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The Journal of the Acoustical Society of America2015; 138(2); 594-604; doi: 10.1121/1.4923366

Conventional, Bayesian, and Modified Prony’s methods for characterizing fast and slow waves in equine cancellous bone.

Abstract: Conventional, Bayesian, and the modified least-squares Prony's plus curve-fitting (MLSP + CF) methods were applied to data acquired using 1 MHz center frequency, broadband transducers on a single equine cancellous bone specimen that was systematically shortened from 11.8 mm down to 0.5 mm for a total of 24 sample thicknesses. Due to overlapping fast and slow waves, conventional analysis methods were restricted to data from sample thicknesses ranging from 11.8 mm to 6.0 mm. In contrast, Bayesian and MLSP + CF methods successfully separated fast and slow waves and provided reliable estimates of the ultrasonic properties of fast and slow waves for sample thicknesses ranging from 11.8 mm down to 3.5 mm. Comparisons of the three methods were carried out for phase velocity at the center frequency and the slope of the attenuation coefficient for the fast and slow waves. Good agreement among the three methods was also observed for average signal loss at the center frequency. The Bayesian and MLSP + CF approaches were able to separate the fast and slow waves and provide good estimates of the fast and slow wave properties even when the two wave modes overlapped in both time and frequency domains making conventional analysis methods unreliable.
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Publication Date: 2015-09-04 PubMed ID: 26328678PubMed Central: PMC4529434DOI: 10.1121/1.4923366Google Scholar: Lookup
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  • Comparative Study
  • Journal Article
  • Research Support
  • N.I.H.
  • Extramural
  • Research Support
  • Non-U.S. Gov't

Summary

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The research investigates the performance of three different methods: conventional, Bayesian, and a combination of modified least-squares Prony’s plus curve-fitting, in analyzing the properties of fast and slow waveforms in horse bone samples. The results suggest that the Bayesian and the mixed method are superior in processing samples of more varied thicknesses and in dealing with overlapping waves compared to the conventional method.

Research experiment and application of three methods

  • The experiment was conducted using a single horse bone sample that was methodically reduced in thickness from 11.8 mm to 0.5 mm for a total of 24 differing sample sizes.
  • Broadband assessments were performed on these samples using a transducer with a 1 MHz center frequency.
  • The conventional method of analysis was only capable of analyzing data from bone sample thicknesses that ranged from 11.8 mm to 6.0 mm, due to overlapping fast and slow waveforms.
  • Both the Bayesian method and the modified least squares Prony’s plus curve-fitting approach were not hindered by this restriction and could cope with sample thicknesses from 11.8 mm to 3.5 mm.

Outcome of comparison

  • Comparisons were made for the phase velocity at the central frequency and for the gradient of the attenuation coefficient, both for the fast and slow wave types.
  • There was comparative agreement among the three methods for average signal loss at the central frequency.
  • The Bayesian and modified least squares Prony’s plus curve-fitting techniques showed superiority in separating the fast and slow waveforms and provided good estimates of the waveform attributes even when the two types of waves overlapped in both domains of time and frequency.

Implications of findings

  • The research suggests that the Bayesian and modified least squares Prony’s plus curve-fitting techniques are more versatile and reliable in this context. They can process diverse sample thicknesses and successfully separate and evaluate overlapping waveforms.
  • This is significant in providing valuable insights into the ultrasonic properties of the bone, which could greatly enhance our understanding and facilitate the design of advanced, reliable and efficient diagnostic and treatment methods in veterinary and human medicine.

