Ramp-hold relaxation solutions for the KVFD model applied to soft viscoelastic media

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.

Label-free multimodal electro-thermo-mechanical (ETM) phenotyping as a novel biomarker to differentiate between normal, benign, and cancerous breast biopsy tissues

BACKGROUND

Technologies for quick and label-free diagnosis of malignancies from breast tissues have the potential to be a significant adjunct to routine diagnostics. The biophysical phenotypes of breast tissues, such as its electrical, thermal, and mechanical properties (ETM), have the potential to serve as novel markers to differentiate between normal, benign, and malignant tissue.

RESULTS

We report a system-of-biochips (SoB) integrated into a semi-automated mechatronic system that can characterize breast biopsy tissues using electro-thermo-mechanical sensing. The SoB, fabricated on silicon using microfabrication techniques, can measure the electrical impedance (Z), thermal conductivity (K), mechanical stiffness (k), and viscoelastic stress relaxation (%R) of the samples. The key sensing elements of the biochips include interdigitated electrodes, resistance temperature detectors, microheaters, and a micromachined diaphragm with piezoresistive bridges. Multi-modal ETM measurements performed on formalin-fixed tumour and adjacent normal breast biopsy samples from N = 14 subjects were able to differentiate between invasive ductal carcinoma (malignant), fibroadenoma (benign), and adjacent normal (healthy) tissues with a root mean square error of 0.2419 using a Gaussian process classifier. Carcinoma tissues were observed to have the highest mean impedance (110018.8 ± 20293.8 Ω) and stiffness (0.076 ± 0.009 kNm-1) and the lowest thermal conductivity (0.189 ± 0.019 Wm-1 K-1) amongst the three groups, while the fibroadenoma samples had the highest percentage relaxation in normalized load (47.8 ± 5.12%).

CONCLUSIONS

The work presents a novel strategy to characterize the multi-modal biophysical phenotype of breast biopsy tissues to aid in cancer diagnosis from small-sized tumour samples. The methodology envisions to supplement the existing technology gap in the analysis of breast tissue samples in the pathology laboratories to aid the diagnostic workflow.

Ramp-Creep Ultrasound Viscoelastography for Measuring Viscoelastic Parameters of Materials

Several ultrasound-based methods have been developed to evaluate the viscoelastic properties of materials. The purpose of this study is to introduce a novel viscoelastography method based on ultrasound acoustic radiation force for measuring the parameters relevant to the viscoelastic properties of materials, named ramp-creep ultrasound viscoelastography (RC viscoelastography). RC viscoelastography uses two different ultrasound excitation modes to cause ramp and creep strain responses in the material. By combining and analyzing the information obtained from these two modes of excitation, the viscoelastic parameters of the material can be quantitatively evaluated. Finite element computer simulation demonstrated that RC viscoelastography can accurately evaluate the viscoelastic parameters of the material, including the relaxation and creep time constants as well as the ratio of viscous fluids to solids in the material, except for the region near the top surface of the material. The novelty of RC viscoelastography is that there is no need to know the magnitude of acoustic radiation force and induced stress in the material in order to evaluate the viscoelastic parameters. In the future, experiments are necessary to test the performance of RC viscoelastography in real biomaterials and biological tissues.

Viscoelasticity in simple indentation-cycle experiments: a computational study

Instrumented indentation has become an indispensable tool for quantitative analysis of the mechanical properties of soft polymers and biological samples at different length scales. These types of samples are known for their prominent viscoelastic behavior, and attempts to calculate such properties from the indentation data are constantly made. The simplest indentation experiment presents a cycle of approach (deepening into the sample) and retraction of the indenter, with the output of the force and indentation depth as functions of time and a force versus indentation dependency (force curve). The linear viscoelastic theory based on the elastic–viscoelastic correspondence principle might predict the shape of force curves based on the experimental conditions and underlying relaxation function of the sample. Here, we conducted a computational analysis based on this theory and studied how the force curves were affected by the indenter geometry, type of indentation (triangular or sinusoidal ramp), and the relaxation functions. The relaxation functions of both traditional and fractional viscoelastic models were considered. The curves obtained from the analytical solutions, numerical algorithm and finite element simulations matched each other well. Common trends for the curve-related parameters (apparent Young’s modulus, normalized hysteresis area, and curve exponent) were revealed. Importantly, the apparent Young’s modulus, obtained by fitting the approach curve to the elastic model, demonstrated a direct relation to the relaxation function for all the tested cases. The study will help researchers to verify which model is more appropriate for the sample description without extensive calculations from the basic curve parameters and their dependency on the indentation rate.

