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Published in final edited form as: IEEE Trans Ultrason Ferroelectr Freq Control. 2008 Nov;55(11):2418–2425. doi: 10.1109/TUFFC.949

Mechanisms for Attenuation in Cancellous-Bone-Mimicking Phantoms

Keith A Wear 1
PMCID: PMC6935503  NIHMSID: NIHMS1064089  PMID: 19049921

Abstract

Broadband ultrasound attenuation (BUA) in cancellous bone is useful for prediction of osteoporotic fracture risk, but its causes are not well understood. In order to investigate attenuation mechanisms, nine 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 three separable components: 1) a linear (with frequency) component attributable to absorption in the soft-tissue-mimicking fluid, 2) a quasi-linear (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 nine 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 three components of attenuation in cancellous bone-mimicking phantoms.

Keywords: attenuation cancellous bone phantom

I. INTRODUCTION

Prospective clinical trials [1–8], retrospective clinical trials [9–19], and pre-clinical experiments [20–57] have established that broadband ultrasound attenuation (BUA) (the slope of attenuation coefficient vs. frequency) and speed of sound (SOS) in calcaneus are effective for prediction of osteoporotic fracture risk. However, the mechanisms responsible for BUA in cancellous bone are not well understood. BUA is the combined result of absorption and scattering [58–94]. Cancellous bone contains approximately cylindrically-shaped scatterers (trabeculae) and plate-like structures arrayed in a mesh. See Figure 1. The spaces between the trabeculae are filled with marrow (in vivo) or water (in vitro).

Figure 1.

Figure 1.

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Micro Computed Tomogram of calcaneus. Some trabeculae appear to terminate as they move into and out of the imaging plane. Image acquired by Andres Laib, Scanco Medical AG, Brüttisellen, Switzerland.

2D simulation studies in human cancellous calcaneus suggest that scattering is greater in magnitude than absorption between 300 and 900 kHz [46, 83]. 3D simulation studies in human cancellous femur suggest that 1) absorption is greater than scattering at low frequencies but is less than scattering at high frequencies (with equality achieved around 600 kHz) and 2) longitudinal-shear (LS) mode conversion may be a significant source of attenuation [79, 84, 85, 95, 96]. The 3D studies therefore suggest that absorption is probably the largest component of clinical (300–700 kHz) BUA. 3D simulation studies also suggest the presence of a significant scattering mechanism that varies approximately linearly with frequency [95]. These 2D and 3D simulation studies appear to include LS mode conversion as a form of scattering. If shear waves are rapidly absorbed as they propagate (as has been suggested [97, 104]), LS mode conversion could alternatively be regarded as effectively an absorptive mechanism, with ultrasonic energy briefly taking the form of a transient shear wave prior to absorption. (See Discussion section.)

In the diagnostic frequency range (300 – 700 kHz), attenuation coefficient in cancellous bone is approximately proportional to frequency to the first power [20–57] while longitudinal-longitudinal (LL) backscatter coefficient is approximately proportional to frequency to the third power [60, 61, 64]. If LL total scattering (i.e., the integral of LL scattering over all angles) also varies substantially nonlinearly with frequency, then LL scattering could only represent a minor contribution to attenuation coefficient in the diagnostic frequency range [60, 64, 68]. (Evidence for nonlinear total scattering is provided by the Faran Cylinder model, which predicts that total LL scattering, like LL backscatter, varies approximately as frequency to the third power [60]).

Experiments on graphite-fiber-in-gelatin phantoms may help elucidate mechanisms of attenuation in cancellous bone. Graphite-fiber-in-gelatin phantoms [97] resemble cancellous bone somewhat in that they contain a mixture of hard scatterers (graphite fibers) embedded in a fluid (gelatin). Measurements of attenuation coefficient in graphite-fiber-in-gelatin phantoms [97] have shown that the combination of absorption within the fluid (gelatin) and LS mode conversion from the graphite fibers produces a quasi-linear frequency dependence of attenuation when ultrasound propagates parallel to the fibers and a slightly higher than linear frequency dependence of attenuation when ultrasound propagates perpendicular to the fibers (consistent with theoretical predications [98]). See Ref. 97, Figure 8.

The objective of the work described below was to experimentally separate three components of attenuation in cancellous-bone-mimicking phantoms: 1) a linear (with frequency) component attributable to absorption in the soft-tissue-mimicking fluid, 2) a quasi-linear (with frequency) component, which may include absorption in and LS mode conversion by the nylon filaments, and 3) a nonlinear (with frequency) component, which may be closely associated with LL scattering from the nylon filaments.

