Human Calcaneus Research Articles

Fundamental precision limitations for measurements of frequency dependence of backscatter: applications in tissue-mimicking phantoms and trabecular bone.

Various models for ultrasonic scattering from trabecular bone have been proposed. They may be evaluated to a certain extent by comparison with experimental measurements. In order to appreciate limitations of these comparisons, it is important to understand measurement precision. In this article, an approach proposed by Lizzi and co-workers is adapted to model precision of estimates of frequency-dependent backscatter for scattering targets (such as trabecular bone) that contain many scatterers per resolution cell. This approach predicts uncertainties in backscatter due to the random nature of the interference of echoes from individual scatterers as they are summed at the receiver. The model is validated in experiments on a soft-tissue-mimicking phantom and on 24 human calcaneus samples interrogated in vitro. It is found that while random interference effects only partially explain measured variations in the magnitude of backscatter, they are virtually entirely responsible for observed variations in the frequency dependence (exponent of a power law fit) of backscatter.

Ossification in the human calcaneus: a model for spatial bone development and ossification

Perichondral bone, the circumferential grooves of Ranvier and cartilage canals are features of endochondral bone development. Cartilage canals containing connective tissue and blood vessels are found in the epiphysis of long bones and in cartilaginous anlagen of small and irregular bones. The pattern of cartilage canals seems to be integral to bone development and ossification. The canals may be concerned with the nourishment of large masses of cartilage, but neither their role in the formation of ossification centres nor their interaction with the circumferential grooves of Ranvier has been established. The relationships between cartilage canals, perichondral bone and the ossification centre were studied in the calcaneus of 9 to 38-wk-old human fetuses, by use of epoxy resin embedding, three-dimensional computer reconstructions and immunhistochemistry on paraffin sections. We found that cartilage canals are regularly arranged in shells surrounding the ossification centre. Whereas most of the shell canals might be involved in the nourishment of the cartilage, the inner shell is directly connected with the perichondral ossification groove of Ranvier and with large vessels from outside. In this way the inner shell canal imports extracellular matrix, cells and vessels into the cartilage. With the so-called communicating canals it is also connected to the endochondral ossification centre to which it delivers extracellular matrix, cells and vessels. The communicating canals can be considered as inverted 'internal' ossification grooves. They seem to be responsible for both build up intramembranous osteoid and for the direction of growth and thereby for orientation of the ossication centre.

Quantitative Ultrasound and Trabecular Architecture in the Human Calcaneus

Relationships between quantitative ultrasound (QUS), density (bone volume density [BV/TV]), and trabecular architecture were investigated in 69 calcaneal cancellous bone cubes. Ultrasound signal velocity, phase velocity, attenuation, and broadband ultrasonic attenuation (BUA) measurements were made along the mediolateral axis. Density and architectural parameters were measured using microcomputed tomography (microCT). Density yielded the best correlations with QUS (r2 = 73-77%). Of the individual architectural parameters, correlations with QUS were highest for the Structure Model Index (SMI), a parameter quantifying the relative proportion of rods and plates (r2 = 57-63%). After adjustment for density, significant associations with QUS remained for SMI, trabecular spacing (Tb.Sp), and trabecular number (Tb.N), although the variance in QUS attributable uniquely to individual architectural parameters was at best 4%. In multivariate regression models, combinations of density and architectural parameters explained 76-82% of the variance in QUS, representing an r2 increase of, at most, 8% compared with using density alone. However, multivariate models using combinations of architectural parameters alone (i.e., density excluded) also had a good predictive ability for QUS (r2 = 73-81%). Thus, although these data show modest but significant density-independent relationships between QUS and trabecular architecture in the human calcaneus for the first time, the causal relationships behind the variation in acoustic properties remain obscure. Given the relative weakness and complexity of the emerging associations between QUS and architecture, it is prudent to regard QUS measurements in calcaneal bone primarily as an indicator of bone density.