Towards microvascular pressure estimation using ultrasound and photoacoustic imaging

Microvascular pressure drives perfusion in tissues but is difficult to measure. A method is proposed here to estimate relative pressures in microvessels using photoacoustic and ultrasound tracking of small vessels during calibrated tissue compression. A photoacoustic-ultrasound dual imaging transducer is used to directly compress on tissue in vivo. Photoacoustic signals from blood vessels diminish as an external load is applied and eventually reaches a minimum or vanishes when external pressure is sufficiently greater than the internal pressure. Two methods were proposed to estimate relative pressures. In the first approach, vessels were tracked during compression and when the vessel photoacoustic signals vanished below a set threshold, the internal pressures were assigned as the external loading pressure at the respective collapse point. In this approach pressures required to collapse vessel signatures completely were found to be much greater than physiological blood pressures. An alternative approach was to track the cross-sectional area of small vessels with changing external load and fitting the data to a known Shapiro model for thin-walled vessel compression. This approach produced estimates of internal pressures which were much more realistic. Both approaches produced the same rank-ordering of relative pressures of various vessels in vivo. Approaches thus far require future work to become fully quantitative but the present contributions represent steps towards this goal.

Feasibility study of using the dispersion of surface acoustic wave impulse for viscoelasticity characterization in tissue mimicking phantoms

The aim of this study was to investigate the feasibility of utilizing the phase velocity dispersion of impulse surface acoustic wave (SAW) for viscoelasticity characterization of soft materials. The focused ultrasound transducer and the phase-sensitive optical coherence tomography were applied as the impulse SAW inducer and tracker, respectively. Three types of liquid-paraffin-based cream-in-agar phantoms were tested. Phase velocity dispersion curve was extracted using a Fourier transform-based phase velocity analysis algorithm. Viscoelastic parameters were obtained by fitting the dispersion curve of SAW into Rayleigh wave dispersion equation. The estimated viscoelasticity was compared with that from spherical indenter, ramp-hold relaxation testing for validation. Both results show an increasing trend in the elasticity and decreasing trend in the viscosity with the concentration of liquid-paraffin-based cream increasing in the samples. The proposed method has the capability of evaluating the viscoelastic properties of homogeneous soft tissue. By combining viscoelastic parameters estimated from the proposed method, the dispersive SAW-impulse-based viscosity-compensated elastography could be further developed.

Correlation between stress drop and applied strain as a biomarker for tumor detection

This is the first study to measure the viscoelastic behavior of tumor tissues using stepwise compression-relaxation testing, and investigate the measured (Δσ-ε) relation between stress drop (Δσ) and applied strain (ε) as a biomarker for tumor detection. Stepwise compression-relaxation testing was implemented via a 2D tactile sensor to measure stress drop at each applied strain of a sample. Pearson correlation analysis was conducted to quantify the measured Δσ-ε relation as slope of stress drop versus applied strain (m=Δσ/ε) and coefficient of determination (R²). The measured results on soft materials revealed no dependency of coefficient of determination on the testing parameters and dependency of slope on them. Three groups of tissues: five mouse breast tumor (BT) tissues ex vivo, two mouse pancreatic tumor (PT) tissues in vivo and six normal tissues, were measured by using different testing parameters. Coefficient of determination was found to show significant difference among the center, edge and outside sites of all the BT tissues, and no difference between the BT outside sites and the normal tissues. Coefficient of determination also revealed significant difference between before and after treatment of the PT tissues, and no difference between the PT tissues after treatment and the normal tissues. Moreover, coefficient of determination of the PT tissues before treatment was found to be significantly different from that of the BT center sites, but slope failed to capture their difference. Dummy tumors made of silicon rubbers were found to behave differently from the native tumors. By removing the need of fitting the time-dependent data with a viscoelastic model, this study offered a time-efficient solution to quantifying the viscosity for tumor detection.

