The fractional viscoelastic response of human breast tissue cells

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.

Biomechanical Modelling of Porcine Kidney

In this study, the viscoelastic properties of porcine kidney in the upper, middle and lower poles were investigated using oscillatory shear tests. The viscoelastic properties were extracted in the form of the storage modulus and loss modulus in the frequency and time domain. Measurements were taken as a function of frequency from 0.1 Hz to 6.5 Hz at a shear strain amplitude of 0.01 and as function of strain amplitude from 0.001 to 0.1 at a frequency of 1 Hz. Measurements were also taken in the time domain in response to a step shear strain. Both the frequency and time domain data were fitted to a conventional Standard Linear Solid (SLS) model and a semi-fractional Kelvin-Voigt (SFKV) model with a comparable number of parameters. The SFKV model fitted the frequency and time domain data with a correlation coefficient of 0.99. Although the SLS model well fitted the time domain data and the storage modulus data in the frequency domain, it was not able to capture the variation in loss modulus with frequency with a correlation coefficient of 0.53. A five parameter Maxwell-Wiechert model was able to capture the frequency dependence in storage modulus and loss modulus better than the SLS model with a correlation of 0.85.

Ultrasound Viscosity Imaging in Breast Lesions: A Multicenter Prospective Study

RATIONALE AND OBJECTIVES

To explore and validate the clinical value of ultrasound (US) viscosity imaging in differentiating breast lesions by combining with BI-RADS, and then comparing the diagnostic performances with BI-RADS alone.

MATERIALS AND METHODS

This multicenter, prospective study enrolled participants with breast lesions from June 2021 to November 2022. A development cohort (DC) and validation cohort (VC) were established. Using histological results as reference standard, the viscosity-related parameter with the highest area under the receiver operating curve (AUC) was selected as the optimal one. Then the original BI-RADS would upgrade or not based on the value of this parameter. Finally, the results were validated in the VC and total cohorts. In the DC, VC and total cohorts, all breast lesions were divided into the large lesion, small lesion and overall groups respectively.

RESULTS

A total of 639 participants (mean age, 46 years ± 14) with 639 breast lesions (372 benign and 267 malignant lesions) were finally enrolled in this study including 392 participants in the DC and 247 in the VC. In the DC, the optimal viscosity-related parameter in differentiating breast lesions was calculated to be A'-S2-Vmax, with the AUC of 0.88 (95% CI: 0.84, 0.91). Using > 9.97 Pa.s as the cutoff value, the BI-RADS was then modified. The AUC of modified BI-RADS significantly increased from 0.85 (95% CI: 0.81, 0.88) to 0.91 (95% CI: 0.87, 0.93), 0.85 (95% CI: 0.80, 0.89) to 0.90 (95% CI: 0.85, 0.93) and 0.85 (95% CI: 0.82, 0.87) to 0.90 (95% CI: 0.88, 0.92) in the DC, VC and total cohorts respectively (P < .05 for all).

CONCLUSION

The quantitative viscous parameters evaluated by US viscosity imaging contribute to breast cancer diagnosis when combined with BI-RADS.

Electropneumatic system for the simulation of the pulmonary viscoelastic effect in a mechanical ventilation scenario

The viscoelastic properties of the lung have important implications during respiratory mechanics in terms of lung movement or work of breathing, for example. However, this property has not been well characterized due to several reasons, such as the complex nature of the lung, difficulty accessing its tissues, and the lack of physical simulators that represent viscoelastic effects. This research proposes an electropneumatic system and a method to simulate the viscoelastic effect from temporary forces generated by the opposition of magnetic poles. The study was tested in a mechanical ventilation scenario with inspiratory pause, using a Hamilton-S1 mechanical ventilator (Hamilton Medical) and a simulator of the human respiratory system (SAMI-SII). The implemented system was able to simulate the stress relaxation response of a Standard Linear Solid model in the Maxwell form and showed the capacity to control elastic and viscous parameters independently. To the best of our knowledge, this is the first system incorporated into a physical lung simulator that represents the viscoelastic effect in a mechanical ventilation scenario.