Computer and experimental simulation of a cortical end-plate phase cancellation artefact in the measurement of BUA at the calcaneus

It has been experimentally demonstrated that for the measurement of broadband ultrasound attenuation (BUA) at the human calcaneus the cortical end-plate creates a measurement artefact of the order of 7 dB MHz−1. It has been suggested that the origin of this artefact may be a phase cancellation of the ultrasound pulse resulting from inconsistencies in propagation time across the ultrasound beam.Experimental and computer simulations were performed on samples of varying degrees of curvature and hence varying propagation times across the ultrasound beam. The experimental simulation incorporated Perspex samples of 35, 50 and 75 mm radius. The computer simulation was implemented using Matlab and Simulink, with the propagation time represented by a transport delay. The wavelet-based simulation incorporated a digitized transmitted ultrasound pulse derived from the experimental simulation.The experimental and computer-derived frequency spectra for the varying radii samples were comparable, demonstrating, firstly, that there is a significant dependence of measured BUA upon radius of curvature and, secondly, that the response in measured BUA to radius of curvature is similar in magnitude and trend for both experimental and computer simulations. The current study suggests that the BUA artefact observed in vitro corresponds to a radius of approximately 58 mm. Although the radius of curvature was not recorded in the original in vitro study, this value appears to be reasonable.This study indicates that the assumptions within the computer simulation were manifested within the experimental validation, and, hence, the observed BUA measurement artefact is related to the presence of the calcaneal cortical end-plate and is due to phase cancellation of the propagating ultrasound pulse.

Autocorrelation analysis of bone structure.

We propose a method called spatial autocorrelation analysis (SACA) to determine the spatial anisotropy of the trabecular bone in order to investigate osteoporosis. For demonstrating the potential of SACA we first evaluate the method on rectangular, simulated test patterns as a simple model for the anisotropic pore structure of the bone. As a next step towards biomedical application, photographic reference images of human vertebral bone were investigated by SACA. Osteoporotic bone structure could be clearly differentiated from non-osteoporotic sample images. Moreover, for demonstration of the applicability and potential of the method for in vivo characterization of osteoporosis, the microstructure of the human calcaneus was investigated by MR-microimaging on a young healthy male subject and an osteoporotic female. The measurements were performed using a high-field (3T) whole-body MR tomograph equipped with a special, strong head gradient system. The signal was acquired with a surface coil mounted on an in-house-built device for convenient immobilization of the subject's foot. Using a 3D gradient echo sequence a resolution of 0.254 x 0.254 x 2.188 mm3 was achieved in vivo. Selected images were inverted, gradient corrected for the inhomogeneous but sensitive detection by the surface coil, and subsequently analyzed by SACA. The anisotropy of bone structure detected by SACA is a possible candidate for noninvasive determination of the osteoporotic status, potentially complementing standard bone mineral density measurements.

Ultrasonic attenuation in human calcaneus from 0.2 to 1.7 MHz.

Ultrasonic attenuation has been demonstrated to be a useful measurement in the diagnosis of osteoporosis. Most studies have employed ultrasound in a range of frequencies from about 200 kHz-300 kHz to 600 kHz-1 MHz, and many have assumed a linear dependence of attenuation on frequency. In order to investigate the attenuation properties of human calcaneus at higher frequencies, 16 defatted human calcanea were interrogated in vitro using two matched pairs of transducers with center frequencies of 500 kHz and 2.25 MHz. The linear dependence of attenuation on frequency seems to extend up to at least 1.7 MHz. The correlation between attenuation coefficient and frequency from 400 kHz to 1.7 MHz was r = 0.999 (95% confidence interval, CI, = 0.998-1.00). The measurements suggest that some deviations from linear frequency dependence of attenuation may occur at lower frequencies (below 400 kHz), however.

A numerical method to predict the effects of frequency-dependent attenuation and dispersion on speed of sound estimates in cancellous bone.