II. METHODS

A. Phantoms

Nine phantoms containing nylon wires (simulating trabeculae) in proprietary soft tissue-mimicking material (simulating marrow) (CIRS Inc., Norfolk, VA) were interrogated. Two reference phantoms containing only soft tissue-mimicking material were also interrogated. Table 1 shows the phantom properties. Two different kinds of nylon wire (designated below by their colors “green” and “clear” in Table 1) were used. Two batches of proprietary soft tissue-mimicking material (“CIRS #1” and “CIRS #2”) were used. Three of the phantoms used nylon filaments with diameter equal to 152 μm, which is reasonably close to the mean trabecular thickness in human calcananeus, 127 μm [102]. Figure 2 shows the phantom containing green nylon wires along with its reference phantom.

Table 1.

Properties of phantoms.

Nylon Fluid Filler Diameter (μm) Length (mm) Scatter Number Density (# per cc) Volume Fraction (%) Frequency Range for Linear Fit (MHz)
- CIRS #1 - - - - 0.5 – 0.8
Green CIRS #1 203 12 100 3.9 0.5 – 0.8
- CIRS #2 - - - - 0.3 – 0.7
Clear CIRS #2 152 10 100 1.8 0.3 – 0.7
Clear CIRS #2 203 10 100 3.2 0.3 – 0.7
Clear CIRS #2 229 10 100 4.1 0.3 – 0.7
Clear CIRS #2 330 10 100 8.5 0.3 – 0.5
Clear CIRS #2 356 10 100 9.9 0.3 – 0.5
Clear CIRS #2 152 12 100 2.2 0.3 – 0.7
Clear CIRS #2 229 12 100 3.3 0.3 – 0.7
Clear CIRS #2 152 12 200 4.4 0.3 – 0.7
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Figure 2.

Figure 2.

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Phantoms. Both phantoms contained soft-tissue-mimicking material. The phantom on the right also contained green nylon filaments to simulate trabeculae.

B. Ultrasonic Methods

The phantoms containing clear nylon filaments were interrogated in through-transmission mode in a water tank using 3 pairs of coaxially-aligned Panametrics (Waltham, MA) focused transducers. See Table 2. The phantom containing green nylon filaments was only interrogated at 2.25 MHz. The propagation path between transducers was twice the focal length. Attenuation coefficient and group velocity were measured as described previously [63].

Table 2.

Transducers.

Transducer Center Frequency (MHz) Diameter (mm) Focal Length (mm)
V391 0.5 29 53
V302 1 25 51
V305 2.25 19 51
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In order to investigate the contribution of LL scattering to attenuation coefficient, the phantoms containing clear nylon filaments were also interrogated in pulse-echo mode in a water tank using a 2.25 MHz center frequency transducer. The phantom was placed at the focal plane of the transducer. A reference-phantom method was used to compensate for transducer electro-mechanical properties and diffraction so that backscatter coefficient could be computed [60].

A Panametrics 5800 pulser/receiver was used. Received radio frequency (RF) signals were digitized (8 bit, 10 MHz) using a LeCroy (Chestnut Ridge, NY) 9310C Dual 400 MHz oscilloscope and stored on computer (via GPIB) for off-line analysis.

Frequency-dependent attenuation coefficients, α(f), were decomposed into 3 components.

α(f)=αFL(f)+αL2(f)+αNL(f)

where αFL(f), the linear (with frequency) absorption in the soft-tissue-mimicking fluid, was measured directly in the reference phantoms (i.e., phantoms without nylon filaments). The attenuation above and beyond that due to absorption in the soft-tissue-mimicking fluid was decomposed into linear and nonlinear components, αL2(f) and αNL(f). αL2(f) was measured by performing a least-squares linear regression fit to measured α(f) in the low-frequency linear regime and then subtracting αFL(f). αNL(f) was then computed from αNL(f) = α(f) – αFL(f) - αL2(f). Attenuation slope was defined as the sum of the slopes of linear regressions to αFL(f) vs. frequency and αL2(f) vs. frequency.

The low frequency range for the linear fit was usually the clinical range of 300 – 700 kHz. See Table 2. For phantoms containing clear nylon filaments with diameters 330 and 356 μm, however, the upper limit was reduced to 500 kHz because their nonlinear (with frequency) attenuation components became prominent at lower frequencies. For the phantom containing green nylon filaments, the range was 500 – 800 kHz, which corresponded to the low end of the usable frequency band obtainable with the 2.25 MHz center frequency transducer.

