A Mathematical Model of Spatial Self-Organization in a Mechanically Active Cellular Medium

A general continual model of a medium composed of mechanically active cells is proposed. The medium is considered to be formed by three phases: cells, extracellular fluid, and an additional phase that is responsible for active interaction forces between cells and, for instance, may correspond to a system of protrusions that provide the development of active contractile forces. The deformation of the medium, which is identified with the deformation of the cell phase, consists of two components: elastic deformation of individual cells and cell rearrangements. The elastic deformation is associated with stresses in the cell phase. The spherical component of the stress tensor describes the nonlinear resistance of the cellular medium, which leads to the impossibility of its excessive compression. The constitutive equation for pressure in the cell phase is taken in the form of a nonlinear dependence on the volume cell density. The rearrangement of cells is considered as a flow controlled by stresses in the cell phase, active stresses, and fluid pressure. The tensor of active stresses is assumed to be spherical and nonlocally dependent on the cell density. Assuming that the process of biological tissue deformation is slow, we obtained a reduced model that neglects the elastic deformation of cells, compared to the inelastic deformation. A linear stability analysis of a spatially uniform steady-state solution was performed. The hydrostatic pressure of fluid is present among the parameters that are responsible for the loss of stability of the steady-state solution: an increase in it has a destabilizing effect owing to the action of the component of the interphase interaction force that is determined by the fluid pressure. The model we obtained can be used to describe the process of cavity formation in an initially homogeneous cell spheroid. The role of local and nonlocal mechanisms of active stress generation in the formation of cavity is investigated.     

Cell cytoskeleton and tether extraction

We perform a detailed investigation of the force × deformation curve in tether extraction from 3T3 cells by optical tweezers. Contrary to conventional wisdom about tethers extracted from cells, we find that actin filaments are present within them, so that a revised theory of tether pulling from cells is called for. We also measure steady and maximum tether force values significantly higher than previously published ones for 3T3 cells. Possible explanations for these differences are investigated. Further experimental support of the theory of force barriers for membrane tube extension is obtained. The potential of studies on tether pulling force × deformation for retrieving information on membrane-cytoskeleton interaction is emphasized.     

A new method to study shape recovery of red blood cells using multiple optical trapping.

In this new method for studying the shape recovery of deformed red blood cells, three optical traps ("optical tweezers") induce a parachute-shaped red cell deformation, which is comparable to the deformation in small capillaries. The shape recovery is recorded, and a relaxation time is obtained for each individual red blood cell. The sensitivity of this technique for the detection of differences in relaxation times is demonstrated on subpopulations of density-separated red blood cells: "young" cells have shorter (162 ms) and "old" cells have longer (353 ms) relaxation times compared with the total population (271 ms). The relaxation time is remarkably shorter (114 ms) when the plasma surrounding the cells is replaced by a phosphate-buffered saline solution. The main advantages of this technique are the relatively short measuring and preparation time and the physiological type of deformation and shape recovery in which all relevant cell properties play a role. Therefore, especially when automated further, the technique may be a powerful tool for the study of (sub)populations of pathological red blood cells.     

A phenomenological model for cell and nucleus deformation during cancer metastasis

Cell migration plays an essential role in cancer metastasis. In cancer invasion through confined spaces, cells must undergo extensive deformation, which is a capability related to their metastatic potentials. Here, we simulate the deformation of the cell and nucleus during invasion through a dense, physiological microenvironment by developing a phenomenological computational model. In our work, cells are attracted by a generic emitting source (e.g., a chemokine or stiffness signal), which is treated by using Green’s Fundamental solutions. We use an IMEX integration method where the linear parts and the nonlinear parts are treated by using an Euler backward scheme and an Euler forward method, respectively. We develop the numerical model for an obstacle-induced deformation in 2D or/and 3D. Considering the uncertainty in cell mobility, stochastic processes are incorporated and uncertainties in the input variables are evaluated using Monte Carlo simulations. This quantitative study aims at estimating the likelihood for invasion and the length of the time interval in which the cell invades the tissue through an obstacle. Subsequently, the two-dimensional cell deformation model is applied to simplified cancer metastasis processes to serve as a model for in vivo or in vitro biomedical experiments.     

