Mechanical and failure properties of single attached cells under compression

PneumaOCT: Pneumatic optical coherence tomography endoscopy for targeted distortion-free imaging in tortuous and narrow internal lumens

The complex anatomy of internal luminal organs, like bronchioles, poses challenges for endoscopic optical coherence tomography (OCT). These challenges include limited steerability for targeted imaging and nonuniform rotation distortion (NURD) with proximal scanning. Using rotary micromotors for distal scanning could address NURD but raises concerns about electrical safety and costs. We present pneumaOCT, the first pneumatic OCT endoscope, comprising a steerable catheter with a soft pneumatic actuator and an imaging probe with a miniature pneumatic turbine. With a diameter of 2.8 mm, pneumaOCT allows for a bending angle of up to 237°, facilitating navigation through narrow turns. The pneumatic turbine enables adjustable imaging speeds from 51 to 446 revolutions per second. We demonstrate the pneumaOCT in vivo imaging of mouse esophagus and colon, as well as targeted and distortion-free imaging of peripheral bronchioles in a bronchial phantom and a porcine lung. This advancement substantially improves endoscopic OCT for navigational imaging in curved and narrow lumens.

Assessment by finite element analysis modelling of tissue strains associated with the use of two different nasogastric tube securement devices

OBJECTIVES

Nasogastric tube use can lead to pressure injury. Some nasogastric tube securement devices (NG-SD) include hard plastic components. In the current study, we assessed the differences in strain profiles for two NG-SD, one with hard segments and one without hard segments, using finite element analysis (FEA) to measure strain and deformation occurring at the nasogastric tube-tissue interface.

METHODS

FEA in silico models of devices were based on device mechanical test data and clinically relevant placements. Peak strain values were determined by modelling different scenarios using Abaqus software whereby the tubing is moved during wear.

RESULTS

The modelling showed peak strains ranging from 52% to 434% for the two NG-SD depending on the tubing placement and device type. Peak strain was always higher for the hard plastic device. Tissue strain energy was a minimum of 133.8 mJ for the NG-SD with no hard parts and a maximum of 311.6 mJ for the NG-SD with hard parts.

CONCLUSIONS

This study provided evidence through in silico modelling that NG-SD without hard components may impart less strain and stress to tissues which may provide an option for tube securement that is less likely to cause medical device-related pressure injury.

Mechanical models and measurement methods of solid stress in tumors

In addition to genetic mutations, biomechanical factors also affect the structures and functions of the tumors during tumor growth, including solid stress, interstitial fluid pressure, stiffness, and microarchitecture. Solid stress affects tumors by compressing cancer and stromal cells and deforming blood and lymphatic vessels which reduce supply of oxygen, nutrients and drug delivery, making resistant to treatment. Researchers simulate the stress by creating mechanical models both in vitro and in vivo. Cell models in vitro are divided into two dimensions (2D) and three dimensions (3D). 2D models are simple to operate but exert pressure on apical surface of the cells. 3D models, the multicellular tumor spheres, are more consistent with the actual pathological state in human body. However, the models are more difficult to establish compared with the 2D models. Besides, the procedure of the animal models in vivo is even more complex and tougher to operate. Then, researchers challenged to quantify the solid stress through some measurement methods. We compared the advantages and limitations of these models and methods, which may help to explore new therapeutic targets for normalizing the tumor's physical microenvironment. KEY POINTS: •This is the first review to conclude the mechanical models and measurement methods in tumors. •The merit and demerit of these models and methods are compared. •Insights into further models are discussed.

Assessing friction and damage of cell monolayers on soft substrates in vitro

In the area of surgical applications, understanding the interaction between medical device materials and tissue is important since this interaction may cause complications. The interaction often consists of a cell monolayer touching the medical device that can be mimicked in vitro. Prominent examples of this are contact lenses, where epithelial cells interact with the contact lens, or stents and catheters, which are in contact with endothelial cells. To investigate those interactions, in previous studies, expensive microtribometers were used to avoid pressures in the contact area far beyond physiologically relevant levels. Here, we aim to present a new methodology that is cost- and time-efficient, more accessible than those used previously and allows for the application of more realistic pressures, while permitting a quantification of the damage caused to the monolayer. For this, a soft polydimethylsiloxane is employed that better mimics the mechanical properties of blood vessels than materials used in other studies. Furthermore, a technique to account for misalignments within the experiment set-up is presented. This is carried out using the raw spatial and force data recorded by the tribometer and adjusting for misalignments. The methodology is demonstrated using an endothelial cell (human umbilical vein endothelial cells) monolayer.

A Simulation of the Mechanical Testing of the Cell Membrane and Cytoskeleton

Cell models play a crucial role in analyzing the mechanical response of cells and quantifying cellular damage incurred during micromanipulation. While traditional models can capture the overall mechanical behavior of cells, they often lack the ability to discern among distinct cellular components. Consequently, by employing dissipative particle dynamics, this study constructed a triangular network-like representation of the cell membrane along with cross-linked cytoskeletal chains. The mechanical properties of both the membrane and cytoskeleton were then analyzed through a series of simulated mechanical tests, validated against real-world experiments. The investigation utilized particle-tracking rheology to monitor changes in the mean square displacements of membrane particles over time, facilitating the analysis of the membrane's storage and loss moduli. Additionally, the cytoskeletal network's storage and loss moduli were examined via a double-plate oscillatory shear experiment. The simulation results revealed that both the membrane and cytoskeleton exhibit viscoelastic behavior, as evidenced by the power-law dependency of their storage and loss moduli on frequency. Furthermore, indentation and microinjection simulations were conducted to examine the overall mechanical properties of cells. In the indentation experiments, an increase in the shear modulus of the membrane's WLCs correlated with a higher Young's modulus for the entire cell. Regarding the microinjection experiment, augmenting the microinjection speed resulted in reduced deformation of the cell at the point of membrane rupture and a lower percentage of high strain.

