Kelvin-Voigt Research Articles

Prediction of single cell mechanical properties in microchannels based on deep learning

Traditional methods for measuring single-cell mechanical characteristics face several challenges, including lengthy measurement times, low throughput, and a requirement for advanced technical skills. To overcome these challenges, a novel machine learning (ML) approach is implemented based on the convolutional neural networks (CNNs), aiming at predicting cells’ elastic modulus and constitutive equations from their deformations while passing through micro-constriction channels. In the present study, the computational fluid dynamics technology is used to generate a dataset within the range of the cell elastic modulus, incorporating three widely-used constitutive models that characterize the cellular mechanical behavior, i.e., the Mooney-Rivlin (M-R), Neo-Hookean (N-H), and Kelvin-Voigt (K-V) models. Utilizing this dataset, a multi-input convolutional neural network (MI-CNN) algorithm is developed by incorporating cellular deformation data as well as the time and positional information. This approach accurately predicts the cell elastic modulus, with a coefficient of determination R2 of 0.999, a root mean square error of 0.218, and a mean absolute percentage error of 1.089%. The model consistently achieves high-precision predictions of the cellular elastic modulus with a maximum R2 of 0.99, even when the stochastic noise is added to the simulated data. One significant feature of the present model is that it has the ability to effectively classify the three types of constitutive equations we applied. The model accurately and reliably predicts single-cell mechanical properties, showcasing a robust ability to generalize. We demonstrate that incorporating deformation features at multiple time points can enhance the algorithm’s accuracy and generalization. This algorithm presents a possibility for high-throughput, highly automated, real-time, and precise characterization of single-cell mechanical properties.

A modified parametric model to predict visco-elastic properties of magneto-rheological elastomers at non-LVE region

The magneto-rheological elastomer is mostly used in vibration isolation, for which higher modulus and lower Payne effect factors are crucial parameters. Strain amplitudes and frequencies influence many applications under dynamic modes. In this work, the dynamic viscoelastic properties of MRE, fabricated using electrolyte iron (EI) particles, were measured for varying strain amplitude, magnetic field and frequency. A fractional Kelvin-Voigt (KV) model is used in a frequency region from 0.01 to 40 Hz to predict the rheological behaviour. However, the available models failed to explain the observed behaviour at low frequencies and high magnetic fields and increasing strain amplitude (i.e. in the non-viscoelastic region). Therefore, a new modified KV model is proposed in this work to incorporate the drawbacks and hence can validate for varying frequency, magnetic field and strain amplitudes. The added terms can also be used in the fractional derivative Maxwell model to explain the effect of strain amplitude and magnetic field at various frequencies. The proposed model significantly improves the quality of experimental prediction in the low-frequency range, corresponding to a slow dissipative process at different strain amplitudes.

Analysis of shear creep properties of wood via modified Burger models and off-axis compression test method

In this study, the rheological Burger model combining Maxwell and Voigt–Kelvin model units as well as modified mechanical models were employed to analyze the shear creep mechanism of wood. Off-axis compression tests were conducted on Japanese Hinoki cypress specimens (Chamaecyparis obtusa), and a mechanical analysis of the shear creep mechanism was performed. First, the measured creep compliance curves [JTL(t)] were fitted using this Burger model, which is a typical model used to explain the creep behavior of wood. Furthermore, three modified Burger models with non-Newtonian dashpots were proposed to explain the measured data more accurately: model 1—only the dashpot in the permanent strain unit is non-Newtonian; model 2—both dashpots are non-Newtonian; and model 3—only the dashpot in the delayed elastic strain unit is non-Newtonian. The mean value of the coefficient of determination was highest for model 1. The number of specimens that could be fitted with a tolerance error of 0.1% was 43 out of 50 with the Burger model, 45 with model 1, 25 with model 2, and 45 with model 3. The Burger model exhibited large discrepancies between the theoretical and measured values, model 2 could not be used to explain several specimens, and model 3 exhibited a delayed elastic strain behavior that was inconsistent with the definition. Therefore, we conclude that model 1 is the most appropriate for studying the shear creep behavior of wood.

