3-D FDTD simulation of shear waves for evaluation of complex modulus imaging

Using torsional wave elastography to evaluate spring pot parameters in skin tumor mimicking phantoms

Estimating the tissue parameters of skin tumors is crucial for diagnosis and effective therapy in dermatology and related fields. However, identifying the most sensitive biomarkers require an optimal rheological model for simulating skin behavior this remains an ongoing research endeavor. Additionally, the multi-layered structure of the skin introduces further complexity to this task. In order to surmount these challenges, an inverse problem methodology, in conjunction with signal analysis techniques, is being employed. In this study, a fractional rheological model is presented to enhance the precision of skin tissue parameter estimation from the acquired signal from torsional wave elastography technique (TWE) on skin tumor-mimicking phantoms for lab validation and the estimation of the thickness of the cancerous layer. An exhaustive analysis of the spring-pot model (SP) solved by the finite difference time domain (FDTD) is conducted. The results of experiments performed using a TWE probe designed and prototyped in the laboratory were validated against ultrafast imaging carried out by the Verasonics Research System. Twelve tissue-mimicking phantoms, which precisely simulated the characteristics of skin tissue, were prepared for our experimental setting. The experimental data from these bi-layer phantoms were measured using a TWE probe, and the parameters of the skin tissue were estimated using inverse problem-solving. The agreement between the two datasets was evaluated by comparing the experimental data obtained from the TWE technique with simulated data from the SP- FDTD model using Pearson correlation, dynamic time warping (DTW), and time-frequency representation. Our findings show that the SP-FDTD model and TWE are capable of determining the mechanical properties of both layers in a bilayer phantom, using a single signal and an inverse problem approach. The ultrafast imaging and the validation of TWE results further demonstrate the robustness and reliability of our technology for a realistic range of phantoms. This fusion of the SP-FDTD model and TWE, as well as inverse problem-solving methods has the potential to have a considerable impact on diagnoses and treatments in dermatology and related fields.

Healthy human skin Kelvin-Voigt fractional and spring-pot biomarkers reconstruction using torsional wave elastography

This paper presents a novel method for reconstructing skin parameters using Probabilistic Inverse Problem (PIP) techniques and Torsional Wave Elastography (TWE) rheological modeling. A comprehensive examination was conducted to compare and analyze the theoretical, time-of-flight (TOF), and full-signal waveform (FSW) approaches. The objective was the identification of the most effective method for the estimation of mechanical parameters. Initially, the most appropriate rheological model for the simulation of skin tissue behavior was determined through the application and comparison of two models, spring pot (SP) and Kevin Voigt fractional derivative (KVFD). A numerical model was developed using the chosen rheological models. The collection of experimental data from 15 volunteers utilizing a TWE sensor was crucial for obtaining significant information for the reconstruction process. The study sample consisted of five male and ten female subjects ranging in age from 25 to 60 years. The procedure was performed on the ventral forearm region of the participants. The process of reconstructing skin tissue parameters was carried out using PIP techniques. The experimental findings were compared with the numerical results. The three methods considered (theoretical, TOF, FSW) have been used. The efficacy of TOF and FSW was then compared with theoretical method. The findings of the study demonstrate that the FSW and TOF techniques successfully reconstructed the parameters of the skin tissue in all of the models. The SP model's the skin tissue η values ranged from 8 to 12 P a · s , as indicated by the TOF reconstruction parameters. η values found by the KVFD model ranged from 4.1 to 9.3 P a · s . The μ values generated by the KVFD model range between 0.61 and 96.86 kPa. However, FSW parameters reveal that skin tissue η values for the SP model ranged from 7.8 to 12 P a · s . The KVFD model determined η values between 6.3 and 9.5 P a · s . The KVFD model presents μ values ranging between 26.02 and 122.19 kPa. It is shown that the rheological model that best describes the nature of the skin is the SP model and its simplicity as it requires only two parameters, in contrast to the three parameters required by the KVFD model. Therefore, this work provides a valuable addition to the area of dermatology, with possible implications for clinical practice.