An ex vivo animal model to study the effect of transverse mechanical loading on skeletal muscle

In many populations like wheelchair and prosthetic users, the soft tissue is subject to excessive or repetitive loading, making it prone to Deep Tissue Injury (DTI). To study the skeletal muscle response to physical stress, numerous in vitro and in vivo models exist. Yet, accuracy, variability, and ethical considerations pose significant trade-offs. Here, we present an ex vivo approach to address these limitations and offer additional quantitative information on cellular damage. In this study, skeletal muscle tissue from Sprague Dawley rats was isolated and transversely loaded. Histological analysis and fluorescence staining demonstrated that the setup was suitable to keep the tissue alive throughout the experimental procedure. Mechanically induced cell damage was readily distinguishable through morphological changes and uptake of a membrane impermeable dye. Our comparably simple experimental setup can be adapted to different loading conditions and tissues to assess the cell response to mechanical loading in future studies.

Magnetic soft microfiberbots for robotic embolization

Cerebral aneurysms and brain tumors are leading life-threatening diseases worldwide. By deliberately occluding the target lesion to reduce the blood supply, embolization has been widely used clinically to treat cerebral aneurysms and brain tumors. Conventional embolization is usually performed by threading a catheter through blood vessels to the target lesion, which is often limited by the poor steerability of the catheter in complex neurovascular networks, especially in submillimeter regions. Here, we propose magnetic soft microfiberbots with high steerability, reliable maneuverability, and multimodal shape reconfigurability to perform robotic embolization in submillimeter regions via a remote, untethered, and magnetically controllable manner. Magnetic soft microfiberbots were fabricated by thermal drawing magnetic soft composite into microfibers, followed by magnetizing and molding procedures to endow a helical magnetic polarity. By controlling magnetic fields, magnetic soft microfiberbots exhibit reversible elongated/aggregated shape morphing and helical propulsion in flow conditions, allowing for controllable navigation through complex vasculature and robotic embolization in submillimeter regions. We performed in vitro embolization of aneurysm and tumor in neurovascular phantoms and in vivo embolization of a rabbit femoral artery model under real-time fluoroscopy. These studies demonstrate the potential clinical value of our work, paving the way for a robotic embolization scheme in robotic settings.

Adaptive wireless millirobotic locomotion into distal vasculature

Microcatheters have enabled diverse minimally invasive endovascular operations and notable health benefits compared with open surgeries. However, with tortuous routes far from the arterial puncture site, the distal vascular regions remain challenging for safe catheter access. Therefore, we propose a wireless stent-shaped magnetic soft robot to be deployed, actively navigated, used for medical functions, and retrieved in the example M4 segment of the middle cerebral artery. We investigate shape-adaptively controlled locomotion in phantoms emulating the physiological conditions here, where the lumen diameter shrinks from 1.5 mm to 1 mm, the radius of curvature of the tortuous lumen gets as small as 3 mm, the lumen bifurcation angle goes up to 120°, and the pulsatile flow speed reaches up to 26 cm/s. The robot can also withstand the flow when the magnetic actuation is turned off. These locomotion capabilities are confirmed in porcine arteries ex vivo. Furthermore, variants of the robot could release the tissue plasminogen activator on-demand locally for thrombolysis and function as flow diverters, initiating promising therapies towards acute ischemic stroke, aneurysm, arteriovenous malformation, dural arteriovenous fistulas, and brain tumors. These functions should facilitate the robot's usage in new distal endovascular operations.

In silico stress fibre content affects peak strain in cytoplasm and nucleus but not in the membrane for uniaxial substrate stretch

Existing in silico models for single cell mechanics feature limited representations of cytoskeletal structures that contribute substantially to the mechanics of a cell. We propose a micromechanical hierarchical approach to capture the mechanical contribution of actin stress fibres. For a cell-specific fibroblast geometry with membrane, cytoplasm and nucleus, the Mori-Tanaka homogenization method was employed to describe cytoplasmic inhomogeneities and constitutive contribution of actin stress fibres. The homogenization was implemented in a finite element model of the fibroblast attached to a substrate through focal adhesions. Strain in cell membrane, cytoplasm and nucleus due to uniaxial substrate stretch was assessed for different stress fibre volume fractions and different elastic modulus of the substrate. A considerable decrease of the peak strain with increasing stress fibre content was observed in cytoplasm and nucleus but not the membrane, whereas the peak strain in cytoplasm, nucleus and membrane increased for increasing elastic modulus of the substrate. Finite element mesh of reconstructed human fibroblast and intracellular strain distribution in cell subjected to substrate stretch.

Molecular cancer cell responses to solid compressive stress and interstitial fluid pressure

Alterations to the mechanical properties of the microenvironment are a hallmark of cancer. Elevated mechanical stresses exist in many solid tumors and elicit responses from cancer cells. Uncontrolled growth in confined environments gives rise to elevated solid compressive stress on cancer cells. Recruitment of leaky blood vessels and an absence of functioning lymphatic vessels causes a rise in the interstitial fluid pressure. Here we review the role of the cancer cell cytoskeleton and the nucleus in mediating both the initial and adaptive cancer cell response to these two types of mechanical stresses. We review how these mechanical stresses alter cancer cell functions such as proliferation, apoptosis, and migration.

Finite element analysis reveals an important role for cell morphology in response to mechanical compression

Mechanical loading naturally controls cell phenotype, development, motility and various other biological functions; however, prolonged or substantial loading can cause cell damage and eventual death. Loading-induced mechanobiological and mechanostructural responses of different cell types affect their morphology and the internal architecture and the mechanics of the cellular components. Using single, mesenchymal stem cells, we have developed a cell-specific three-dimensional finite-element model; cell models were developed from phase-contrast microscopy images. This allowed us to evaluate the mechanostructural response of the naturally occurring variety of cell morphologies to increase sustained compressive loading. We focus on the morphology of the cytoplasm and the nucleus, as the main mechanically responsive elements, and evaluate formation of tensional strains and area changes in cells undergoing increasing uniaxial compressions. Here, we study mesenchymal stem cells as a model, due to their important role in tissue engineering and regenerative medicine; the method and findings are, however, applicable to any cell type. We observe variability in the cell responses to compression, which correlate directly with the morphology of the cells. Specifically, in cells with or without elongated protrusions (i.e., lamellipodia) tensional strains were, respectively, distributed mostly in the thin extensions or concentrated around the stiff nucleus. Thus, through cell-specific computational modeling of mechanical loading we have identified an underlying cause for stiffening (by actin recruitment) along the length of lamellipodia as well as a role for cell morphology in inducing cell-to-cell variability in mechanostructural response to loading.

