Traveling-wave optical coherence elastography (OCE) is a promising technique to measure the stiffness of biological tissues. While OCE has been applied to relatively homogeneous samples, tissues with significantly varying elasticity through depth pose a challenge, requiring depth-resolved measurement with sufficient resolution and accuracy. Here, we develop a broadband Rayleigh-wave OCE technique capable of measuring the elastic moduli of the 3 major skin layers (epidermis, dermis, and hypodermis) reliably by analyzing the dispersion of leaky Rayleigh surface waves over a wide frequency range of 0.1-10 kHz. We show that a previously unexplored, high frequency range of 4-10 kHz is critical to resolve the thin epidermis, while a low frequency range of 0.2-1 kHz is adequate to probe the dermis and deeper hypodermis. We develop a dual bilayer-based inverse model to determine the elastic moduli in all 3 layers and verify its high accuracy with finite element analysis and skin-mimicking phantoms. Finally, the technique is applied to measure the forearm skin of healthy volunteers. The Young's modulus of the epidermis (including the stratum corneum) is measured to be $\sim$ 4 MPa at 4-10 kHz, whereas Young's moduli of the dermis and hypodermis are about 40 and 15 kPa, respectively, at 0.2-1 kHz. Besides dermatologic applications, this method may be useful for the mechanical analysis of various other layered tissues with sub-mm depth resolution.
Knowing the stress within a soft material is of fundamental interest to basic research and practical applications, such as soft matter devices, biomaterial engineering, and medical sciences. However, it is challenging to measure stress fields in situ in a non-invasive way. It becomes even more difficult if the mechanical properties of the material are unknown or altered by the stress. Here we present a robust non-destructive technique capable of measuring in situ stress and strain in elastically deformed thin films without the need to know their material properties. The technique is based on measuring elastic wave speeds, and then using a universal dispersion curve we derived for Lamb wave to predict the local stress and strain. Using optical coherence tomography, we experimentally verified the method for a rubber sheet, a cling film, and the leather skin of a musical instrument.
The clinical and economic burdens of cardiovascular diseases pose a global challenge. Growing evidence suggests an early assessment of arterial stiffness can provide insights into the pathogenesis of cardiovascular diseases. However, it remains difficult to quantitatively characterize local arterial stiffness in vivo. Here we utilize guided axial waves continuously excited and detected by ultrasound to probe local blood pressures and mechanical properties of common carotid arteries simultaneously. In a pilot study of 17 healthy volunteers, we observe a ~20% variation in the group velocities of the guided axial waves (5.16±0.55 m/s in systole and 4.31±0.49 m/s in diastole) induced by the variation of the blood pressures. A linear relationship between the square of group velocity and blood pressure is revealed by the experiments and finite element analysis, which enables us to measure the waveform of the blood pressures by the group velocities. Furthermore, we propose a wavelet analysis-based method to extract the dispersion relations of the guided axial waves. We then determined the shear modulus by fitting the dispersion relations in diastole with the leaky Lamb wave model. The average shear modulus of all the volunteers is 166.3±32.8 kPa. No gender differences are found. This study shows the group velocity and dispersion relation of the guided axial waves can be utilized to probe blood pressure and arterial stiffness locally in a noninvasive manner and thus promising for early diagnosis of cardiovascular diseases.
Probing the mechanical properties of cells is critical for understanding their deformation behaviors and biological functions. Although some methods have been proposed to characterize the elastic properties of cells, it is still difficult to measure their time-dependent properties. This paper investigates the use of atomic force microscope (AFM) to determine the reduced relaxation modulus of cells. In principle, AFM is hard to perform an indentation relaxation test that requires a constant indenter displacement during load relaxation, whereas the real AFM indenter displacement usually varies with time during relaxation due to the relatively small bending stiffness of its cantilever. We investigate this issue through a combined theoretical, computational, and experimental effort. A protocol relying on the choice of appropriate cantilever bending stiffness is proposed to perform an AFM-based indentation relaxation test of cells, which enables the measurement of reduced relaxation modulus with high accuracy. This protocol is first validated by performing nanoindentation relaxation tests on a soft material and by comparing the results with those from independent measurements. Then indentation tests of cartilage cells are conducted to demonstrate this method in determining time-dependent properties of living cells. Finally, the change in the viscoelasticity of MCF-7 cells under hyperthermia is investigated.