III. RESULTS

Figure 3 shows measurements of attenuation coefficient vs. frequency for the phantom containing green nylon filaments (*’s) and its reference phantom (i.e., phantom without nylon filaments) (o’s). The attenuation coefficient for the reference phantom appeared to be approximately linear with frequency up to at least 3 MHz. The slope of the linear least-squares regression fit to the reference phantom attenuation coefficient data vs. frequency was 0.7 ± 0.1 dB/cmMHz (mean ± standard error). The slope of the linear least-squares regression fit to the attenuation coefficient data from the phantom containing green nylon filaments over the range from 0.5 to 0.8 MHz was 2.3 ± 0.2 dB/cmMHz, or about three times the value for its reference phantom (see dashed line in Fig. 3). Therefore, there seems to have been a substantial quasi-linear (with frequency) attenuation mechanism operating in the phantom containing green nylon filaments, in addition to the linear (with frequency) attenuation attributable to absorption in the proprietary soft-tissue mimicking material. The group velocities were 1555 ± 5 m/s (phantom containing green nylon filaments) and 1545 ± 1 m/s (reference phantom).

Figure 3.

Figure 3.

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Attenuation coefficient vs. frequency in the phantom containing green nylon filaments (*) and in the reference (i.e. without nylon filaments) phantom (o). The dashed line corresponds to a linear regression fit at low frequencies.

Figure 4 shows results for 5 phantoms containing 10-mm-long clear nylon filaments. The left panel shows measurements of total attenuation coefficient vs. frequency. The dotted lines correspond to frequency dependent attenuation coefficients measured from the reference phantom (i.e. phantom without nylon filaments). The dashed lines correspond to linear fits of attenuation coefficient vs. frequency at low frequencies. It can be seen that there was a substantial quasi-linear (with frequency) component of attenuation above and beyond the attenuation due to the soft-tissue-mimicking fluid (dotted line), especially for the phantoms with filaments with diameters of 229, 330, and 356 μm. The middle column of Figure 4 shows the nonlinear component of attenuation coefficient, αNL(f), which is the difference between α(f) (left panel) and the low-frequency linear fit to α(f) (left panel, dashed line). The right column of Figure 4 shows measurements of backscatter coefficient, η(f). Comparison of the middle and right columns of Figure 4 shows that for each filament diameter, the frequencies of rapid onset of αNL(f) and η(f) are very similar, suggesting that LL scattering may be a significant source of αNL(f).

Figure 4.

Figure 4.

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Results for the 5 phantoms containing 10 mm clear nylon filaments. The left panel shows measurements of attenuation coefficient vs. frequency. The dotted lines correspond to frequency-dependent attenuation coefficients measured from the reference phantom (i.e., phantom without nylon filaments). The dashed lines correspond to linear fits of attenuation coefficient vs. frequency at low frequencies. The middle panel shows the nonlinear component of attenuation coefficient, αNL(f), which is the difference between α(f) (left panel) and the low-frequency linear fit to α(f) (left panel, dashed line). The right panel shows measurements of backscatter coefficient, η(f).

Figure 5 shows attenuation slope plotted vs. volume fraction for the phantoms containing clear nylon filaments. A least-squares linear regression fit is also shown. The correlation coefficient to the least-squares fit was r = 0.96. The 95% confidence interval for r was (0.82, 0.99).

Figure 5.

Figure 5.

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Attenuation slope plotted vs. volume fraction for the phantoms containing clear nylon filaments. A least-squares linear regression fit is also shown.

IV. DISCUSSION

This work represents the first experimental separation of three distinct components of attenuation in cancellous bone-mimicking phantoms. The rate of change of the total linear (with frequency) attenuation coefficient, αFL(f) + αL2(f), with frequency was found to increase linearly with volume fraction, consistent with previous measurements on cancellous bone.

Figures 3 and 4 show that some phantoms exhibited a substantial quasi-linear (with frequency) component of attenuation above and beyond the absorption in the soft-tissue-mimicking fluid. This quasi-linear (with frequency) excess attenuation may include absorption in and LS mode conversion by the nylon filaments. The latter source of quasi-linear (with frequency) attenuation is consistent with 1) 3D simulations that consider only non-absorptive mechanisms [95], and 2) measurements on graphite-fiber-in-gelatin phantoms that include absorption within the fluid (gelatin) and LS mode conversion from the graphite fibers [97].

