Short ultrasonic waves in cancellous bone

The modeling of ultrasonic propagation in cancellous bone is relevant to the study of clinical bone assessment. Historical experiments revealed the importance of both the viscous effects of bone marrow and the anisotropy of the porous microstructure. Of those propagation models previously applied to cancellous bone, Biot's theory incorporates viscosity, but has only been applied in isotropic form, while Schoenberg's anisotropic model does not include viscosity. In this paper we present an approach that incorporates the merits of both models, by utilizing the tortuosity, a key parameter describing pore architecture. An angle-dependent tortuosity for a layered structure is used in Biot's theory to generate the "Stratified Biot Model" for cancellous bone, which is compared with published bone data. While the Stratified Biot model was inferior to Schoenberg's model for slow wave velocity prediction, the proposed model improved agreement fast wave velocity at high propagation angles, particularly when sorted for porosity. An attempt was made to improve the fast wave agreement at low angles by introducing an angle-dependent Young's Modulus, which, while improving the agreement of predicted fast wave velocity at low angles, degraded agreement at high angles. In this paper the utility of the tortuosity in characterizing the architecture of cancellous bone is highlighted.

Section: Schoenberg's Theory For Stratified Mediasupporting

confidence: 63%

Investigation of an anisotropic tortuosity in a Biot model of ultrasonic propagation in cancellous bone

Hughes

Leighton

White

et al. 2007

“…23,24 The difference between the fast and the slow wave speeds is smaller in this study than in other studies that have reported the speed of sound for both waves. 7,16,[25][26][27] This result is expected because the fast and slow wave speeds are most similar when propagating perpendicular to the predominant fiber direction. [7][8][9][10][11]16,28 The solid lines are linear best fit lines.…”

Section: A Phase Velocitymentioning

confidence: 85%

Cancellous bone fast and slow waves obtained with Bayesian probability theory correlate with porosity from computed tomography

Hoffman

Nelson

Holland

et al. 2012

A Bayesian probability theory approach for separating overlapping ultrasonic fast and slow waves in cancellous bone has been previously introduced. The goals of this study were to investigate whether the fast and slow waves obtained from Bayesian separation of an apparently single mode signal individually correlate with porosity and to isolate the fast and slow waves from medial-lateral insonification of the calcaneus. The Bayesian technique was applied to trabecular bone data from eight human calcanei insonified in the medial-lateral direction. The phase velocity, slope of attenuation (nBUA), and amplitude were determined for both the fast and slow waves. The porosity was assessed by micro-computed tomography (microCT) and ranged from 78.7% to 94.1%. The method successfully separated the fast and slow waves from medial-lateral insonification of the calcaneus. The phase velocity for both the fast and slow wave modes showed an inverse correlation with porosity (R 2 ¼ 0.73 and R 2 ¼ 0.86, respectively). The slope of attenuation for both wave modes also had a negative correlation with porosity (fast wave: R 2 ¼ 0.73, slow wave: R 2 ¼ 0.53). The fast wave amplitude decreased with increasing porosity (R 2 ¼ 0.66). Conversely, the slow wave amplitude modestly increased with increasing porosity (R 2 ¼ 0.39).

“…The propagation of two longitudinal waves in poroelastic media is predicted by Biot theory (Biot 1956a(Biot ,b,c, 1962(Biot , 1963, which has been reviewed by Haire and Langton (1999). After early applications of Biot theory to cancellous bone (McKelvie and Palmer 1991;Williams 1992), the presence of two waves was confirmed experimentally by Otani (1997, 1998), Kaczmarek et al (2002), and Cardoso et al (2003). Theoretical investigations of Biot theory in the context of cancellous bone have been reported by Cowin (1999); Pakula and Kubik (2002); Lee et al (2003Lee et al ( , 2006; Hughes et al (2003); Hughes et al (2007); Fellah et al (2004); , Sebaa et al (2006); Sebaa et al (2008); Aygun et al (2009) ;Cardoso and Cowin (2011); Cowin and Cardoso (2011); and Buchanan et al (2012).…”

Section: Introductionmentioning

confidence: 98%

“…Through-transmission ultrasound measurements on cancellous bone in vitro suggest that the fast and slow waves have different frequency-dependent attenuation coefficients (Hosokawa and Otani, 1997;Kaczmarek et al, 2002;Cardoso et al, 2003). Fast wave velocity in bovine cancellous bone depends on structural anisotropy and is maximum when propagation is parallel to the predominant trabecular orientation (Mizuno et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Estimation of fast and slow wave properties in cancellous bone using Prony's method and curve fitting

Wear

2013

The presence of two longitudinal waves in poroelastic media is predicted by Biot's theory and has been confirmed experimentally in through-transmission measurements in cancellous bone. Estimation of attenuation coefficients and velocities of the two waves is challenging when the two waves overlap in time. The modified least squares Prony's (MLSP) method in conjuction with curve-fitting (MLSP + CF) is tested using simulations based on published values for fast and slow wave attenuation coefficients and velocities in cancellous bone from several studies in bovine femur, human femur, and human calcaneus. The search algorithm is accelerated by exploiting correlations among search parameters. The performance of the algorithm is evaluated as a function of signal-to-noise ratio (SNR). For a typical experimental SNR (40 dB), the root-mean-square errors (RMSEs) for one example (human femur) with fast and slow waves separated by approximately half of a pulse duration were 1 m/s (slow wave velocity), 4 m/s (fast wave velocity), 0.4 dB/cm MHz (slow wave attenuation slope), and 1.7 dB/cm MHz (fast wave attenuation slope). The MLSP + CF method is fast (requiring less than 2 s at SNR = 40 dB on a consumer-grade notebook computer) and is flexible with respect to the functional form of the parametric model for the transmission coefficient. The MLSP + CF method provides sufficient accuracy and precision for many applications such that experimental error is a greater limiting factor than estimation error.