Reverse time migration and genetic algorithms Combined for Reconstruction in Transluminal Shear Wave Elastography: An In Silico Case Study

A new reconstruction approach that combines Reverse Time Migration (RTM) and Genetic Algorithms (GAs) is proposed for solving the inverse problem associated with transluminal shear wave elastography. The transurethral identification of the first thermal lesion generated by transrectal High Intensity Focused Ultrasound (HIFU) for the treatment of prostate cancer, was used to preliminarily test in silico the combined reconstruction method. The RTM method was optimised by comparing reconstruction images from several cross-correlation techniques, including a new proposed one, and different device configurations in terms of the number and arrangement of emitters and receivers of the conceptual transurethral probe. The best results were obtained for the new proposed cross-correlation method and a device configuration with 3 emitters and 32 receivers. The RTM reconstructions did not completely contour the shape of the HIFU lesion, however, as planned for the combined approach, the areas in the RTM images with high level of correlation were used to narrow down the search space in the GA-based technique. The GA-based technique was set to find the location of the HIFU lesion and the increment in stiffness and viscosity due to thermal damage. Overall, the combined approach achieves lower level of error in the reconstructed values, and in a shorter computational time, compared to the GA-based technique alone. The lowest errors were accomplished for the location of HIFU lesion, followed by the contrast ratio of stiffness between thermally treated tissue and non-treated normal tissue. The homologous ratio of viscosity obtained higher level of error. Further investigation considering diverse scenarios to be reconstructed and with experimental data is required to fully evaluate the feasibility of the combined approach.

Shear wave imaging and classification using extended Kalman filter and decision tree algorithm

Shear wave ultrasound elastography is a quantitative imaging approach in soft tissues based on viscosity-elastic properties. Complex shear modulus (CSM) estimation is an effective solution to analyze tissues' physical properties for elasticity and viscosity based on the wavenumber and attenuation coefficient. CSM offers a way to detect and classify some types of soft tissues. However, CSM-based elastography inherits some obstacles, such as estimation precision and calculation complexity. This work proposes an approach for two-dimensional CSM estimation and soft tissue classification using the Extended Kalman Filter (EKF) and Decision Tree (DT) algorithm, named the EKF-DT approach. CSM estimation is obtained by applying EKF to exploit shear wave propagation at each spatial point. Afterward, the classification of tissues is done by a direct and efficient decision tree algorithm categorizing three types of normal, cirrhosis, and fibrosis liver tissues. Numerical simulation scenarios have been employed to illustrate the recovered quality and practicality of the proposed method's liver tissue classification. With the EKF, the estimated wave number and attenuation coefficient are close to the ideal values, especially the estimated wave number. The states of three liver tissue types were automatically classified by applying the DT coupled with two proposed thresholds of elasticity and viscosity: (2.310 kPa, 1.885 Pa.s) and (3.620 kPa 3.146 Pa.s), respectively. The proposed method shows the feasibility of CSM estimation based on the wavenumber and attenuation coefficient by applying the EKF. Moreover, the DT can automate the classification of liver tissue conditions by proposing two thresholds. The proposed EKF-DT method can be developed by 3D image reconstruction and empirical data before applying it in medical practice.

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.

Why Are Viscosity and Nonlinearity Bound to Make an Impact in Clinical Elastographic Diagnosis?

The adoption of multiscale approaches by the biomechanical community has caused a major improvement in quality in the mechanical characterization of soft tissues. The recent developments in elastography techniques are enabling in vivo and non-invasive quantification of tissues' mechanical properties. Elastic changes in a tissue are associated with a broad spectrum of pathologies, which stems from the tissue microstructure, histology and biochemistry. This knowledge is combined with research evidence to provide a powerful diagnostic range of highly prevalent pathologies, from birth and labor disorders (prematurity, induction failures, etc.), to solid tumors (e.g., prostate, cervix, breast, melanoma) and liver fibrosis, just to name a few. This review aims to elucidate the potential of viscous and nonlinear elastic parameters as conceivable diagnostic mechanical biomarkers. First, by providing an insight into the classic role of soft tissue microstructure in linear elasticity; secondly, by understanding how viscosity and nonlinearity could enhance the current diagnosis in elastography; and finally, by compounding preliminary investigations of those elastography parameters within different technologies. In conclusion, evidence of the diagnostic capability of elastic parameters beyond linear stiffness is gaining momentum as a result of the technological and imaging developments in the field of biomechanics.

Kelvin-Voigt Parameters Reconstruction of Cervical Tissue-Mimicking Phantoms Using Torsional Wave Elastography

The reconstruction of viscous properties of soft tissues, and more specifically, of cervical tissue is a challenging problem. In this paper, a new method is proposed to reconstruct the viscoelastic parameters of cervical tissue-mimicking phantoms by a Torsional Wave Elastography (TWE) technique. The reconstruction method, based on a Probabilistic Inverse Problem (PIP) approach, is presented and experimentally validated against Shear Wave Elastography (SWE). The anatomy of the cervical tissue has been mimicked by means of a two-layer gelatine phantom that simulates the epithelial and connective layers. Five ad hoc oil-in-gelatine phantoms were fabricated at different proportion to test the new reconstruction technique. The PIP approach was used for reconstructing the Kelvin-Voigt (KV) viscoelastic parameters by comparing the measurements obtained from the TWE technique with the synthetic signals from a Finite Difference Time Domain (FDTD) KV wave propagation model. Additionally, SWE tests were realized in order to characterize the viscoelastic properties of each batch of gelatine. Finally, validation was carried out by comparing the KV parameters inferred from the PIP with those reconstructed from the shear wave dispersion curve obtained from the SWE measurements. In order to test the degree of agreement between both techniques, a Student's T-test and a Pearson's correlation study were performed. The results indicate that the proposed method is able to reconstruct the KV viscoelastic properties of the cervical tissue, for both the epithelial and connective layers, as well as the thickness of the first layer with acceptable accuracy.