Differences between the cancellous-bone-mimicking phantoms interrogated here and cancellous bone should be acknowledged:

First, the longitudinal sound speed in nylon (2600 m/s) is somewhat lower than that for mineralized bone material (2800 – 4000 m/s, near 500 kHz) [100] (but still far greater than that for water or marrow—near 1500 m/s). However, nylon may still be a reasonable material to simulate trabeculae for this application because previous studies have shown that phantoms consisting of parallel nylon wires in water exhibit similar dependences of LL scattering [77] and phase velocity [101] on frequency and scatterer thickness as cancellous bone.

Second, the cancellous bone phantom investigated here lacked cross-links that can connect nearby trabeculae in cancellous bone. However, again, the parallel-nylon-wire phantoms mentioned in the previous paragraph also lacked cross-links but still exhibited similar acoustic properties to cancellous bone [77, 101].

Third, while scatterers were essentially randomly oriented in the phantom, they tend to align along preferred directions in cancellous bone. However, the phantom may still be a useful model for this application because attenuation due to LS mode conversion tends to be quasi-linear with frequency regardless of whether ultrasound propagates parallel or perpendicular to the scatterers, according to theory [98] and measurements on phantoms containing graphite fibers in gelatin [97].

Fourth, nylon wires may have lower absorption than trabeculae. However, as stated earlier, this may not be a serious limitation because simulations that ignore absorption are able to reproduce experimental results for trabecular bone [79].

The present study is more relevant to cancellous bone than the previously-mentioned graphite-fiber-in-gelatin study [97] (which was intended to model soft tissue, not bone) in terms of scatterer diameter (152 – 356 vs. 8 μm), scatterer length (10 – 12 mm vs. 100μm), and volume fraction (1.8 – 9.9% vs. unspecified). (The mean trabecular thickness in human calcaneus is 127 μm [102]. Volume fractions in human calcaneus range from 3% to 14% [103]) Another advantage of the present study over the previous study [97] is that LL backscattering was measured independently of attenuation in order to investigate the effects of LL scattering on frequency-dependent attenuation.

Although shear waves may arise from mode conversion at scatterer interfaces, they may be extremely transient. For example, shear attenuation coefficients in bovine cancellous bone have been estimated to be approximately 17 dB/mm (at 1 MHz) [104], implying that shear wave power is reduced by approximately 98% for each mm of propagation. Similarly, shear waves generated from graphite particles suspended in gelatin have been described as “evanescent” [97]. Therefore, the relative roles of absorption and scattering in cancellous bone will depend on the relative roles of absorption and scattering of mode-converted shear waves. If the rapid attenuation of mode-converted shear waves is primarily due to absorption, then absorption would be the dominant loss mechanism, albeit with the caveat that the ultrasonic energy briefly takes the form of a very short-lived shear wave prior to absorption.

ACKNOWLEDGEMENTS

The author thanks 1) Professor James Miller, Physics Department, Washington University, St. Louis, MO, for helpful discussions, 2) Laura Perfetti and Heather Pierce, C.I.R.S., Norfolk, VA, for assistance in phantom design and construction, and 3) Andres Laib, Scanco Medical AG, Brüttisellen, Switzerland, for providing the micro computed tomogram in Figure 1. The mention of commercial products, their sources, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the Food and Drug Administration.

Biography

Keith A. Wear graduated from the University of California at San Diego with a B.A. in Applied Physics in 1980. He received his M.S. and Ph.D. in Applied Physics with a Ph.D. minor in Electrical Engineering from Stanford University in 1982 and 1987.

He was a post-doctoral research fellow with the Physics department at Washington University, St. Louis from 1987–1989. He has been a research physicist at the FDA Center for Devices and Radiological Health since 1989. His research has included measurements of ultrasonic scattering properties from tissues, high-resolution spectral estimation, magnetic resonance spectroscopic image reconstruction methods, analysis of statistical properties of ultrasonic echoes from tissues, and improved measurement methodology in bone sonometry.

He is an adjunct professor of Radiology at Georgetown University. He is a Fellow of the American Institute for Medical and Biological Engineering (AIMBE) and the American Institute of Ultrasound in Medicine (AIUM). He is a senior member of IEEE. He is a member of the Acoustical Society of America, IEEE Ultrasonics Society and the AIUM Technical Standards Committee. He served as Vice-Chairman (2002–2004) and Chairman (2004–2006) of the AIUM Basic Science and Instrumentation Section. He is an associate editor of IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control.

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