Nenadic, Ivan

Introduction: Ultrasound radiation force-based methods can quantitatively evaluate tissue viscoelastic material properties. A limitation of current methods includes neglecting the inherent anisotropy nature of tissue. To explore this phenomenon, we created a phantom incorporating fibrous material that has preferential orientations. Methods: Two phantoms were made in a cube-shaped mold using a fibrous material arranged in multiple layers and embedded in porcine gelatin using two different concentrations of the gelatin (8%, 14%). Shear wave measurements were made in the phantoms at different angles by rotating the phantom, where 0° and 180° were defined along the fibers, and 90° and 270° across the fibers. Measurements were performed using a Verasonics ultrasound system equipped with a linear array transducer. Results/Discussion: The mean shear wave speeds and mean standard deviations for 8% and 14% gelatin along the fibers (0°) were (3.60 ± 0.03 and 4.10 ± 0.11 m/s) and across the fibers (90°) were (3.18 ± 0.12 and 3.90 ± 0.02 m/s), respectively. Conclusion: The fibrous gelatin-based phantoms exhibited anisotropy that could be measured using quantitative shear waves speed measurements. Increasing the gelatin percentage increases the shear wave speed and anisotropic moduli. [This study was supported by NIH grant DK092255.]

Diastolic dysfunction is the impaired ability of the left ventricle (LV) to passively fill during diastole and maintain its stroke volume at physiologic filling pressures and is associated with impaired relaxation and reduced compliance of LV. Knowledge of the quantitative values of the myocardial viscoelastic properties would improve the clinician’s ability to evaluate diastolic dysfunction in patients. To gain better understanding of the viscoelastic properties of the LV as a function of geometry, we studied Lamb wave propagation in different directions in excised porcine free-wall myocardium. The phantom consisting of a dissected porcine LV free-wall embedded in gelatin was fixed in a water tank. A mechanical shaker was used for harmonic excitation over a range of 40–500 Hz and a 7.5 MHz ultrasound transducer was used for motion measurements. Motion amplitude and phase at different depths of the sample were analyzed to obtain dispersion curves in four orthogonal directions. The data were fitted to the Lamb wave equations and shear elasticity and viscosity coefficients were estimated. The values of μ1 and μ2 were 13.75 ± 0.96 and 5.86 ± 0.75 Pa s. Our results suggest that the viscoelastic characteristics of the porcine LV free-wall in orthogonal directions were similar.

The cardiovascular diseases such as atherosclerosis, coronary artery disease, hypertension and diastolic dysfunction have been associated with arterial stiffening and decreased ventricular compliance. Noninvasive techniques capable of quantifying elasticity and viscosity of cardiovascular tissues could facilitate early diagnosis and improve treatment. Here, we present a technique that uses focused ultrasound radiation force to excite mechanical waves in the tissue of interest and pulse echo to track the tissue deformation. Analysis of tissue deformation as a function of time using Fourier transforms allows calculation of the phase wave velocity dispersion (change of velocity as a function of frequency) of various modes of deformation. Continuum mechanics equations governing the motion of a viscoelastic plate and a tube are used to model the myocardial wall and arteries, respectively. Dispersion equations are derived for the two geometries and fit to the measured velocity dispersion to estimate tissue elasticity and viscosity. ECG-gated in vivo measurements of porcine myocardial and arterial elasticity and viscosity through a heart cycle are reported. The results show that both elasticity and viscosity increase during systole and decrease during diastole in the myocardium and arteries, consistent with underlying physiology.

In the past several decades, the fields of ultrasound and magnetic resonance elastography have shown promising results in noninvasive estimates of mechanical properties of soft tissues. These techniques often rely on measuring shear wave velocity due to an external or internal source of force and relating the velocity to viscoelasticity of the tissue. The mathematical relationship between the measured velocity and material properties of the myocardial wall, arteries, and other organs with non-negligible boundary conditions is often complicated and computationally expensive. A simple relationship between the Lamb–Rayleigh dispersion and the shear wave dispersion is derived for both the velocity and attenuation. The relationship shows that the shear wave velocity is around 20% higher than the Lamb–Rayleigh velocity and that the shear wave attenuation is about 20% lower than the Lamb–Rayleigh attenuation. Results of numerical simulations in the frequency range 0–500 Hz are presented.

Diastolic dysfunction is characterized by the stiffening of the left-ventricular myocardium. An imaging technique capable of quantifying viscoelasticity of the left-ventricle would aid clinicians in evaluating diastolic function. Lamb wave dispersion ultrasound vibrometry (LDUV) is an ultrasound-based method for measuring viscoelasticity of plate-like materials by exciting Lamb waves and measuring change of wave velocity as a function of frequency (dispersion). Lamb wave dispersion equation is fit to the dispersion data to estimate mechanical properties. We report in vivo transthoracic studies aimed at quantifying elasticity and viscosity of a beating porcine left-ventricle using LDUV. A single ultrasound probe operating at 5 MHz was used for impulse excitation in the myocardium and to track the wave motion. A Fourier space-time analysis of the motion was used to obtain Lamb wave velocity dispersion. ECG-gated transthoracic in vivo measurements of group velocity, elasticity, and viscosity throughout a single heart cycle were obtained. Group velocity, elasticity, and viscosity in the frequency range from 50 to 500 Hz increased by at least two-fold from diastole to systole, consistent with contraction and relaxation of the myocardium.