Acoustic radiation force-induced longitudinal shear wave for ultrasound-based viscoelastic evaluation

Acoustic radiation force (ARF) is widely used to induce shear waves for evaluating the mechanical properties of biological tissues. Two shear waves can be generated when exciting with ARF: a transverse shear wave, also simply called shear wave (SW), and a longitudinal shear wave (LSW). Shear waves (SWs) have been broadly used to assess the mechanical properties. Some articles have reported that the LSW can be used to evaluate mechanical properties locally. However, existing LSW studies are mainly focused on the group velocity evaluation using optical coherence tomography (OCT). Here, we report that a LSW generated with ARF can be used to probe viscoelastic properties, including shear modulus and viscosity, using ultrasound. We took advantage of the surface boundary effect to reflect the LSW, named RLSW, to address the energy deficiency of LSW induced by ARF. We systematically evaluated the experiments with tissue-mimicking viscoelastic phantoms and validated by numerical simulations. Phase velocity and dispersion comparison between the results induced by a RLSW and a SW exhibit good agreement in both the numerical simulations and experimental results. The Kelvin-Voigt (KV) model was used to determine the shear modulus and viscosity. RLSW shows great potential to evaluate localized viscoelastic properties, which could benefit various biomedical applications such as evaluating the viscoelasticity of heterogeneous materials or microscopic lesions of tissues.

MOC-Z Model of Transient Cavitating Flow in Viscoelastic Pipe

In this paper, a unitary method for the solution of transient cavitating flow in viscoelastic pipes is proposed in the framework of the method of characteristics (MOC) and a Z-mirror numerical scheme (MOC-Z model). Assuming a standard form of the continuity equation allows the unified treatment of both viscoelasticity and cavitation. An extension of the MOC-Z is used for Courant numbers less than 1 to overcome a few cases with numerical instabilities. Four viscoelastic models were considered: a Kelvin–Voigt (KV) model without the instantaneous strain, and three generalised Kelvin–Voigt models with one, two, and three KV elements (GKV1, GKV2, and GKV3, respectively). The use of viscoelastic parameters of KV and GKV models calibrated for transient flow tests without cavitation allows good comparisons between experimental and numerical pressure versus time for transient tests with cavitation. Whereas for tests without cavitation, the mean absolute error (MAE) always decreases when the complexity of the model increases (from KV to GKV1, GKV2, and GKV3) for all the considered tests, this does not happen for tests with cavitation, probably because the decreasing capacity of parameter generalization for the increasing complexity of the model. In particular, in the examined cases, the KV model performs better than the GKV1 and the GKV3 models in three cases out of five, and the GKV2 model performs better than the GKV3 model in three cases out of five. Furthermore, the GKV2 model performs better than the KV model only in three cases out of five.

Exact analytical solution for shear horizontal wave propagation through locally periodic structures realized by viscoelastic functionally graded materials

The paper presents a novel comprehensive exact analytical solution for modeling linear shear-horizontal (SH) wave propagation in an isotropic inhomogeneous layer made of functionally graded material, using local Heun functions. The layer is a composite of two materials with varying properties represented by spatial variations following the square of the sine function. The Voigt–Kelvin model is used to account for material losses. The study focuses on SH waves incident at a specific angle and employs the wave splitting technique to analyze forward and backward waves, facilitating the computation of reflection and transmission coefficients at any point in the inhomogeneous structure. The proposed solution utilizes the periodic nature of material functions and employs the Floquet–Bloch theory to derive an exact analytical solution. This approach is particularly suited for cases where SH waves encounter locally periodic functionally graded material. A Riccati equation-based verification is conducted to compare the frequency-dependent modulus of the reflection coefficient obtained from the analytical solution with numerically solved results. The presented work provides a comprehensive and versatile analytical solution for studying linear SH wave propagation in locally inhomogeneous isotropic layers, contributing to the theoretical understanding of elastic wave fields and practical applications.

On the Characterization of Viscoelastic Parameters of Polymeric Pipes for Transient Flow Analysis

The behaviour of polymeric pipes in transient flows has been proved to be viscoelastic. Generalized Kelvin–Voigt (GKV) models perform very well when simulating the experimental pressure. However, in the literature, no general indications on the evaluation of the model parameters are given. In the present study, the calibration of GKV model parameters is carried out using a micro-genetic algorithm for experimental tests of transient flows in polymeric pipes taken from the literature. The results confirm that the higher the number of Kelvin–Voigt elements, the better the reproduction of experimental tests, but it is difficult to search for general rules for parameter characterization. Assuming a Kelvin–Voigt (KV) model with a single element, it is shown that the retardation time is related to the oscillation period that can be obtained from the elastic modulus and from easily evaluable pipe characteristics. A simple procedure is then proposed for the characterization of the viscoelastic parameters that can be used by manufacturers and technicians. Considering the limits of such a model, the procedure has to be considered as a first step for the characterization of the viscoelastic parameters of more complex models.