Calculation of the force field required for nucleus deformation during cell migration through constrictions

During cell migration in confinement, the nucleus has to deform for a cell to pass through small constrictions. Such nuclear deformations require significant forces. A direct experimental measure of the deformation force field is extremely challenging. However, experimental images of nuclear shape are relatively easy to obtain. Therefore, here we present a method to calculate predictions of the deformation force field based purely on analysis of experimental images of nuclei before and after deformation. Such an inverse calculation is technically non-trivial and relies on a mechanical model for the nucleus. Here we compare two simple continuum elastic models of a cell nucleus undergoing deformation. In the first, we treat the nucleus as a homogeneous elastic solid and, in the second, as an elastic shell. For each of these models we calculate the force field required to produce the deformation given by experimental images of nuclei in dendritic cells migrating in microchannels with constrictions of controlled dimensions. These microfabricated channels provide a simplified confined environment mimicking that experienced by cells in tissues. Our calculations predict the forces felt by a deforming nucleus as a migrating cell encounters a constriction. Since a direct experimental measure of the deformation force field is very challenging and has not yet been achieved, our numerical approaches can make important predictions motivating further experiments, even though all the parameters are not yet available. We demonstrate the power of our method by showing how it predicts lateral forces corresponding to actin polymerisation around the nucleus, providing evidence for actin generated forces squeezing the sides of the nucleus as it enters a constriction. In addition, the algorithm we have developed could be adapted to analyse experimental images of deformation in other situations.     

Purkyn?'s description of pressure phosphenes and modern neurophysiological studies on the generation of phosphenes by eyeball deformation

(a) When a subject indents one of his eyeballs in total darkness, he immediately perceives light extending slowly across the whole visual field of the indented eye. The appearance and the time course of these pressure or deformation phosphenes are described. (b) With simultaneous binocular indentation of the eyeballs a flickering patterned phosphene is observed. (c) A short history of the research on pressure phosphenes and its consequences for the theories of vision is presented. (d) Purkyn?'s observations of monocular deformation phosphenes are described. He repeatedly noted patterned light structures, which most observers only perceive with simultaneous binocular eyeball deformation. It is suggested that Purkyn?'s deviating observations were caused by amblyopia of one eye. (e) The neurophysiological basis of the monocular pressure phosphenes was investigated by means of microelectrode recordings from single optic tract fibers. The activity of single retinal ganglion cells (on-center, off-center neurons, latency class I [Y-neurons] or latency class II [X-neurons]), was recorded in anaesthetized cats. Eyeball deformation in total darkness led to an activation of the on-center ganglion cells, while the off-center ganglion cells were inhibited. The latency and strength of this activation or inhibition varied considerably between different neurons, but were fairly constant in the same neuron when the eyeball indentation was repeated after a pause of 1-3 min. The latency and strength of neuronal activation or inhibition seemed to be dependent mainly upon the neuron location relative to the point of eyeball indentation. Some on-center neurons also exhibited a short activation at "deformation off". (f) The antagonistic response type of on-center and off-center ganglion cells was also observed when the eyeball was deformed as a hydrostatic open system and the intraocular pressure was kept at 25 mm Hg basic pressure. (g) Dark adaptation up to 45 min affected the deformation responses of retinal neurons only to a small degree, if at all. This corresponds to the observation that deformation phosphenes in a human observer changed little during the course of dark adaptation. (h) We assume that the activation of on-center and inhibition of off-center ganglion cells by eyeball deformation are caused by retinal stretching, which also leads to horizontal cell stretch. Stretching the horizontal cell membrane probably generates an increase in membrane sodium conductivity and a depolarization of the membrane potential. This depolarization of the horizontal cell membrane potential is transmitted either directly or indirectly (via receptor synapses) from the horizontal to the bipolar cells.(ABSTRACT TRUNCATED AT 400 WORDS)     