Cite This Article

APA
Groopman AM, Katz JI, Holland MR, Fujita F, Matsukawa M, Mizuno K, Wear KA, Miller JG. (2015). Conventional, Bayesian, and Modified Prony’s methods for characterizing fast and slow waves in equine cancellous bone. J Acoust Soc Am, 138(2), 594-604. https://doi.org/10.1121/1.4923366

Publication

The Journal of the Acoustical Society of America
ISSN: 1520-8524
NlmUniqueID: 7503051
Country: United States
Language: English
Volume: 138
Issue: 2
Pages: 594-604

Researcher Affiliations

Groopman, Amber M
  • Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA.
Katz, Jonathan I
  • Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA.
Holland, Mark R
  • Department of Radiology and Imaging Sciences, Indiana University-Purdue University School of Medicine, Indianapolis, Indiana 46202, USA.
Fujita, Fuminori
  • Laboratory of Ultrasonic Electronics, Research Center for Wave Electronics, Doshisha University, Kyotanabe, 610-0321 Kyoto, Japan.
Matsukawa, Mami
  • Laboratory of Ultrasonic Electronics, Research Center for Wave Electronics, Doshisha University, Kyotanabe, 610-0321 Kyoto, Japan.
Mizuno, Katsunori
  • Underwater Technology Research Center, The University of Tokyo, Meguro-ku, Tokyo 153-8505, Japan.
Wear, Keith A
  • Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, Maryland 20993, USA.
Miller, James G
  • Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA.

MeSH Terms

  • Acoustics
  • Algorithms
  • Animals
  • Bayes Theorem
  • Bone Conduction / physiology
  • Horses / anatomy & histology
  • Horses / physiology
  • Least-Squares Analysis
  • Porosity
  • Radio Waves
  • Radius / ultrastructure
  • Sound
  • Ultrasonics