A comparative analysis between viscoacoustic forward and adjoint wave equations based on Maxwell, Kelvin-Voigt, and SLS rheological models

Most seismic imaging applications still consider the subsurface as a perfect acoustic or elastic medium, ignoring the viscosity of rocky materials. That viscosity converts part of the mechanical energy of seismic waves into heat, affecting the amplitude and phase of the wavefield when propagating through the physical medium. In this work, we derive, implement and analyze a set of forward and adjoint viscoacoustic equations based on the Maxwell, Kelvin-Voigt (KV), and standard linear solid (SLS) rheological models. These equations are described in the time–space domain allowing us to solve with the finite difference method. For this implementation, we used Devito - a domain-specific language (DSL) and code generation framework to design highly optimized finite difference kernels for use in inversion methods. We analyzed the attenuating behavior, comparing each equation’s dissipation and dispersion effects in these models, both forward modeling equations through comparisons between snapshots, seismograms, and traces, and adjoint equations through RTM images.

Optical micro-elastography with magnetic excitation for high frequency rheological characterization of soft media

The propagation of shear waves in elastography at high frequency (>3 kHz) in viscoelastic media has not been extensively studied due to the high attenuation and technical limitations of current techniques. An optical micro-elastography (OME) technique using magnetic excitation for generating and tracking high frequency shear waves with enough spatial and temporal resolution was proposed. Ultrasonics shear waves (above 20 kHz) were generated and observed in polyacrylamide samples. A cutoff frequency, from where the waves no longer propagate, was observed to vary depending on the mechanical properties of the samples. The ability of the Kelvin–Voigt (KV) model to explain the high cutoff frequency was investigated. Two alternative measurement techniques, Dynamic Mechanical Analysis (DMA) and Shear Wave Elastography (SWE), were used to complete the whole frequency range of the velocity dispersion curve while avoid capturing guided waves in the low frequency range (<3 kHz). The combination of the three measurement techniques provided rheology information from quasi-static to ultrasonic frequency range. A key observation was that the full frequency range of the dispersion curve was necessary if one wanted to infer accurate physical parameters from the rheological model. By comparing the low frequency range with the high frequency range, the relative errors for the viscosity parameter could reach 60 % and they could be higher with higher dispersive behavior. The high cutoff frequency may be predicted in materials that follow a KV model over their entire measurable frequency range. The mechanical characterization of cell culture media could benefit from the proposed OME technique.

Parametric evaluation of Kelvin-Voigt dispersion curve fitting

Ultrasound shear wave elastography (SWE) is a useful technique for non-invasive tissue assessment. For effective quantitative analysis the employment of physical models is necessary for rheological parameter estimation, such as the Kelvin-Voigt (KV) model. From SWE data, the frequency response can be calculated, and the shear wave velocity dispersion can be fit, yielding the shear elasticity and shear viscosity, μ1 and μ2, respectively. In this study, a parametric evaluation is performed using staggered-grid finite-difference simulations of materials with μ1 = 1–25 kPa (increment: 1 kPa) and μ2 = 0–10 Pa s (increment: 0.5 Pa s), with an acoustic radiation force push of f-number equal to 2. The novel Stockwell transform combined with a slant frequency-wavenumber analysis (GST-SFK) was compared with the two-dimensional Fourier transform for dispersion curve estimation over a variety of frequency ranges. Regardless of dispersion curve estimation technique, the accuracy of estimating μ1 is confounded for μ2 values above 5 Pa s. It was found that KV fitting benefits from wider frequency ranges (up to 1kHz), with lower μ1 and μ2 estimation errors. The GST-SFK was the best dispersion curve calculation technique, yet the KV fitting process was found to be unreliable for parameter estimation in highly viscous media.

