Bernal, Miguel

Evaluation of tissue engineering constructs is performed by a series of different tests. In many cases it is important to match the mechanical properties of these constructs to those of native tissues. However, many mechanical testing methods are destructive in nature which increases cost for evaluation because of the need for additional samples reserved for these assessments. A wave propagation method is proposed for characterizing the shear elasticity of thin layers bounded by a rigid substrate and fluid-loading, similar to the configuration for many tissue engineering applications. An analytic wave propagation model was derived for this configuration and compared against finite element model simulations and numerical solutions from the software package Disperse. The results from the different models found very good agreement. Experiments were performed in tissue-mimicking gelatin phantoms with thicknesses of 1 and 4 mm and found that the wave propagation method could resolve the shear modulus with very good accuracy, no more than 4.10% error. This method could be used in tissue engineering applications to monitor tissue engineering construct maturation with a nondestructive wave propagation method to evaluate the shear modulus of a material.

The objective of this study was to assess the potential for noninvasively identifying viscoelastic material properties in arterial vessels using ultrasound radiation force and modern computational inverse problem techniques. A rubber tube embedded in gelatin was excited at different points along the axis using impulsive ultrasound radiation force. The resulting mechanical waves were measured using a laser vibrometer and pulse-echo ultrasound. The inverse problem was cast as an optimization problem, in which the discrepancy between the measured dynamic response and the computed finite element model response was minimized with respect to viscoelastic material parameters. The model was very sensitive to the tube’s viscoelastic parameters and relatively insensitive to those of the gelatin. The viscoelastic properties of the tube obtained from the inverse problem were compared to the results obtained from a dynamic mechanical analyzer (DMA). For the overlapping range of frequencies (130–190 Hz), the results of the inverse problem gave an equivalent modulus that range from 7.3–8.5 MPa, while the DMA values range from 6.0–9.2 MPa. These results have important implications for using ultrasound radiation force in noninvasive characterization of the viscoelastic properties of arteries in vivo. [This work was supported in part by Grant No. EB002640 from NIH.]

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.

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.]

Arterial elasticity is an independent predictor of cardiovascular disease and mortality. Measurment of waves in thin shells can be used to estimate the circumferential and the longitudinal elastic moduli. Latex tubes and excised pig arteries were used as isotropic and anisotropic models. Waves were generated using focused ultrasound (1 ms, 3 MHz) in different locations of the wall. The modes of propagation of the waves were detected with a laser vibrometer or an ultrasound pulse echo tool while the excitation was moved known distances. Bending waves were predominant when exciting in the center of the wall, while a combination of torsion and bending waves resulted from exciting off center. Wave speeds of 15 m/s and 5 m/s respectively, were measured for the bending waves. Using the Moens-Korteweg equation, values of 1.1 and 0.350 MPa were found for the longitudinal elastic modulus in the tube and artery respectively. Generation of different modes in the tubes and arteries is possible using focused ultrasound. Elastic components of the tubes and vessels in the longitudinal and the circumferential direction can be estimated from the speed of propagation and the frequency of the bending and the torsional waves.