Modeling tissue-selective cavitation damage

The destructive growth and collapse of cavitation bubbles are used for therapeutic purposes in focused ultrasound procedures and can contribute to tissue damage in traumatic injuries. Histotripsy is a focused ultrasound procedure that relies on controlled cavitation to homogenize soft tissue. Experimental studies of histotripsy cavitation have shown that the extent of ablation in different tissues depends on tissue mechanical properties and waveform parameters. Variable tissue susceptibility to the large stresses, strains, and strain rates developed by cavitation bubbles has been suggested as a basis for localized liver tumor treatments that spare large vessels and bile ducts. However, field quantities developed within microns of cavitation bubbles are too localized and transient to measure in experiments. Previous numerical studies have attempted to circumvent this challenge but made limited use of realistic tissue property data. In this study, numerical simulations are used to calculate stress, strain, and strain rate fields produced by bubble oscillation under histotripsy forcing in a variety of tissues with literature-sourced viscoelastic and acoustic properties. Strain field calculations are then used to predict a theoretical damage radius using tissue ultimate strain data. Simulation results support the hypothesis that differential tissue responses could be used to design tissue-selective treatments. Results agree with studies correlating tissue ultimate fractional strain with resistance to histotripsy ablation and are also consistent with experiments demonstrating smaller lesion size under exposure to higher frequency waveforms. Methods presented in this study provide an approach for modeling tissue-selective cavitation damage in general.

A shear assay study of single normal/breast cancer cell deformation and detachment from poly-di-methyl-siloxane (PDMS) surfaces

This paper presents the results of a combined experimental and analytical/computational study of viscoelastic cell deformation and detachment from poly-di-methyl-siloxane (PDMS) surfaces. Fluid mechanics and fracture mechanics concepts are used to model the detachment of biological cells observed under shear assay conditions. The analytical and computational models are used to compute crack driving forces, which are then related to crack extension during the detachment of normal breast cells and breast cancer cells from PDMS surfaces that are relevant to biomedical implants. The interactions between cells and the extracellular matrix, or the extracellular matrix and the PDMS substrate, are then characterized using force microscopy measurements of the pull-off forces that are used to determine the adhesion energies. Finally, fluorescence microscopy staining of the cytosketelal structures (actin, micro-tubulin and cyto-keratin), transmembrane proteins (vimentin) and the ECM structures (Arginin Glycine Aspartate - RGD) is used to show that the detachment of cells during the shear assay experiments occurs via interfacial cracking between (between the ECM and the cell membranes) with a high incidence of crack bridging by transmembrane vinculin structures that undergo pull-out until they detach from the actin cytoskeletal structure. The implications of the results are discussed for the design of interfaces that are relevant to implantable biomedical devices and normal/cancer tissue.

Mechanical principles of nuclear shaping and positioning

Positioning and shaping the nucleus represents a mechanical challenge for the migrating cell because of its large size and resistance to deformation. Cells shape and position the nucleus by transmitting forces from the cytoskeleton onto the nuclear surface. This force transfer can occur through specialized linkages between the nuclear envelope and the cytoskeleton. In response, the nucleus can deform and/or it can move. Nuclear movement will occur when there is a net differential in mechanical force across the nucleus, while nuclear deformation will occur when mechanical forces overcome the mechanical resistance of the various structures that comprise the nucleus. In this perspective, we review current literature on the sources and magnitude of cellular forces exerted on the nucleus, the nuclear envelope proteins involved in transferring cellular forces, and the contribution of different nuclear structural components to the mechanical response of the nucleus to these forces.

Are elastic moduli of biological cells depth dependent or not? Another explanation using a contact mechanics model with surface tension

Atomic force microscopy (AFM) has become the most commonly used tool to measure the mechanical properties of biological cells. In AFM indentation experiments, the Hertz and Sneddon models of contact mechanics are usually adopted to extract the elastic modulus by analyzing the load-indent depth curves for spherical and conical tips, respectively. However, the effects of surface tension, neglected in existing contact models, become more significant in indentation responses due to the lower elastic moduli of living cells. Here, we present two simple yet robust relations between load and indent depth considering surface tension effects for spherical and conical indentations, through dimensional analysis and finite element simulations. When the indent depth is smaller than the intrinsic length defined as the ratio of surface tension to elastic modulus, the elastic modulus obtained by classical contact mechanics theories would be overestimated. Contrary to the majority of reported results, we find that the elastic modulus of a cell could be independent of indent depths if surface tension is taken into account. Our model seems to be in agreement with experimental data available. A comprehensive comparison will be done in the future.

Micropipette aspiration method for characterizing biological materials with surface energy

Many soft biological tissues possess a considerable surface stress, which plays a significant role in their biophysical functions, but most previous methods for characterizing their mechanical properties have neglected the effects of surface stress. In this work, we investigate the micropipette aspiration method to measure the mechanical properties of soft tissues and cells with surface effects. The neo-Hookean constitutive model is adopted to describe the hyperelasticity of the measured biological material, and the surface effect is taken into account by the finite element method. It is found that when the pipette radius or aspiration length is comparable to the elastocapillary length, surface energy may distinctly alter the aspiration response. Generally, both the aspiration length and the bulk normal stress decrease with increasing surface energy, and thus neglecting the surface energy would lead to an overestimation of elastic modulus. Through dimensional analysis and numerical simulations, we provide an explicit relation between the imposed pressure and the aspiration length. This method can be applied to determine the mechanical properties of soft biological tissues and organs, e.g., livers, tumors and embryos.