Reconstruction of Viscosity Maps in Ultrasound Shear Wave Elastography

Change in viscoelastic properties of biological tissues may often be symptomatic of a dysfunction that can be correlated to tissue pathology. Shear wave elastography is an imaging method mainly used to assess stiffness but with the potential to measure viscoelasticity of biological tissues. This can enable tissue characterization; and thus, can be used as a marker to improve diagnosis of pathological lesions. In this study, a frequency-shift method based framework is presented for the reconstruction of viscosity by analyzing the spectral properties of acoustic radiation force-induced shear waves. The aim of the study was to investigate the feasibility of viscosity reconstruction maps in homogeneous as well as heterogeneous samples. Experiments were performed in four in vitro phantoms, two ex vivo porcine liver samples, two ex vivo fatty duck liver samples, and one in vivo fatty goose liver. Successful viscosity maps were reconstructed in homogeneous and heterogeneous phantoms with embedded mechanical inclusions having different geometries. Quantitative values of viscosity obtained for two porcine liver tissues, two fatty duck liver samples, and one goose fatty liver were (mean ± SD) 0.61 ± 0.21, 0.52 ± 0.35; 1.28 ± 0.54, 1.36 ± 0.73, and 1.67 ± 0.70 Pa.s, respectively.

GPU-based Green's function simulations of shear waves generated by an applied acoustic radiation force in elastic and viscoelastic models

Shear wave calculations induced by an acoustic radiation force are very time-consuming on desktop computers, and high-performance graphics processing units (GPUs) achieve dramatic reductions in the computation time for these simulations. The acoustic radiation force is calculated using the fast near field method and the angular spectrum approach, and then the shear waves are calculated in parallel with Green's functions on a GPU. This combination enables rapid evaluation of shear waves for push beams with different spatial samplings and for apertures with different f/#. Relative to shear wave simulations that evaluate the same algorithm on an Intel i7 desktop computer, a high performance nVidia GPU reduces the time required for these calculations by a factor of 45 and 700 when applied to elastic and viscoelastic shear wave simulation models, respectively. These GPU-accelerated simulations also compared to measurements in different viscoelastic phantoms, and the results are similar. For parametric evaluations and for comparisons with measured shear wave data, shear wave simulations with the Green's function approach are ideally suited for high-performance GPUs.

Development of an intravascular ultrasound elastography based on a dual-element transducer

The ability to measure the elastic properties of plaques and vessels would be useful in clinical diagnoses, particularly for detecting a vulnerable plaque. This study demonstrates the feasibility of the combination of intravascular ultrasound (IVUS) and acoustic radiation force elasticity imaging for detecting the distribution of stiffness within atherosclerotic arteries ex vivo. A dual-frequency IVUS transducer with two elements was used to induce the propagation of the shear wave (by the 8.5 MHz pushing element) which could be simultaneously monitored by the 31 MHz imaging element. The wave-amplitude image and the wave-velocity image were reconstructed by measuring the peak displacement and wave velocity of shear wave propagation, respectively. System performance was verified using gelatin phantoms. The phantom results demonstrate that the stiffness differences of shear modulus of 1.6 kPa can be distinguished through the wave-amplitude and wave-velocity images. The stiffness distributions of the atherosclerotic aorta from a rabbit were obtained, for which the values of peak displacement and the shear wave velocity were 3.7 ± 1.2 µm and 0.38 ± 0.19 m s^-1 for the lipid-rich plaques, and 1.0 ± 0.2 µm and 3.45 ± 0.45 m s^-1 for the arterial walls, respectively. These results indicate that IVUS elasticity imaging can be used to distinguish the elastic properties of plaques and vessels.

