US velocity, we obtain the highest correlation coefficient with SoS (R2 = 0.84; Fig. 8).
We performed the FFTs of all the signals recorded. For each sample during decalcification the same alteration of the spectrum was observed; before decalcification the Fourier spectrum presents a peak at high frequencies, with central frequency in the range of 0.9-1.1 MHz (Fig. 9, spectrum A); during decalcification (at T1) in the spectrum alongside the peak at high frequencies, a peak at lower frequencies, less than 0.7 MHz, becomes evident (Fig. 9, spectrum B); and at the end of the decalcifying process the main frequency is the low frequency (Fig. 9, spectrum C). For the six samples that reached T2 (5 days of decalcification) the main frequency values observed in the Fourier spectra were 0.98 ± 0.08 MHz at T0 and 0.54 ± 0.13 MHz at T2.
We then moved on to the quantitative analysis of the US signal by evaluation of the ultrasonographic parameters; the variations during decalcification of all the ultrasonographic parameters considered (Fig. 10, UPA, W_Slope, energy, and UPA first peak). We then observed how these parameters correlated with density and stiffness coefficient; the regression correlation coefficients are shown in Table 1.
UPA and W_Slope are correlated closely with the stiffness coefficient, whereas the amplitude of the first peak (UPA first peak) seems to be more correlated with the density than with the stiffness coefficient. Even after weighting the regressions for the density, UPA (R2 = 0.53; p < 0.0001), energy (R2 = 0.31; p < 0.005), W_Slope (R2 = 0.34; p < 0.005), and UPA first peak (R2 = 0.19; p < 0.05), they still remain significantly correlated with the stiffness coefficient, differently from SoS. In the multivariate model applied to each one of the US parameters using as independent variables density and stiffness coefficient, we found that stiffness coefficient remains the only significant variable in the model for UPA (p < 0.0001), W_Slope (p < 0.005), and energy (p < 0.005). In these cases, density does not improve the model significantly. In the case of UPA first peak, density and stiffness coefficient both contribute significantly to the model (p < 0.005 and p < 0.05, respectively), even if density has a larger relevance with respect to stiffness coefficient. Subsequently, using polynomial regressions in the analysis of these data we obtained higher correlation values, as shown in Table 1.
In recent years, the QUS technique has been studied in the field of osteoporosis as a less expensive alternative to X-ray absorptiometric technique and one that avoids the problem of the ionizing radiation to which the patient is exposed during measurement. (8–12) This is why great emphasis has been placed on the ability of this technique to determine BMD in the same way as X-ray densitometric techniques. (35–39) Indeed, it was relegated to a position of less importance than the potential of the US technique to supply further information on the bone tissue analyzed, independent of the mineral density but closely linked with the stiffness of the material.
For this reason, in the present study we investigated different new aspects of the interaction of the US signal through bone tissue, and we focused on the influence exerted separately by density and elastic characteristics of the material. In particular, we attempted to interpret the information provided by the US signal that should be independent on the density characteristics of the bone commonly studied with these devices. We used samples of bone tissue taken from pig phalanxes gradually decalcified with EDTA, thus leaving the trabecular structure unchanged. We have shown by microradiographic analysis of four specimens that the decalcification occurred homogeneously throughout the specimen over time in our experimental conditions.