A viscoelastic constitutive model for human femoropopliteal arteries

High failure rates present challenges for surgical and interventional therapies for peripheral artery disease of the femoropopliteal artery (FPA). The FPA's demanding biomechanical environment necessitates complex interactions with repair devices and materials. While a comprehensive understanding of the FPA's mechanical characteristics could improve medical treatments, the viscoelastic properties of these muscular arteries remain poorly understood, and the constitutive model describing their time-dependent behavior is absent. We introduce a new viscoelastic constitutive model for the human FPA grounded in its microstructural composition. The model is capable of detailing the contributions of each intramural component to the overall viscoelastic response. Our model was developed utilizing fractional viscoelasticity and tested using biaxial experimental data with hysteresis and relaxation collected from 10 healthy human subjects aged 57 to 65 and further optimized for high throughput and automation. The model accurately described the experimental data, capturing significant nonlinearity and hysteresis that were particularly pronounced circumferentially, and tracked the contribution of passive smooth muscle cells to viscoelasticity that was twice that of the collagen fibers. The high-throughput parameter estimation procedure we developed included a specialized objective function and modifications to enhance convergence for the common exponential-type fiber laws, facilitating computational implementation. Our new model delineates the time-dependent behavior of human FPAs, which will improve the fidelity of computational simulations investigating device-artery interactions and contribute to their greater physical accuracy. Moreover, it serves as a useful tool to investigate the contribution of arterial constituents to overall tissue viscoelasticity, thereby expanding our knowledge of arterial mechanophysiology. STATEMENT OF SIGNIFICANCE: The demanding biomechanical environment of the femoropopliteal artery (FPA) necessitates complex interactions with repair devices and materials, but the viscoelastic properties of these muscular arteries remain poorly understood with the constitutive model describing their time-dependent behavior being absent. We hereby introduce the first viscoelastic constitutive model for the human FPA grounded in its microstructures. This model was tested using biaxial mechanical data collected from 10 healthy human subjects between the ages of 57 to 65. It can detail the contributions of each intramural component to the overall viscoelastic response, showing that the contribution of passive smooth muscle cells to viscoelasticity is twice that of collagen fibers. The usefulness of this model as tool to better understand arterial mechanophysiology was demonstrated.

Methodologies and models for measuring viscoelastic properties of cancer cells: Towards a universal classification

Different methods and several physical models exist to study cell viscoelasticity with the atomic force microscope (AFM). In search of a robust mechanical classification of cells through AFM, in this work, viscoelastic parameters of the cancer cell lines MDA-MB-231, DU-145, and MG-63 are obtained using two methodologies; through force-distance and force-relaxation curves. Four mechanical models were applied to fit the curves. The results show that both methodologies agree qualitatively on the parameters that quantify elasticity but disagree on the parameters that account for energy dissipation. The Fractional Zener (FZ) model represents well the information given by the Solid Linear Standard and Generalized Maxwell models. The Fractional Kelvin (FK) model concentrates the viscoelastic information mainly in two parameters, which could be an advantage over the other models. Therefore, the FZ and FK models are proposed as the basis for the classification of cancer cells. However, more research using these models is needed to obtain a broader view of the meaning of each parameter and to be able to establish a relationship between the parameters and the cellular components.

Cellular-automaton model for tumor growth dynamics: Virtualization of different scenarios

Mathematical Oncology has emerged as a research field that applies either continuous or discrete models to mathematically describe cancer-related phenomena. Such methods are usually expressed in terms of differential equations, however tumor composition involves specific cellular structure and can demonstrate probabilistic nature, often requiring tailor-made approaches. In this context, cell-based models allow monitoring independent single parameters, which might vary in both time and space. By relying on extant tumor growth models in the literature, this study introduces cellular-automata simulation strategies that admit heterogeneous cell population while capturing both single-cell and cluster-cell behaviors. In this agent-based computational model, tumor cells are limited to follow four possible courses of action, namely: proliferation, migration, apoptosis or quiescence. Despite the apparent simplicity of those actions, the model can represent different complex tumor features depending on parameter settings. This study virtualized five different scenarios, showcasing model capabilities of representing tumor dynamics including alternate dormancy periods, cell death instability and cluster formation. Implementation techniques are also explored together with prospective model expansion towards deterministic features. The proposed stochastic cellular automaton model is able to effectively simulate different scenarios regarding tumor growth effectively, figuring as an interesting tool for in silico modeling, with promising capabilities of expansion to support research in mathematical oncology, thus improving diagnosis tools and/or personalized treatment.