A computational study of leukocyte adhesion and its effect on flow pattern in microvessels

Three-dimensional computational modeling and simulation are presented on the adhesive rolling of deformable leukocytes over a P-selectin coated surface in parabolic shear flow in microchannels. The computational model is based on the immersed boundary method for cell deformation and Monte Carlo simulation for receptor/ligand interaction. The simulations are continued for at least 1 s of leukocyte rolling during which the instantaneous quantities such as cell deformation index, cell/substrate contact area, and fluid drag remain statistically stationary. The characteristic ‘stop-and-go’ motion of rolling leukocytes, and the ‘tear-drop’ shape of adherent leukocytes as observed in experiments are reproduced by the simulations. We first consider the role of cell deformation and cell concentration on rolling characteristics. We observe that compliant cells roll slower and more stably than rigid cells. Our simulations agree with previous in vivo observation that the hydrodynamic interactions between nearby leukocytes affect cell rolling, and that the rolling velocity decreases inversely with the separation distance, irrespective of cell deformability. We also find that cell deformation decreases, and the cells roll more stably with reduced velocity fluctuation, as the cell concentration is increased. However, the effect of nearby cells on the rolling characteristics is found to be more significant for rigid cells than compliant cells. We then address the effect of cell deformability and rolling velocity on the flow resistance due to, and the fluid drag on, adherent leukocytes. While several earlier computational works have addressed this problem, two key features of leukocyte adhesion, such as cell deformation and rolling, were often neglected. Our results suggest that neglecting cell deformability and rolling velocity may significantly overpredict the flow resistance and drag force. Increasing the cell concentration is shown to increase the flow resistance and reduce the fluid drag. The reduced drag then results in slower and more stable rolling of the leukocytes with longer pause time and shorter step distance. But the increase/decrease in the flow resistance/fluid drag due to the increase in the cell concentration is observed to be more significant in case of rigid cells than compliant cells.     

Deformation of leukocytes on a hematological blood film

Human leukocytes in a blood film exhibit a significantly larger diameter than in the circulation. This is due to the fact that white cells are highly deformed during preparation of a blood film. Instead of having the usual spherical shape, the cells are compressed to "pancake" forms with a thickness of about 1 micron. Hematological investigation is usually performed on these compressed cells, but in the circulation they are not observed. The deformation of the cells on a blood film is due to compression by the glass edge used to spread the blood. After deformation leukocytes do not have enough time to recover since the blood film usually dries in a shorter period than is needed for cell recovery. The shape and size of the leukocyte on the blood film is not only determined by cell volume but also by the cell membrane area. This is shown for each kind of leukocyte by independent prediction of the pancake dimensions from previous measurements of cell volume and membrane area. Leukocytes which are strongly compressed during blood film preparation may exhibit mechanical damage with rupture of membranes.     

An improved texture correlation algorithm to measure substrate-cytoskeletal network strain transfer under large compressive strain

Force-induced deformation of tissues is transduced to the cytoskeletal (CSK) network within cells via focal adhesions. Previous studies have characterized transfer of strains of less than 15% from the substrate to the cell, using mitochondria as surrogate markers for CSK deformation. However, it is unclear if intracellular strains determined from mitochondrial displacement accurately reflect CSK network deformation. Furthermore, previous studies have not characterized substrate-CSK network strain transfer for strain magnitudes exceeding 15%, as can occur in vivo and in cell culture studies. Here, we developed and characterized a texture correlation algorithm to address the image distortion problem caused by large strain. We then used this algorithm to characterize large compressive strain (-40%) transfer from the substrate to the CSK in living cells, using fluorescently tagged actin to perform the tracking and both fluorescently tagged actin and talin to make validation measurements. With this approach, we were able to demonstrate explicitly that substrate strain transfers directly to CSK deformation in living cells undergoing large compressive deformation, and that the strain transfer ratios are independent of cell alignment. The tools and approaches developed here enable improved characterization of cell-matrix interactions under large deformation and in doing so, may reveal new insights into mechanotransduction mechanisms in such circumstances.     

