Modeling high strain-rate microcavitation in soft materials: the role of material behavior in bubble dynamics.

Inertial Microcavitation Rheometry (IMR) is a promising tool for characterizing the mechanical behavior of soft materials at high strain rates. In IMR, an isolated, spherical microbubble is generated inside a soft material, using either a spatially-focused pulsed laser or focused ultrasound, to probe the mechanical behavior of the soft material at high strain rates (>103 s-1). Then, a theoretical modeling framework for inertial microcavitation, incorporating all the dominant physics, is used to extract information regarding the mechanical behavior of the soft material by fitting model predictions to the experimentally measured bubble dynamics. To model the cavitation dynamics, approaches based on extensions of the Rayleigh-Plesset equation are commonly used; however, these approaches cannot consider bubble dynamics that involves appreciable compressible behavior and place a limit on the nonlinear viscoelastic constitutive models that may be employed to describe the soft material. To circumvent these limitations, in this work, we develop a finite-element-based numerical simulation capability for inertial microcavitation of spherical bubbles that enables appreciable compressibility to be accounted for and more complex viscoelastic constitutive laws to be incorporated. We first apply the numerical simulation capability to understanding the role of material compressibility during violent spherical bubble collapse, and based on finite-element simulations, we propose a Mach-number-based threshold of 0.08, beyond which bubble collapse is violent, and the bubble dynamics involves compressibility not accounted for in Rayleigh-Plesset-based approaches. Second, we consider more complex viscoelastic constitutive models for the surrounding material, including nonlinear elastic and power-law viscous behavior, and apply IMR by fitting computational results to experimental data from inertial microcavitation of polyacrylamide (PA) gels in order to determine material parameters for PA gels at high strain rates.

Mechanophenotyping of 3D multicellular clusters using displacement arrays of rendered tractions.

Epithelial tissues mechanically deform the surrounding extracellular matrix during embryonic development, wound repair, and tumor invasion. Ex vivo measurements of such multicellular tractions within three-dimensional (3D) biomaterials could elucidate collective dissemination during disease progression and enable preclinical testing of targeted antimigration therapies. However, past 3D traction measurements have been low throughput due to the challenges of imaging and analyzing information-rich 3D material deformations. Here, we demonstrate a method to profile multicellular clusters in a 96-well-plate format based on spatially heterogeneous contractile, protrusive, and circumferential tractions. As a case study, we profile multicellular clusters across varying states of the epithelial-mesenchymal transition, revealing a successive loss of protrusive and circumferential tractions, as well as the formation of localized contractile tractions with elongated cluster morphologies. These cluster phenotypes were biochemically perturbed by using drugs, biasing toward traction signatures of different epithelial or mesenchymal states. This higher-throughput analysis is promising to systematically interrogate and perturb aberrant mechanobiology, which could be utilized with human-patient samples to guide personalized therapies.

Acoustic cavitation rheometry.

Characterization of soft materials is challenging due to their high compliance and the strain-rate dependence of their mechanical properties. The inertial microcavitation-based high strain-rate rheometry (IMR) method [Estrada et al., J. Mech. Phys. Solids, 2018, 112, 291-317] combines laser-induced cavitation measurements with a model for the bubble dynamics to measure local properties of polyacrylamide hydrogel under high strain-rates from 103 to 108 s-1. While promising, laser-induced cavitation involves plasma formation and optical breakdown during nucleation, a process that could alter local material properties before measurements are obtained. In the present study, we extend the IMR method to another means to generate cavitation, namely high-amplitude focused ultrasound, and apply the resulting acoustic-cavitation-based IMR to characterize the mechanical properties of agarose hydrogels. Material properties including viscosity, elastic constants, and a stress-free bubble radius are inferred from bubble radius histories in 0.3% and 1% agarose gels. An ensemble-based data assimilation is used to further help interpret the obtained estimates. The resulting parameter distributions are consistent with available measurements of agarose gel properties and with expected trends related to gel concentration and high strain-rate loading. Our findings demonstrate the utility of applying IMR and data assimilation methods with single-bubble acoustic cavitation data for measurement of viscoelastic properties.

Characterizing viscoelastic materials via ensemble-based data assimilation of bubble collapse observations.