Surface waves play important roles in many fundamental and applied areas from seismic detection to material characterizations. Supershear surface waves with propagation speeds greater than bulk shear waves have recently been reported, but their properties are not well understood. In this Letter, we describe theoretical and experimental results on supershear surface waves in rubbery materials. We find that supershear surface waves can be supported in viscoelastic materials with no restriction on the shear quality factor. Interestingly, the effect of prestress on the speed of the supershear surface wave is opposite to that of the Rayleigh surface wave. Furthermore, anisotropy of material affects the supershear wave much more strongly than the Rayleigh surface wave. We offer heuristic interpretation as well as theoretical verification of our experimental observations. Our work points to the potential applications of supershear waves for characterizing the bulk mechanical properties of soft solid from the free surface.
When a point force travels in a solid with a speed greater than the velocity of the elastic wave induced, the interfering elastic wave fronts will form a Mach cone. This phenomenon is called the elastic Cherenkov effect (ECE). In this study, the ECE in soft matter was investigated with emphasis on backward Mach cone formation. Phase diagrams were proposed based on the theoretical analysis to elucidate key features of the ECE in a wide material parameter space, including the critical conditions for the onset of backward Mach cones and the cone angles. Subsequently, finite element models were developed to validate the theoretical solutions. Our results show that backward Mach cones can be formed in some typical soft tissues under the described conditions, which is important for the use of the ECE in characterizing the mechanical properties of these soft tissues in vivo. Our method and results also illustrate that backward Mach cones can be generated in soft phononic crystals with periodic microstructures, indicating that they are promising material systems for studying the ECE in soft matter.
Ultrasound shear wave elastography (USWE) enables us to quantitatively characterize the mechanical properties of solid tumors and is of clinical importance in differentiating malignant tumors from benign ones. However, limited by the resolution of USWE, it remains challenging in evaluating the elastic properties of tumors with small dimensions. Here we study the size effect in USWE of tumors via phantom experiments. Gelatin phantoms consisted of spherical inclusions and softer matrix were fabricated to model the tumors embedded in surrounding soft tissues. Our results show that elastic moduli E of the phantom tumors measured with conventional USWE are highly related to their diameters d (r > 0.96, P < 0.001). The elastic moduli of stiffer phantom tumors were heavily underestimated when the dimension of a tumor is smaller than 1.5 cm, indicating that the size effect should be considered in interpreting USWE of solid tumors. Based on dimension analysis and our phantom experiments, an empirical formula has been proposed to predict the size effect. The method and the results reported here may not only help quantitatively understand the size effect encountered in USWE of solid tumors, but also provide a promising approach to characterize the mechanical properties of soft matter composites in situ.
Measuring stress levels in loaded structures is crucial to assess and monitor structure health and to predict the length of remaining structural life. Many ultrasonic methods are able to accurately predict in-plane stresses inside a controlled laboratory environment but struggle to be robust outside, in a real-world setting. That is because these methods rely either on knowing beforehand the material constants (which are difficult to acquire) or require significant calibration for each specimen. This paper presents an ultrasonic method to evaluate the in-plane stress in situ directly, without knowing any material constants. The method is simple in principle, as it only requires measuring the speed of two angled shear waves. It is based on a formula that is exact for incompressible solids, such as soft gels or tissues, and is approximately true for compressible "hard"solids, such as steel and other metals. The formula is validated by finite element simulations, showing that it displays excellent accuracy, with a small error on the order of 1%.
The occurrence and development of many diseases are accompanied by a change in the mechanical properties of the human body across different length scales. The word “elastodiagnosis” coined in this review paper indicates that the elastic cue, i.e., the variation in the elastic properties (including linear elastic, viscoelastic, hyperelastic, poroelastic properties and so on) of cells, tissues or organs, can be used in the diagnosis of a disease. This review is organized into sections based on the use of elastodiagnosis in different diseases, including monitoring the development of liver fibrosis, assessing artery stiffening, determining the stage of chronic kidney disease (CKD) and detecting cancers. Emphasis is given to the challenges involved in understanding and characterizing the variation in the mechanical properties of both healthy and diseased tissues, and future perspectives for improving and developing elastodiagnosis methods are discussed.