Many studies have demonstrated that time-domain speed-of-sound (SOS) measurements in calcaneus are predictive of osteoporotic fracture risk. However, there is a lack of standardization for this measurement. Consequently, different investigators using different measurement systems and analysis algorithms obtain disparate quantitative values for calcaneal SOS, impairing and often precluding meaningful comparison and/or pooling of measurements. A numerical method has been developed to model the effects of frequency-dependent attenuation and dispersion on transit-time-based SOS estimates. The numerical technique is based on a previously developed linear system analytic model for Gaussian pulses propagating through linearly attenuating, weakly dispersive media. The numerical approach is somewhat more general in that it can be used to predict the effects of arbitrary pulse shapes and dispersion relationships. The numerical technique, however, utilizes several additional assumptions (compared with the analytic model) which would be required for the practical task of correcting existing clinical databases. These include a single dispersion relationship for all calcaneus samples, a simple linear model relating phase velocity to broadband ultrasonic attenuation, and a constant calcaneal thickness. Measurements on a polycarbonate plate and 30 human calcaneus samples were in good quantitative agreement with numerical predictions. In addition, the numerical approach predicts that in cancellous bone, frequency-dependent attenuation tends to be a greater contributor to variations in transit-time-based SOS estimates than dispersion. This approach may be used to adjust previously acquired individual measurements so that SOS data recorded with different devices using different algorithms may be compared in a meaningful fashion.

Quantitative ultrasound does not reflect mechanically induced damage in human cancellous bone.

This study investigated the ability of quantitative ultrasound (QUS) to detect reductions in the elastic modulus of cancellous bone caused by mechanical damage. Ultrasonic velocity and attenuation were measured using an in-house parametric imaging system in 46 cancellous bone cores from the human calcaneus. Each core was subjected to a mechanical testing regime to (a) determine the predamage elastic modulus, (b) induce damage by applying specified strains in excess of the yield strain, and (c) measure the postdamage elastic modulus. The specimens were divided into four groups: a control group subjected to a nominally nondestructive 0.7% maximum strain (epsilonm) and three damage groups subjected to increasing strain levels (epsilonm = 1.5, 3.0, and 4.5%). QUS measurements before and after the mechanical testing showed no significant differences between the control group and damage groups, despite highly significant (p < 0.001) reductions in the elastic modulus of up to 72%. These results indicate that current QUS techniques do not intrinsically reflect the elastic properties of cancellous bone. This is consistent with ultrasonic properties being determined by other factors (apparent density and/or architecture), which normally are associated strongly with elastic properties, but only when bone is mechanically intact. Clinically, this implies that ultrasound cannot be expected to detect bone fragility in the absence of major changes in bone density and/or trabecular architecture.

Relationships of ultrasonic backscatter with ultrasonic attenuation, sound speed and bone mineral density in human calcaneus

Ultrasonic attenuation and sound speed have been investigated in trabecular bone by numerous authors. Ultrasonic backscatter has received much less attention. To investigate relationships among these three ultrasonic parameters and bone mineral density (BMD), 30 defatted human calcanei were investigated in vitro. Normalized broadband ultrasonic attenuation (nBUA), sound speed (SOS), and logarithm of ultrasonic backscatter coefficient (LBC) were measured. Bone mineral density was assessed using single-beam dual energy x-ray absorptiometry (DEXA). The correlation coefficients of least squares linear regressions of the three individual ultrasound (US) parameters with BMD were 0.84 (nBUA), 0.84 (SOS) and 0.79 (LBC). The 95% confidence intervals for the correlation coefficients were 0.69–0.92 (nBUA), 0.68–0.92 (SOS) and 0.60–0.90 (LBC). The correlations among pairs of US variables ranged from 0.63–0.79. Variations in nBUA accounted for r 2 = 62% of the variations in LBC. Variations in SOS accounted for r 2 = 40% of the variations in LBC. These results suggest that ultrasonic backscattering properties may contain substantial information not already contained in nBUA and SOS. A multiple regression model including all three US variables was somewhat more predictive of BMD than a model including only nBUA and SOS.

The relationship between ultrasonic backscatter and bone mineral density in human calcaneus

Backscatter and attenuation coefficients were measured from 24 human calcanei in vitro. The logarithm of the backscatter coefficient at 500 kHz showed moderate correlations with bone mineral density (r=0.81, 95% confidence interval: 0.59-0.91) and attenuation (r=0.79, 95% CI: 0.56-0.91). These results suggest that backscatter measurements may be useful in the diagnosis of osteoporosis.

