Zoujun Dai

Estimating material viscoelastic properties based on surface wave measurements: A comparison of techniques and modeling assumptions

Previous studies of the first author and others have focused on low audible frequency (<1 kHz) shear and surface wave motion in and on a viscoelastic material comprised of or representative of soft biological tissue. A specific case considered has been surface (Rayleigh) wave motion caused by a circular disk located on the surface and oscillating normal to it. Different approaches to identifying the type and coefficients of a viscoelastic model of the material based on these measurements have been proposed. One approach has been to optimize coefficients in an assumed viscoelastic model type to match measurements of the frequency-dependent Rayleigh wave speed. Another approach has been to optimize coefficients in an assumed viscoelastic model type to match the complex-valued frequency response function (FRF) between the excitation location and points at known radial distances from it. In the present article, the relative merits of these approaches are explored theoretically, computationally, and experimentally. It is concluded that matching the complex-valued FRF may provide a better estimate of the viscoelastic model type and parameter values; though, as the studies herein show, there are inherent limitations to identifying viscoelastic properties based on surface wave measurements.

Sound transmission in the chest under surface excitation - An experimental and computational study with diagnostic applications

Chest physical examination often includes performing chest percussion, which involves introducing sound stimulus to the chest wall and detecting an audible change. This approach relies on observations that underlying acoustic transmission, coupling, and resonance patterns can be altered by chest structure changes due to pathologies. More accurate detection and quantification of these acoustic alterations may provide further useful diagnostic information. To elucidate the physical processes involved, a realistic computer model of sound transmission in the chest is helpful. In the present study, a computational model was developed and validated by comparing its predictions with results from animal and human experiments which involved applying acoustic excitation to the anterior chest, while detecting skin vibrations at the posterior chest. To investigate the effect of pathology on sound transmission, the computational model was used to simulate the effects of pneumothorax on sounds introduced at the anterior chest and detected at the posterior. Model predictions and experimental results showed similar trends. The model also predicted wave patterns inside the chest, which may be used to assess results of elastography measurements. Future animal and human tests may expand the predictive power of the model to include acoustic behavior for a wider range of pulmonary conditions.

A model of lung parenchyma stress relaxation using fractional viscoelasticity

Some pulmonary diseases and injuries are believed to correlate with lung viscoelasticity changes. Hence, a better understanding of lung viscoelastic models could provide new perspectives on the progression of lung pathology and trauma. In the presented study, stress relaxation measurements were performed to quantify relaxation behavior of pig lungs. Results have uncovered certain trends, including an initial steep decay followed by a slow asymptotic relaxation, which would be better described by a power law than exponential decay. The fractional standard linear solid (FSLS) and two integer order viscoelastic models - standard linear solid (SLS) and generalized Maxwell (GM) - were used to fit the stress relaxation curves; the FSLS was found to be a better fit. It is suggested that fractional order viscoelastic models, which have nonlocal, multi-scale attributes and exhibit power law behavior, better capture the lung parenchyma viscoelastic behavior.

Pneumothorax effects on pulmonary acoustic transmission

Pneumothorax (PTX) is an abnormal accumulation of air between the lung and the chest wall. It is a relatively common and potentially life-threatening condition encountered in patients who are critically ill or have experienced trauma. Auscultatory signs of PTX include decreased breath sounds during the physical examination. The objective of this exploratory study was to investigate the changes in sound transmission in the thorax due to PTX in humans. Nineteen human subjects who underwent video-assisted thoracic surgery, during which lung collapse is a normal part of the surgery, participated in the study. After subjects were intubated and mechanically ventilated, sounds were introduced into their airways via an endotracheal tube. Sounds were then measured over the chest surface before and after lung collapse. PTX caused small changes in acoustic transmission for frequencies below 400 Hz. A larger decrease in sound transmission was observed from 400 to 600 Hz, possibly due to the stronger acoustic transmission blocking of the pleural air. At frequencies above 1 kHz, the sound waves became weaker and so did their changes with PTX. The study elucidated some of the possible mechanisms of sound propagation changes with PTX. Sound transmission measurement was able to distinguish between baseline and PTX states in this small patient group. Future studies are needed to evaluate this technique in a wider population.

Investigation of pulmonary acoustic simulation: comparing airway model generation techniques

Alterations in the structure and function of the pulmonary system that occur in disease or injury often give rise to measurable spectral, spatial and/or temporal changes in lung sound production and transmission. These changes, if properly quantified, might provide additional information about the etiology, severity and location of trauma, injury, or pathology. With this in mind, the authors are developing a comprehensive computer simulation model of pulmonary acoustics, known as The Audible Human Project™. Its purpose is to improve our understanding of pulmonary acoustics and to aid in interpreting measurements of sound and vibration in the lungs generated by airway insonification, natural breath sounds, and external stimuli on the chest surface, such as that used in elastography. As a part of this development process, finite element (FE) models were constructed of an excised pig lung that also underwent experimental studies. Within these models, the complex airway structure was created via two methods: x-ray CT image segmentation and through an algorithmic means called Constrained Constructive Optimization (CCO). CCO was implemented to expedite the segmentation process, as airway segments can be grown digitally. These two approaches were used in FE simulations of the surface motion on the lung as a result of sound input into the trachea. Simulation results were compared to experimental measurements. By testing how close these models are to experimental measurements, we are evaluating whether CCO can be used as a means to efficiently construct physiologically relevant airway trees.