Grant Funding

  • R01 AR057433 / NIAMS NIH HHS
  • R01 HL040302 / NHLBI NIH HHS

References

This article includes 44 references
  1. Anderson CC, Bauer AQ, Holland MR, Pakula M, Laugier P, Bretthorst GL, Miller JG. Inverse problems in cancellous bone: estimation of the ultrasonic properties of fast and slow waves using Bayesian probability theory.. J Acoust Soc Am 2010 Nov;128(5):2940-8.
    doi: 10.1121/1.3493441pmc: PMC3003723pubmed: 21110589google scholar: lookup
  2. Anderson CC, Marutyan KR, Holland MR, Wear KA, Miller JG. Interference between wave modes may contribute to the apparent negative dispersion observed in cancellous bone.. J Acoust Soc Am 2008 Sep;124(3):1781-9.
    doi: 10.1121/1.2953309pmc: PMC2597053pubmed: 19045668google scholar: lookup
  3. Bauer AQ, Anderson CC, Holland MR, Miller JG. Bone sonometry: reducing phase aberration to improve estimates of broadband ultrasonic attenuation.. J Acoust Soc Am 2009 Jan;125(1):522-9.
    doi: 10.1121/1.3035841pmc: PMC2677275pubmed: 19173437google scholar: lookup
  4. Bauer AQ, Marutyan KR, Holland MR, Miller JG. Is the Kramers-Kronig relationship between ultrasonic attenuation and dispersion maintained in the presence of apparent losses due to phase cancellation?. J Acoust Soc Am 2007 Jul;122(1):222-8.
    doi: 10.1121/1.2735803pubmed: 17614481google scholar: lookup
  5. Bauer AQ, Marutyan KR, Holland MR, Miller JG. Negative dispersion in bone: the role of interference in measurements of the apparent phase velocity of two temporally overlapping signals.. J Acoust Soc Am 2008 Apr;123(4):2407-14.
    doi: 10.1121/1.2839893pmc: PMC2677307pubmed: 18397043google scholar: lookup
  6. Biot M. Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. J. Acoust. Soc. Am. 28, 168–178.
    doi: 10.1121/1.1908239google scholar: lookup
  7. Biot M. Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J. Acoust. Soc. Am. 28, 179–191.
    doi: 10.1121/1.1908241google scholar: lookup
  8. Cardoso L, Teboul F, Sedel L, Oddou C, Meunier A. In vitro acoustic waves propagation in human and bovine cancellous bone.. J Bone Miner Res 2003 Oct;18(10):1803-12.
    doi: 10.1359/jbmr.2003.18.10.1803pubmed: 14584891google scholar: lookup
  9. Cheng J, Serra-Hsu F, Tian Y, Lin W, Qin YX. Effects of phase cancellation and receiver aperture size on broadband ultrasonic attenuation for trabecular bone in vitro.. Ultrasound Med Biol 2011 Dec;37(12):2116-25.
    doi: 10.1016/j.ultrasmedbio.2011.08.009pmc: PMC3223273pubmed: 22033134google scholar: lookup
  10. Dencks S, Barkmann R, Gluer CC, Schmitz G. Model-based parameter estimation in the frequency domain for quantitative ultrasound measurement of bone. Proceedings of the IEEE International Ultrasonics Symposium pp. 554–557.
  11. Dencks S, Schmitz G. Estimation of multipath transmission parameters for quantitative ultrasound measurements of bone.. IEEE Trans Ultrason Ferroelectr Freq Control 2013 Sep;60(9):1884-95.
    doi: 10.1109/TUFFC.2013.2773pubmed: 24658719google scholar: lookup
  12. Fellah ZE, Chapelon JY, Berger S, Lauriks W, Depollier C. Ultrasonic wave propagation in human cancellous bone: application of Biot theory.. J Acoust Soc Am 2004 Jul;116(1):61-73.
    doi: 10.1121/1.1755239pubmed: 15295965google scholar: lookup
  13. Fujita F, Mizuno K, Matsukawa M. An experimental study on the ultrasonic wave propagation in cancellous bone: waveform changes during propagation.. J Acoust Soc Am 2013 Dec;134(6):4775.
    doi: 10.1121/1.4824970pubmed: 25669289google scholar: lookup
  14. Haire TJ, Langton CM. Biot theory: a review of its application to ultrasound propagation through cancellous bone.. Bone 1999 Apr;24(4):291-5.
    doi: 10.1016/S8756-3282(99)00011-3pubmed: 10221540google scholar: lookup
  15. Hasegawa S, Nagatani Y, Mizuno K, Matsukawa M. Wavelet transform analysis of ultrasonic wave propagation in cancellous bone. Jpn. J. Appl. Phys. 49, 07HF28.
