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

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) = 0.73 and R(2) = 0.86, respectively). The slope of attenuation for both wave modes also had a negative correlation with porosity (fast wave: R(2) = 0.73, slow wave: R(2) = 0.53). The fast wave amplitude decreased with increasing porosity (R(2) = 0.66). Conversely, the slow wave amplitude modestly increased with increasing porosity (R(2) = 0.39).

Echocardiographic-based assessment of myocardial fiber structure in individual, excised hearts.

The objective of this study was to assess the feasibility of using echocardiographic imaging as an approach for determining the myocardial fiber structure of intact, individual hearts. Seven formalin-fixed, ex vivo sheep hearts were imaged using a commercially available echocardiographic imaging system, and the intrinsic fiber structure for the reconstructed short-axis cross section was determined for a specific distance from the apex of each heart. Diffusion tensor magnetic resonance (DT-MR) images of each heart were acquired and fiber maps were created for comparison with the fiber structure obtained from the corresponding reconstructed echocardiographic images. These two methods of obtaining the fiber structure showed relatively good agreement, suggesting that measurements of fiber orientation for individual hearts can be derived from echocardiographic images. Further development of this method may provide a clinically useful approach for mapping the fiber orientation in individual patients over the heart cycle.

Inverse problems in cancellous bone: estimation of the ultrasonic properties of fast and slow waves using Bayesian probability theory.

Quantitative ultrasonic characterization of cancellous bone can be complicated by artifacts introduced by analyzing acquired data consisting of two propagating waves (a fast wave and a slow wave) as if only one wave were present. Recovering the ultrasonic properties of overlapping fast and slow waves could therefore lead to enhancement of bone quality assessment. The current study uses Bayesian probability theory to estimate phase velocity and normalized broadband ultrasonic attenuation (nBUA) parameters in a model of fast and slow wave propagation. Calculations are carried out using Markov chain Monte Carlo with simulated annealing to approximate the marginal posterior probability densities for parameters in the model. The technique is applied to simulated data, to data acquired on two phantoms capable of generating two waves in acquired signals, and to data acquired on a human femur condyle specimen. The models are in good agreement with both the simulated and experimental data, and the values of the estimated ultrasonic parameters fall within expected ranges.