Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones

The use of guided waves has recently drawn significant interest in the ultrasonic characterization of bone aiming at supplementing the information provided by traditional velocity measurements. This work presents a three-dimensional finite element study of guided wave propagation in intact and healing bones. A model of the fracture callus was constructed and the healing course was simulated as a three-stage process. The dispersion of guided modes generated by a broadband 1-MHz excitation was represented in the time-frequency domain. Wave propagation in the intact bone model was first investigated and comparisons were then made with a simplified geometry using analytical dispersion curves of the tube modes. Then, the effect of callus consolidation on the propagation characteristics was examined. It was shown that the dispersion of guided waves was significantly influenced by the irregularity and anisotropy of the bone. Also, guided waves were sensitive to material and geometrical changes that take place during healing. Conversely, when the first-arriving signal at the receiver corresponded to a nondispersive lateral wave, its propagation velocity was almost unaffected by the elastic symmetry and geometry of the bone and also could not characterize the callus tissue throughout its thickness. In conclusion, guided waves can enhance the capabilities of ultrasonic evaluation.     

Application of an effective medium theory for modeling ultrasound wave propagation in healing long bones

Quantitative ultrasound has recently drawn significant interest in the monitoring of the bone healing process. Several research groups have studied ultrasound propagation in healing bones numerically, assuming callus to be a homogeneous and isotropic medium, thus neglecting the multiple scattering phenomena that occur due to the porous nature of callus. In this study, we model ultrasound wave propagation in healing long bones using an iterative effective medium approximation (IEMA), which has been shown to be significantly accurate for highly concentrated elastic mixtures. First, the effectiveness of IEMA in bone characterization is examined: (a) by comparing the theoretical phase velocities with experimental measurements in cancellous bone mimicking phantoms, and (b) by simulating wave propagation in complex healing bone geometries by using IEMA. The original material properties of cortical bone and callus were derived using serial scanning acoustic microscopy (SAM) images from previous animal studies. Guided wave analysis is performed for different healing stages and the results clearly indicate that IEMA predictions could provide supplementary information for bone assessment during the healing process. This methodology could potentially be applied in numerical studies dealing with wave propagation in composite media such as healing or osteoporotic bones in order to reduce the simulation time and simplify the study of complicated geometries with a significant porous nature.     

Comment on "Mutual suppression in the 6 kHz region of sensitive chinchilla cochleae" [J. Acoust. Soc. Am. 121, 2805-2818 (2007)

Rhode [J. Acoust. Soc. Am. 121, 2805-2818 (2007)] acknowledges that two-tone neural rate responses for low-side suppression differ from those measured in basilar membrane mechanics, making one question whether this aspect of suppression has a mechanical correlate. It is suggested here that signal coding between mechanical and neural processing stages may be responsible for the fact that the total rate response (but not the basilar membrane response) for low-frequency suppressors is smaller than that for the probe-alone condition. For example, the velocity dependence of inner hair cell (IHC) transduction, membrane/synaptic filtering and the sensitivity difference between ac and dc components of the IHC receptor potential all serve to reduce excitability for low-side suppressors at the single-unit level. Hence, basilar membrane mechanics may well be the source of low-side suppression measured in the auditory nerve.     

Comment on "silent research vessels are not quiet" [J. Acoust. Soc. Am. 121, EL145-EL150

The recent paper by Ona et al. [J. Acoust. Soc. Am. 121, EL145-EL150] compared avoidance reactions by herring (Clupea harengus) to a traditional and a "silent" research vessel. Surprisingly, the latter evoked the strongest avoidance, leading to the conclusion that "candidate stimuli for vessel avoidance remain obscure." In this Comment, it is emphasized that the otolith organs in fish are linear acceleration detectors with extreme sensitivity to infrasonic particle acceleration. Near-field particle motions generated by a moving hull are mainly in the infrasonic range, and infrasound is particularly potent in evoking directional avoidance responses in several species of fish. The stimuli initiating vessel avoidance may thus include infrasonic particle acceleration.     

Comment on "Analysis of the time-reversal operator for scatterers of finite size," by D. H. Chambers [J. Acoust. Soc. Am. 112, 411-419 (2002)

This letter concerns the paper "Analysis of the time-reversal operator for scatterers of finite size" [J. Acoust. Soc. Am. 112, 411-419 (2002)]. The number of possible eigenvalues and eigenfunctions of the time reversal operator for a finite sphere given in the paper is much more than the correct number, which is proven to be the total number of multipole moments induced inside the finite sphere.     

Comment on "The directionality of acoustic T-phase signals from small magnitude submarine earthquakes" [J. Acoust. Soc. Am. 119, 3669-3675 (2006)

In a recent paper, Chapman and Marrett [J. Acoust. Soc. Am. 119, 3669-3675 (2006)] examined the tertiary (T-) waves associated with three subduction-related earthquakes within the South Fiji Basin. In that paper it is argued that acoustic energy is radiated into the sound channel by downslope propagation along abyssal seamounts and ridges that lie distant to the epicenter. A reexamination of the travel-time constraints indicates that this interpretation is not well supported. Rather, the propagation model that is described would require the high-amplitude T-wave components to be sourced well to the east of the region identified, along a relatively flat-lying seafloor.     