In the field of tissue engineering, monitoring the elasticity of developing tissue cultures is important for evaluating their growth and maturation. In this work, we used wave propagation methods to measure the elasticity of thin tissue-mimicking layers to test the feasibility of measuring the elasticity of developing tissue cultures. We developed finite element and analytical models for investigating this problem and found good agreement between the results from both models. We used ultrasound radiation force to induce propagating waves, and the waves are measured using high frame rate ultrasound imaging at 10 kHz. The wave modes were identified and compared with an analytic model for Rayleigh wave propagation in a thin elastic layer bound to a solid substrate. The same gelatin mixture was used to make phantoms 1, 4, and 50 mm thick, where the phantom with 50 mm thickness was used as control and evaluated with shear wave imaging methods. The analytic model was used to fit data from experiments in the large block and thin layers of 1 and 4 mm thick, and the measured shear moduli were 22.7, 21.8, and 22.5 kPa, respectively. These results provide a validation for measurement of elasticity in thin elastic layers.

The response of an embedded sphere in a viscoelastic medium excited by acoustic radiation force has been studied in both the time- and frequency-domains. This model is important because it can be used to characterize the viscoelastic properties of the medium by fitting the response to the theoretical model. The Kelvin–Voigt model has been used exclusively in these models. An extension to the previously reported models is described so that any viscoelastic rheological model can be used. This theoretical development describes the generalized embedded sphere response both in the time and frequency domains. Comparing the results from derivations in both domains showed very good agreement with a median absolute error (MAE) ranging from 0.0044 to 0.0072. Good agreement is demonstrated with finite element model simulations and the theory with a MAE of 0.006. Lastly, results for characterization of gelatin and rubber materials with the new theory are shown where the MAE values were used to determine which rheological model best describes the measured responses.

Arterial elasticity has been proposed as an independent predictor of cardiovascular diseases and mortality. Identification of the different propagating modes in thin shells can be used to characterize the elastic properties. Ultrasound radiation force was used to generate local mechanical waves in the wall of a urethane tube or an excised pig carotid artery. The waves were tracked using pulse-echo ultrasound. A modal analysis using two-dimensional discrete fast Fourier transform was performed on the time–space signal. This allowed the visualization of different modes of propagation and characterization of dispersion curves for both structures. The urethane tube/artery was mounted in a metallic frame, embedded in tissue-mimicking gelatin, cannulated, and pressurized over a range of 10–100 mmHg. The k-space and the dispersion curves of the urethane tube showed one mode of propagation, with no effect of transmural pressure. Fitting of a Lamb wave model estimated Young’s modulus in the urethane tube around 560 kPa. Young’s modulus of the artery ranged from 72 to 134 kPa at 10 and 100 mmHg, respectively. The changes observed in the artery dispersion curves suggest that this methodology of exciting mechanical waves and characterizing the modes of propagation has potential for studying arterial elasticity.

Arterial elasticity has gained importance in the past decades as it has been shown to be an independent predictor of cardiovascular diseases. Ultrasound radiation force has been used to excite propagating waves in arterial vessels in order to measure the wave speeds and characterize the elastic properties of the vessels. Excised pig carotid arteries were excited with impulsive radiation force using 3-MHz tonebursts of length 200, and the propagating waves were measured along the length of the artery over a distance of 2 cm. A 2-D fast Fourier transform was performed on the spatiotemporal data for identification of several propagating modes in the vessel. Multiple propagating modes could be visualized from the spatiotemporal data that varied with the transmural pressure of the artery under investigation over a range of 10–100 mm Hg. The modes present in the data were fitted with a theoretical model to estimate the elasticity of the arteries. The comparison with the model provides insight into characterizing the elastic properties of the artery. [This work was supported in part by NIH Grant no. EB002640.]

Characterization of viscoelastic soft tissues and materials has been a subject of active research for the past two decades. Techniques involving measuring the motion of embedded spheres in viscoelastic media have been employed to measure the viscoelastic material properties of the media surrounding the sphere. The published work using this technique has been restricted to using the Kelvin–Voigt model, which has worked for gelatin-based materials. We report an extension of this method using different viscoelastic rheological models such as the Maxwell, generalized Maxwell, Zener, and Kelvin–Voigt fractional derivative models. We performed experiments using a focused 3-MHz transducer to produce radiation force and a 7.5-MHz pulse-echo transducer to measure the sphere motion. Two phantoms were tested; one made of gelatin and another made of rubber with stainless steel spheres embedded in the materials. The response was fitted with the generalized theoretical model to find the material properties over bandwidths of 25–3000 Hz. The median absolute errors ranged from 0.0036–0.0421 and 0.0365–0.0879 for the gelatin and rubber phantoms, respectively. This generalized method offers added flexibility to characterize different types of viscoelastic materials using the most appropriate rheological model. [Work supported in part by NIH Grant nos. EB002167 and DK082408.]