Red blood cell deformation in shear flow. Effects of internal and external phase viscosity and of in vivo aging.

Shear deformation of young and old human red blood cells was examined over a range of shear stresses and suspending phase viscosities (eta o) using a cone-plate Rheoscope. The internal viscosities (eta i) of these cell types differ, and further changes in internal viscosity were induced by alteration of suspension osmolality and hence cell volume. For low suspending viscosities (0.0555 or 0.111 P) old cells tended to tumble in shear flow, whereas young cells achieved stable orientation and deformed. Changes in osmolality, at these external viscosities, altered the percentage of cells deforming, and for each cell type threshold osmolalities (Osm-50) were determined where 50% of cells deformed. The threshold osmolalities were higher for younger cells than for older cells, but the internal viscosities of the two cell types were similar at their respective Osm-50. Threshold osmolalities were also higher for the higher external viscosity, but the ratio of internal to external viscosities (i.e., eta i/eta o) was nearly constant for both external viscosities. Deformation of stably oriented cells increased with increasing shear stress and approached a value limited by cell surface area and volume. For isotonic media, over a wide range of external viscosities and shear stresses, deformation was greater for younger cells than for older cells. However, deformation vs. shear stress data for the two cell types became nearly coincident if young cells were osmotically shrunk to have their internal viscosity close to that for old cells. Increases in external viscosity, at constant shear stress, caused greater deformation for all cells. This effect of external viscosity was not equal for young and old cells; the ratio of old/young cell deformation increased with increasing eta o. However, if deformation was plotted as a function of the ratio lambda = eta i/eta o, at constant shear stress, young and old cell data followed similar paths. Thus the ratio lambda is a major determinant of cell deformation as well as a critical factor affecting stable orientation in shear flow.     

Deformability and stability of erythrocytes in high-frequency electric fields down to subzero temperatures.

High-frequency electric fields can be used to induce deformation of red blood cells. In the temperature domain T = 0 degrees to -15 degrees C (supercooled suspension) and for 25 degrees C this paper examines for human erythrocytes (discocytes, young cell population suspended in a low ionic strength solution with conductivity sigma(25 degrees) = 154 microS/cm) in a sinusoidal electric field (nu = 1 MHz, E0 = 0-18 kV/cm) the following properties and effects as a function of field strength and temperature: 1) viscoelastic response, 2) (shear) deformation (steady-state value obtained from the viscoelastic response time), 3) stability (by experimentally observed breakdown of cell polarization and hemolysis), 4) electrical membrane breakdown and field-induced hemolysis (theoretical calculations for ellipsoidal particles), and 5) mechanical hemolysis. The items 2-4 were also examined for the frequency nu = 100 kHz and for a nonionic solution of very low conductivity (sigma(25 degrees) = 10 microS/cm) to support our interpretations of the results for 1 MHz. Below 0 degrees C with decreasing temperature the viscoelastic response time tau(res)(T) for the cells to reach steady-state deformation values d(infinity,E) increases and the deformation d(infinity,E)(T) decreases strongly. Both effects are especially high for low field strengths. The longest response time of approximately 30 s was obtained for -15 degrees C and small deformations. For 1 MHz the cells can be highly elongated up to 2.3 times their initial diameter a0 for 25 degrees and 0 degrees C, 2.1a0 for -10 degrees C and still 1.95a0 for -15 degrees C. For T > or = 0 degrees C the deformation is limited by hemolysis of the cells, which sets in for E0(lysis)(25 degrees) approximately 8 kV/cm and E0(lysis)(0 degrees) approximately 14 kV/cm. These values are approximately three times higher than the corresponding calculated critical field strengths for electrically induced pore formation. Nevertheless, the observed depolarization and hemolysis of the cells is provoked by electrical membrane breakdown rather than by mechanical forces due to the high deformation. For the nonionic solution, where no electrical breakdown is expected in the whole range for E0, the cells can indeed be deformed to even higher values with a low hemolytic rate. Below 0 degrees C we observe no hemolysis at all, not even for the frequency 100 kHz, where the cells hemolyze at 25 degrees C for the much lower field strength E0(lysis) approximately 2.5 kV/cm. Obviously, pore formation and growth are weak for subzero temperatures.     