Localized Elastography Map of Human Cornea Through Surface Vibrations

Elastography techniques are being developed to diagnose and monitor the progression and treatment of diseases that correlate with changes in soft tissue stiffness. The objective of this paper is to outline the application of vibrations to the human cornea in order to reconstruct a stiffness map. Having a localized stiffness map is useful for early diagnosis of cornea related diseases such as glaucoma and keratoconus. Experimental data was collected by directly vibrating the excised cornea axisymetrically along the edge and measuring wave propagation inward with the use of laser vibrometry. Different methods have been implemented to increase the reflectivity of the cornea for laser vibrometry. To corroborate the data, as well as to test feasibility, experiments have been done on phantoms constructed from silicone-based polymers. To reconstruct the data into a stiffness map, an appropriate analytical model has to be derived. This paper outlines the derivation of the analytical model for the cornea starting with simple circular plates and moving towards the curved geometry of the cornea. To verify the analytical model, finite element simulations were used to replicate the results. These results have also been checked against experimental data to help determine any external variables that affect results. Overall, the feasibility and application of a process has been determined. Future goals include increasing in-vivo application to make the process safe and cost-effective.Copyright

Wideband optical elastography of in vivo human skin using geometrically focused surface waves

Viscoelastic models are fit to shear moduli derived from geometrically focused surface waves (GFS) on human skin using viscoelastic wave theory. Unlike in previous studies on the analytical solution and experimental measurement of radially outward traveling surface waves, measurable radially inward traveling GFS waves can be generated over a wider range of frequencies as attenuation is countered by the converging nature of the wavefront. This enables a more accurate and broader assessment of both the shear storage and loss moduli of the material, which are expected to vary with frequency. In the present study, GFS waves are applied to human skin on the posterior side of the forearm using a scanning LASER Doppler vibrometer. Surface wave measurements can then be used to estimate the complex frequency dependent viscoelastic properties of biological tissue, which are affected by numerous pathologies. Using a phantom gel this technique was validated through comparison with other studies. It was found that spring-pot and fractional Voigt models yield a potentially stable model parameter for skin, but more study is needed to confirm. [Work supported by NIH: Grant # EB012142.]

MEASURING AND MODELING ELASTOGRAPHY OF HUMAN CORNEA USING SCANNING LASER DOPPLER VIBROMETRY

Our interest is in noninvasively mapping the viscoelastic properties of the human cornea with the aid of a Scanning Laser Doppler Vibrometer (SLDV). Mechanical properties of the cornea can be used to predict early onset of diseases, such as glaucoma and keratoconus. By applying mechanical vibration near the cornea and measuring the dynamic wave propagation across the cornea, an elastographic map can be reconstructed. To effectively reconstruct the data, an appropriate analytical solution is needed to interpret the measured motion; in the present article, we review initial measurements and modeling of phantom cornea models. Several viscoelastic plate phantoms were constructed using silicone gels to simulate corneal structures. Comprehensive frequency sweeps were performed on these phantoms. The material can be represented using a fractional order model of viscoelasticity. Similar experiments have been completed on ex-vivo human cornea from donor eyes. The design shows proof of concept and is now being modified to a more applicable manner for in vivo experiments.© 2013 ASME

Poro-visco-elastic modeling of mechanical wave motion in the lungs

Noninvasive measurement of mechanical wave motion (sound and vibration) in the lungs may be of diagnostic value, as it can provide information about the mechanical properties of the lungs, which in turn are affected by disease and injury. In this study, two theoretical models of the vibro-acoustic behavior of the lung parenchyma are compared: (1) a Biot theory of poroviscoelasticity and (2) a simplified “bubble swarm” model for compression wave behavior. A “slow” compression wave speed predicted by the Biot theory formulation agrees well with the bubbly swarm theory in both analytical calculations and computational simulation. Biot theory also predicts a fast compression wave and a shear wave. The relative contributions of all three wave types are assessed. The effect of the air volume fraction is also investigated. Preliminary experimental measurements of the slow compression wave speed in the lung parenchyma are carried out and agree with theoretical predictions.© 2012 ASME

Estimation of local viscoelasticity of lungs based on surface waves

The viscoelastic properties of lung tissue are of interest in medicine as they have been shown to be affected by various pathologies. Identifying the mechanical properties of lung tissue first requires a means of quantitatively measuring phenomena, such as mechanical wave motion, that are affected by these properties. In the present study, lung surface motion is measured on excised pig lungs to determine suitable viscoelastic models. The relation between the surface wave speed and the frequency is analyzed and different viscoelastic models are used to fit this relation. Also a more comprehensive method to evaluate the frequency-dependent shear modulus of the pig lung measuring the propagation of surface waves on the surface of the lung is presented and viscoelastic models (both of integer and fractional order) are compared to experimental results over the frequency range of 100–500 Hz.Copyright