Frontiers of Complex Disease Mechanisms: Membrane Surface Tension May Link Genotype to Phenotype in Glaucoma

Although many monogenic diseases are understood based upon structural changes of gene products, less progress has been made concerning polygenic disease mechanisms. This article presents a new interdisciplinary approach to understand complex diseases, especially their genetic polymorphisms. I focus upon primary open angle glaucoma (POAG). Although elevated intraocular pressure (IOP) and oxidative stress are glaucoma hallmarks, the linkages between these factors and cell death are obscure. Reactive oxygen species (ROS) promote the formation of oxidatively truncated phosphoglycerides (OTP), free fatty acids, lysophosphoglycerides, oxysterols, and other chemical species that promote membrane disruption and decrease membrane surface tension. Several POAG-linked gene polymorphisms identify proteins that manage damaged lipids and/or influence membrane surface tension. POAG-related genes expected to participate in these processes include: ELOVL5, ABCA1, APOE4, GST, CYP46A1, MYOC, and CAV. POAG-related gene products are expected to influence membrane surface tension, strength, and repair. I propose that heightened IOP overcomes retinal ganglion cell (RGC) membrane compressive strength, weakened by damaged lipid accumulation, to form pores. The ensuing structural failure promotes apoptosis and blindness. The linkage between glaucoma genotype and phenotype is mediated by physical events. Force balancing between the IOP and compressive strength regulates pore nucleation; force balancing between pore line tension and membrane surface tension regulates pore growth. Similar events may contribute to traumatic brain injury, Alzheimer's disease, and macular degeneration.

Cellular mechanosensitivity to substrate stiffness decreases with increasing dissimilarity to cell stiffness

Computational modelling has received increasing attention to investigate multi-scale coupled problems in micro-heterogeneous biological structures such as cells. In the current study, we investigated for a single cell the effects of (1) different cell-substrate attachment (2) and different substrate modulus [Formula: see text] on intracellular deformations. A fibroblast was geometrically reconstructed from confocal micrographs. Finite element models of the cell on a planar substrate were developed. Intracellular deformations due to substrate stretch of [Formula: see text], were assessed for: (1) cell-substrate attachment implemented as full basal contact (FC) and 124 focal adhesions (FA), respectively, and [Formula: see text]140 KPa and (2) [Formula: see text], 140, 1000, and 10,000 KPa, respectively, and FA attachment. The largest strains in cytosol, nucleus and cell membrane were higher for FC (1.35[Formula: see text], 0.235[Formula: see text] and 0.6[Formula: see text]) than for FA attachment (0.0952[Formula: see text], 0.0472[Formula: see text] and 0.05[Formula: see text]). For increasing [Formula: see text], the largest maximum principal strain was 4.4[Formula: see text], 5[Formula: see text], 5.3[Formula: see text] and 5.3[Formula: see text] in the membrane, 9.5[Formula: see text], 1.1[Formula: see text], 1.2[Formula: see text] and 1.2[Formula: see text] in the cytosol, and 4.5[Formula: see text], 5.3[Formula: see text], 5.7[Formula: see text] and 5.7[Formula: see text] in the nucleus. The results show (1) the importance of representing FA in cell models and (2) higher cellular mechanical sensitivity for substrate stiffness changes in the range of cell stiffness. The latter indicates that matching substrate stiffness to cell stiffness, and moderate variation of the former is very effective for controlled variation of cell deformation. The developed methodology is useful for parametric studies on cellular mechanics to obtain quantitative data of subcellular strains and stresses that cannot easily be measured experimentally.

Mechanical Criterion for the Rupture of a Cell Membrane under Compression

We investigate the mechanical conditions leading to the rupture of the plasma membrane of an endothelial cell subjected to a local, compressive force. Membrane rupture is induced by tilted microindentation, a technique used to perform mechanical measurements on adherent cells. In this technique, the applied force can be deduced from the measured horizontal displacement of a microindenter's tip, as imaged with an inverted microscope and without the need for optical sensors to measure the microindenter's deflection. We show that plasma membrane rupture of endothelial cells occurs at a well-defined value of the applied compressive stress. As a point of reference, we use numerical simulations to estimate the magnitude of the compressive stresses exerted on endothelial cells during the deployment of a stent.

An integrated enhancement and reconstruction strategy for the quantitative extraction of actin stress fibers from fluorescence micrographs

BACKGROUND

The stress fibers are prominent organization of actin filaments that perform important functions in cellular processes such as migration, polarization, and traction force generation, and whose collective organization reflects the physiological and mechanical activities of the cells. Easily visualized by fluorescence microscopy, the stress fibers are widely used as qualitative descriptors of cell phenotypes. However, due to the complexity of the stress fibers and the presence of other actin-containing cellular features, images of stress fibers are relatively challenging to quantitatively analyze using previously developed approaches, requiring significant user intervention. This poses a challenge for the automation of their detection, segmentation, and quantitative analysis.

RESULT

Here we describe an open-source software package, SFEX (Stress Fiber Extractor), which is geared for efficient enhancement, segmentation, and analysis of actin stress fibers in adherent tissue culture cells. Our method made use of a carefully chosen image filtering technique to enhance filamentous structures, effectively facilitating the detection and segmentation of stress fibers by binary thresholding. We subdivided the skeletons of stress fiber traces into piecewise-linear fragments, and used a set of geometric criteria to reconstruct the stress fiber networks by pairing appropriate fiber fragments. Our strategy enables the trajectory of a majority of stress fibers within the cells to be comprehensively extracted. We also present a method for quantifying the dimensions of the stress fibers using an image gradient-based approach. We determine the optimal parameter space using sensitivity analysis, and demonstrate the utility of our approach by analyzing actin stress fibers in cells cultured on various micropattern substrates.

CONCLUSION

We present an open-source graphically-interfaced computational tool for the extraction and quantification of stress fibers in adherent cells with minimal user input. This facilitates the automated extraction of actin stress fibers from fluorescence images. We highlight their potential uses by analyzing images of cells with shapes constrained by fibronectin micropatterns. The method we reported here could serve as the first step in the detection and characterization of the spatial properties of actin stress fibers to enable further detailed morphological analysis.

On the determination of elastic moduli of cells by AFM based indentation

The atomic force microscopy (AFM) has been widely used to measure the mechanical properties of biological cells through indentations. In most of existing studies, the cell is supposed to be linear elastic within the small strain regime when analyzing the AFM indentation data. However, in experimental situations, the roles of large deformation and surface tension of cells should be taken into consideration. Here, we use the neo-Hookean model to describe the hyperelastic behavior of cells and investigate the influence of surface tension through finite element simulations. At large deformation, a correction factor, depending on the geometric ratio of indenter radius to cell radius, is introduced to modify the force-indent depth relation of classical Hertzian model. Moreover, when the indent depth is comparable with an intrinsic length defined as the ratio of surface tension to elastic modulus, the surface tension evidently affects the indentation response, indicating an overestimation of elastic modulus by the Hertzian model. The dimensionless-analysis-based theoretical predictions, which include both large deformation and surface tension, are in good agreement with our finite element simulation data. This study provides a novel method to more accurately measure the mechanical properties of biological cells and soft materials in AFM indentation experiments.