Online we were able to follow the effect of the in vitro decalcification on the transmission of the US signal. We succeeded in confirming that the transmission of the US is closely linked—especially its velocity—with the degree of mineralization. At the same time, the use of mechanical compression tests enabled us to correlate, with one another, the stiffness of the sample, its density, and SoS. In particular, when the parameters are combined together in the bar wave equation, high values of R2 are obtained: R2 = 0.84. This result suggests that linear models are not always able to give an exhaustive account of the relations between the measured magnitudes of a particular phenomenon. Often, to the contrary, it is useful to consider the mathematical models suggested by the theory. Nevertheless, analysis of the partial correlation between velocity and stiffness coefficient weighted for density show a low degree of correlation (R2 = 0.16; p = 0.05), whereas the partial correlation between SoS and density, weighted for stiffness coefficient, is still highly significant (R2 = 0.31; p < 0.005). In the multivariate model including density and stiffness as variables, both variables significantly contribute to improve the R2 correlation of the model. These results allow us to conclude that velocity is related more strictly to density than to stiffness. Nevertheless, stiffness coefficient significantly contributes to increase the R2 of the multivariate model also. Similar results have been obtained by Hans et al.(13) with the same device. They used cubes excised from cadaveric lumbar vertebrae and they found that the variability of SoS is explained mostly by density and to a small extent by elasticity or anisotropy. Their results, in terms of correlation coefficients, are similar, even if they found a higher correlation between SoS and density and a lower correlation between SoS and elasticity, with respect to our results. This can be caused by a number of effects: the different origin of the specimens (human and pig specimens), the different methods used in the evaluation of sample density (QCT and weight/volume ratio), and the difference in the geometry used for mechanical tests. Other studies have addressed the issue of the association among density, elasticity, and US velocity with similar results; although their correlations are higher, these differences can be attributed to the specific experimental conditions used: US frequencies, animal specimens, geometrical conditions, etc.(14, 17–20)
An important and original aspect of this work consisted of studying the characteristics of the US signal produced at the receiving probe and particularly in the application of signal processing techniques. Use of the FFT technique applied to the received and digitized US signal represents the preliminary approach to addressing correctly and with theoretical bases the study of the analysis of a discrete time signal such as the US signal considered here. Initial analysis on the frequency spectrum of the signal enabled us to observe a typical trend of the maximum amplitude peaks during decalcification that was reproducible and detectable in all the samples decalcified. In a very reproducible way, we observed that the main frequency (that of maximum amplitude) in the Fourier spectrum of the US signal during decalcification shifts toward lower values, from 0.98 to 0.54 MHz. The shift toward low frequencies of the US signal after decalcification is different from that reported by other authors studying the BUA of the whole signal, always below 1 MHz.(33) This difference can be explained if we consider that in this study we have investigated the part of the signal in which velocity exceeds 1700 m/s. Thus, the US signal considered here refers to fast US waves, traveling mostly in the bone material, not taking into consideration the slow US waves mainly propagating through intertrabecular spaces. Furthermore, another aspect should be taken into consideration: the nonlinearity of the association of BUA with porosity of the bone. In fact, a negative association between BUA and density above 600 mg/cm3 has been observed by Han et al.(40) Our specimens cover a range between 200 and 1400 mg/cm3, with a majority above 600 mg/cm3; this aspect also may help to explain our results.
From the methodological point of view, this undoubtedly qualitative-type analysis enabled us to investigate the phenomenon in a quantitative way, defining and studying the behavior of certain parameters calculated on morphological aspects of the US signal received. We thus evidenced how it is possible to identify certain parameters of the received US signal that are linked more closely with the stiffness characteristics of the bone tissue independently of the density. These observations on the changes of the characteristics of the US signal suggest that the bone tissue should be viewed not merely as a means of transport, but as a material that actively modifies the US signal,(28) which, from a bioengineering point of view, could be described as a low-pass band filter. Langton has developed an electronic phantom, on the basis of the low-pass filter properties of the cancellous bone.(41) Thus, the experimental model and the US signal analysis techniques applied here could represent a first step for the development of an electrical model of the bone, which could be used to describe the interaction between US and bone tissue. From these observations, it can clearly be understood how the detection of the interaction between bone tissue and US is much more complex as compared with DXA and it should be investigated using appropriate signal processing techniques. Only an in depth analysis can effectively supply information on the structural, densitometric, and elastic characteristics that combine to define the mechanical properties of bone tissue.(26, 30, 31, 42, 43)
The main limitation of the study is the unknown clinic relevance of these results. Nevertheless, clinical studies are now focusing on the changes of the US signal after bone resorption in different pathologies.(31, 42, 43) Another limitation of the study was undoubtedly the impossibility of comparing the values of the stiffness coefficient with the values of the Young modulus commonly determined by means of mechanical tests. In spite of using the same methodology in performing the mechanical tests, an undoubted difference in the geometry of the samples makes such comparison impossible and also makes it impossible for us to use the term “Young modulus” in order to define the result of our mechanical tests.
This study enables us to show that the potentiality of the analysis of the US signal, a technique commonly used in clinical echography, is much more extensive as compared with the present common use of these techniques in US devices for diagnosing osteoporosis. Further studies are needed in order to better define the values obtained by signal processing that in a more significant way are able to supply useful information for various clinical requirements. In particular, the clinical relevance of this new approach for the study of osteoporosis remains to be established. Nevertheless, some preliminary reports are clearly promising.(42)