Viscoelastic parameters of invasive breast cancer in correlation with porous structure and elemental analysis data

BACKGROUND AND OBJECTIVE

Invasive ductal carcinoma (IDC) is the most common and aggressive type of breast cancer. As many clinical diagnoses are concerned with the tumor behavior at the compression, the IDC characterization using a compression test is performed in the present study. In the field of tissue characterization, most of the previous studies have focused on healthy and cancerous breast tissues at the cellular level; however, characterization of cancerous tissue at the tissue level has been under-represented, which is the target of the present study.

METHODS

Throughout this article, 18 IDC samples are tested using a ramp-relaxation test. The strain rate in the ramp phase is similar for all samples, whereas the strain level is set at 2,4 and 6%. The experimental stress-time data is interpolated by a viscoelastic model. Two relaxation times, as well as the instantaneous and long-term shear moduli, are calculated for each specimen.

RESULTS

The results show that the long-term and instantaneous shear moduli vary in the range of 0.31-17.03 kPa and 6.03-55.13 kPa, respectively. Our assessment of the viscoelastic parameters is accompanied by observing structural images of the IDCs and inspecting their elemental composition. It is concluded that IDCs with lower Magnesium to Calcium ratio (Mg:Ca) have smaller shear modulus and longer relaxation time, with a p-value of 0.001 and 0.01 for the correlation between Mg:Ca and long-term shear modulus, and Mg:Ca and early relaxation time.

CONCLUSIONS

Our identification of the IDC viscoelastic parameters can contribute to the IDC inspection at the tissue level. The results also provide useful information for modeling of breast cancer.

Recent advances in AFM-based biological characterization and applications at multiple levels

Atomic force microscopy (AFM) has found a wide range of bio-applications in the past few decades due to its ability to measure biological samples in natural environments at a high spatial resolution. AFM has become a key platform in biomedical, bioengineering and drug research fields, enabling mechanical and morphological characterization of live biological systems. Hence, we provide a comprehensive review on recent advances in the use of AFM for characterizing the biomechanical properties of multi-scale biological samples, ranging from molecule, cell to tissue levels. First, we present the fundamental principles of AFM and two AFM-based models for the characterization of biomechanical properties of biological samples, covering key AFM devices and AFM bioimaging as well as theoretical models for characterizing the elasticity and viscosity of biomaterials. Then, we elaborate on a series of new experimental findings through analysis of biomechanics. Finally, we discuss the future directions and challenges. It is envisioned that the AFM technique will enable many remarkable discoveries, and will have far-reaching impacts on bio-related studies and applications in the future.

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.

Fractional viscoelastic models for power-law materials

Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad distribution of time-scales present in their complex internal structure. A promising tool to accurately describe the rheological behaviour of soft materials is fractional calculus. However, its use in the scientific community remains limited due to the unusual notation and non-trivial properties of fractional operators. This review aims to provide a clear and accessible description of fractional viscoelastic models for a broad audience and to demonstrate the ability of these models to deliver a unified approach for the characterisation of power-law materials. The use of a consistent framework for the analysis of rheological data would help classify the empirical behaviours of soft and biological materials, and better understand their response.