Modeling of the axon membrane skeleton structure and implications for its mechanical properties

Super-resolution microscopy recently revealed that, unlike the soma and dendrites, the axon membrane skeleton is structured as a series of actin rings connected by spectrin filaments that are held under tension. Currently, the structure-function relationship of the axonal structure is unclear. Here, we used atomic force microscopy (AFM) to show that the stiffness of the axon plasma membrane is significantly higher than the stiffnesses of dendrites and somata. To examine whether the structure of the axon plasma membrane determines its overall stiffness, we introduced a coarse-grain molecular dynamics model of the axon membrane skeleton that reproduces the structure identified by super-resolution microscopy. Our proposed computational model accurately simulates the median value of the Young’s modulus of the axon plasma membrane determined by atomic force microscopy. It also predicts that because the spectrin filaments are under entropic tension, the thermal random motion of the voltage-gated sodium channels (Na_v), which are bound to ankyrin particles, a critical axonal protein, is reduced compared to the thermal motion when spectrin filaments are held at equilibrium. Lastly, our model predicts that because spectrin filaments are under tension, any axonal injuries that lacerate spectrin filaments will likely lead to a permanent disruption of the membrane skeleton due to the inability of spectrin filaments to spontaneously form their initial under-tension configuration.

Super-resolution microscopy has suggested that the actin cytoskeleton structure differ between various neuronal subcompartments. To determine the possible implication of the differing actin cytoskeleton structure, we determined the stiffness of the plasma membrane of neuronal subcompartments using atomic force microscopy (AFM). We found that axons are almost ~6 fold stiffer than the soma and ~2 fold stiffer than dendrites. By using a particle-based model for the surface membrane skeleton of the axon that comprises actin rings connected with spring filaments to represent the axonal structure, we show that regions neighboring actin rings are stiffer than areas between these rings. In these in between sub-regions, the spectrin filaments determine stiffness. Our modeling also shows that because the spectrin filaments are under tension, the thermal jitter of the actin-associated ankyrin particles, connected to the middle area of spectrin filaments, is minimal. As a result, we propose that the sodium channels bound to ankyrin particles will maintain an ordered distribution along the axon. We also predict that laceration of the spectrin filaments due to injury will cause a permanent damage to the axon since spontaneous repair of the spectrin network is not possible as spectrin filaments are under entropic tension.

Computational simulation of static/cyclic cell stimulations to investigate mechanical modulation of an individual mesenchymal stem cell using confocal microscopy

It has been found that cells react to mechanical stimuli, while the type and magnitude of these cells are different in various physiological and pathological conditions. These stimuli may affect cell behaviors via mechanotransduction mechanisms. The aim of this study is to evaluate mechanical responses of a mesenchymal stem cell (MSC) to a pressure loading using finite elements method (FEM) to clarify procedures of MSC mechanotransduction. The model is constructed based on an experimental set up in which statics and cyclic compressive loads are implemented on a model constructed from a confocal microscopy 3D image of a stem cell. Both of the applied compressive loads are considered in the physiological loading regimes. Moreover, a viscohyperelastic material model was assumed for the cell through which the finite elements simulation anticipates cell behavior based on strain and stress distributions in its components. As a result, high strain and stress values were captured from the viscohyperelastic model because of fluidic behavior of cytosol when compared with the obtained results through the hyperelastic models. It can be concluded that the generated strain produced by cyclic pressure is almost 8% higher than that caused by the static load and the von Mises stress distribution is significantly increased to about 150kPa through the cyclic loading. In total, the results does not only trace the efficacy of an individual 3D model of MSC using biomechanical experiments of cell modulation, but these results provide knowledge in interpretations from cell geometry. The current study was performed to determine a realistic aspect of cell behavior.

Cell stretching devices as research tools: engineering and biological considerations

Cells within the human body are subjected to continuous, cyclic mechanical strain caused by various organ functions, movement, and growth. Cells are well known to have the ability to sense and respond to mechanical stimuli. This process is referred to as mechanotransduction. A better understanding of mechanotransduction is of great interest to clinicians and scientists alike to improve clinical diagnosis and understanding of medical pathology. However, the complexity involved in in vivo biological systems creates a need for better in vitro technologies, which can closely mimic the cells' microenvironment using induced mechanical strain. This technology gap motivates the development of cell stretching devices for better understanding of the cell response to mechanical stimuli. This review focuses on the engineering and biological considerations for the development of such cell stretching devices. The paper discusses different types of stretching concepts, major design consideration and biological aspects of cell stretching and provides a perspective for future development in this research area.

Single cell active force generation under dynamic loading - Part II: Active modelling insights

In Part I of this two-part study a novel single cell AFM experimental investigation reveals a complex force-strain response of cells to cyclic loading. The biomechanisms underlying such complex behaviour cannot be fully understood without a detailed mechanistic analysis incorporating the key features of active stress generation and remodelling of the actin cytoskeleton. In order to simulate untreated contractile cells an active bio-chemo-mechanical model is developed, incorporating the key features of stress fibre (SF) remodelling and active tension generation. It is demonstrated that a fading memory SF contractility model accurately captures the transient response of cells to dynamic loading. Simulations reveal that high stretching forces during unloading half-cycles (probe retraction) occur due to tension actively generated by axially oriented SFs. On the other hand, hoop oriented SFs generate tension during loading half-cycles, providing a coherent explanation for the elevated compression resistance of contractile cells. Finally, it is also demonstrated that passive non-linear visco-hyperelastic material laws, traditionally used to simulate cell mechanical behaviour, are not appropriate for untreated contractile cells, and their use should be limited to the simulation of cells in which the active force generation machinery of the actin cytoskeleton has been chemically disrupted. In summary, our active modelling framework provides a coherent understanding of the biomechanisms underlying the complex patterns of experimentally observed single cell force generation presented in the first part of this study.