    doi: 10.1143/JJAP.49.07HF28google scholar: lookup
  16. Hoffman JJ, Nelson AM, Holland MR, Miller JG. Cancellous bone fast and slow waves obtained with Bayesian probability theory correlate with porosity from computed tomography.. J Acoust Soc Am 2012 Sep;132(3):1830-7.
    doi: 10.1121/1.4739455pmc: PMC3460989pubmed: 22978910google scholar: lookup
  17. Hosokawa A, Otani T. Ultrasonic wave propagation in bovine cancellous bone.. J Acoust Soc Am 1997 Jan;101(1):558-62.
    doi: 10.1121/1.418118pubmed: 9000743google scholar: lookup
  18. Hosokawa A, Otani T. Acoustic anisotropy in bovine cancellous bone.. J Acoust Soc Am 1998 May;103(5 Pt 1):2718-22.
    doi: 10.1121/1.422790pubmed: 9604363google scholar: lookup
  19. Hughes ER, Leighton TG, White PR, Petley GW. Investigation of an anisotropic tortuosity in a biot model of ultrasonic propagation in cancellous bone.. J Acoust Soc Am 2007 Jan;121(1):568-74.
    doi: 10.1121/1.2387132pubmed: 17297810google scholar: lookup
  20. Kaufman J, Xu W, Chiabrera A, Siffert R. Diffraction effects in insertion mode estimation of ultrasonic group velocity. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42(2), 232–242.
    doi: 10.1109/58.365237google scholar: lookup
  21. Langton CM, Subhan M. Computer and experimental simulation of a cortical end-plate phase cancellation artefact in the measurement of BUA at the calcaneus.. Physiol Meas 2001 Aug;22(3):581-7.
    doi: 10.1088/0967-3334/22/3/314pubmed: 11556676google scholar: lookup
  22. Lashkari B, Manbachi A, Mandelis A, Cobbold RS. Slow and fast ultrasonic wave detection improvement in human trabecular bones using Golay code modulation.. J Acoust Soc Am 2012 Sep;132(3):EL222-8.
    doi: 10.1121/1.4742729pubmed: 22979836google scholar: lookup
  23. Laugier P, Haïat G. Bone Quantitative Ultrasound. Chap. 3, pp. 47–71.
  24. Lee KI, Hughes ER, Humphrey VF, Leighton TG, Choi MJ. Empirical angle-dependent Biot and MBA models for acoustic anisotropy in cancellous bone.. Phys Med Biol 2007 Jan 7;52(1):59-73.
    doi: 10.1088/0031-9155/52/1/005pubmed: 17183128google scholar: lookup
  25. Maruo S, Hosokawa A. A generalized harmonic analysis of ultrasound waves propagating in cancellous bone. Jpn. J. Appl. Phys. 53, 07KF06.
    doi: 10.7567/JJAP.53.07KF06google scholar: lookup
  26. Marutyan KR, Bretthorst GL, Miller JG. Bayesian estimation of the underlying bone properties from mixed fast and slow mode ultrasonic signals.. J Acoust Soc Am 2007 Jan;121(1):EL8-15.
    doi: 10.1121/1.2401198pubmed: 17297820google scholar: lookup
  27. Marutyan KR, Holland MR, Miller JG. Anomalous negative dispersion in bone can result from the interference of fast and slow waves.. J Acoust Soc Am 2006 Nov;120(5 Pt 1):EL55-61.
    doi: 10.1121/1.2357187pubmed: 17139755google scholar: lookup
  28. Mizuno K, Matsukawa M, Otani T, Takada M, Mano I, Tsujimoto T. Effects of structural anisotropy of cancellous bone on speed of ultrasonic fast waves in the bovine femur.. IEEE Trans Ultrason Ferroelectr Freq Control 2008 Jul;55(7):1480-7.
    doi: 10.1109/TUFFC.2008.823pubmed: 18986937google scholar: lookup
  29. Nagatani Y, Mizuno K, Saeki T, Matsukawa M, Sakaguchi T, Hosoi H. Numerical and experimental study on the wave attenuation in bone--FDTD simulation of ultrasound propagation in cancellous bone.. Ultrasonics 2008 Nov;48(6-7):607-12.
    doi: 10.1016/j.ultras.2008.04.011pubmed: 18589470google scholar: lookup
  30. Nagatani Y, Tachibana RO. Multichannel instantaneous frequency analysis of ultrasound propagating in cancellous bone.. J Acoust Soc Am 2014 Mar;135(3):1197-206.
    doi: 10.1121/1.4864464pubmed: 24606262google scholar: lookup
  31. Nelson AM, Hoffman JJ, Anderson CC, Holland MR, Nagatani Y, Mizuno K, Matsukawa M, Miller JG. Determining attenuation properties of interfering fast and slow ultrasonic waves in cancellous bone.. J Acoust Soc Am 2011 Oct;130(4):2233-40.