A collection of wet beam models for wave–ice interaction

Abstract. Theoretical models for the prediction of decay rate and dispersion process of gravity waves traveling into an integrated ice cover expanded over a long way are introduced. The term “wet beam” is chosen to refer to these models as they are developed by incorporating water-based damping and added mass forces. Presented wet beam models differ from each other according to the rheological behavior considered for the ice cover. Two-parameter viscoelastic solid models accommodating Kelvin–Voigt (KV) and Maxwell mechanisms along with a one-parameter elastic solid model are used to describe the rheological behavior of the ice layer. Quantitative comparison between the landfast ice field data and model predictions suggests that wet beam models, adopted with both KV and Maxwell mechanisms, predict the decay rate more accurately compared to a dry beam model. Furthermore, the wet beam models, adopted with both KV and Maxwell mechanisms, are found to construct decay rates of disintegrated ice fields, though they are built for a continuous ice field. Finally, it is found that wet beam models can accurately construct decay rate curves of freshwater ice, though they cannot predict the dispersion process of waves accurately. To overcome this limitation, three-parameter solid models, termed standard linear solid (SLS) mechanisms, are suggested to be used to re-formulate the dispersion relationship of wet beam models, which were seen to construct decay rates and dispersion curves of freshwater ice with an acceptable level of accuracy. Overall, the two-parameter wet beam dispersion relationships presented in this research are observed to predict decay rates and dispersion process of waves traveling into actual ice covers, though three-parameter wet beam models were seen to reconstruct the those of freshwater ice formed in a wave flume. The wet beam models presented in this research can be implemented in spectral models on a large geophysical scale.

Forward and Adjoint Modeling of Three Viscoacoustic Equations Based on Rheological Models Using DEVITO

Disregarding the effect of seismic signal attenuation in gas and hydrocarbon zones leads to a final image with low resolution. However, a range of equations called viscoacoustics overcome such limitations. We use three secondorder equations based on Maxwell, Kelvin-Voigt (KV), and Standard Linear Solid (SLS) models. We analyze the dissipation and dispersion effects on each of them through seismograms. We also perform Reverse Time Migration (RTM) using the exact adjoint operators (Q-RTAM). All numerical experiments were implemented using Devito - a domain-specific language (DSL) and code generation framework to design highly optimized finite difference kernels for use in inversion methods.

A Transparent Teleoperated Robotic Surgical System with Predictive Haptic Feedback and Force Modelling.

In recent years, robotic minimally invasive surgery has transformed many types of surgical procedures and improved their outcomes. Implementing effective haptic feedback into a teleoperated robotic surgical system presents a significant challenge due to the trade-off between transparency and stability caused by system communication time delays. In this paper, these time delays are mitigated by implementing an environment estimation and force prediction methodology into an experimental robotic minimally invasive surgical system. At the slave, an exponentially weighted recursive least squares (EWRLS) algorithm estimates the respective parameters of the Kelvin-Voigt (KV) and Hunt-Crossley (HC) force models. The master then provides force feedback by interacting with a virtual environment via the estimated parameters. Palpation experiments were conducted with the slave in contact with polyurethane foam during human-in-the-loop teleoperation. The experimental results indicated that the prediction RMSE of error between predicted master force feedback and measured slave force was reduced to 0.076 N for the Hunt-Crossley virtual environment, compared to 0.356 N for the Kelvin-Voigt virtual environment and 0.560 N for the direct force feedback methodology. The results also demonstrated that the HC force model is well suited to provide accurate haptic feedback, particularly when there is a delay between the master and slave kinematics. Furthermore, a haptic feedback approach that incorporates environment estimation and force prediction improve transparency during teleoperation. In conclusion, the proposed bilateral master-slave robotic system has the potential to provide transparent and stable haptic feedback to the surgeon in surgical robotics procedures.

Dynamic Response of Vibratory Piling Machines for Ground Foundations

Vibrating technological equipment for the introduction of piles and columns into the ground of construction foundations (named vibratory piling machines) is crucial in the process of building stable and resilient foundations for civil engineering, hydrotechnical construction, special construction (e.g., military constructions), bridges, roads and industrial platforms. During the works carried out by the construction companies in various geographical areas of Romania, particularities of the dynamic technological regimes influenced by the nature of the land were identified at the deep introduction of the construction elements in the form of piles or circular (tubular) columns. The results of applied research, rheological modeling and optimization of vibrating equipment, highlight the need for an analytical approach that takes into account the parametric variations of the elastic and damping characteristics of some categories of soils on the depth of piles or foundation columns. In this context, the paper presents the calculation model with the dynamic response for the vibrating equipment of insertion with disturbing forces of 200–1250 kN for piles or columns with lengths of 10–30 m. The novelty of the research study consists in the linear rheological model, which was adopted in the form of a Maxwell–Voigt–Kelvin schematic of the type (E-V)–(E|V), with a discrete variation in four values for stiffness and damping of the soil, as the piles or columns vibrate and advance in the ground foundation. Practical experience of the authors in the field of using vibrogenerators for the introduction of piles in various types of ground foundations led to the adoption of the rheological model with variable damping coefficients depending on the depth of penetration into the soil. The curves of the dissipated power confirm the experimental data obtained in situ, in accordance with the rheological indoor tests of the different types of soil foundations.

