Viscoelastic Soft Tissue Research Articles

Power-Law Modeling for Swift Viscoelastic Assessment in Biological Soft Tissues

In addressing the viscoelastic behavior of biological soft tissues, the precise and expeditious measurement methodologies hold paramount significance, given the intrinsic softness and heightened aqueous content of such substrates. We have introduced an expeditious modality for the characterization of viscoelasticity in biological soft tissues, hinged upon a power-law model. This method has been rigorously validated through ramp–hold tests conducted on mechanically stable hydrogels. Notably, during the Ramp phase, the viscoelastic parameters of the material can be readily extracted. Furthermore, we applied unconfined compression stress-relaxation/creep tests with three different ramp–strain rates, namely [Formula: see text], on both white and gray matter to enable rapid quantification. The results indicate that the predicted curves during the Hold phase exhibit notable consistency with experimental data. Moreover, under quasi-static loading conditions, an increase in strain rate significantly enhances the predictive adaptability. Nonetheless, it is crucial to be mindful of the sensitivity to initial stress conditions. This study offers a promising avenue for the expeditious characterization of soft tissue viscoelasticity. It underscores the feasibility of mechanical characterization metrics from a phenomenological model for the assessment of physiological variations and pathological mechanisms in tissue states.

Automated model discovery for muscle using constitutive recurrent neural networks

The stiffness of soft biological tissues not only depends on the applied deformation, but also on the deformation rate. To model this type of behavior, traditional approaches select a specific time-dependent constitutive model and fit its parameters to experimental data. Instead, a new trend now suggests a machine-learning based approach that simultaneously discovers both the best model and best parameters to explain given data. Recent studies have shown that feed-forward constitutive neural networks can robustly discover constitutive models and parameters for hyperelastic materials. However, feed-forward architectures fail to capture the history dependence of viscoelastic soft tissues. Here we combine a feed-forward constitutive neural network for the hyperelastic response and a recurrent neural network for the viscous response inspired by the theory of quasi-linear viscoelasticity. Our novel rheologically-informed network architecture discovers the time-independent initial stress using the feed-forward network and the time-dependent relaxation using the recurrent network. We train and test our combined network using unconfined compression relaxation experiments of passive skeletal muscle and compare our discovered model to a neo Hookean standard linear solid, to an advanced mechanics-based model, and to a vanilla recurrent neural network with no mechanics knowledge. We demonstrate that, for limited experimental data, our new constitutive recurrent neural network discovers models and parameters that satisfy basic physical principles and generalize well to unseen data. We discover a Mooney–Rivlin type two-term initial stored energy function that is linear in the first invariant I1 and quadratic in the second invariant I2 with stiffness parameters of 0.60 kPa and 0.55 kPa. We also discover a Prony-series type relaxation function with time constants of 0.362s, 2.54s, and 52.0s with coefficients of 0.89, 0.05, and 0.03. Our newly discovered model outperforms both the neo Hookean standard linear solid and the vanilla recurrent neural network in terms of prediction accuracy on unseen data. Our results suggest that constitutive recurrent neural networks can autonomously discover both model and parameters that best explain experimental data of soft viscoelastic tissues. Our source code, data, and examples are available at https://github.com/LivingMatterLab.

Fractional Dual-Phase-Lag Model for Nonlinear Viscoelastic Soft Tissues

The primary goal of this paper is to create a new fractional boundary element method (BEM) model for bio-thermomechanical problems in functionally graded anisotropic (FGA) nonlinear viscoelastic soft tissues. The governing equations of bio-thermomechanical problems are briefly presented, including the fractional dual-phase-lag (DPL) bioheat model and Biot’s model. The more complex shapes of nonlinear viscoelastic soft tissues can be handled by the boundary element method, which also avoids the need for the interior domain to be discretized. The fractional dual-phase-lag bioheat equation was solved using the general boundary element method (GBEM) based on the local radial basis function collocation method (LRBFCM). The poroelastic fields are then calculated using the convolution quadrature boundary element method (CQBEM) The numerical findings show that our proposed numerical model is valid, efficient, and accurate.