Characterizing the viscoelasticity of extra- and intra-parenchymal lung bronchi

Pulmonary disease is known to cause remodeling of tissue structure, resulting in altered viscoelastic properties; yet the foundation for understanding this phenomenon is still nascent and will enable scientific insights regarding lung functionality. In order to characterize the viscoelastic response of pulmonary airways, uniaxial tensile experiments are conducted on porcine extra- and intra-parenchymal bronchial regions, measuring both axially and circumferentially oriented tissue. Anisotropic and heterogeneous effects on preconditioning and hysteresis are substantial, linking to energy dissipation expectancies. Stress relaxation is rheologically modeled using several classical configurations of discrete spring and dashpot elements; among them, Standard Linear Solid (SLS) and Maxwell-Weichart exhibit better fit performance. Enhanced fractional order derivative SLS (FSLS) model is also evaluated through use of a hybrid spring-pot of order α. FSLS outperforms the conventional models, demonstrating superior representation of the stress-relaxation curve's initial value and non-linear asymptotic decent. FSLS parameters exhibit notable orientation- and region-specific values, trending with observed tissue structural constituents, such as glycosaminoglycan and collagen. To the best of our knowledge, this work is the first to characterize proximal and distal bronchial energy efficiency and contextualize tissue biochemical composition in view of experimental measures and viscoelastic trends. Results provide a foundation for future investigations, particularly for understanding the role of viscoelasticity in diseased states.

Fluidity and elasticity form a concise set of viscoelastic biomarkers for breast cancer diagnosis based on Kelvin-Voigt fractional derivative modeling

Cancer progression involves biomechanical changes within transformed cells and the surrounding extracellular matrix (ECM). The viscoelastic features of fluidity and elasticity that are based on a novel Kelvin-Voigt fractional derivative (KVFD) model were found capable of discriminating normal, benign and malignant breast biopsy tissues on the cellular scale. The improved specificity of KVFD model parameters derives from greater accuracy of fitting the entire approaching force-indentation measurement curve ([Formula: see text] > 0.99) compared with traditional elastic models ([Formula: see text] < 0.86). Moreover, model parameters can be interpreted in terms of histopathological features. First, statistical comparisons reveal there are significant differences (p < 0.001) in elasticity E₀, fluidity [Formula: see text], and viscosity [Formula: see text] among healthy, benign, and malignant groups. Malignant breast tissues show low-value, broad-distributions in E₀ and with high fluidity [Formula: see text] as compared with healthy and benign tissues. Second, histograms of E₀ and [Formula: see text] provide distinctive features by fitting to Gaussian mixture (GM) models. The histograms of E₀ and [Formula: see text] are best fit by two kernels GM for malignant tissues, indicating that the cells are soft but with high fluidity and the ECM is stiff but with low fluidity. However, the data suggest one-kernel GM model for benign tissue and a patched uniform distribution for healthy tissue. Third, using fluidity [Formula: see text] as the test statistic, the area under the receiver operator characteristic curve (AUC) is 0.701 ± 0.012 (p < 0.0001) for control versus malignant and 0.706 ± 0.013 (p < 0.0001) for benign versus malignant group. Variations in tissue fluidity and elasticity offer a concise set of viscoelastic biomarkers that correlate well with histopathological features.

Measuring viscoelasticity of soft biological samples using atomic force microscopy

Mechanical properties play important roles at different scales in biology. At the level of a single cell, the mechanical properties mediate mechanosensing and mechanotransduction, while at the tissue and organ levels, changes in mechanical properties are closely connected to disease and physiological processes. Over the past three decades, atomic force microscopy (AFM) has become one of the most widely used tools in the mechanical characterization of soft samples, ranging from molecules, cell organoids and cells to whole tissue. AFM methods can be used to quantify both elastic and viscoelastic properties, and significant recent developments in the latter have been enabled by the introduction of new techniques and models for data analysis. Here, we review AFM techniques developed in recent years for examining the viscoelastic properties of cells and soft gels, describe the main steps in typical data acquisition and analysis protocols, and discuss relevant viscoelastic models and how these have been used to characterize the specific features of cellular and other biological samples. We also discuss recent trends and potential directions for this field.

