Rayleigh-Lamb wave propagation on a fractional order viscoelastic plate.

A previous study of the authors published in this journal focused on mechanical wave motion in a viscoelastic material representative of biological tissue [Meral et al., J. Acoust. Soc. Am. 126, 3278-3285 (2009)]. Compression, shear and surface wave motion in and on a viscoelastic halfspace excited by surface and sub-surface sources were considered. It was shown that a fractional order Voigt model, where the rate-dependent damping component that is dependent on the first derivative of time is replaced with a component that is dependent on a fractional derivative of time, resulted in closer agreement with experiment as compared with conventional (integer order) models, such as those of Voigt and Zener. In the present study, this analysis is extended to another configuration and wave type: out-of-plane response of a viscoelastic plate to harmonic anti-symmetric Lamb wave excitation. Theoretical solutions are compared with experimental measurements for a polymeric tissue mimicking phantom material. As in the previous configurations the fractional order modeling assumption improves the match between theory and experiment over a wider frequency range. Experimental complexities in the present study and the reliability of the different approaches for quantifying the shear viscoelastic properties of the material are discussed.

Sound transmission in human thorax through airway insonification: an experimental and computational study with diagnostic applications.

Pulmonary diseases and injury lead to structural and functional changes in the lung parenchyma and airways, often resulting in measurable sound transmission changes on the chest wall surface. Additionally, noninvasive imaging of externally driven mechanical wave motion in the chest (e.g., using magnetic resonance elastography) can provide information about lung stiffness and other structural property changes which may be of diagnostic value. In the present study, a comprehensive computational simulation (in silico) model was developed to simulate sound wave propagation in the airways, parenchyma, and chest wall under normal and pathological conditions that create distributed structural (e.g., pneumothoraces) and diffuse material (e.g., fibrosis) changes, as well as a localized structural and material changes as may be seen with a neoplasm. Experiments were carried out in normal subjects to validate the baseline model. Sound waves with frequency content from 50 to 600 Hz were introduced into the airways of three healthy human subjects through the mouth, and transthoracic transmitted waves were measured by scanning laser Doppler vibrometry at the chest wall surface. The computational model predictions of a frequency-dependent decreased sound transmission due to pneumothorax were consistent with experimental measurements reported in previous work. Predictions for the case of fibrosis show that while shear wave motion is altered, changes to compression wave propagation are negligible, and thus, insonification, which primarily drives compression waves, is not ideal to detect the presence of fibrosis. Results from the numerical simulation of a tumor show an increase in the wavelength of propagating waves in the immediate vicinity of the tumor region. Graphical abstract.

Surface response of a fractional order viscoelastic halfspace to surface and subsurface sources.

Previous studies by the second author published in this journal focused on low audible frequency (40-400 Hz) shear and surface wave motion in and on a viscoelastic material representative of biological tissue. Specific cases considered were that of surface wave motion on a halfspace caused by a finite rigid circular disk located on the surface and oscillating normal to it [Royston et al., J. Acoust. Soc. Am. 106, 3678-3686 (1999)] and compression, shear, and surface wave motion in a halfspace generated by a subsurface finite dipole [Royston et al., J. Acoust. Soc. Am. 113, 1109-1121 (2003)]. In both studies, a Voigt model of viscoelasticity was assumed in the theoretical treatment, which resulted in agreement between theoretical predictions and experimental measurements over a limited frequency range. In the present article, the linear viscoelastic assumption in these two prior works is revisited to consider a (still linear) fractional order Voigt model, where the rate-dependent damping component that is dependent on the first derivative of time is replaced with a component that is dependent on a fractional derivative of time. It is shown that in both excitation source configurations, the fractional order Voigt model assumption improves the match of theory to experiment over a wider frequency range (in some cases up to the measured range of 700 Hz).

Microstructural and strength evaluation of regenerate tissue during the consolidation period after vertical mandibular ramus distraction.

Mandibular ramus height restoration by distraction osteogenesis (DO) is a key procedure in mandibular hypoplasia reconstruction. The objective of this study was to evaluate short-term skeletal changes in the regenerated bone after vertical mandibular ramus DO using a buried distraction device. Eight subadult beagle dogs underwent bilateral vertical mandibular ramus DO. After a 7-day latency period, distraction was performed at a rate of 0.5 mm twice a day for 12 days. Four dogs were killed at 1 month and four dogs at 2 months after the end of distraction. One intact beagle was included as an unoperated control. After sacrifice, micro computed tomography (muCT) and mechanical testing of distracted sites were used to measure bone volume (BV), total volume (TV), and mechanical peak load strength, respectively. The muCT images showed wide variation in the response, with some animals demonstrating considerable bone formation and reconstitution of the canal for the inferior alveolar nerve. Quantitatively, BV was no more than 67% and BV/TV was less than 25% of the intact control, and strength was approximately 33% of the intact control value. The 1 and 2 month values were similar. These results suggest that internal distractors can successfully reconstitute bone but that the regenerated tissue did not regain structural and mechanical characteristics of native bone within the 2 month study period.

The effect of pulsed ultrasound on mandibular distraction.

This study evaluated the effect of pulsed ultrasound on tissue repair and bone growth during mandibular osteodistraction. Twenty-one rabbits were divided into three groups of 7. The distraction started 72 h after surgically severing both sides of the mandible and proceeded at a rate of 1.5 mm/12 h for 5 days. Group I received pulsed ultrasound (nominally 200 micros pulse of 1.5 MHz at a 1.1 kHz pulse repetition frequency, 30 mW/cm2) for 20 min on both sides of the mandible every other day (alternating sides). Group 2 received the same pulsed ultrasound treatment on one side of the mandible every day for 20 min. Group 3 did not receive any ultrasound treatment. Bone formation at the distraction site was assessed by photodensitometry on head radiographs, a vibratory coherence test across the distraction site, a postmortem three-point bending mechanical stiffness test, and a postmortem histological examination. Statistical analyses performed using analysis of variance revealed that pulsed ultrasound enhanced bone formation at the distraction site with a high level of significance when assessed by the increase in new bone photodensity (p = 0.001), vibratory coherence (p = 0.001), mechanical stiffness (p = 0.003), and qualitative histological studies, especially when the pulsed ultrasound treatment was directly applied daily.