STATEMENT OF SIGNIFICANCE

A novel computational investigation into the active and passive response of cells to dynamic loading is performed. An active formulation that considers key features of actin cytoskeleton active contractility and remodelling throughout the cytoplasm is implemented. Simulations provide new insights into the sub-cellular biomechanical response, providing a coherent explanation for the complex patterns of cell force uncovered experimentally in the first part of this study. Our computational models also reveal that passive non-linear visco-hyperelastic material laws, traditionally used to simulate cell mechanical behaviour, are not appropriate for untreated contractile cells, and their use should be limited to the simulation of cells in which the active force generation machinery of the actin cytoskeleton has been chemically disrupted.

Creased hydrogels as active platforms for mechanical deformation of cultured cells

Cells cultured in vitro using traditional substrates often change their behavior due to the lack of mechanical deformation they would naturally experience in vivo. To mimic the in vivo mechanical environment, we design temperature-responsive hydrogels with patterned surface creases as dynamic cell stretching devices. A one-step photolithographic method is first employed to pattern integrin-binding peptides on the gel, causing single cells or several-cell clusters to adhere to the surface in registry with creases. A variety of crease patterns are prescribed on a single substrate, enabling the mechanical deformation of cultured myoblast cells with different strain states and achieving tensile strain as high as 0.2. As creases provide large amplitude local deformation of the gel surface without the need for macroscopic deformation, can be formed on gels covering a wide range of modulus, and can be actuated using a variety of stimuli, they hold the potential to enable the design of high throughput and versatile platforms for mechano-biological studies.

The effects of oxidative stress on the compressive damage thresholds of C2C12 mouse myoblasts: implications for deep tissue injury

Deep tissue injury (DTI) is a severe kind of pressure ulcers formed by sustained deformation of muscle tissues over bony prominences. As a major clinical issue, DTI affects people with physical disabilities, and is obviously related to the load-bearing capacity of muscle cells in various in vivo conditions. It has been hypothesized that oxidative stress, either induced by reperfusion immediately following tissue unloading or in chronic inflammatory conditions, may affect the cellular capacity against subsequent mechanical damages. In this study, we measured the compressive damage threshold of C2C12 mouse myoblasts with or without pre-treatment of hydrogen peroxide as an oxidative agent to understand how changes in the oxidative environment may contribute to the development of DTI. Spherical indentation was applied onto a layer of agarose gel (3 mm thick) covering a monolayer of C2C12 myoblasts. Cell damage was recognized by using a cell membrane damage assay, propidium iodide. The spatial profile of the measured percentage cell damage was correlated with the radially varying stress field as determined by finite element analysis to estimate the compressive stress threshold for cell damage. Results supported the hypothesis that chronic exposure to high-dosage oxidative stress could compromise the capability of muscle cells to withstand compressive damages, while short exposure to low-dosage oxidative stress could enhance such capability.

The mechanics of hyaluronic acid/adipic acid dihydrazide hydrogel: towards developing a vessel for delivery of preadipocytes to native tissues

Promising treatment approaches in repairing tissue defects include implementation of regenerative medicine strategies, particularly delivery of preadipocytes to sites where adipose tissue damage needs to be repaired or where fat needs to be generated. In this study, we suggest that the injectable hyaluronic acid/adipic acid dihydrazide (HA/ADH) hydrogel may be an adipose-tissue-like material in terms of biological compatibility as well as mechanical behavior. First, we show that the hydrogel enables and supports growth, proliferation and differentiation of 3T3-L1 preadipocytes. Second, given that adipose tissue is a weight-bearing biological structure, we investigate the large deformation mechanical behavior of the hydrogel with and without embedded preadipocytes, by performing confined and unconfined compression tests and then calibrating a strain energy density (SED) function to the results. Four test groups were examined: (1) Hydrogel specimens right after the preparation without cells, (2) and (3) 3-days-cultured hydrogel specimens with and without cells, respectively, and (4) 6-days-cultured hydrogel specimens with cells. A one-term Ogden SED was found to adequately describe the hyperelastic behavior of the hydrogel specimens in all experimental groups. Importantly, we found that the mechanical properties of the hydrogel, when subjected to compression, are in good agreement with those of native adipose tissue, with the better fit occurring 3-6 days after preparation of the hydrogel. Third, computational finite element studies of the mechanical (stress-strain) behavior of the HA/ADH hydrogel when containing mature adipocytes indicated that the stiffnesses of the constructs were mildly affected by the presence of the adipocytes. Hence, we conclude that injectable HA/ADH hydrogel may serve as a vessel for protecting preadipocytes during, and at a short-term after delivery to native tissues, e.g. in research towards regenerative medicine in tissue reconstructions.

A linear programming approach to reconstructing subcellular structures from confocal images for automated generation of representative 3D cellular models

This paper presents a novel computer vision algorithm to analyze 3D stacks of confocal images of fluorescently stained single cells. The goal of the algorithm is to create representative in silico model structures that can be imported into finite element analysis software for mechanical characterization. Segmentation of cell and nucleus boundaries is accomplished via standard thresholding methods. Using novel linear programming methods, a representative actin stress fiber network is generated by computing a linear superposition of fibers having minimum discrepancy compared with an experimental 3D confocal image. Qualitative validation is performed through analysis of seven 3D confocal image stacks of adherent vascular smooth muscle cells (VSMCs) grown in 2D culture. The presented method is able to automatically generate 3D geometries of the cell's boundary, nucleus, and representative F-actin network based on standard cell microscopy data. These geometries can be used for direct importation and implementation in structural finite element models for analysis of the mechanics of a single cell to potentially speed discoveries in the fields of regenerative medicine, mechanobiology, and drug discovery.

Experimental and computational investigation of the role of stress fiber contractility in the resistance of osteoblasts to compression

The mechanical behavior of the actin cytoskeleton has previously been investigated using both experimental and computational techniques. However, these investigations have not elucidated the role the cytoskeleton plays in the compression resistance of cells. The present study combines experimental compression techniques with active modeling of the cell's actin cytoskeleton. A modified atomic force microscope is used to perform whole cell compression of osteoblasts. Compression tests are also performed on cells following the inhibition of the cell actin cytoskeleton using cytochalasin-D. An active bio-chemo-mechanical model is employed to predict the active remodeling of the actin cytoskeleton. The model incorporates the myosin driven contractility of stress fibers via a muscle-like constitutive law. The passive mechanical properties, in parallel with active stress fiber contractility parameters, are determined for osteoblasts. Simulations reveal that the computational framework is capable of predicting changes in cell morphology and increased resistance to cell compression due to the contractility of the actin cytoskeleton. It is demonstrated that osteoblasts are highly contractile and that significant changes to the cell and nucleus geometries occur when stress fiber contractility is removed.