Viscoelastic properties of doxorubicin-treated HT-29 cancer cells by atomic force microscopy: the fractional Zener model as an optimal viscoelastic model for cells

The malignancy of cancer cells and their response to drug treatments have been traditionally studied using solely their elastic properties. However, the study of the combined viscous and elastic properties provides a richer description of the mechanics of the cell, and achieves a more precise assessment of the effect exerted by anti-cancer treatments. We used an atomic force microscope to obtain the morphological, elastic and viscous properties of HT-29 colorectal cancer cells. Changes in these parameters were observed during exposure of the cells to doxorubicin at different times. The elastic properties were analyzed using the Hertz and Sneddon models. Furthermore, we analyzed the data to study the viscoelasticity of the cells comparing the models known as the standard linear solid, fractional Zener, generalized Maxwell, and power law. A discussion about the optimal model based in the accuracy and physical assumptions for this particular system is included. From the morphological data and viscoelasticity of HT-29 cells exposed to doxorubicin, we found that some parameters were affected differently at shorter or longer exposure times. For instance, the relaxation time suggests a measure of the cell to self-heal and it was observed to increase at shorter exposure times and then to reduce for longer exposure times to the drug. The fractional Zener model better described the mechanical properties of the cell due to the reduced number of parameters and the quality of the fit to experimental data.

Model-Free Rheo-AFM Probes the Viscoelasticity of Tunable DNA Soft Colloids

Atomic force microscopy rheological measurements (Rheo-AFM) of the linear viscoelastic properties of single, charged colloids having a star-like architecture with a hard core and an extended, deformable double-stranded DNA (dsDNA) corona dispersed in aqueous saline solutions are reported. This is achieved by analyzing indentation and relaxation experiments performed on individual colloidal particles by means of a novel model-free Fourier transform method that allows a direct evaluation of the frequency-dependent linear viscoelastic moduli of the system under investigation. The method provides results that are consistent with those obtained via a conventional fitting procedure of the force-relaxation curves based on a modified Maxwell model. The outcomes show a pronounced softening of the dsDNA colloids, which is described by an exponential decay of both the Young's and the storage modulus as a function of the salt concentration within the dispersing medium. The strong softening is related to a critical reduction of the size of the dsDNA corona, down to ≈70% of its size in a salt-free solution. This can be correlated to significant topological changes of the dense star-like polyelectrolyte forming the corona, which are induced by variations in the density profile of the counterions. Similarly, a significant reduction of the stiffness is obtained by increasing the length of the dsDNA chains, which we attribute to a reduction of the DNA density in the outer region of the corona.

The mechanical behavior of brain surrogates manufactured from silicone elastomers

The ongoing conflict against terrorism has resulted in an escalation of blast-induced traumatic brain injuries (bTBI) caused by improvised explosive devices (IEDs). The destructive IEDs create a blast wave that travels through the atmosphere. Blast-induced traumatic brain injuries, attributed to the blast wave, can cause life-threatening injuries and fatalities. This study aims to find a surrogate brain material for assessing the effectiveness of head protection systems designed to mitigate bTBI. Polydimethylsiloxane (PDMS) is considered as the surrogate brain material. The stiffness of PDMS (Sylgard 184, Dow Corning Corp.) can be controlled by varying the ratio of base and curing agent. Cylindrical PDMS specimen with ratios of 1:10, 1:70, and 1:80 were subjected to unconfined compression experiments at linear rates of 5 mm/min, 50 mm/min, and 500 mm/min. A ramp-hold strain profile was used to simulate a stress relaxation experiment. The fractional Zener viscoelastic model was used to describe the stress relaxation response, after optimization of the material constants for the brain surrogate and shock wave exposure brain tissue. The results show that the low cost PDMS can be used as a surrogate brain material to study the dynamic brain response to blast wave exposure.

A viscoelastic nonlinear compressible material model of lung parenchyma - Experiments and numerical identification