Modeling Ramp-hold Indentation Measurements based on Kelvin-Voigt Fractional Derivative Model

Interpretation of experimental data from micro- and nano-scale indentation testing is highly dependent on the constitutive model selected to relate measurements to mechanical properties. The Kelvin-Voigt Fractional Derivative model (KVFD) offers a compact set of viscoelastic features appropriate for characterizing soft biological materials. This paper provides a set of KVFD solutions for converting indentation testing data acquired for different geometries and scales into viscoelastic properties of soft materials. These solutions, which are mostly in closed-form, apply to ramp-hold relaxation, load-unload and ramp-load creep-testing protocols. We report on applications of these model solutions to macro- and nano-indentation testing of hydrogels, gastric cancer cells and ex vivo breast tissue samples using an Atomic Force Microscope (AFM). We also applied KVFD models to clinical ultrasonic breast data using a compression plate as required for elasticity imaging. Together the results show that KVFD models fit a broad range of experimental data with a correlation coefficient typically R2 > 0.99. For hydrogel samples, estimation of KVFD model parameters from test data using spherical indentation versus plate compression as well as ramp relaxation versus load-unload compression all agree within one standard deviation. Results from measurements made using macro- and nano-scale indentation agree in trend. For gastric cell and ex vivo breast tissue measurements, KVFD moduli are, respectively, 1/3 - 1/2 and 1/6 of the elasticity modulus found from the Sneddon model. In vivo breast tissue measurements yield model parameters consistent with literature results. The consistency of results found for a broad range of experimental parameters suggest the KVFD model is a reliable tool for exploring intrinsic features of the cell/tissue microenvironments.

Tissue perfusion rate estimation with compression-based photoacoustic-ultrasound imaging

Tissue perfusion is essential for transporting blood oxygen and nutrients. Measurement of tissue perfusion rate would have a significant impact in clinical and preclinical arenas. However, there are few techniques to image this important parameter and they typically require contrast agents. A label-free methodology based on tissue compression and imaging with a high-frequency photoacoustic-ultrasound system is introduced for estimating and visualizing tissue perfusion rates. Experiments demonstrate statistically significant differences in depth-resolved perfusion rates in a human subject with various temperature exposure conditions.

Assessing composition and structure of soft biphasic media from Kelvin-Voigt fractional derivative model parameters

Kelvin-Voigt fractional derivative (KVFD) model parameters have been used to describe viscoelastic properties of soft tissues. However, translating model parameters into a concise set of intrinsic mechanical properties related to tissue composition and structure remains challenging. This paper begins by exploring these relationships using a biphasic emulsion materials with known composition. Mechanical properties are measured by analyzing data from two indentation techniques - ramp-stress relaxation and load-unload hysteresis tests. Material composition is predictably correlated with viscoelastic model parameters. Model parameters estimated from the tests reveal that elastic modulus E₀ closely approximates the shear modulus for pure gelatin. Fractional-order parameter α and time constant τ vary monotonically with the volume fraction of the material's fluid component. α characterizes medium fluidity and the rate of energy dissipation, and τ is a viscous time constant. Numerical simulations suggest that the viscous coefficient η is proportional to the energy lost during quasi-static force-displacement cycles, E_A . The slope of E_A versus η is determined by α and the applied indentation ramp time T_r. Experimental measurements from phantom and ex vivo liver data show close agreement with theoretical predictions of the η - E_A relation. The relative error is less than 20% for emulsions 22% for liver. We find that KVFD model parameters form a concise features space for biphasic medium characterization that described time-varying mechanical properties.

Sample, testing and analysis variables affecting liver mechanical properties: A review

Given the critical role of liver mechanics in regulating cell response and directing the development of tissue fibrosis, accurately characterising its mechanical behaviour is of relevance for both diagnostic purposes as well as for tissue engineering and for the development of in-vitro models. Determining and quantifying the mechanical behaviour of soft biological tissues is, however, highly challenging due to their intrinsic labile nature. Indeed, a unique set of values of liver mechanical properties is still lacking to date; testing conditions can significantly affect sample status and hence the measured behaviour and reported results are strongly dependent on the adopted testing method and configuration as well as sample type and status. This review aims at summarising the bulk mechanical properties of liver described in the literature, discussing the possible sources of variation and their implications on the reported results. We distinguish between the intrinsic mechanical behaviour of hepatic tissue, which depends on sample variables, and the measured mechanical properties which also depend on the testing and analysis methods. Finally, the review provides guidelines on tissue preparation and testing conditions for generating reproducible data which can be meaningfully compared across laboratories.

STATEMENT OF SIGNIFICANCE

Soft tissue mechanics is widely investigated, but poorly understood. This review identifies and discusses sample and testing variables which can influence the mechanical behaviour of hepatic tissue and consequently the measured mechanical properties. To encourage the biomaterial community towards more standardized testing of soft tissues and enable comparisons between data from different laboratories, we have established new testing methods and experimental recommendations for sample preparation and testing. The review could be of wide interest to scientists involved in biomaterials research because it addresses and proposes guidelines for several issues related to the mechanical testing of soft tissues whose implications have not been considered together before.