Q. He, G.-Y. Li, F.-F. Lee, Q. Zhang, Y. Cao, and J. Luo. 2017. “Novel Method for Vessel Cross-Sectional Shear Wave Imaging.” Ultrasound in Medicine and Biology, 43, 7.Abstract
Many studies have investigated the applications of shear wave imaging (SWI) to vascular elastography, mainly on the longitudinal section of vessels. It is important to investigate SWI in the arterial cross section when evaluating anisotropy of the vessel wall or complete plaque composition. Here, we proposed a novel method based on the coordinate transformation and directional filter in the polar coordinate system to achieve vessel cross-sectional shear wave imaging. In particular, ultrasound radiofrequency data were transformed from the Cartesian to the polar coordinate system; the radial displacements were then estimated directly. Directional filtering was performed along the circumferential direction to filter out the reflected waves. The feasibility of the proposed vessel cross-sectional shear wave imaging method was investigated through phantom experiments and ex vivo and in vivo studies. Our results indicated that the dispersion relation of the shear wave (i.e., the guided circumferential wave) within the vessel can be measured via the present method, and the elastic modulus of the vessel can be determined.
Y.-L. Liu, G.-Y. Li, P. He, Z.-Q. Mao, and Y. Cao. 2017. “Temperature-dependent elastic properties of brain tissues measured with the shear wave elastography method.” Journal of the Mechanical Behavior of Biomedical Materials, 65.Abstract
Determining the mechanical properties of brain tissues is essential in such cases as the surgery planning and surgical training using virtual reality based simulators, trauma research and the diagnosis of some diseases that alter the elastic properties of brain tissues. Here, we suggest a protocol to measure the temperature-dependent elastic properties of brain tissues in physiological saline using the shear wave elastography method. Experiments have been conducted on six porcine brains. Our results show that the shear moduli of brain tissues decrease approximately linearly with a slope of −0.041±0.006 kPa/°C when the temperature T increases from room temperature ($\sim$23 °C) to body temperature ($\sim$37 °C). A case study has been further conducted which shows that the shear moduli are insensitive to the temperature variation when T is in the range of 37 to 43 °C and will increase when T is higher than 43 °C. With the present experimental setup, temperature-dependent elastic properties of brain tissues can be measured in a simulated physiological environment and a non-destructive manner. Thus the method suggested here offers a unique tool for the mechanical characterization of brain tissues with potential applications in brain biomechanics research.
Y. Cao, G.-Y. Li, X. Zhang, and Y.-L. Liu. 2017. “Tissue-mimicking materials for elastography phantoms: A review.” Extreme Mechanics Letters, 17.Abstract
Ultrasound imaging can generate real-time images and is a low-cost, safe, and mobile imaging modality, which has broad applications in clinical radiology. During the past decade, ultrasound-based elastography has emerged as a highly useful technique for characterizing the mechanical properties of living soft tissues. Tissue-mimicking phantoms play an essential role in the development, validation, and use of elastography methods. Phantoms with desired acoustic and mechanical properties that are stable over time and can be stored in a broad range of temperatures have been pursued over the years. In this paper, we provide a brief overview of the typical phantom materials reported in the literature; in particular, we discuss the progress made in recent years and the open issues that deserve further investigation.
G.-Y. Li, Q. He, G. Xu, L. Jia, J. Luo, and Y. Cao. 2017. “An ultrasound elastography method to determine the local stiffness of arteries with guided circumferential waves.” Journal of Biomechanics, 51.Abstract
Arterial stiffness is highly correlated with the functions of the artery and may serve as an important diagnostic criterion for some cardiovascular diseases. To date, it remains a challenge to quantitatively assess local arterial stiffness in a non-invasive manner. To address this challenge, we investigated the possibility of determining arterial stiffness using the guided circumferential wave (GCW) induced in the arterial wall by a focused acoustic radiation force. The theoretical model for the dispersion analysis of the GCW is presented, and a finite element model has been established to calculate the dispersion curve. Our results show that under described conditions, the dispersion relations of the GCW are basically independent of the curvature of the arterial wall and can be well-described using the Lamb wave (LW) model. Based on this conclusion, an inverse method is proposed to characterize the elastic modulus of artery. Both numerical experiments and phantom experiments had been performed to validate the proposed method. We show that our method can be applied to the cases in which the artery has local stenosis and/or the geometry of the artery cross-section is irregular; therefore, this method holds great potential for clinical use.