Baseline mechanical characterization of J774 macrophages

Macrophage cell lines like J774 cells are ideal model systems for establishing the biophysical foundations of autonomous deformation and motility of immune cells. To aid comparative studies on these and other types of motile cells, we report measurements of the cortical tension and cytoplasmic viscosity of J774 macrophages using micropipette aspiration. Passive J774 cells cultured in suspension exhibited a cortical resting tension of ∼0.14 mN/m and a viscosity (at room temperature) of 0.93 kPa·s. Both values are about one order of magnitude higher than the respective values obtained for human neutrophils, lending support to the hypothesis that a tight balance between cortical tension and cytoplasmic viscosity is a physical prerequisite for eukaryotic cell motility. The relatively large stiffness of passive J774 cells contrasts with their capacity for a more than fivefold increase in apparent surface area during active deformation in phagocytosis. Scanning electron micrographs show how microscopic membrane wrinkles are smoothed out and recruited into the apparent surface area during phagocytosis of large targets.     

In vitro studies of deformation and adhesion properties of transformed cells.

The micropipet aspiration technique and the parallel-plate flow chamber were used to investigate the deformation and detachment properties, respectively, of normal and transformed rat fibroblasts. The normal Cloned Rat Embryo Fibroblasts (CREF) cell line was transfected with the T24 ras oncogene to produce the transformed cell line CREF T24. The CREF T24 cell line was transfected with a Kirsten ras revertant gene (K-rev 1a suppressor) to produce the CT24HKB1 cells, which have the same morphological characteristics as the cells in the CREF line. The cells utilized in this investigation were derived from the parent cell line CREF, the only differences being the presence or absence of the T24 ras oncogene and the Kirsten ras revertant gene. The detachment and deformation properties, therefore, could be related to the metastatic phenotype of the cell rather than inherent differences between disparate cell lines. Results indicated that transfecting the CREF cell line with the ras oncogene greatly modified the detachment and deformation properties. The CREF T24 cells were more easily detached from normal cells and were 50% more deformable. Both CREF and CT24HKB1 showed similar detachment properties. Based on these results, it is speculated that K-rev 1a reversed ras-induced membrane alterations in these cells. Preliminary investigations have demonstrated that both CREF and CREF T24 cells in different phases of the cell cycle differed in morphological characteristics. However, the majority of the cells within a given cell line showed similar deformation characteristics. Current investigations are focusing on characterization of both detachment and deformation properties of these cells as a function of the cell cycle using synchronization techniques.     

Theoretical model and experimental study of red blood cell (RBC) deformation in microchannels

The motion and deformation of red blood cells (RBCs) flowing in a microchannel were studied using a theoretical model and a novel automated rheoscope. The theoretical model was developed to predict the cells deformation under shear as a function of the cells geometry and mechanical properties. Fluid dynamics and membrane mechanics are incorporated, calculating the traction and deformation in an iterative manner. The model was utilized to evaluate the effect of different biophysical parameters, such as: inner cell viscosity, membrane shear modulus and surface to volume ratio on deformation measurements. The experimental system enables the measurement of individual RBCs velocity and their deformation at defined planes within the microchannel. Good agreement was observed between the simulation results, the rheoscope measurements and published ektacytometry results. The theoretical model results imply that such deformability measuring techniques are weakly influenced by changes in the inner viscosity of the cell or the ambient fluid viscosity. However, these measurements are highly sensitive to RBC shear modulus. The shear modulus, estimated by the model and the rheoscope measurements, falls between the values obtained by micropipette aspiration and laser trapping. The study demonstrates the integration of a theoretical model with a microfabricated device in order to achieve a better understanding of RBC mechanics and their measurement using microfluidic shear assays. The system and the model have the potential of serving as quantitative clinical tools for diagnosing deformability disorders in RBCs.     

