Ultrasonic scattering from cancellous bone: a review.

This paper reviews theory, measurements, and computer simulations of scattering from cancellous bone reported by many laboratories. Three theoretical models (binary mixture, Faran cylinder, and weak scattering) for scattering from cancellous bone have demonstrated some consistency with measurements of backscatter. Backscatter is moderately correlated with bone mineral density in human calcaneus in vitro (r(2) = 0.66 - 0.68). Backscatter varies approximately as frequency cubed and trabecular thickness cubed in human calcaneus and femur in vitro. Backscatter from human calcaneus and bovine tibia exhibits substantial anisotropy. So far, backscatter has demonstrated only modest clinical utility. Computer simulation models have helped to elucidate mechanisms underlying scattering from cancellous bones.

A method for improved standardization of in vivo calcaneal time-domain speed-of-sound measurements.

Although calcaneal speed of sound (SOS) is an effective predictor of osteoporotic fracture risk, clinical SOS measurements exhibit a high degree of inter-system variability. Calcaneal SOS is usually computed from time-of-flight measurements of broadband ultrasound pulses that propagate through the foot. In order to minimize the effects of multi-path interference, many investigators measure time-of-flight from markers near the leading edge of the pulse. The calcaneus is a highly attenuating, highly inhomogeneous bone that distorts propagating ultrasound pulses via frequency-dependent attenuation, reverberation, dispersion, multiple scattering, and refraction. This pulse distortion can produce errors in leading-edge transit-time marker-based SOS measurements. In this paper, an equation to predict dependence of time-domain SOS measurements on system parameters (center frequency and bandwidth), transit-time marker location, and bone properties (attenuation coefficient and thickness) is validated with through-transmission measurements in a bone-mimicking phantom and in 73 women in vivo, using a clinical bone sonometer. In order to test the utility of the formula for suppressing system dependence of SOS measurements, a wideband laboratory data acquisition system was used to make a second set of through-transmission measurements on the phantom. The compensation formula reduced system-dependent leading-edge transit-time marker-based SOS measurements in the phantom from 41 m/s to 5 m/s and reduced average transit-time marker-related SOS variability in 73 women from 40 m/s to 10 m/s. The compensation formula can be used to improve standardization in bone sonometry.

A stratified model to predict dispersion in trabecular bone.

Frequency-dependent phase velocity (dispersion) has previously been measured in trabecular bone by several groups. In contrast to most biologic tissues, phase velocity in trabecular bone tends to decrease with frequency. A stratified model, consisting of alternating layers of bone and marrow (in vivo) or water (in vitro), has been employed in an attempt to explain this phenomenon. Frequency-dependent phase velocity was measured from 300 to 700 kHz in 1) phantoms consisting of regularly spaced thin parallel layers of polystyrene sheets in water and 2) 30 calcaneus samples in vitro. For the polystyrene phantoms, the agreement between theory and experiment was good. For the calcaneus samples, the model has some limited usefulness (uncertainty of about 5%) in predicting average phase velocity. More importantly, the model seems to perform consistently well for predicting the frequency dependence of phase velocity in calcaneus.

Relationships among calcaneal backscatter, attenuation, sound speed, hip bone mineral density, and age in normal adult women.

The present study was undertaken in order to investigate the use of calcaneal ultrasonic backscatter for the application of diagnosis of osteoporosis. Broadband ultrasonic attenuation (BUA), speed of sound (SOS), the average backscatter coefficient (ABC), and the hip bone mineral density (BMD) were measured in calcanea in 47 women (average age: 58 years, standard deviation: 13 years). All three ultrasound variables had comparable correlations with hip BMD (around 0.5). As reported previously by others, BUA and SOS were rather highly correlated with each other. The logarithm of the ABC was only moderately correlated with the other two. The three ultrasound parameters exhibited similar moderate negative correlations with age. These results taken collectively suggest that the ABC may carry important diagnostic information independent of that contained in BUA and SOS and, therefore, may be useful as an adjunct measurement in the diagnosis of osteoporosis.

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.

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.

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.

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.

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.

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 degrees C to 40 degrees C. The temperature-related variation was -0.18 dB/cm MHz degrees C (95% confidence interval: -0.27 dB/cm MHz degrees C, -0.10 dB/cm MHz degrees 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.

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.

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.

Interlaboratory comparison of ultrasonic backscatter, attenuation, and speed measurements.

In a study involving 10 different sites, independent results of measurements of ultrasonic properties on equivalent tissue-mimicking samples are reported and compared. The properties measured were propagation speed, attenuation coefficients, and backscatter coefficients. Reasonably good agreement exists for attenuation coefficients, but less satisfactory results were found for propagation speeds. As anticipated, agreement was not impressive in the case of backscatter coefficients. Results for four sites agreed rather well in both absolute values and frequency dependence, and results from other sites were lower by as much as an order of magnitude. The study is valuable for laboratories doing quantitative studies.