In vivo mechanical characterization of soft biological tissues has broad applications ranging from disease diagnosis to tissue engineering. Shear wave elastography based on the bulk wave theory has been widely used to measure the mechanical properties of soft tissues. Given that most soft tissues basically have layered structures, the dispersive feature of elastic waves should be considered when the thickness of the interested layer is comparable to or smaller than the wavelength. Bearing this fundamental issue in mind, we propose an ultrasound-based guided wave elastography (GWE) method to characterize the mechanical properties of layered soft tissues. The dispersion relations of guided waves in layered structures were derived first, and its explicit expression was achieved. An inverse approach based on the dispersion relation to characterize the mechanical properties of layered soft tissues was then established. Both finite element analysis (FEA) and phantom experiments were carried out to validate the new method. In vivo experiments on forearm skin demonstrate the usefulness of the present method in characterizing layered soft tissues. Statement of significance: Layered soft tissues and artificial soft materials are ubiquitous in both nature and engineering. Imaging their in vivo/in situ mechanical properties finds important applications and remains a great challenge to date. Here, we propose an ultrasound-based guided wave elastography method to in vivo/in situ characterize the elastic properties of layered soft materials. We validate the method via finite element analysis and phantom experiments and further demonstrate its usefulness in practice by performing in vivo measurements on forearm skins. Given that the dispersive feature of elastic waves in layered soft media is considered in our method, it provides the opportunity to assess the intrinsic elastic properties of an individual layer in a non-destructive manner as shown in our experiments.
Determining time-dependent mechanical properties of soft materials is essential in understanding their deformation behaviors under various stimuli. This paper investigates the use of indentation creep tests to measure the viscoelastic properties of soft materials at local areas. A simple scaling law between the reduced creep function and the creep displacement of the indenter is revealed in this paper based on a theoretical analysis. We show that the scaling relation can be used to interpret indentation creep tests of viscoelastic soft solids with arbitrary surface profile provided that the contact area does not change. Both numerical and practical experiments have been performed to validate the theory and the analytical solution. In our experiments, a low-cost portable indentation system is proposed to measure the reduced creep function. Our results show that the low-cost instrument and the analytical solution to interpret the experimental data reported here represent a useful testing method to deduce the intrinsic viscoelastic properties of soft materials in a non-destructive manner.
Functionally graded soft materials (FGSMs) with microstructures and mechanical properties exhibiting gradients across a spatial volume to satisfy specific functions have received interests in recent years. How to characterize the mechanical properties of these FGSMs in vivo/in situ and/or in a non-destructive manner is a great challenge. This paper investigates the use of ultrasound elastography in the mechanical characterization of FGSMs. An efficient finite-element model was built to calculate the dispersion relation for surface waves in FGSMs. For FGSMs with large elastic gradients, the measured dispersion relation can be used to identify mechanical parameters. In the case where the elastic gradient is smaller than a certain critical value calculated here, our analysis on transient wave motion in FGSMs shows that the group velocities measured at different depths can infer the local mechanical properties. Experiments have been performed on polyvinyl alcohol (PVA) cryogel to demonstrate the usefulness of the method. Our analysis and the results may not only find broad applications in mechanical characterization of FGSMs but also facilitate the use of shear wave elastography in clinics because many diseases change the local elastic properties of soft tissues and lead to different material gradients.
It has been reported that ex vivo viscoelastic properties of liver tissues usually differ from those measured in in vivo state due to the reasons such as the effects of perfusion, temperature, and native pre-stress. Therefore, the development of an appropriate ex vivo protocol, which enables the measurement of liver mechanical properties close to those in vivo, is of great importance and has been pursued over the years. In this paper, we propose a simple protocol by ligating the liver when performing ex vivo indentation relaxation tests. Our results show that the viscoelastic kernel function, which measures the intrinsic time-dependent mechanical behavior of a viscoelastic material, determined with the present protocol can describe the in vivo viscoelasticity of liver tissues well in comparison with the ex vivo result measured on a liver without ligation and that obtained in vitro. The performance of the protocol reported here is similar to the ex vivo perfusion system developed by Kerdok et al. (2006). However, the present experimental set-up is much easier to realize.
Determining the mechanical properties of brain tissues is essential in the field of brain biomechanics. In this paper, we use ultrasound-based shear wave elastography to measure both in vivo and ex vivo elastic properties of brain tissues. Our results demonstrate that the shear modulus from in vivo measurements is about 47% higher than that given by the ex vivo measurements (p value = 0.0063). The change in ex vivo elastic properties within 60-min post-mortem is negligible. The results also show that within 60-min post-mortem and in a temperature range of 37–23 °C, the elastic properties of brain tissues approximately linearly depend on the temperature in both cooling and re-heating processes.