Coordination of Membrane and Actin Cytoskeleton Dynamics during Filopodia Protrusion

Leading edge protrusion of migrating cells involves tightly coordinated changes in the plasma membrane and actin cytoskeleton. It remains unclear whether polymerizing actin filaments push and deform the membrane, or membrane deformation occurs independently and is subsequently stabilized by actin filaments. To address this question, we employed an ability of the membrane-binding I-BAR domain of IRSp53 to uncouple the membrane and actin dynamics and to induce filopodia in expressing cells. Using time-lapse imaging and electron microscopy of IRSp53-I-BAR-expressing B16F1 melanoma cells, we demonstrate that cells are not able to protrude or maintain durable long extensions without actin filaments in their interior, but I-BAR-dependent membrane deformation can create a small and transient space at filopodial tips that is subsequently filled with actin filaments. Moreover, the expressed I-BAR domain forms a submembranous coat that may structurally support these transient actin-free protrusions until they are further stabilized by the actin cytoskeleton. Actin filaments in the I-BAR-induced filopodia, in contrast to normal filopodia, do not have a uniform length, are less abundant, poorly bundled, and display erratic dynamics. Such unconventional structural organization and dynamics of actin in I-BAR-induced filopodia suggests that a typical bundle of parallel actin filaments is not necessary for generation and mechanical support of the highly asymmetric filopodial geometry. Together, our data suggest that actin filaments may not directly drive the protrusion, but only stabilize the space generated by the membrane deformation; yet, such stabilization is necessary for efficient protrusion.     

A tensegrity model of the cytoskeleton in spread and round cells.

Measurements on adherent cells have shown that spreading affects their mechanics. Highly spread cells are stiffer than less spread cells. The stiffness increases approximately linearly with increasing applied stress and more so in highly spread cells than in less spread cells. In this study, a six-strut tensegrity model of the cytoskeleton is used to analyze the effect of spreading on cellular mechanics. Two configurations are considered: a "round" configuration where a spherically shaped model is anchored to a flat rigid surface at three joints, and a "spread" configuration, where three additional joints of the model are attached to the surface. In both configurations a pulling force is applied at a free joint, distal from the anchoring surface, and the corresponding deformation is determined from equations of equilibrium. The model stiffness is obtained as the ratio of applied force to deformation. It is found that the stiffness changes with spreading consistently with the observations in cells. These findings suggest the possibility that the spreading-induced changes of the mechanical properties of the cell are the result of the concomitant changes in force distribution and microstructural geometry of the cytoskeleton.     

A computational model for the transit of a cancer cell through a constricted microchannel

We propose a three-dimensional computational model to simulate the transient deformation of suspended cancer cells flowing through a constricted microchannel. We model the cell as a liquid droplet enclosed by a viscoelastic membrane, and its nucleus as a smaller stiffer capsule. The cell deformation and its interaction with the suspending fluid are solved through a well-tested immersed boundary lattice Boltzmann method. To identify a minimal mechanical model that can quantitatively predict the transient cell deformation in a constricted channel, we conduct extensive parametric studies of the effects of the rheology of the cell membrane, cytoplasm and nucleus and compare the results with a recent experiment conducted on human leukaemia cells. We find that excellent agreement with the experiment can be achieved by employing a viscoelastic cell membrane model with the membrane viscosity depending on its mode of deformation (shear versus elongation). The cell nucleus limits the overall deformation of the whole cell, and its effect increases with the nucleus size. The present computational model may be used to guide the design of microfluidic devices to sort cancer cells, or to inversely infer cell mechanical properties from their flow-induced deformation.