Comment on paper entitled, "An inversion of Freedman's 'image pulse' model in air". Acoust. Soc. Am. 119(2), 965-975 (2006)

Echolocation (i.e., perceiving objects using acoustic echoes) is well-known in underwater detection and to a lesser extent in robot guidance and machine perception. The paper by Tsakiris and McKerrow is concerned with machine perception in air using Freedman's asymptotic model, which was originally developed to predict the backscattering multiple-echo effect observed in sonar detection. This effect was subsequently shown to be due to the elastic response of underwater targets. Freedman's model can be used in air because the acoustic target is assumed to be rigid. Also, the model's prediction of multiple echoes can be used to obtain information about the shape of the target. This is the so-called inversion of the Freedman model by Tsakiris and McKerrow. In their paper, various simple bodies are tested in air using ultrasound and it is shown that the model provides relatively poor information about body shape. Several explanations are given. However, one explanation is not considered, namely that the model itself is not satisfactory. First, there is poor agreement with exact backscattering theory. Second, deriving information about target shape from the multiple echoes predicted by the model is a highly questionable procedure. Both these aspects are examined here.     

Comment on "Auditory-nerve first-spike latency and auditory absolute threshold: a computer model" [J. Acoust. Soc. Am. 119, 406-417 (2006)

A recent paper by Meddis [J. Acoust. Soc. Am. 119, 406-417 (2006)] shows that an existing model of the auditory nerve [Meddis and O'Mard, J. Acoust. Soc. Am. 117, 3787-3798 (2005)] is consistent with experimentally-measured first-spike latencies in the auditory nerve [Heil and Neubauer, J. Neurosci. 21, 7404-7415 (2001)]. The paper states that this consistency emerges because in the model, the calcium concentration inside the inner hair cell builds up over long periods of time (up to at least 200 ms) during tone presentation. It further states that integration over long time-scales happens despite the very short time constants (< 1 ms) used for the calcium dynamics. This letter demonstrates that these statements are incorrect. It is shown by simulation that calcium concentration inside the hair cell stage of the Meddis model rapidly reaches a steady state within a few milliseconds of a stimulus onset, exactly as expected from the short time-constant in the simple first-order differential equation used to model the calcium concentration. The success of the Meddis model in fitting experimental data actually confirms earlier results [Krishna, J. Comput. Neurosci. 13, 71-91 (2002a)] that show that the experimental data are a natural result of stochasticity in the synaptic events leading up to spike-generation in the auditory nerve; integration over long time scales is not necessary to model the experimental data.     

Comment on "Increase in voice level and speaker comfort in lecture rooms" [J. Acoust. Soc. Am. 125, 2072-2082 (2009)] (L)

Recently, a paper written by Brunskog Gade, Paya?-Ballester and Reig-Calbo, "Increase in voice level and speaker comfort in lecture rooms" [J. Acoust. Soc. Am. 125, 2072-2082 (2009)] related teachers' variation in vocal intensity during lecturing to the room acoustic conditions, introducing an objective parameter called "room gain" to describe these variations. In a failed attempt to replicate the objective measurements by Brunskog et al., a simplified and improved method for the calculation of room gain is proposed, in addition with an alternative magnitude called "voice support." The measured parameters are consistent with those of other studies and are used here to build two empirical models relating the voice power levels measured by Brunskog et al., to the room gain and the voice support.     

Comment on "Optimum absorption and aperture parameters for realistic coupled volume spaces determined from computational analysis and subjective testing results" [J. Acoust. Soc. Am. 127, 223-232 (2010)

A recent paper [D. T. Bradley and L. M. Wang, J. Acoust. Soc. Am. 127, 223-232 (2010)] has reported inconsistencies between the results of two different approaches for characterizing non-exponential decays in coupled-volume systems. This letter aims to expose the origin of these inconsistencies, which are due to a limitation in the methodology utilized for the analysis presented in the paper referenced above.     

Comment on "A geometric representation of spectral and temporal vowel features: quantification of vowel overlap in three linguistic varieties" [J. Acoust. Soc. Am. 119, 2334-2350 (2006)

In a recent paper by Wassink [J. Acoust Soc. Am. 119, 2334-2350 (2006)] the spectral overlap assessment metric (SOAM) was proposed for quantifying the degree of acoustic overlap between vowels. The SOAM does not fully take account of probability densities. An alternative metric is proposed which is based on quadratic discriminant analysis and takes account of probability densities in the form of a posteriori probabilities. Unlike the SOAM, the a posteriori probability-based metric allows for a direct comparison of vowel overlaps calculated using different numbers of dimensions, e.g., three dimensions (Fl, F2, and duration) versus two dimensions (Fl and F2).