Surface acoustic wave (SAW) devices have found a wide variety of technical applications, including SAW filters, SAW resonators, microfluidic actuators, biosensors, flow measurement devices, and seismic wave shields. Stretchable/flexible electronic devices, such as sensory skins for robotics, structural health monitors, and wearable communication devices, have received considerable attention across different disciplines. Flexible SAW devices are essential building blocks for these applications, wherein piezoelectric films may need to be integrated with the compliant substrates. When piezoelectric films are much stiffer than soft substrates, SAWs are usually leaky and the devices incorporating them suffer from acoustic losses. In this study, the propagation of SAWs in a wrinkled bilayer system is investigated, and our analysis shows that non-leaky modes can be achieved by engineering stress patterns through surface wrinkles in the system. Our analysis also uncovers intriguing bandgaps (BGs) related to the SAWs in a wrinkled bilayer system; these are caused by periodic deformation patterns, which indicate that diverse wrinkling patterns could be used as metasurfaces for controlling the propagation of SAWs.
Determining the mechanical properties of soft biological tissues can be of great importance. For example, the microstructures of many soft tissues, such as those of the human Achilles tendon, have been identified as typical anisotropic materials. This paper proposes an inverse approach that uses guided wave elastography to determine the anisotropic elastic and hyperelastic parameters of thin-walled transversely isotropic biological soft tissues. This approach was developed from the theoretical solutions for the dispersion relations of guided waves, which were derived based on a constitutive model suitable for describing the deformation behavior of such tissues. The properties of these solutions were investigated; in particular, sensitivity to data errors was addressed by introducing the concept of the condition number. To further validate the proposed inverse approach, the guided wave elastography of thin-walled transversely isotropic soft tissues was investigated using numerical experiments. The results indicated that the four constitutive parameters (other than the tensile modulus along the direction of the fibers, EL) could be determined with a good level of accuracy using this method.
We investigate the edge wrinkling of a soft ridge with gradient thickness under axial compression. Our experiments show that the wrinkling wavelength undergoes a considerable increase with increasing load. Simple scaling laws are derived based on an upper-bound analysis to predict the critical buckling conditions and the evolution of wrinkling wavelength during the post-buckling stage, and the results show good accordance with our finite element simulations and experiments. We also report a pattern transformation triggered by the edge wrinkling of soft ridge arrays. The results and method not only help understand the correlation between the growth and form observed in some natural systems but also inspire a strategy to fabricate advanced functional surfaces.
In vivo measurement of the mechanical properties of thin-walled soft tissues (e.g., mitral valve, artery and bladder) and in situ mechanical characterization of thin-walled artificial soft biomaterials in service are of great challenge and difficult to address via commonly used testing methods. Here we investigate the properties of guided waves generated by focused acoustic radiation force in immersed pre-stressed plates and tubes, and show that they can address this challenge. To this end, we carry out both (i) a theoretical analysis based on incremental wave motion in finite deformation theory and (ii) finite element simulations. Our analysis leads to a novel method based on the ultrasound elastography to image the elastic properties of pre-stressed thin-walled soft tissues and artificial soft materials in a non-destructive and non-invasive manner. To validate the theoretical and numerical solutions and demonstrate the usefulness of the corresponding method in practical measurements, we perform (iii) experiments on polyvinyl alcohol cryogel phantoms immersed in water, using the Verasonics V1 System equipped with a L10-5 transducer. Finally, potential clinical applications of the method have been discussed.
Many cardiovascular diseases can alter arterial stiffness; therefore, measurement of arterial wall stiffness can provide valuable information for both diagnosis of such diseases in the clinic and evaluation of the effectiveness of relevant drugs. However, quantitative assessment of the in vivo elastic properties of arterial walls in a non-invasive manner remains a great challenge. In this study, we found that the elastic modulus of the arterial wall can be extracted from the dispersion curve of the guided axial wave (GAW) measured using the ultrasound elastography method. It is shown that the GAW in the arterial wall can be well described with the Lamb wave (LW) model when the frequency exceeds a critical value fc, whose explicit form is determined here based on dimensional analysis method and systematic finite-element simulations. Further, an inverse procedure is proposed to determine both fc and the elastic modulus of the arterial wall. Phantom experiments have been performed to validate the inverse method and illustrate its potential use in the clinic.
Ultrasound elastography enables in vivo measurement of the mechanical properties of living soft tissues in a non-destructive and non-invasive manner and has attracted considerable interest for clinical use in recent years. Continuum mechanics plays an essential role in understanding and improving ultrasound-based elastography methods and is the main focus of this review. In particular, the mechanics theories involved in both static and dynamic elastography methods are surveyed. They may help understand the challenges in and opportunities for the practical applications of various ultrasound elastography methods to characterize the linear elastic, viscoelastic, anisotropic elastic and hyperelastic properties of both bulk and thin-walled soft materials, especially the in vivo characterization of biological soft tissues. 2017 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License.