GPU-accelerated study of the inertial cavitation threshold in viscoelastic soft tissue using a dual-frequency driving signal

Inertial cavitation thresholds under two forms of ultrasonic excitation (the single- and dual-frequency ultrasound modes) are studied numerically. The Gilmore–Akulichev model coupled with the Zener viscoelastic model is used to model the bubble dynamics. The threshold pressures are determined with two criteria, one based on the bubble radius and the other on the bubble collapse speed. The threshold behavior is investigated for different initial bubble sizes, acoustic signal modes, frequencies, tissue viscosities, tissue elasticities, and all their combinations. Due to the large number of parameters and their many combinations (around 1.5 billion for each threshold criterion), all simulations were executed on graphics processing units to speed up the calculations. We used our own code written in the C++ and CUDA C languages. The results obtained demonstrate that using the dual-frequency signal mode can help to reduce the inertial cavitation threshold (in comparison to the single-frequency mode). The criterion based on the bubble size gives a lower threshold than the criterion using the bubble collapse speed. With an increase of the elasticity, the threshold pressure also increases, whereas changing the viscosity has a very small impact on the optimal threshold, unlike the elasticity. A detailed analysis of the optimal ultrasound frequencies for a dual-frequency driving signal found that for viscosities less than 0.02 Pa·s, the first optimal frequency, in general, is much smaller than the second optimal frequency, which can reach 1 MHz. However, for high viscosities, both optimal frequencies are similar and varied in the range 0.01–0.05 MHz. Overall, this study presents a detailed analysis of inertial cavitation in soft tissue under dual-frequency signal excitation. It may be helpful for the further development of different applications of biomedical ultrasound.

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.

Improved two-point frequency shift power method for measurement of shear wave attenuation

Quantitative assessment of mechanical properties of biological soft tissues is frequently evaluated using a noninvasive modality, called ultrasound shear wave elastography (SWE). SWE typically exerts an acoustic radiation force (ARF) to produce shear waves propagating in the lateral direction for which velocities and attenuations are measured. The tissue viscoelasticity is commonly studied by investigating the shear wave phase velocity curves. Viscoelastic tissue properties can also be characterized through utilizing various shear wave attenuation techniques. In this study, we propose an improved method for measuring the shear wave attenuation, called two-point frequency shift power (2P-FSP), which is an improved version of the two-point frequency shift (2P-FS) method. The technique is fully data driven and does not use a rheological model for mathematical modeling. The 2P-FSP method utilizes the power spectra frequency shift of shear waves measured at two spatial positions, which provides robustness to noise. The conceptual basis for the 2P-FSP is provided and tested with numerical and experimental data. We investigated how the location of the first signal and the distance interval between the two locations influence the shear wave attenuation measurement in the 2P-FSP technique. We utilized the 2P-FSP method on numerical phantom data generated using a finite-difference-based method in tissue-mimicking viscoelastic media. Moreover, we tested the 2P-FSP method with data from custom-made tissue-mimicking viscoelastic phantom experiments, and ex vivo porcine liver. We compared results from the proposed technique with results from 2P-FS and analytical values in the case of simulations. The results showed that the 2P-FSP method provides improved results over the 2P-FS technique for lower signal-to-noise ratio (SNR) and locations farther from the push location considered, and can be used to measure attenuation of viscoelastic soft tissues.

Gpu-Accelerated Study of the Inertial Cavitation Threshold in Viscoelastic Soft Tissue Using a Dual-Frequency Driving Signal

Gpu-Accelerated Study of the Inertial Cavitation Threshold in Viscoelastic Soft Tissue Using a Dual-Frequency Driving Signal

GPU-Accelerated Study of the Inertial Cavitation Threshold in Viscoelastic Soft Tissue Using a Dual-Frequency Driving Signal

GPU-Accelerated Study of the Inertial Cavitation Threshold in Viscoelastic Soft Tissue Using a Dual-Frequency Driving Signal

Comparison of the Effects of Passive Accessory Joint Mobilization and Active Stretching on Balance in Stroke Patients with Limited Ankle Dorsiflexion

Background: Patients with stroke may show impaired balance due to the limited range of motion of the ankle resulting from abnormal soft tissues surrounding the ankle joint. Changes in the viscoelasticity of soft tissues and decreased mobility of the ankle impair the balance and lead to problems in the daily life of patients with stroke. Joint mobilization and stretching are effective methods of improving balance by increasing the viscoelasticity of soft tissues and range of motion of the ankle. Objectives: To effects of ankle joint mobilization and calf muscle stretching on balance in patients with stroke. Design: A randomized controlled trial. Methods: A total of 20 patients with stroke were randomly assigned into two groups. The joint mobilization group (JMG) underwent anteroposterior joint mobilization of the talocrural joint, while the stretching group (SG) received calf muscle stretching. Functional reach test (FRT), berg balance scale (BBS), and timed up and go test (TUG) were used to assess balance. Results: The FRT, BBS, and TUG results significantly improved in the JMG and SG after invention (P<.05). However, the improvements were greater in the JMG group than those in the SG group (P<.05). Conclusion: Joint mobilization was an effective intervention to improve soft tissue performance and range of motion of the ankle, thereby improving balance in patients with stroke.