Y. Zheng, G.-Y. Li, Y. Cao, and X.-Q. Feng. 2017. “Wrinkling of a stiff film resting on a fiber-filled soft substrate and its potential application as tunable metamaterials.” Extreme Mechanics Letters, 11.Abstract
Mechanical self-assembly of ordered patterns via spontaneous buckling of thin-film/soft-substrate systems has received considerable interests in recent years. Here we study the wrinkling of a stiff film resting on a fiber-filled soft substrate. In particular, the effects of the cross-section dimension, spacing, and positions of fibers on the wrinkling patterns in the film/substrate bilayer system are investigated. We show that diverse wrinkling patterns, including sinusoidal wrinkling, period-doubling, period-tripling and mountain ridge modes, may occur at a small or moderate overall compression strain due to the inhomogeneous deformation in the substrate and they can be well controlled by tuning geometrical and physical parameters of the system. To illustrate the potential use of the wrinkling patterns revealed in this study, we investigate the elastic wave propagation in such a wrinkled bilayer using the Bloch wave theory. Our computational results show that diverse stress patterns generated in the soft composites give rise to a rich variety of band structures. Desired bandgaps of elastic waves can be achieved and tuned by simply designing the geometric parameters and controlling the external stimuli imposed on the soft metamaterials.
G.-Y. Li, Y. Zheng, Y. Cao, X.-Q. Feng, and W. Zhang. 2016. “Controlling elastic wave propagation in a soft bilayer system: Via wrinkling-induced stress patterns.” Soft Matter, 12, 18.Abstract
Compression of a film/substrate bilayer system with different surface/interfacial structures can lead to diverse buckling patterns including sinusoidal wrinkles, ridges, folds, creases and tilted sawteeth wrinkles. In this paper, we show that elastic wave band gaps in the film/substrate bilayer system largely depend on the wrinkling patterns. More interestingly, we find that different wrinkling patterns investigated here can coexist and evolve in one bilayer system and the elastic wave propagation behaviors can be controlled by manipulating the hybrid wrinkling patterns. Our analysis also reveals that the periodic stress pattern plays a dominant role in tuning the bandgap structures in comparison to geometrical patterns caused by surface instability. A careful investigation of the transmission spectra of the composite systems has validated the main findings given by the analysis based on the Bloch wave theory. Potential use of the method and materials reported here to gain wide attenuation frequency ranges and the design of nesting Fibonacci superlattices have been demonstrated.
G.-Y. Li, Q. He, L.-X. Qian, H. Geng, Y. Liu, X.-Y. Yang, J. Luo, and Y. Cao. 2016. “Elastic Cherenkov effects in transversely isotropic soft materials-II: Ex vivo and in vivo experiments.” Journal of the Mechanics and Physics of Solids, 94.Abstract
In part I of this study, we investigated the elastic Cherenkov effect (ECE) in an incompressible transversely isotropic (TI) soft solid using a combined theoretical and computational approach, based on which an inverse method has been proposed to measure both the anisotropic and hyperelastic parameters of TI soft tissues. In this part, experiments were carried out to validate the inverse method and demonstrate its usefulness in practical measurements. We first performed ex vivo experiments on bovine skeletal muscles. Not only the shear moduli along and perpendicular to the direction of muscle fibers but also the elastic modulus EL and hyperelastic parameter c2 were determined. We next carried out tensile tests to determine EL, which was compared with the value obtained using the shear wave elastography method. Furthermore, we conducted in vivo experiments on the biceps brachii and gastrocnemius muscles of ten healthy volunteers. To the best of our knowledge, this study represents the first attempt to determine EL of human muscles using the dynamic elastography method and inverse analysis. The significance of our method and its potential for clinical use are discussed.
G.-Y. Li, Y. Zheng, Y. Liu, M. Destrade, and Y. Cao. 2016. “Elastic Cherenkov effects in transversely isotropic soft materials-I: Theoretical analysis, simulations and inverse method.” Journal of the Mechanics and Physics of Solids, 96.Abstract
A body force concentrated at a point and moving at a high speed can induce shear-wave Mach cones in dusty-plasma crystals or soft materials, as observed experimentally and named the elastic Cherenkov effect (ECE). The ECE in soft materials forms the basis of the supersonic shear imaging (SSI) technique, an ultrasound-based dynamic elastography method applied in clinics in recent years. Previous studies on the ECE in soft materials have focused on isotropic material models. In this paper, we investigate the existence and key features of the ECE in anisotropic soft media, by using both theoretical analysis and finite element (FE) simulations, and we apply the results to the non-invasive and non-destructive characterization of biological soft tissues. We also theoretically study the characteristics of the shear waves induced in a deformed hyperelastic anisotropic soft material by a source moving with high speed, considering that contact between the ultrasound probe and the soft tissue may lead to finite deformation. On the basis of our theoretical analysis and numerical simulations, we propose an inverse approach to infer both the anisotropic and hyperelastic parameters of incompressible transversely isotropic (TI) soft materials. Finally, we investigate the properties of the solutions to the inverse problem by deriving the condition numbers in analytical form and performing numerical experiments. In Part II of the paper, both ex vivo and in vivo experiments are conducted to demonstrate the applicability of the inverse method in practical use.