Characterizing material properties of lung parenchyma is essential in order to describe and predict the mechanical behavior of the lung in health and disease. Hence, we aim to identify the viscoelastic constitutive behavior of viable lung parenchyma with a particular focus on the nonlinear, compressible, and frequency-dependent material properties. To quantify the viscoelastic material behavior of rat lung parenchyma experimentally, we performed uniaxial tension tests with different frequencies, including the whole range of physiological frequencies, in combination with full-field displacement measurements (a total of 120 tests on 30 samples of 5 rats). By means of these experimental measurements, we identified the material parameters of two viscoelastic material models applicable to large three-dimensional deformations, i.e., the standard linear solid model and the model of fractional viscoelasticity. Our aim is to identify one set of material parameters that describes the whole range of physiological frequencies; therefore, we utilized a coupled inverse analysis, which equally incorporates all different tensile tests performed on one sample. The model most suitable for the description of the viscoelastic, nonlinear, and compressible material behavior of viable rat lung parenchyma is the strain energy function [Formula: see text] in combination with the model of fractional viscoelasticity (τ=0.06454s,α=0.5378, and β=1.856). This material model was validated to describe the complex nonlinear and compressible viscoelastic material behavior of lung parenchyma and can be utilized in finite element simulations of the whole range of physiological frequencies. Based on this model, it will be possible to quantify the stresses and strains of lung tissue during spontaneous and artificial breathing more reliable in the future.

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.

Atomic Force Microscopy in Characterizing Cell Mechanics for Biomedical Applications: A Review

Cell mechanics is a novel label-free biomarker for indicating cell states and pathological changes. The advent of atomic force microscopy (AFM) provides a powerful tool for quantifying the mechanical properties of single living cells in aqueous conditions. The wide use of AFM in characterizing cell mechanics in the past two decades has yielded remarkable novel insights in understanding the development and progression of certain diseases, such as cancer, showing the huge potential of cell mechanics for practical applications in the field of biomedicine. In this paper, we reviewed the utilization of AFM to characterize cell mechanics. First, the principle and method of AFM single-cell mechanical analysis was presented, along with the mechanical responses of cells to representative external stimuli measured by AFM. Next, the unique changes of cell mechanics in two types of physiological processes (stem cell differentiation, cancer metastasis) revealed by AFM were summarized. After that, the molecular mechanisms guiding cell mechanics were analyzed. Finally the challenges and future directions were discussed.

Measuring nanoscale viscoelastic parameters of cells directly from AFM force-displacement curves

Force-displacement (F-Z) curves are the most commonly used Atomic Force Microscopy (AFM) mode to measure the local, nanoscale elastic properties of soft materials like living cells. Yet a theoretical framework has been lacking that allows the post-processing of F-Z data to extract their viscoelastic constitutive parameters. Here, we propose a new method to extract nanoscale viscoelastic properties of soft samples like living cells and hydrogels directly from conventional AFM F-Z experiments, thereby creating a common platform for the analysis of cell elastic and viscoelastic properties with arbitrary linear constitutive relations. The method based on the elastic-viscoelastic correspondence principle was validated using finite element (FE) simulations and by comparison with the existed AFM techniques on living cells and hydrogels. The method also allows a discrimination of which viscoelastic relaxation model, for example, standard linear solid (SLS) or power-law rheology (PLR), best suits the experimental data. The method was used to extract the viscoelastic properties of benign and cancerous cell lines (NIH 3T3 fibroblasts, NMuMG epithelial, MDA-MB-231 and MCF-7 breast cancer cells). Finally, we studied the changes in viscoelastic properties related to tumorigenesis including TGF-β induced epithelial-to-mesenchymal transition on NMuMG cells and Syk expression induced phenotype changes in MDA-MB-231 cells.

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.

Single-Cell Mechanical Characteristics Analyzed by Multiconstriction Microfluidic Channels

A microfluidic device composed of variable numbers of multiconstriction channels is reported in this paper to differentiate a human breast cancer cell line, MDA-MB-231, and a nontumorigenic human breast cell line, MCF-10A. Differences between their mechanical properties were assessed by comparing the effect of single or multiple relaxations on their velocity profiles which is a novel measure of their deformation ability. Videos of the cells were recorded via a microscope using a smartphone, and imported to a tracking software to gain the position information on the cells. Our results indicated that a multiconstriction channel design with five deformation (50 μm in length, 10 μm in width, and 8 μm in height) separated by four relaxation (50 μm in length, 40 μm in width, and 30 μm in height) regions was superior to a single deformation design in differentiating MDA-MB-231 and MCF-10A cells. Velocity profile criteria can achieve a differentiation accuracy around 95% for both MDA-MB-231 and MCF-10A cells.