    doi: 10.1121/1.3625241pmc: PMC3206914pubmed: 21973378google scholar: lookup
  32. Njeh CF, Hans D, Fuerst T, Gluer CC, Genant HK. Quantitative Ultrasound: Assessment of Osteoporosis and Bone Status. Chap. 4, pp. 67–77.
  33. O'Donnell M, Jaynes ET, Miller JG. Kramers–Kronig relationship between ultrasonic attenuation and phase velocity. J. Acoust. Soc. Am. 69, 696–701.
    doi: 10.1121/1.385566google scholar: lookup
  34. Ophir J, Jaeger P. Spectral shifts of ultrasonic propagation through media with nonlinear dispersive attenuation.. Ultrason Imaging 1982 Jul;4(3):282-9.
    doi: 10.1177/016173468200400304pubmed: 6889773google scholar: lookup
  35. Waters KR, Hoffmeister BK. Kramers-Kronig analysis of attenuation and dispersion in trabecular bone.. J Acoust Soc Am 2005 Dec;118(6):3912-20.
    doi: 10.1121/1.2126934pubmed: 16419833google scholar: lookup
  36. Waters KR, Hughes MS, Mobley J, Miller JG. Differential forms of the Kramers-Krönig dispersion relations.. IEEE Trans Ultrason Ferroelectr Freq Control 2003 Jan;50(1):68-76.
    doi: 10.1109/TUFFC.2003.1176526pubmed: 12578137google scholar: lookup
  37. Waters KR, Mobley J, Miller JG. Causality-imposed (Kramers-Kronig) relationships between attenuation and dispersion.. IEEE Trans Ultrason Ferroelectr Freq Control 2005 May;52(5):822-33.
    doi: 10.1109/TUFFC.2005.1503968pubmed: 16048183google scholar: lookup
  38. Wear KA. The effect of phase cancellation on estimates of calcaneal broadband ultrasound attenuation in vivo.. IEEE Trans Ultrason Ferroelectr Freq Control 2007 Jul;54(7):1352-9.
    doi: 10.1109/TUFFC.2007.395pmc: PMC6935505pubmed: 17718324google scholar: lookup
  39. Wear KA. The effect of phase cancellation on estimates of broadband ultrasound attenuation and backscatter coefficient in human calcaneus in vitro.. IEEE Trans Ultrason Ferroelectr Freq Control 2008 Feb;55(2):384-90.
    doi: 10.1109/TUFFC.2008.656pmc: PMC6931155pubmed: 18334344google scholar: lookup
  40. Wear KA. Decomposition of two-component ultrasound pulses in cancellous bone using modified least squares prony method--phantom experiment and simulation.. Ultrasound Med Biol 2010 Feb;36(2):276-87.
    doi: 10.1016/j.ultrasmedbio.2009.06.1092pubmed: 20113862google scholar: lookup
  41. Wear KA. Estimation of fast and slow wave properties in cancellous bone using Prony's method and curve fitting.. J Acoust Soc Am 2013 Apr;133(4):2490-501.
    doi: 10.1121/1.4792935pubmed: 23556613google scholar: lookup
  42. Wear KA. Time-domain separation of interfering waves in cancellous bone using bandlimited deconvolution: simulation and phantom study.. J Acoust Soc Am 2014 Apr;135(4):2102-12.
    doi: 10.1121/1.4868473pubmed: 25235007google scholar: lookup
  43. Wear K, Nagatani Y, Mizuno K, Matsukawa M. Fast and slow wave detection in bovine cancellous bone in vitro using bandlimited deconvolution and Prony's method.. J Acoust Soc Am 2014 Oct;136(4):2015-24.
    doi: 10.1121/1.4895668pubmed: 25324100google scholar: lookup
  44. Xu W, Kaufman JJ. Diffraction correction methods for insertion ultrasound attenuation estimation.. IEEE Trans Biomed Eng 1993 Jun;40(6):563-70.
    doi: 10.1109/10.237676pubmed: 8262538google scholar: lookup

Citations

This article has been cited 3 times.
  1. Wear K. Scattering in Cancellous Bone. Adv Exp Med Biol 2022;1364:163-175.
    doi: 10.1007/978-3-030-91979-5_8pubmed: 35508875google scholar: lookup
  2. Mizuno K, Nagatani Y, Mano I. Ultrasonic Assessment of Cancellous Bone Based on the Two-Wave Phenomenon. Adv Exp Med Biol 2022;1364:119-143.
    doi: 10.1007/978-3-030-91979-5_6pubmed: 35508873google scholar: lookup
  3. Wear KA. Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review. IEEE Trans Ultrason Ferroelectr Freq Control 2020 Mar;67(3):454-482.
    doi: 10.1109/TUFFC.2019.2947755pubmed: 31634127google scholar: lookup
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