Anisotropy of ultrasonic backscatter and attenuation from human calcaneus: implications for relative roles of absorption and scattering in determining attenuation.

Although bone sonometry has been demonstrated to be useful in the diagnosis of osteoporosis, much remains to be learned about the processes governing the interactions between ultrasound and bone. In order to investigate these processes, ultrasonic attenuation and backscatter in two orientations were measured in 43 human calcaneal specimens in vitro at 500 kHz. In the mediolateral (ML) orientation, the ultrasound propagation direction is approximately perpendicular to the trabecular axes. In the anteroposterior (AP) orientation, a wide range of angles between the ultrasound propagation direction and trabecular axes is encountered. Average attenuation slope was 18% greater while average backscatter coefficient was 50% lower in the AP orientation compared with the ML orientation. Backscatter coefficient in both orientations approximately conformed to a cubic dependence on frequency, consistent with a previously reported model. These results support the idea that absorption is a greater component of attenuation than scattering in human calcaneal trabecular bone.

Measurements of phase velocity and group velocity in human calcaneus

Ultrasonic velocity in calcaneus correlates highly with bone mineral density, which is a good predictor of osteoporotic fracture risk. Several commercial bone sonometers perform a velocity measurement based on the transit time of a broadband pulse to assess skeletal status. This approach is somewhat problematic, however, because several authors have reported ambiguities in measurements in calcaneus. Phase velocity is an alternative that may be less dependent on device spectral characteristics. In addition, dispersion (the frequency-dependence of phase velocity) is a fundamental property worth investigating to increase understanding of interaction between ultrasound and bone. To compare two group-velocity measurement methods and one phase-velocity measurement method, a polycarbonate sample (for method validation) and 24 human calcanei were investigated in vitro. Phase velocity in calcaneus at 500 kHz was 1511 m/s ± 30 m/s (mean ± standard deviation). Average phase velocity decreased approximately linearly with frequency (−18 m/s MHz). The two group velocity measurements were comparable and tended to be slightly lower than phase velocity. The magnitude of dispersion showed little correlation with bone mineral density.

Temperature dependence of ultrasonic attenuation in human calcaneus

Ultrasonic attenuation in calcaneus has been shown to be a useful measurement for the diagnosis of osteoporosis. Several studies indicate that this measurement is affected by temperature fluctuations, although the fundamental causes for this are currently not well understood. To investigate this phenomenon, six defatted human calcanei were interrogated in vitro at six temperatures ranging from 10°C to 40°C. The temperature-related variation was −0.18 dB/cmMHz°C (95% confidence interval: −0.27 dB/cmMHz°C, −0.10 dB/cmMHz°C). This study reinforces the notion, advanced by other investigators, that temperature-related effects need to be taken into account when performing diagnostic measurements that require high precision (such as monitoring responses to drug intervention), will aid in the interpretation of in vivo experiments designed to investigate temperature-dependent precision limitations, will facilitate comparisons between in vitro studies normally carried out at room temperature with in vivo studies carried out at body temperature, and fills a gap in the compendium of measurements of temperature-dependences of acoustic properties of biologic tissues.

Internal Architecture of the Calcaneus: Implications for Calcaneus Fractures

Fourteen cadaveri specimens were sectioned to analyze the internal architecture of the human calcaneus. We described the arrangement and orientation of trabecular patterns within the calcaneus and made multiple measurements of its cortical thickness. To characterize the internal architecture of the calcaneus and correlate these findings with well-described patterns of calcaneus fracture in order to better understand the fracture mechanics of this common fracture. Fourteen dry, frozen, human calcanei were sectioned using a saw. In each the coronal, sagittal and axial planes, we sectioned separate specimens into slices of 0.5 mm thickness. High-resolution radiographic images were taken of the sectioned specimens. The internal trabecular arrays were described and measurements of cortical thickness were recorded. The correlation between these findings and the known pattern of calcaneal fractures was analyzed. A dominant trabecular pattern running antero-posteriorly along the long axis of the calcaneus was observed. In the posterior tuberosity the trabeculae were arranged parallel to the posterior border. There was an area of sparse or absent mineralization in the anterior part of the calcaneus corresponding to the "neutral triangle" described by Wood and Harty 10, 23. The thickest sites of the calcaneal cortex were the lower pole of the posterior tuberosity, the upper surface at the angle of Gissane, and the lateral surface below the anterior portion of the posterior facet. The trabecular architecture of the calcaneus is created by applied stress in concordance with Wolff's law. The weakest plane of resistance to stress is parallel to these organized trabeculae or through areas lacking trabeculae. This study demonstrates that the primary and secondary fracture lines commonly encountered in calcaneus fractures correlates with the internal architectural map of the calcaneal trabecular patterns.