A computational approach to understand phenotypic structure and constitutive mechanics relationships of single cells

The goal of this study is to construct a representative 3D finite element model (FEM) of individual cells based on their sub-cellular structures that predicts cell mechanical behavior. The FEM simulations replicate atomic force microscopy (AFM) nanoindentation experiments on live vascular smooth muscle cells. Individual cells are characterized mechanically with AFM and then imaged in 3D using a spinning disc confocal microscope. Using these images, geometries for the FEM are automatically generated via image segmentation and linear programming algorithms. The geometries consist of independent structures representing the nucleus, actin stress fiber network, and cytoplasm. These are imported into commercial software for mesh refinement and analysis. The FEM presented here is capable of predicting AFM results well for 500 nm indentations. The FEM results are relatively insensitive to both the exact number and diameter of fibers used. Despite the localized nature of AFM nanoindentation, the model predicts that stresses are distributed in an anisotropic manner throughout the cell body via the actin stress fibers. This pattern of stress distribution is likely a result of the geometric arrangement of the actin network.

Stability enhancement of an atomic force microscope for long-term force measurement including cantilever modification for whole cell deformation

Atomic force microscopy (AFM) is widely used in the study of both morphology and mechanical properties of living cells under physiologically relevant conditions. However, quantitative experiments on timescales of minutes to hours are generally limited by thermal drift in the instrument, particularly in the vertical (z) direction. In addition, we demonstrate the necessity to remove all air-liquid interfaces within the system for measurements in liquid environments, which may otherwise result in perturbations in the measured deflection. These effects severely limit the use of AFM as a practical tool for the study of long-term cell behavior, where precise knowledge of the tip-sample distance is a crucial requirement. Here we present a readily implementable, cost effective method of minimizing z-drift and liquid instabilities by utilizing active temperature control combined with a customized fluid cell system. Long-term whole cell mechanical measurements were performed using this stabilized AFM by attaching a large sphere to a cantilever in order to approximate a parallel plate system. An extensive examination of the effects of sphere attachment on AFM data is presented. Profiling of cantilever bending during substrate indentation revealed that the optical lever assumption of free ended cantilevering is inappropriate when sphere constraining occurs, which applies an additional torque to the cantilevers "free" end. Here we present the steps required to accurately determine force-indentation measurements for such a scenario. Combining these readily implementable modifications, we demonstrate the ability to investigate long-term whole cell mechanics by performing strain controlled cyclic deformation of single osteoblasts.

Cell-to-cell variability in deformations across compressed myoblasts

Many biological consequences of external mechanical loads applied to cells depend on localized cell deformations rather than on average whole-cell-body deformations. Such localized intracellular deformations are likely to depend, in turn, on the individual geometrical features of each cell, e.g., the local surface curvatures or the size of the nucleus, which always vary from one cell to another, even within the same culture. Our goal here was to characterize cell-to-cell variabilities in magnitudes and distribution patterns of localized tensile strains that develop in the plasma membrane (PM) and nuclear surface area (NSA) of compressed myoblasts, in order to identify resemblance or differences in mechanical performances across the cells. For this purpose, we utilized our previously developed confocal microscopy-based three-dimensional cell-specific finite element modeling methodology. Five different C2C12 undifferentiated cells belonging to the same culture were scanned confocally and modeled, and were then subjected to compression in the simulation setting. We calculated the average and peak tensile strains in the PM and NSA, the percentage of PM area subjected to tensile strains above certain thresholds and the coefficient of variation (COV) in average and peak strains. We found considerable COV values in tensile strains developing at the PM and NSA (up to ~35%) but small external compressive deformations induced greater variabilities in intracellular strains across cells compared to large deformations. Interestingly, the external deformations needed to cause localized PM or NSA strains exceeding each threshold were very close across the different cells. Better understanding of variabilities in mechanical performances of cells-either of the same type or of different types-is important for interpreting experimental data in any experiments involving delivery of mechanical loads to cells.

Real time responses of fibroblasts to plastically compressed fibrillar collagen hydrogels

In vitro reconstituted type I collagen hydrogels are widely utilized for tissue engineering studies. However, highly hydrated collagen (HHC) gels exhibit insufficient mechanical strength and unstable geometrical properties, thereby limiting their therapeutic application. Plastic compression (PC) is a simple and reproducible approach for the immediate production of dense fibrillar collagen (DC) scaffolds which demonstrate multiple improvements for tissue engineered constructs including extracellular matrix (ECM)-like meso scale characteristics, increased mechanical properties (modulus and strength), enhanced cell growth and differentiation, and reduced long-term scaffold deformation. In order to determine at which stage these benefits become apparent, and the underlying mechanisms involved, the immediate response of NIH/3T3 fibroblasts to PC as well as longer-term cell growth within DC scaffolds were examined herein. The real time three-dimensional (3D) distribution of fluorescently labelled cells during PC was sequentially monitored using confocal laser scanning microscopy (CLSM), observing excellent cell retention and negligible numbers of expelled cells. Relative to cells grown in HHC gels, a significant improvement in cell survival within DC scaffolds was evident as early as day 1. Cell growth and metabolic activity within DC gels were significantly increased over the course of one week. While cells within DC scaffolds reached confluency, an inhomogeneous distribution of cells was present in HHC gels, as detected using x-ray computed micro-tomography analysis of phosphotungstic acid labelled cells and CLSM, which both showed a significant cell loss within the HHC core. Therefore, PC generates a DC gel scaffold without detrimental effects towards seeded cells, surpassing HHC gels as a 3D scaffold for tissue engineering.