Ultrasound elastography using shear wave interference patterns: a finite element study of affecting factors.

Elastography as one of the non-invasive medical imaging techniques which can help determine the stiffness of organs and other structures is currently attracting more attention. An interesting imaging rate-independent technique which has been discussed in literature uses shear wave interference patterns (SWIP). In this method, two external continuous harmonic vibration sources were used to induced SWIP and the resulting tissue displacements are mapped using ultrasonic imaging called sonoelastography. In this paper, a finite element model (FEM) of viscoelastic soft tissue with circular stiffer lesion inside, is simulated for testing the effect of stimulation characteristics on the propagation of SWIPs and shear speed map reconstruction. Also, we proposed an elastography probe, including miniature vibration sources and ultrasound transducer, which can be appropriate for experimental tests. The elastographic average speed ratio (ASR) and some scores like Dice coefficient, related to the binary image of shear speed map, are calculated for quantitatively measuring the effect of different contributing harmonic vibration parameters. Results show that the potential of providing useful diagnostic information can be improved if the preferable parameters are considered for implementation. According to these results the ASR, Dice and Jaccard scores would diverge from the ground truth of FEA if the parameter level is not selected correctly. Particularly, the Dice and Jaccard coefficients are obtained about 0.9 and 0.8, respectively, for the best vibration parameters level choice.

A Recruitment Model of Tendon Viscoelasticity That Incorporates Fibril Creep and Explains Strain-Dependent Relaxation.

Soft tissues exhibit complex viscoelastic behavior, including strain-rate dependence, hysteresis, and strain-dependent relaxation. In this paper, a model for soft tissue viscoelasticity is developed that captures all of these features and is based upon collagen recruitment, whereby fibrils contribute to tissue stiffness only when taut. We build upon existing recruitment models by additionally accounting for fibril creep and by explicitly modeling the contribution of the matrix to the overall tissue viscoelasticity. The fibrils and matrix are modeled as linear viscoelastic and each fibril has an associated critical strain (corresponding to its length) at which it becomes taut. The model is used to fit relaxation tests on three rat tail tendon fascicles and predict their response to cyclic loading. It is shown that all of these mechanical tests can be reproduced accurately with a single set of constitutive parameters, the only difference between each fascicle being the distribution of their fibril crimp lengths. By accounting for fibril creep, we are able to predict how the fibril length distribution of a fascicle changes over time under a given deformation. Furthermore, the phenomenon of strain-dependent relaxation is explained as arising from the competition between the fibril and matrix relaxation functions.

Optical coherence tomography for evaluating capillary waves in blood and plasma

Capillary waves are associated with fluid mechanical properties. Optical coherence tomography (OCT) has previously been used to determine the viscoelasticity of soft tissues or cornea. Here we report that OCT was able to evaluate phase velocities of capillary waves in fluids. The capillary waves of water, porcine whole blood and plasma on the interfacial surface, air-fluid in this case, are discussed in theory, and phase velocities of capillary waves were estimated by both our OCT experiments and theoretical calculations. Our experiments revealed highly comparable results with theoretical calculations. We concluded that OCT would be a promising tool to evaluate phase velocities of capillary waves in fluids. The methods described in this study could be applied to determine surface tensions and viscosities of fluids for differentiating hematological diseases in the future potential biological applications.

Towards a consensus on rheological models for elastography in soft tissues

A rising wave of technologies and instruments are enabling more labs and clinics to make a variety of measurements related to tissue viscoelastic properties. These instruments include elastography imaging scanners, rheological shear viscometers, and a variety of calibrated stress–strain analyzers. From these many sources of disparate data, a common step in analyzing results is to fit the measurements of tissue response to some viscoelastic model. In the best scenario, this places the measurements within a theoretical framework and enables meaningful comparisons of the parameters against other types of tissues. However, there is a large set of established rheological models, even within the class of linear, causal, viscoelastic solid models, so which of these should be chosen? Is it simply a matter of best fit to a minimum mean squared error of the model to several data points? We argue that the long history of biomechanics, including the concept of the extended relaxation spectrum, along with data collected from viscoelastic soft tissues over an extended range of times and frequencies, and the theoretical framework of multiple relaxation models which model the multi-scale nature of physical tissues, all lead to the conclusion that fractional derivative models represent the most succinct and meaningful models of soft tissue viscoelastic behavior. These arguments are presented with the goal of clarifying some distinctions between, and consequences of, some of the most commonly used models, and with the longer term goal of reaching a consensus among different sub-fields in acoustics, biomechanics, and elastography that have common interests in comparing tissue measurements.