The effects of frequency-dependent attenuation and dispersion on sound speed measurements: applications in human trabecular bone

Sound speed may be measured by comparing the transit time of a broadband ultrasonic pulse transmitted through an object with that transmitted through a reference water path. If the speed of sound in water and the thickness of the sample are known, the speed of sound in the object may be computed. To measure the transit time differential, a marker such as a zero-crossing, may be used. A sound speed difference between the object and water shifts all markers backward or forward. Frequency-dependent attenuation and dispersion may alter the spectral characteristics of the waveform, thereby distorting the locations of markers and introducing variations in sound-speed estimates. Theory is derived to correct for this distortion for Gaussian pulses propagating through linearly attenuating, weakly dispersive media. The theory is validated using numerical analysis, measurements on a tissue mimicking phantom, and on 24 human calcaneus samples in vitro. Variations in soft tissue-like media are generally not exceptionally large for most applications but can be substantial, particularly for high bandwidth pulses propagating through media with high attenuation coefficients. At 500 kHz, variations in velocity estimates in bone can be very substantial, on the order of 40 to 50 m/s because of the high attenuation coefficient of bone. In trabecular bone, the effects of frequency-dependent attenuation are considerable, and the effects of dispersion are negligible.

Frequency dependence of ultrasonic backscatter from human trabecular bone: theory and experiment.

A model describing the frequency dependence of backscatter coefficient from trabecular bone is presented. Scattering is assumed to originate from the surfaces of trabeculae, which are modeled as long thin cylinders with radii small compared with the ultrasonic wavelength. Experimental ultrasonic measurements at 500 kHz, 1 MHz, and 2.25 MHz from a wire target and from trabecular bone samples from human calcaneus in vitro are reported. In both cases, measurements are in good agreement with theory. For mediolateral insonification of calcaneus at low frequencies, including the typical diagnostic range (near 500 kHz), backscatter coefficient is proportional to frequency cubed. At higher frequencies, the frequency response flattens out. The data also suggest that at diagnostic frequencies, multiple scattering effects on the average are relatively small for the samples investigated. Finally, at diagnostic frequencies, the data suggest that absorption is likely to be a larger component of attenuation than scattering.

Bone properties as estimated by mineral density, ultrasound attenuation, and velocity

Quantitative ultrasound (QUS) analysis of bone has been suggested to have a level of performance equal to dual-energy X-ray absorptiometry (DXA) for the assessment of fracture risk. In this study, QUS and DXA measurements were conducted on bovine trabecular bone in vitro using commercially available clinical instruments. The samples were then mechanically tested to obtain Young’s modulus and ultimate strength. In addition, QUS and DXA parameters of the human calcaneus (n = 34) were measured in vivo. The measurements revealed a significant effect of bovine bone size on broadband ultrasound attenuation (BUA) and speed of sound (SOS) in vitro. By normalizing the DXA and QUS results with bone thickness we could systematically improve their ability to predict bone strength. However, in bovine trabecular bone, BUA showed no significant linear correlation with either bone mineral density (BMD), Young’s modulus, or ultimate strength. This finding may be typical of only high-density and low-porosity bovine bone. We significantly improved prediction of ultimate strength by combining density and ultrasound velocity results as compared with assessments of volumetric BMD vol ( p < 0.05) or SOS ( p < 0.001) alone. However, the improvement was not significant if BMD vol, instead of wet density, was used. Altogether, 88% of the variation in the ultimate strength of bovine bone could be explained by combined density and ultrasound velocity. In vivo, SOS showed a weak negative correlation with heel width ( r = −0.350). The in vivo measurements also showed a close correlation for BUA with BMD in the human calcaneus. This suggests that BUA is more suitable for quantitative analysis of low-density trabecular bone.