Actuation means for the mechanical stimulation of living cells via microelectromechanical systems: A critical review

Within a living body, cells are constantly exposed to various mechanical constraints. As a matter of fact, these mechanical factors play a vital role in the regulation of the cell state. It is widely recognized that cells can sense, react and adapt themselves to mechanical stimulation. However, investigations aimed at studying cell mechanics directly in vivo remain elusive. An alternative solution is to study cell mechanics via in vitro experiments. Nevertheless, this requires implementing means to mimic the stresses that cells naturally undergo in their physiological environment. In this paper, we survey various microelectromechanical systems (MEMS) dedicated to the mechanical stimulation of living cells. In particular, we focus on their actuation means as well as their inherent capabilities to stimulate a given amount of cells. Thereby, we report actuation means dependent upon the fact they can provide stimulation to a single cell, target a maximum of a hundred cells, or deal with thousands of cells. Intrinsic performances, strengths and limitations are summarized for each type of actuator. We also discuss recent achievements as well as future challenges of cell mechanostimulation.

Atomic force microscopy in mechanobiology: measuring microelastic heterogeneity of living cells

Recent findings clearly demonstrate that cells feel mechanical forces, and respond by altering their -phenotype and modulating their mechanical environment. Atomic force microscope (AFM) indentation can be used to mechanically stimulate cells and quantitatively characterize their elastic properties, providing critical information for understanding their mechanobiological behavior. This review focuses on the experimental and computational aspects of AFM indentation in relation to cell biomechanics and pathophysiology. Key aspects of the indentation protocol (including preparation of substrates, selection of indentation parameters, methods for contact point detection, and further post-processing of data) are covered. Historical perspectives on AFM as a mechanical testing tool as well as studies of cell mechanics and physiology are also highlighted.

Force propagation and force generation in cells

Determining how forces are produced by and propagated through the cytoskeleton (CSK) of the cell is of great interest as dynamic processes of the CSK are intimately correlated with many molecular signaling pathways. We are presenting a novel approach for integrating measurements on cell elasticity, transcellular force propagation, and cellular force generation to obtain a comprehensive description of dynamic and mechanical properties of the CSK under force loading. This approach uses a combination of scanning force microscopy (SFM) and Total Internal Reflection Fluorescence (TIRF) microscopy. We apply well-defined loading schemes onto the apical cell membrane of fibroblasts using the SFM and simultaneously use TIRF microscopy to image the topography of the basal cell membrane. The locally distinct changes of shape and depth of the cytoskeletal imprints onto the basal membrane are interpreted as results of force propagation through the cytoplasm. This observation provides evidence for the tensegrity model and demonstrates the usefulness of our approach that does not depend on potentially disturbing marker compounds. We confirm that the actin network greatly determines cell stiffness and represents the substrate that mediates force transduction through the cytoplasm of the cell. The latter is an essential feature of tensegrity. Most importantly, our new finding that, both intact actin and microtubule networks are required for enabling the cell to produce work, can only be understood within the framework of the tensegrity model. We also provide, for the first time, a direct measurement of the cell's mechanical power output under compression at two femtowatts.

Biomechanics of Pressure Ulcer in Body Tissues Interacting with External Forces during Locomotion

Forces acting on the body via various external surfaces during locomotion are needed to support the body under gravity, control posture, and overcome inertia. Examples include the forces acting on the body via the seating surfaces during wheelchair propulsion, the forces acting on the plantar foot tissues via the insole during gait, and the forces acting on the residual-limb tissues via the prosthetic socket during various movement activities. Excessive exposure to unwarranted stresses at the body-support interfaces could lead to tissue breakdowns commonly known as pressure ulcers, often presented as deep-tissue injuries around bony prominences or as surface damage on the skin. In this article, we review the literature that describes how the involved tissues respond to epidermal loading, taking into account both experimental and computational findings from in vivo and in vitro studies. In particular, we discuss related literature about internal tissue deformation and stresses, microcirculatory responses, and histological, cellular, and molecular observations.

Biomechanical properties of single chondrocytes and chondrons determined by micromanipulation and finite-element modelling

A chondrocyte and its surrounding pericellular matrix (PCM) are defined as a chondron. Single chondrocytes and chondrons isolated from bovine articular cartilage were compressed by micromanipulation between two parallel surfaces in order to investigate their biomechanical properties and to discover the mechanical significance of the PCM. The force imposed on the cells was measured directly during compression to various deformations and then holding. When the nominal strain at the end of compression was 50 per cent, force relaxation showed that the cells were viscoelastic, but this viscoelasticity was generally insignificant when the nominal strain was 30 per cent or lower. The viscoelastic behaviour might be due to the mechanical response of the cell cytoskeleton and/or nucleus at higher deformations. A finite-element analysis was applied to simulate the experimental force-displacement/time data and to obtain mechanical property parameters of the chondrocytes and chondrons. Because of the large strains in the cells, a nonlinear elastic model was used for simulations of compression to 30 per cent nominal strain and a nonlinear viscoelastic model for 50 per cent. The elastic model yielded a Young's modulus of 14 ± 1 kPa (mean ± s.e.) for chondrocytes and 19 ± 2 kPa for chondrons, respectively. The viscoelastic model generated an instantaneous elastic modulus of 21 ± 3 and 27 ± 4 kPa, a long-term modulus of 9.3 ± 0.8 and 12 ± 1 kPa and an apparent viscosity of 2.8 ± 0.5 and 3.4 ± 0.6 kPa s for chondrocytes and chondrons, respectively. It was concluded that chondrons were generally stiffer and showed less viscoelastic behaviour than chondrocytes, and that the PCM significantly influenced the mechanical properties of the cells.

Applications of atomic force microscopy in biophysical chemistry of cells

This article addresses the question of what information and new insights atomic force microscopy (AFM) provides that are of importance and relevance to cellular biophysical chemistry research. Three enabling aspects of AFM are discussed: (a) visualization of membrane structural features with nanometer resolution, such as microvilli, ridges, porosomes, lamellapodia, and filopodia; (b) revealing structural evolution associated with cellular signaling pathways by time-dependent and high-resolution imaging of the cellular membrane in correlation with intracellular components from simultaneous optical microscopy; and (c) qualitative and quantitative measurements of single cell mechanics by acquisition of force-deformation profiles and extraction of Young's moduli for the membrane as well as cytoskeleton. A future prospective of AFM is also presented.