Two-Point Frequency Shift Method for Shear Wave Attenuation Measurement.

Ultrasound shear wave elastography (SWE) is an increasingly used noninvasive modality for quantitative evaluation of tissue mechanical properties. SWE typically uses an acoustic radiation force to produce laterally propagating shear waves that are tracked in the spatial and temporal domains, in order to obtain the wave velocity. One of the ways to study the viscoelasticity is through studying the shear wave phase velocity dispersion curves. Shear wave attenuation can be also characterized in viscoelastic tissues with methods that use multiple lateral data samples. In this article, we present an alternative method for measuring the shear wave attenuation without using a rheological model two-point frequency shift (2P-FS). The technique uses information related to the amplitude spectra FS of shear waves measured at only two lateral locations. The theoretical basis for the 2P-FS is derived and validated. We examined how the first signal position and the distance between the two locations affect the shear wave attenuation estimation in the 2P-FS method. We tested this new method on digital phantom data created using the local interaction simulation approach (LISA) in viscoelastic media. Moreover, we tested data acquired from custom-made tissue-mimicking viscoelastic phantom experiments and ex vivo porcine liver measurements. We compared results from the 2P-FS method with the other two techniques used for assessing a shear wave attenuation: the FS-based method and the attenuation-measuring ultrasound shear wave elastography (AMUSE) technique. In addition, we evaluated the 2P-FS algorithm with different levels of added white Gaussian noise to the shear wave particle velocity using numerical phantoms. Tests conducted showed that the 2P-FS method gives robust results based on only two measurements and can be used to measure attenuation of viscoelastic soft tissues.

A parametric evaluation of shear wave speeds estimated with the time-of-flight approach in viscoelastic media

The time-of-flight approach estimates the shear elasticity in tissue mimicking elastography phantoms and in soft tissue. The time-of-flight approach is effective in elastic phantoms, but the time-of-flight approach tends to overestimate the shear elasticity in viscoelastic phantoms and in viscoelastic soft tissues. To characterize errors in estimated parameters for different values of the shear elasticity and the shear viscosity, three-dimensional (3D) shear wave simulations are evaluated for twelve different parameter combinations. The 3D acoustic radiation force is calculated for an L7-4 transducer using the fast nearfield method and the angular spectrum approach, and then, 3D shear wave propagation in a viscoelastic medium is simulated with Green's functions for a Kelvin-Voigt model. The time-of-flight method is then evaluated within a two-dimensional plane. The results show that the accuracy of the time-of-flight method depends on the values of the shear elasticity and the shear viscosity. In particular, the error in the estimated shear elasticity increases as the shear viscosity increases, where the largest errors are observed when larger values of the shear viscosity are combined with smaller values of the shear elasticity. [Work supported in part by NIH Grants DK092255, EB023051, and EB012079.]

ANTERIOR CRUCIATE LIGAMENT SECTIONING ALTERS CENTER OF PRESSURE WITHIN THE TIBIOFEMORAL JOINT: AN IN VITRO STUDY

Anterior cruciate ligament (ACL) injuries often lead to secondary injuries, joint degradation, and were linked to osteoarthritis. There is little known about how ACL rupture affects the loading and contact characteristics within the tibiofemoral joint. The objective of this study was to evaluate changes in tibiofemoral joint contact pressure and center of pressure (COP) during dynamic motion before and after ACL sectioning in vitro. Six intact cadaveric knees were manipulated through three full cycles of motion ranging from 30∘ to 120∘ of flexion in a custom-built device. A pressure sensor inserted in the tibiofemoral joint measured contact pressure of the medial and lateral compartments as well as COP characteristics of the whole joint before and after the ACL was sectioned. There was a significant decrease in lateral-compartment peak pressure, medial and lateral mean pressure, and total contact area after the ACL was sectioned. In both intact and ACL deficient knees, a posterior-lateral shift in COP was observed during flexion and a medial-anterior shift when returning to extension. Plotting the COP trajectory through the flexion-extension cycle resulted in a distinct hysteresis curve due to the viscoelastic soft tissue properties. Following sectioning, the COP trajectory had a diminished area compared to the intact condition. The diminished area of contact pressure may be more problematic than the overall magnitude when the integrity of the ACL is compromised. The centralized pressure distribution to a smaller surface area over time may cause focal damage to the cartilage leading to osteoarthritis.