Time domain characteristics of wave motion in dispersive and anisotropic continuum acoustic metamaterials

The authors study the wave propagation in continuum acoustic metamaterials whose all or not all of the principal elements of the mass tensor or the scalar compressibility can be negative due to wave dispersion. Their time-domain wave characteristics are particularly investigated by the finite-difference time-domain (FDTD) method, in which algorithms for the Drude and Lorentz dispersion pertinent to acoustic metamaterials are provided necessarily. Wave propagation nature of anisotropic acoustic metamaterials with all admissible material parameters are analyzed in a general manner. It is found that anomalous negative refraction phenomena can appear in several dispersion regimes, and their unique time-domain signatures have been discovered by the FDTD modeling. It is further proposed that two different metamaterial layers with specially assigned dispersions could comprise a conjugate pair that permits wave propagation only at specific points in the wave vector space. The time-domain pulse simulation verifies that acoustic directive radiation capable of modulating radiation angle with the wave frequency can be realized with this conjugate pair. The study provides the detailed analysis of wave propagation in anisotropic and dispersive acoustic mediums, which makes a further step toward dispersion engineering and transient wave control through acoustic metamaterials.

Sonic Estimation of Elasticity via Resonance: A New Method of Assessing Hemostasis

Uncontrolled bleeding threatens patients undergoing major surgery and in care for traumatic injury. This paper describes a novel method of diagnosing coagulation dysfunction by repeatedly measuring the shear modulus of a blood sample as it clots in vitro. Each measurement applies a high-energy ultrasound pulse to induce a shear wave within a rigid walled chamber, and then uses low energy ultrasound pulses to measure displacements associated with the resonance of that shear wave. Measured displacements are correlated with predictions from finite difference time domain models, with the best fit corresponding to the modulus estimate. In our current implementation each measurement requires 62.4 ms. Experimental data was analyzed using a fixed-viscosity algorithm and a free-viscosity algorithm. In experiments utilizing human blood induced to clot by exposure to kaolin, the free-viscosity algorithm quantified the shear modulus of formed clots with a worst-case precision of 2.5%. Precision was improved to 1.8% by utilizing the fixed-viscosity algorithm. Repeated measurements showed a smooth evolution from liquid blood to a firm clot with a shear modulus between 1.4 and 3.3 kPa. These results show the promise of this technique for rapid, point of care assessment of coagulation.

Single tracking location acoustic radiation force impulse viscoelasticity estimation (STL-VE): A method for measuring tissue viscoelastic parameters

Single tracking location (STL) shear wave elasticity imaging (SWEI) is a method for detecting elastic differences between tissues. It has the advantage of intrinsic speckle bias suppression compared with multiple tracking location variants of SWEI. However, the assumption of a linear model leads to an overestimation of the shear modulus in viscoelastic media. A new reconstruction technique denoted single tracking location viscosity estimation (STL-VE) is introduced to correct for this overestimation. This technique utilizes the same raw data generated in STL-SWEI imaging. Here, the STL-VE technique is developed by way of a maximum likelihood estimation for general viscoelastic materials. The method is then implemented for the particular case of the Kelvin-Voigt Model. Using simulation data, the STL-VE technique is demonstrated and the performance of the estimator is characterized. Finally, the STL-VE method is used to estimate the viscoelastic parameters of ex vivo bovine liver. We find good agreement between the STL-VE results and the simulation parameters as well as between the liver shear wave data and the modeled data fit.

Viscoelastic properties of rodent mammary tumors using ultrasonic shear-wave imaging

Images of tumor mechanical properties provide important insights into malignant-cell processes manifest by extracellular matrix (ECM) stiffening and remodeling. This article presents a pilot study measuring in vivo mechanical-property characteristics of rodent mammary tumors using an ultrasonic shear-wave imaging technique. Shear waves are generated by a needle inserted into the tumor of anesthetized rodents that is vibrated harmonically between 50 and 450 Hz. Particle motion in the tumor associated with the radiation of cylindrical shear waves is imaged using pulsed-Doppler ultrasound techniques. Estimating the spatial gradient of shear-wave phase along the direction of propagation at frequencies in the measurement range yields shear-speed dispersion curves. Measured dispersion curves were fit to those predicted by three different rheological models to estimate the elastic and viscous coefficients of the complex shear modulus. The investigation was performed in vivo on four rat-mammary fibroadenoma tumors and five xenograft mouse-mammary carcinoma tumors. Each tumor was subsequently excised for histological imaging and composition analysis. Collagen composition was measured using hydroxyproline assays that were then correlated with mechanical measurements. The goal was to relate soft-tissue mechanical behavior to biological characteristics of tumor structures, specifically the collagenous ECM protein content. The choice of rheological model and the effects of artifacts induced by shear-wave reflections at internal tissue boundaries are carefully examined in this article. Addressing these issues is of great importance when selecting force-excitation methods and modulus estimation method to assess intrinsic tissue properties responsible for disease-specific elastographic contrast.