G.-Y. Li, Y. Zheng, and Y. Cao. 2016. “Tunable defect mode in a soft wrinkled bilayer system.” Extreme Mechanics Letters, 9.Abstract
Here we study the defect mode in a wrinkled soft bilayer induced by a local geometrical defect introduced into the system. We show that the band gap of the studied composite system depends on the wrinkling-induced stress pattern and is not sensitive to the compression strain $ε$ in the given loading range. However, the frequency of the defect mode apparently varies with $ε$. This interesting phenomenon enables us to widely tune the spatial extension of the defect mode from highly localized to completely extended by simply controlling the imposed external load. Our strategy to create a tunable defect mode in a soft layered composite is simple and straightforward and may find such broad applications as the development of advanced soft metamaterials and corresponding devices.
Y. Jiang, G.-Y. Li, L.-X. Qian, X.-D. Hu, D. Liu, S. Liang, and Y. Cao. 2015. “Characterization of the nonlinear elastic properties of soft tissues using the supersonic shear imaging (SSI) technique: Inverse method, ex vivo and in vivo experiments.” Medical Image Analysis, 20, 1.Abstract
Dynamic elastography has become a new clinical tool in recent years to characterize the elastic properties of soft tissues in vivo, which are important for the disease diagnosis, e.g., the detection of breast and thyroid cancer and liver fibrosis. This paper investigates the supersonic shear imaging (SSI) method commercialized in recent years with the purpose to determine the nonlinear elastic properties based on this promising technique. Particularly, we explore the propagation of the shear wave induced by the acoustic radiation force in a stressed hyperelastic soft tissue described via the Demiray-Fung model. Based on the elastodynamics theory, an analytical solution correlating the wave speed with the hyperelastic parameters of soft tissues is first derived. Then an inverse approach is established to determine the hyperelastic parameters of biological soft tissues based on the measured wave speeds at different stretch ratios. The property of the inverse method, e.g., the existence, uniqueness and stability of the solution, has been investigated. Numerical experiments based on finite element simulations and the experiments conducted on the phantom and pig livers have been employed to validate the new method. Experiments performed on the human breast tissue and human heel fat pads have demonstrated the capability of the proposed method for measuring the in vivo nonlinear elastic properties of soft tissues. Generalization of the inverse analysis to other material models and the implication of the results reported here for clinical diagnosis have been discussed.
C.-C. Luo, L.-X. Qian, G.-Y. Li, Y. Jiang, S. Liang, and Y. Cao. 2015. “Determining the in vivo elastic properties of dermis layer of human skin using the supersonic shear imaging technique and inverse analysis.” Medical Physics, 42, 7.Abstract
Purpose: Human skin consists of several layers including epidermis, dermis, and hypodermis. The determination of the in vivo mechanical properties of an individual skin layer represents a great challenge to date. In this study, the authors explore the use of the supersonic shear imaging (SSI) technique and inverse analysis to determine the in vivo elastic properties of the dermis layer of human skin. Methods: The measurements are conducted on the volar forearms and dorsal forearms of 18 healthy volunteers (nine females and nine males) using the SSI technique that gives the velocities of the shear wave generated by the acoustic force. Finite element analysis is carried out to simulate the propagation of the shear wave in the multilayer soft media and the results are used to interpret the experimental data and deduce the shear modulus of the dermis layer. Results: The shear moduli of the skin dermis layer obtained for the 18 healthy volunteers exhibit significant anisotropy. A standard statistical analysis demonstrates the differences between sexes. Conclusions: This study demonstrates that the SSI technique together with the inverse analysis represents a useful tool to characterize the in vivo elastic properties of human skin.
Y. Zhao, X. Han, G. Li, C. Lu, Y. Cao, X.-Q. Feng, and H. Gao. 2015. “Effect of lateral dimension on the surface wrinkling of a thin film on compliant substrate induced by differential growth/swelling.” Journal of the Mechanics and Physics of Solids, 83.Abstract
Surface wrinkling in thin films on compliant substrates is of considerable interest for applications involving surface patterning, smart adhesion, liquid/cell shaping, particle assembly, design of flexible electronic devices, as well as mechanical characterization of thin film systems. When the in-plane size of the system is infinite, the critical wrinkling strain is known to be governed by the moduli ratio between the film and substrate. Here we show a surprising result that the lateral dimension of the film can play a critical role in the occurrence of surface wrinkling. The basic phenomenon was established through selective UV/Ozone (UVO) exposure of a strain-free PDMS slab via composite copper grids with different meshes, followed by treatment using mixed ethanol/glycerol solvents with different volume fractions of ethanol. To understand the physics behind the experimental observations, finite element (FE) simulations were performed to establish an analytical expression for the distribution of shear tractions at the film-substrate interface. Subsequent theoretical analysis leads to closed-form predictions for the critical growth/swelling strain for the onset of wrinkling. Our analysis reveals that the occurrence of surface wrinkling and post-wrinkling pattern evolution can be controlled by tuning the lateral size of the thin film for a given moduli ratio. These results may find broad applications in preventing surface wrinkling, creating desired surface patterns, evaluating the interfacial shear strength of a film/substrate system and designing flexible electronic devices.