Nonlinear visco-elasticity of soft tissues under cyclic deformations

Nowadays, new experimental set-ups allow to determine the strains which appear in biological tissues under small controlled solicitations as stretch (uniaxial and bi-axial) or shear. Automatically recorded by camera, these data exhibit hysteresis even for very slow and weak forcing. The aim of this work is to revisit the modeling of hyper-elasticity and visco-elasticity for tissues with a rather disordered structure. Despite the weakness of the imposed stretch values, strong nonlinearities are observed for these tissues that polymeric gels do not show under the same conditions. Various classical models have been tested on surgical mammary tissues and it turns out that the simplest Neo-Hookean model with its viscous counter-part explain perfectly the data. Viscosity and elasticity compete quite equivalently showing that, in the selected range of forcing values, visco-elasticity cannot be discarded.

Temperature dependent of viscoelasticity measurement on fat emulsion phantom using acoustic radiation force elasticity imaging method.

During the past two decades, tissue elasticity has been extensively studied and has been used in clinical disease diagnosis. But biological soft tissues are viscoelastic in nature. Therefore, they should be simultaneously characterized in terms of elasticity and viscosity. In addition, the mechanical properties of soft tissues are temperature dependent. However, how the temperature influences the shear wave dispersion and the viscoelasticity of soft tissue are still unclear. The aim of this study is to compare viscoelasticity of fat emulsion phantom with different temperature using acoustic radiation force elasticity imaging method. In our experiment, we produced four proportions of ultrasonic phantom by adding fat emulsion gelatin. Through adjusting the component of the fat emulsion, we change the viscoelasticity of the ultrasonic phantom. We used verasonics system to gather data and voigt model to fit the elasticity and viscosity value of the ultrasonic phantom we made. The influence of temperature to the ultrasonic phantom also measured in our study. The results show that the addition of fat emulsion to the phantom can increase the viscosity of the phantom, and the shear wave phase velocity decreases gradually at each frequency with the temperature increases, which provides a new material for the production of viscoelastic phantom.

Quantitative characterization of viscoelastic behavior in tissue-mimicking phantoms and ex vivo animal tissues.

Viscoelasticity of soft tissue is often related to pathology, and therefore, has become an important diagnostic indicator in the clinical assessment of suspect tissue. Surgeons, particularly within head and neck subsites, typically use palpation techniques for intra-operative tumor detection. This detection method, however, is highly subjective and often fails to detect small or deep abnormalities. Vibroacoustography (VA) and similar methods have previously been used to distinguish tissue with high-contrast, but a firm understanding of the main contrast mechanism has yet to be verified. The contributions of tissue mechanical properties in VA images have been difficult to verify given the limited literature on viscoelastic properties of various normal and diseased tissue. This paper aims to investigate viscoelasticity theory and present a detailed description of viscoelastic experimental results obtained in tissue-mimicking phantoms (TMPs) and ex vivo tissues to verify the main contrast mechanism in VA and similar imaging modalities. A spherical-tip micro-indentation technique was employed with the Hertzian model to acquire absolute, quantitative, point measurements of the elastic modulus (E), long term shear modulus (η), and time constant (τ) in homogeneous TMPs and ex vivo tissue in rat liver and porcine liver and gallbladder. Viscoelastic differences observed between porcine liver and gallbladder tissue suggest that imaging modalities which utilize the mechanical properties of tissue as a primary contrast mechanism can potentially be used to quantitatively differentiate between proximate organs in a clinical setting. These results may facilitate more accurate tissue modeling and add information not currently available to the field of systems characterization and biomedical research.

Deformable Models for Surgical Simulation: A Survey.

This paper presents a survey of the state-of-the-art deformable models studied in the literature, with regard to soft tissue deformable modeling for interactive surgical simulation. It first introduces the challenges of surgical simulation, followed by discussions and analyses on the deformable models, which are classified into three categories: the heuristic modeling methodology, continuum-mechanical methodology, and other methodologies. It also examines linear and nonlinear deformable modeling, model internal forces, and numerical time integrations, together with modeling of soft tissue anisotropy, viscoelasticity, and compressibility. Finally, various issues in the existing deformable models are discussed to outline the remaining challenges of deformable models in surgical simulation.