The impact of sphingosine kinase inhibitor-loaded nanoparticles on bioelectrical and biomechanical properties of cancer cells

Cancer progression and physiological changes within the cells are accompanied by alterations in the biophysical properties. Therefore, the cell biophysical properties can serve as promising markers for cancer detection and physiological activities. To aid in the investigation of the biophysical markers of cells, a microfluidic chip has been developed which consists of a constriction channel and embedded microelectrodes. Single-cell impedance magnitudes at four frequencies and entry and travel times are measured simultaneously during their transit through the constriction channel. This microchip provides a high-throughput, label-free, automated assay to identify biophysical signatures of malignant cells and monitor the therapeutic efficacy of drugs. Here, we monitored the dynamic cellular biophysical properties in response to sphingosine kinase inhibitors (SphKIs), and compared the effectiveness of drug delivery using poly lactic-co-glycolic acid (PLGA) nanoparticles (NPs) loaded with SphKIs versus conventional delivery. Cells treated with SphKIs showed significantly higher impedance magnitudes at all four frequencies. The bioelectrical parameters extracted using a model also revealed that the highly aggressive breast cells treated with SphKIs shifted electrically towards that of a less malignant phenotype; SphKI-treated cells exhibited an increase in cell-channel interface resistance and a significant decrease in specific membrane capacitance. Furthermore, SphKI-treated cells became slightly more deformable as measured by a decrease in their channel entry and travel times. We observed no significant difference in the bioelectrical changes produced by SphKI delivered conventionally or with NPs. However, NPs-packaged delivery of SphKI decreased the cell deformability. In summary, this study showed that while the bioelectrical properties of the cells were dominantly affected by SphKIs, the biomechanical properties were mainly changed by the NPs.

Single cell metastatic phenotyping using pulsed nanomechanical indentations

The existing approach to characterize cell biomechanical properties typically utilizes switch-like models of mechanotransduction in which cell responses are analyzed in response to a single nanomechanical indentation or a transient pulsed stress. Although this approach provides effective descriptors at population-level, at a single-cell-level, there are significant overlaps in the biomechanical descriptors of non-metastatic and metastatic cells which precludes the use of biomechanical markers for single cell metastatic phenotyping. This study presents a new promising marker for biosensing metastatic and non-metastatic cells at a single-cell-level using the effects of a dynamic microenvironment on the biomechanical properties of cells. Two non-metastatic and two metastatic epithelial breast cell lines are subjected to a pulsed stresses regimen exerted by atomic force microscopy. The force-time data obtained for the cells revealed that the non-metastatic cells increase their resistance against deformation and become more stiffened when subjected to a series of nanomechanical indentations. On the other hand, metastatic cells become slightly softened when their mechanical microenvironment is subjected to a similar dynamical changes. This distinct behavior of the non-metastatic and metastatic cells to the pulsed stresses paradigm provided a signature for single-cell-level metastatic phenotyping with a high confidence level of ∼95%.

Sub-cellular force microscopy in single normal and cancer cells

This work investigates the biomechanical properties of sub-cellular structures of breast cells using atomic force microscopy (AFM). The cells are modeled as a triple-layered structure where the Generalized Maxwell model is applied to experimental data from AFM stress-relaxation tests to extract the elastic modulus, the apparent viscosity, and the relaxation time of sub-cellular structures. The triple-layered modeling results allow for determination and comparison of the biomechanical properties of the three major sub-cellular structures between normal and cancerous cells: the up plasma membrane/actin cortex, the mid cytoplasm/nucleus, and the low nuclear/integrin sub-domains. The results reveal that the sub-domains become stiffer and significantly more viscous with depth, regardless of cell type. In addition, there is a decreasing trend in the average elastic modulus and apparent viscosity of the all corresponding sub-cellular structures from normal to cancerous cells, which becomes most remarkable in the deeper sub-domain. The presented modeling in this work constitutes a unique AFM-based experimental framework to study the biomechanics of sub-cellular structures.