Statistics of Envelope of High-Frequency Ultrasonic Backscatter from Trabecular Bone: Simulation Study

Open access


The paper considers the application of statistical properties of backscattered ultrasonic signal for assessment of the trabecular bone status.

Computer simulations were conducted to investigate the properties of the ultrasound pulse-echo signal, as it is received on the transducer surface after scattering in trabecular bone. The micro-architecture of trabecular bone was modeled by a random distribution of long and thin cylindrical scatterers of randomly varying diameters and mechanical properties, oriented perpendicular to the ultrasound beam axis. The received echo signal was calculated as a superposition of echoes from all the scatterers present in the scattering volume.

The simulated signal envelope was used for statistical processing to compute various parameters like the mean amplitude, the amplitude MSR defined as the ratio of the mean to the standard deviation and the amplitude histogram.

Results indicated that while for the well-defined trabeculae properties within the simulated bone structure the signal envelope values are Rayleigh distributed the significant departures from Rayleigh statistics may be expected as the thickness of trabeculae become random. The influence of the variation of mechanical properties of the bone tissue building the trabeculae on the bone backscattered signal parameters was not observed.

Bamber J., Hill C., King J. (1981), Acoustic properties of normal and cancerous human liver, Ultrasound Med. Biol., 7, 121-133.

Chaffai S., Roberjot V., Peyrin F., Berger G., Laugier P. (2000), Frequency dependence of ultrasonic backscattering in cancellous bone: Autocorrelation model and experimental results, J. Acoust. Soc. Am., 108, 5, 2403-2411.

Dagan D., Be'ery M., Gefen A. (2004), Single-trabecula building-block for large-scale finite element models of cancellous bone, Medical & Biological Engineering & Computing, 42, 549-556.

Flax L., Gaunaurd G. C., Uberall H. (1981), Theory of resonance scattering, [in:] Physical Acoustics, Mason W. P., Thurston R. N. [Eds.], vol. 15, pp. 191-294, Academic Press, New York.

Goodman J. (1985), Statistical Optics, John Wiley & Sons.

Hans D., Arlot M., Schott A., Roux J., Kotzki P., Meunier P. (1995), Do ultrasounds measurements on the Os Calcis reflect more the bone microarchitecture than the bone mass?: A two-dimensional histomorfometric study, Bone, 16, 3, 295-300.

Häsler K., Rich P., Smith P., Barry E. (1999), Relationships between static histomorphometry and ultrasound in the human calcaneus, Calcif Tissue Int., 64, 477-480.

Hosokawa A., Otani T. (1997), Ultrasonic wave propagation in bovine cancellous bone, J. Acoustic Soc. Am., 101, 558-562.

Insana M., Wagner R., Brown D., Hall T. (1990), Describing small-scale structure in random media using pulse-echo ultrasound, J. Acoust. Soc. Am., 87, 179-182.

Klimonda Z., Litniewski J., Nowicki A. (2009), Spatial resolution of attenuation imaging, Archives of Acoustics, 34, 4, 461-470.

Kothari M., Keaveny T., Lin J., Newitt D., Majumdar S. (1999), Measurement of intraspecimen variation in vertebral cancellous bone architecture, Bone, 25, 2, 245-250.

Laugier P., Padilla F., Camus E., Chaffai S., Chappard C., Peyrin F., Talmant M., Berger G. (2000), Quantitative ultrasound for Bone Status Assessment, IEEE Ultrasonic Symposium Proceedings, 2, 1341-1350.

Laugier P., Giat P., Chappard C., Roux Ch., Berger G. (1997), Clinical assessment of the backscatter coefficient in osteoporosis, IEEE Ultrasonic Symposium, 1101-1105.

Laugier P., Talmant M., Pham T.-L. (2008), Que vadis, ultrasonics of bone? Present state and future trends, Archives of Acoustics, 33, 4, 553-564.

Litniewski J. (2005), Determination of the elasticity coefficient for a single trabecula of a cancellous bone: Scanning Acoustic Microscopy approach, Ultrasound Med. Biol., 31, 10, 1361-1366.

Litniewski J., Nowicki A., Lewin P. A. (2009), Semi-empirical bone model for determination of trabecular structure properties from backscattered ultrasound, Ultrasonics, 49, 505-513.

Padilla F., Peyrin F., Laugier P. (2003), Prediction of backscattered coefficient in trabecular bones using a numerical model of tree-dimensional microstructure, J. Acoust. Soc. Am., 113, 2, 1122-1129.

Saha P., Wehrli F. (2004), Measurement of Trabecular Bone Thickness in the Limited Resolution Regime of In Vivo MRI by Fuzzy Distance Transform, IEEE Trans. Medical Imaging, 23, 53-62.

Shankar M. (2000), A general statistical model for ultrasonic backscattering from tissue, IEEE Trans. on UFFC, 47, 3, 727-736.

Trebacz H., Natali A. (1999), Ultrasound velocity and attenuation in cancellous bone samples from lumbar vertebra and calcaneus, Osteo. Int., 9, 99-105.

Wagner R., Insana M., Brown D. (1987), Statistical properties of radio-frequency and envelope-detected signals with applications to medical ultrasound, J. Opt. Soc. Am., 4, 5, 910-922.

Wear K. (1999), Frequency dependence of ultrasonic backscatter from human trabecular bone: Theory and experiment, J. Acoust. Soc. Am., 106, 6, 3659-3664.

Wear K., Garra B. (1998), Assessment of bone density using ultrasonic backscatter, Ultrasound Med Biol., 24, 5, 689-695.

Archives of Acoustics

The Journal of Institute of Fundamental Technological of Polish Academy of Sciences

Journal Information

IMPACT FACTOR 2016: 0.816
5-year IMPACT FACTOR: 0.835

CiteScore 2016: 1.15

SCImago Journal Rank (SJR) 2016: 0.432
Source Normalized Impact per Paper (SNIP) 2016: 0.948

Cited By


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 109 77 6
PDF Downloads 47 35 6