Y. Jiang, G. Li, L.-X. Qian, S. Liang, M. Destrade, and Y. Cao. 2015. “Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis.” Biomechanics and Modeling in Mechanobiology, 14, 5.Abstract
We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus $μ$0 varies from 1.8 to 3.2 kPa, the stiffening parameter b of the hyperelastic Demiray–Fung model from 0.13 to 0.73, and the third- (A) and fourth-order (D) constants of weakly nonlinear elasticity from -1.3 to -20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired t test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.
Y.-P. Cao, G.-Y. Li, M.-G. Zhang, and X.-Q. Feng. 2014. “Determination of the reduced creep function of viscoelastic compliant materials using pipette aspiration method.” Journal of Applied Mechanics, Transactions ASME, 81, 7.Abstract
Determining the mechanical properties of soft matter across different length scales is of great importance in understanding the deformation behavior of compliant materials under various stimuli. A pipette aspiration test is a promising tool for such a purpose. A key challenge in the use of this method is to develop explicit expressions of the relationship between experimental responses and material properties particularly when the tested sample has irregular geometry. A simple scaling relation between the reduced creep function and the aspiration length is revealed in this paper by performing a theoretical analysis on the aspiration creep tests of viscoelastic soft solids with arbitrary surface profile. Numerical experiments have been performed on the tested materials with different geometries to validate the theoretical solution. In order to incorporate the effects of the rise time of the creep pressure, an analytical solution is further derived based on the generalized Maxwell model, which relates the parameters in reduced creep function to the aspiration length. Its usefulness is demonstrated through a numerical example and the analysis of the experimental data from literature. The analytical solutions reported here proved to be independent of the geometric parameters of the system under described conditions. Therefore, they may not only provide insight into the deformation behavior of soft materials in aspiration creep tests but also facilitate the use of this testing method to deduce the intrinsic creep/relaxation properties of viscoelastic compliant materials. © 2014 by ASME.
M.-G. Zhang, Y.-P. Cao, G.-Y. Li, and X.-Q. Feng. 2014. “Pipette aspiration of hyperelastic compliant materials: Theoretical analysis, simulations and experiments.” Journal of the Mechanics and Physics of Solids, 68, 1.Abstract
This paper explores the pipette aspiration test of hyperelastic compliant materials. Explicit expressions of the relationship between the imposed pressure and the aspiration length are developed, which serve as fundamental relations to deduce the material parameters from experimental responses. Four commonly used hyperelastic constitutive models, e.g. neo-Hookean, Mooney-Rivlin, Fung, and Arruda-Boyce models, are investigated. Through dimensional analysis and nonlinear finite element simulations, we establish the relations between the experimental responses and the constitutive parameters of hyperelastic materials in explicit form, upon which inverse approaches for determining the hyperelastic properties of materials are developed. The reliability of the results given by the proposed methods has been verified both theoretically and numerically. Experiments have been carried out on an elastomer (polydimethylsiloxane, 1:50) and porcine liver to validate the applicability of the inverse approaches in practical measurements. © 2014 Elsevier Ltd.
M.-G. Zhang, Y.-P. Cao, G.-Y. Li, and X.-Q. Feng. 2014. “Spherical indentation method for determining the constitutive parameters of hyperelastic soft materials.” Biomechanics and Modeling in Mechanobiology, 13, 1.Abstract
A comprehensive study on the spherical indentation of hyperelastic soft materials is carried out through combined theoretical, computational, and experimental efforts. Four widely used hyperelastic constitutive models are studied, including neo-Hookean, Mooney-Rivlin, Fung, and Arruda-Boyce models. Through dimensional analysis and finite element simulations, we establish the explicit relations between the indentation loads at given indentation depths and the constitutive parameters of materials. Based on the obtained results, the applicability of Hertzian solution to the measurement of the initial shear modulus of hyperelastic materials is examined. Furthermore, from the viewpoint of inverse problems, the possibility to measure some other properties of a hyperelastic material using spherical indentation tests, e.g., locking stretch, is addressed by considering the existence, uniqueness, and stability of the solution. Experiments have been performed on polydimethylsiloxane to validate the conclusions drawn from our theoretical analysis. The results reported in this study should help identify the extent to which the mechanical properties of hyperelastic materials could be measured from spherical indentation tests. © 2013 Springer-Verlag Berlin Heidelberg.