Adaptation of the human calcaneus to variations of impact forces during running

Objective. The influence of varied forces under the heel induced by changes in midsole hardness on adaptations of the human calcaneus during running training was investigated. Design. A longitudinal study was conducted over a period of 20 weeks with subjects training for 50 km per week on average. Background. The skeletal systems' metabolism acts highly dynamic, governed by mechanical factors. The amount of running training has been shown to increase the bone mineral density in the calcaneus. Mechanical factors have not been controlled in former investigations. Methods. Bone quality parameters were determined before and after the training by use of an ultrasound system and quantitative MRI while the mechanics of foot-ground contact were controlled. The total group of 26 subjects was divided into three subgroups based upon different magnitude of forces under the heel inside the shoe. Results. The biomechanical testing demonstrate no relationship between midsole hardness and external or in-shoe impacts. Bone parameters showed specific differences for all groups which are pronounced in runners with intermediate impacts. Conclusions. The observed variations reflect metabolic changes in bone marrow which appear to be effected by the impact magnitude and cannot be characterised as negative. Relevance The current data imply that no negative changes of impacts on calcaneal bone were produced by high amounts of training in distance running. The mechanical testing indicates that the potential of modifying calcaneal adaptation directly by varying midsole hardness is limited.

Measurement of airborne ultrasonic slow waves in calcaneal cancellous bone

Measurements of an airborne ultrasonic wave were made in defatted cancellous bone from the human calcaneus using standard ultrasonic equipment. The wave propagating under these conditions was consistent with a decoupled Biot slow wave travelling in the air alone, as previously reported in gas-saturated foams. Reproducible measurements of phase velocity and attenuation coefficient were possible, and an estimate of the tortuosity of the trabecular framework was derived from the high frequency limit of the phase velocity. Thus the method offers a new approach to the acoustic characterisation of bone in vitro which, in contrast to existing techniques, has the potential to yield information directly characterising the trabecular structure.

Determination of a standard site for the measurement of bone mineral density of the human calcaneus

Ultrasound of the calcaneus may be used as a cheap, ionising radiation-free and easy to use indicator of skeletal status, and hence of osteoporotic fracture risk. At present ultrasound is not widely used as it suffers from high precision errors. As ultrasound parameters are determined in part by bone mineral density (BMD), an increase in the accuracy and precision of BMD measurements should reduce the precision error associated with ultrasound measurements. The aim of this study was to define an anatomical site on the calcaneus at which accurate and precise measurements of BMD can be made. Ten dry calcanei and 10 cadaveric feet were scanned using a DXA scanner; 9 anatomically defined regions (1 cm2) were selected in the posterior part of the calcaneus for analysis. The centre of region 1 was positioned halfway along the line joining the anterior border of the calcaneal tubercle and the peak of the posterior superior tubercle, and the remaining 8 regions were placed around this central area. The BMD in these 9 regions was compared with the whole bone BMD and the variability of BMD within each of the 9 regions was measured. The reproducibility of the technique was assessed by taking 10 repeated measurements of 2 bone and 2 cadaveric specimens, each specimen being removed and repositioned between measurements. Region 1 was found to be the most representative of total BMD in cadaveric feet. This region also showed the least variability of BMD and consistently gave the lowest coefficients of variation in the reproducibility study both in the bone and the cadaveric specimens. This region is hence the most suitable site on the calcaneus for measuring absolute values of and changes in BMD. The surface position of region 1 was found to be consistently 5/9 along the line at 45° to the vertical, from the lateral malleolus to the heel. The identification of the surface location of region 1 relative to anatomical landmarks of the foot has enabled the same anatomical site to be measured in all subjects. This allows meaningful intersubject comparisons to be made. Preliminary data suggest that precision errors using ultrasound are also reduced when measurements are taken at this region of the calcaneus. The reduction in the precision error of ultrasound assessment of skeletal status may provide a cheap and safe way to identify individuals at risk from osteoporotic fracture.