     

Mechanical characterization of adult stem cells from bone marrow and perivascular niches

Therapies using adult stem cells often require mechanical manipulation such as injection or incorporation into scaffolds. However, force-induced rupture and mechanosensitivity of cells during manipulation is largely ignored. Here, we image cell mechanical structures and perform a biophysical characterization of three different types of human adult stem cells: bone marrow CD34+ hematopoietic, bone marrow mesenchymal and perivascular mesenchymal stem cells. We use micropipette aspiration to characterize cell mechanics and quantify deformation of subcellular structures under force and its contribution to global cell deformation. Our results suggest that CD34+ cells are mechanically suitable for injection systems since cells transition from solid- to fluid-like at constant aspiration pressure, probably due to a poorly developed actin cytoskeleton. Conversely, mesenchymal stem cells from the bone marrow and perivascular niches are more suitable for seeding into biomaterial scaffolds since they are mechanically robust and have developed cytoskeletal structures that may allow cellular stable attachment and motility through solid porous environments. Among these, perivascular stem cells cultured in 6% oxygen show a developed cytoskeleton but a more compliant nucleus, which can facilitate the penetration into pores of tissues or scaffolds. We confirm the relevance of our measurements using cell motility and migration assays and measure survival of injected cells. Since different types of adult stem cells can be used for similar applications, we suggest considering mechanical properties of stem cells to match optimal mechanical characteristics of therapies.     

In vitro models to study compressive strain-induced muscle cell damage

Skeletal muscle tissue is highly susceptible to sustained compressive straining, eventually leading to tissue breakdown in the form of pressure sores. This breakdown begins at the cellular level and is believed to be triggered by sustained cell deformation. To study the relationship between compressive strain-induced muscle cell deformation and damage, and to investigate the role of cell-cell interactions, cell-matrix interactions and tissue geometry in this process, in vitro models of single cells, monolayers and 3D tissue analogs under compression are being developed. Compression is induced using specially designed loading devices, while cell deformation is visualised with confocal microscopy. Cell damage is assessed from viability tests, vital microscopy and histological or biochemical analyses. Preliminary results from a 3D cell seeded agarose model indicate that cell deformation is indeed an important trigger for cell damage; sustained compression of the model at 20% strain results in a significant increase in cell damage with time of compression, whereas damage in unstrained controls remains constant over time.     

Cell and tissue deformation measurements: Texture correlation with third-order approximation of displacement gradients

Cells remarkably are capable of large deformations during motility and when subjected to mechanical force. Measurement of mechanical deformation (i.e. displacements, strain) is critical to understand functional changes in cells and biological tissues following disease, and to elucidate basic relationships between applied force and cellular biosynthesis. Microscopy-based imaging modalities provide the ability to noninvasively visualize small cell or tissue structures and track their motion over time, often using two-dimensional (2D) digital image (texture) correlation algorithms. For the measurement of complex and nonlinear motion in cells and tissues, implementation of texture correlation algorithms with high order approximations of displacement mapping terms are needed to minimize error. Here, we extend a texture correlation algorithm with up to third-order approximation of displacement mapping terms for the measurement of cell and tissue deformation. We additionally investigate relationships between measurement error and image texture, defined by subset entropy. Displacement measurement error is significantly reduced when the order of displacement mapping terms in the texture correlation algorithm matches or exceeds the order of the deformation observed. Displacement measurement error is also inversely proportional to subset entropy, with well-defined cell and tissue structures leading to high entropy and low error. For cell and tissue studies where complex or nonlinear displacements are expected, texture correlation algorithms with high order terms are required to best characterize the observed deformation.