An artificial damping method for total Lagrangian SPH method with application in biomechanics

Introducing artificial damping into the momentum equation to enhance the numerical stability of the smoothed particle hydrodynamics (SPH) method for large strain dynamics has been well established, however, implementing appropriate damping term in the constitutive model as an alternative stabilization strategy in the context of the SPH method is still not investigated. In this paper, we present a simple stabilization procedure by introducing an artificial damping term into the second Piola–Kirchhoff stress to enhance the numerical stability of the SPH method in total Lagrangian formulation. The key idea is to reformulate the constitutive equation by adding a Kelvin–Voigt (KV) type damper with a scaling factor imitating a von Neumann–Richtmyer type artificial viscosity to alleviate the spurious oscillation in the vicinity of sharp spatial gradients. The proposed method is shown to effectively eliminate the appearance of spurious non-physical instabilities and easy to be implemented into the original total Lagrangian SPH formulation. After validating the numerical stability and accuracy of the present method through a set of benchmark tests with very challenging cases, we demonstrate its applications and potentials in the field of biomechanics by simulating the deformation of complex stent structures and the electromechanical excitation–contraction of the realistic left ventricle.

Comprehensive experimental assessments of rheological models’ performance in elastography of soft tissues

Elastography researchers have utilized several rheological models to characterize soft tissue viscoelasticity over the past thirty years. Due to the frequency-dependent behavior of viscoelastic parameters as well as the different techniques and frequencies employed in various studies of soft tissues, rheological models have value in standardizing disparate techniques via explicit mathematical representations. However, the important question remains: which of the several available models should be considered for widespread adoption within a theoretical framework? We address this by evaluating the performance of three well established rheological models to characterize ex vivo bovine liver tissues: the Kelvin-Voigt (KV) model as a 2-parameter model, and the standard linear solid (SLS) and Kelvin-Voigt fractional derivative (KVFD) models as 3-parameter models. The assessments were based on the analysis of time domain behavior (using stress relaxation tests) and frequency domain behavior (by measuring shear wave speed (SWS) dispersion). SWS was measured over a wide range of frequency from 1 Hz to 1 kHz using three different tests: (i) harmonic shear tests using a rheometer, (ii) reverberant shear wave (RSW) ultrasound elastography scans, and (iii) RSW optical coherence elastography scans, with each test targeting a distinct frequency range. Our results demonstrated that the KVFD model produces the only mutually consistent rendering of time and frequency domain data for liver. Furthermore, it reduces to a 2-parameter model for liver (correspondingly to a 2-parameter “spring-pot” or power-law model for SWS dispersion) and provides the most accurate predictions of the material viscoelastic behavior in time (>98% accuracy) and frequency (>96% accuracy) domains. Statement of SignificanceRheological models are applied in quantifying tissues viscoelastic properties. This study is unique in presenting comprehensive assessments of rheological models:•We employed experimental data in both the frequency domain (shear wave speed (SWS) vs. frequency) and time domain (stress relaxation) to assess rheological models’ performances.•SWS were acquired over a wide frequency range, 1 Hz to 1 kHz, by three independent techniques.•Using the frequency domain analysis, we evaluated how well each model can predict measured time domain behaviors (and vice versa).•This presents wide-ranging experimental proofs as the most comprehensive study of its type in terms of the number of experiments, frequency range, and conjoined assessments of time and frequency domains behaviors, demonstrating the most appropriate rheological model for soft tissues.

Creep characteristics of a fracturing fluid-softened shale investigated by microindentation

The creep of shales affects the fracture conductivity, well production rate, and hence ultimate recovery of hydrocarbons from reservoir formations. This paper presents an experimental study of the creep characteristics of a shale softened by thermo-hydro-mechano-chemical (THMC) treatments that mimic the rock-fluid interactions affected by high temperature, high pressure, and hydraulic fracturing fluids. Microindentation was conducted to characterize the creep behavior of the THMC-treated specimens with the data analyzed by the Kelvin-Voigt (KV) and compliance methods, while X-ray diffraction and scanning electron microscopy were performed to analyze the compositional and microstructural changes respectively to aid interpretation of indentation measurements. Results show that the THMC treatments increase the creep rate by 46–162%, owing to the treatment-induced softening that varies with the treatment time and distance from the fluid-rock interface, while the Young's modulus and hardness decrease with both the THMC-treatment and creep durations. The softened zones become more viscous, as reflected by the decreased KV model's viscoelastic coefficients for the softened specimens. The higher creep rate of the softened zones is primarily attributed to the weakening in cementation bond and increase in microscale porosity due to the dissolution of carbonates. The findings help understand the mechanisms for creep deformation and pertinent proppant embedment in fractured shales, and hence can be used to predict shale gas production and optimize fracturing fluid additives and stimulants.