Uncertainties in estimates of lesion detectability in diagnostic ultrasound.

Statistical properties of estimates of focal lesion detectability for medical ultrasonic imaging systems are investigated. Analytic forms for bias and variance of estimates of detectability of a lesion consisting of fully developed speckle embedded within a speckle background are derived. Bias and variance of estimates of detectability are investigated using a computer simulation and experiments on tissue-mimicking phantoms. This work offers a systematic methodology for interpreting measurements on phantoms in order to assess lesion detectability. In addition, it provides useful results which may be used to improve design of phantoms and experiments for imaging-system performance assessment.

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.

Assessment of bone density using ultrasonic backscatter.

The goal of this project was to investigate the utility of ultrasonic backscatter for the assessment of bone status. Ultrasound offers a low-cost, portable, nonionizing alternative or complement to common X-ray- or radioisotope (gamma ray)-based methods of bone densitometry. Ultrasonic backscatter may provide useful information not revealed by ultrasonic attenuation and sound-speed densitometers. Backscatter is sensitive to microstructural variations in acoustic impedance and should therefore provide information regarding architecture (which is related to fracture risk), as well as density. Ultrasonic backscatter at 2.25 MHz and CT bone densitometric data have been acquired from 10 healthy human volunteers. The degree of correlation between CT and ultrasonic backscatter is high (r = 0.87, p < 0.001). The envelope signal-to-noise ratio was 1.81 +/- 0.08 (mean +/- standard deviation). This suggests that the number of scatterers per resolution cell is large, the radiofrequency signal approximately obeys circular Gaussian statistics, and the envelope obeys Rayleigh statistics. These results indicate promise for ultrasonic backscatter as a substitute for or an adjunct to other ultrasonic measurements (attenuation and sound speed) and X-ray measurements for the assessment of bone status.

Constrained reconstruction applied to 2-D chemical shift imaging.

The method of constrained reconstruction, previously applied to magnetic resonance imaging (MRI), is extended to magnetic resonance spectroscopy. This method assumes a model for the MR signal. The model parameters are estimated directly from the phase encoded data. This process obviates the need for the fast Fourier transform (FFT) (which often exhibits limited resolution and ringing artifact). The technique is tested on simulated data, phantom data, and data acquired from human liver in vivo. In each case, constrained reconstruction offers spatial resolution superior to that obtained with the FFT.

Statistical properties of estimates of signal-to-noise ratio and number of scatterers per resolution cell.

Elementary theory underlying the relationship between the number of scatterers per resolution cell (N) and echo intensity signal-to-noise ratio (SNR) is reviewed. A relationship between the probability density functions for estimates of N and SNR2 is derived. This relationship is validated using a computer simulation. Phantom and in vitro experiments are described. In one set of experiments on phantoms, empirical distributions of estimates of N and SNR2 are measured and compared to theoretical predictions. The utility of SNR2 for discrimination of phantoms with different values for N is assessed using receiver operating characteristic (ROC) analysis. In another set of experiments, the frequency dependence of the SNR2 estimate is investigated for a two-component phantom and for excised dog kidney. It is shown that the frequency dependence of the SNR can help to identify the presence of two or more scattering components that are spatially mixed. With regard to kidney data, measurements performed both parallel and perpendicular to the predominant nephron orientation are reported. The observed anisotropy is compared to the anisotropy of backscatter coefficient encountered in previous investigations.

Measurements of ultrasonic backscatter coefficients in human liver and kidney in vivo.

Ultrasonic backscatter coefficients, in the range of 2.0-4.0 MHz, were measured in normal human livers and kidneys in vivo. In liver, data were acquired and analyzed from 15 normal volunteers and 19 patients with hepatitis. No significant difference between normal and chronic hepatitis was found. The power-law fit to the backscatter coefficient in normal liver as a function of frequency was eta(f) = 4.5 x 10(-5) f1.6 cm-1 Str-1. This is comparable to that measured by other investigators in in vitro preparations of human and animal liver and to that measured by two other teams of investigators in in vivo human liver. In kidney, data were acquired from 11 normal volunteers. The power-law fit to the backscatter coefficient in normal kidney was eta (f) = 2.3 x 10(-5) f2.1 cm-1 Str-1. This is in the range of that measured by other investigators in in vitro preparations of human and animal kidney. In order to assess the system dependence of in vivo abdominal organ backscatter coefficients, measurements were performed using two different ultrasonic data-acquisition systems. The two systems exhibited close agreement.