Field Measurements and Numerical Modeling of Hydraulic Transients in HDPE Pipeline with PRV Interaction

Pressure reducing valves (PRVs) and high-density polyethylene (HDPE) pipes are commonly used in urban water supply systems (UWSS). To study the joint effect of PRV and viscoelasticity on transient wave propagation, extensive experiments have been conducted in a field-scale reservoir-PRV-viscoelastic pipeline system covering a wide range of internal pressure heads (∼10 to 60 m) and air temperatures (12°C–33°C). In addition, a one-dimensional method of characteristics (MOC) based model that incorporates a PRV model and the generalized Kelvin-Voigt (K-V) model for pipe viscoelasticity is developed and validated against field data for the first time. The simulated transient pressures are in good agreement with field measurements. The K-V parameters exhibit a clustered distribution and the mean value for each element can provide a satisfactory simulation. The PRV in hydraulic transients can be interpreted as a quasi-dead-end with a self-adjusting opening, and causes additional positive pressure wave reflections that are gradually damped due to viscoelasticity. The dynamic changes in PRV opening, head loss, pressure wave reflection, and transmission induced by an incident pressure surge are predicted. Due to the joint action of PRV and pipeline viscoelasticity, the pressure oscillations in an intact pipe settle to a value that is considerably higher than the initial PRV set pressure. In a leaking pipe, the downstream pressure reverts to the original set pressure within a few wave cycles. Leaks can be detected by wave reflections in the time domain signals. The existence of leaks is also found to be associated with the the amplification and damping of the frequency response function (FRF) of the system at certain resonance peaks. This study provides new insights into wave propagation in HDPE pipeline with PRV interaction and an original data set for validation of leakage detection methods.

Nanoindentation and Hierarchy Structure of the Bovine Hoof Wall.

The bovine hoof wall with an α-keratin structure protects the bovine foot from impact loads when the cattle are running. Reduced modulus, hardness and creep behavior of the bovine hoof wall have been investigated by a nanoindentation technique. The average reduced modulus of the Transverse Direction (TD) specimens from the outside to inside wall is 3.76 and 2.05 GPa, respectively, while the average reduced modulus of the Longitudinal Direction (LD) specimens from the outside to inside wall is 4.54 and 3.22 GPa, respectively. Obviously, the orientation and the position of the bovine hoof wall have a significant influence on its mechanical properties. The use of the generalized Voigt–Kelvin model can make a good prediction of creep stage. Mechanical properties of the LD specimens are stronger than those of the TD specimens. The bovine hoof wall has a layered structure, which can effectively absorb the energy released by the crack propagation and passivate the crack tip. Therefore, a kind of structural model was designed and fabricated by three-dimensional printing technology, which has a 55% performance improvement on fracture toughness. It is believed that the reported results can be useful in the design of new bionic structure materials which may be used in motorcycle helmets and athletes’ protective equipment to achieve light weight and improved strength at the same time.

Viscoelastic model characterization of human cervical tissue by torsional waves

The understanding of changes in the viscoelastic properties of cervical tissue during the gestation process is a challenging problem. In this work, we explore the importance of considering the multilayer nature (epithelial and connective layers) of human cervical tissue for characterizing the viscoelastic parameters from torsional waves. For this purpose, torsional wave propagations are simulated in three multilayer cervical tissue models (pure elastic, Kelvin–Voigt (KV) and Maxwell) using the finite difference time domain method. High-speed camera measurements have been carried out in tissue-mimicking phantoms in order to obtain the boundary conditions of the numerical simulations. Finally, a parametric modeling study through a probabilistic inverse procedure was performed to rank the most plausible rheological model and to reconstruct the viscoelastic parameters. The procedure consist in comparing the experimental signals obtained in human cervical tissues using the Torsional Wave Elastography (TWE) technique with the synthetic signals from the numerical models. It is shown that the rheological model that best describes the nature of cervical tissue is the Kelvin–Voigt model. Once the most plausible model has been selected, the stiffness and viscosity parameters have been reconstructed of the epithelial and connective layers for the measurements of the 18 pregnant women, along with the thickness of the epithelial layer.