Viscoelastic material properties at high strain rates are needed to model many biological and medical systems. Bubble cavitation can induce such strain rates, and the resulting bubble dynamics are sensitive to the material properties. Thus, in principle, these properties can be inferred via measurements of the bubble dynamics. Estrada et al. (2018) demonstrated such bubble-dynamic high-strain-rate rheometry by using least-squares shooting to minimize the difference between simulated and experimental bubble radius histories. We generalize their technique to account for additional uncertainties in the model, initial conditions, and material properties needed to uniquely simulate the bubble dynamics. Ensemble-based data assimilation minimizes the computational expense associated with the bubble cavitation model, providing a more efficient and scalable numerical framework for bubble-collapse rheometry. We test an ensemble Kalman filter (EnKF), an iterative ensemble Kalman smoother (IEnKS), and a hybrid ensemble-based 4D-Var method (En4D-Var) on synthetic data, assessing their estimations of the viscosity and shear modulus of a Kelvin-Voigt material. Results show that En4D-Var and IEnKS provide better moduli estimates than EnKF. Applying these methods to the experimental data of Estrada et al. (2018) yields similar material property estimates to those they obtained, but provides additional information about uncertainties. In particular, the En4D-Var yields lower viscosity estimates for some experiments, and the dynamic estimators reveal a potential mechanism that is unaccounted for in the model, whereby the apparent viscosity is reduced in some cases due to inelastic behavior, possibly in the form of material damage occurring at bubble collapse.

Influence of Surface Wettability on Discharges from Water Drops in Electric Fields.

It is known that electrified droplets deform and may become unstable when the electric field they are exposed to reaches a certain critical value. These instabilities are accompanied by electric discharges due to the local enhancement of the electric field caused by the deformed droplets. Here we report and highlight an interesting aspect of the behavior of unstable water droplets and discharge generation: by implementing wettability engineering, we can manipulate these discharges. We demonstrate that wettability strongly influences the shape of a droplet that is exposed to an electric field. The difference in shape is directly related to differences in the critical value of the applied electric field at which inception of discharge occurs. Using theoretical models, we can predict and sufficiently support our observations. Thus, by tailoring the wettability of the surface, we can control droplet's behavior from expediting the discharge inception to completely restricting it.

Mean deformation metrics for quantifying 3D cell-matrix interactions without requiring information about matrix material properties.

Mechanobiology relates cellular processes to mechanical signals, such as determining the effect of variations in matrix stiffness with cell tractions. Cell traction recorded via traction force microscopy (TFM) commonly takes place on materials such as polyacrylamide- and polyethylene glycol-based gels. Such experiments remain limited in physiological relevance because cells natively migrate within complex tissue microenvironments that are spatially heterogeneous and hierarchical. Yet, TFM requires determination of the matrix constitutive law (stress-strain relationship), which is not always readily available. In addition, the currently achievable displacement resolution limits the accuracy of TFM for relatively small cells. To overcome these limitations, and increase the physiological relevance of in vitro experimental design, we present a new approach and a set of associated biomechanical signatures that are based purely on measurements of the matrix's displacements without requiring any knowledge of its constitutive laws. We show that our mean deformation metrics (MDM) approach can provide significant biophysical information without the need to explicitly determine cell tractions. In the process of demonstrating the use of our MDM approach, we succeeded in expanding the capability of our displacement measurement technique such that it can now measure the 3D deformations around relatively small cells (∼10 micrometers), such as neutrophils. Furthermore, we also report previously unseen deformation patterns generated by motile neutrophils in 3D collagen gels.

Assessment of Eco-friendly Gases for Electrical Insulation to Replace the Most Potent Industrial Greenhouse Gas SF6.

Gases for electrical insulation are essential for the operation of electric power equipment. This Review gives a brief history of gaseous insulation that involved the emergence of the most potent industrial greenhouse gas known today, namely sulfur hexafluoride. SF6 paved the way to space-saving equipment for the transmission and distribution of electrical energy. Its ever-rising usage in the electrical grid also played a decisive role in the continuous increase of atmospheric SF6 abundance over the last decades. This Review broadly covers the environmental concerns related to SF6 emissions and assesses the latest generation of eco-friendly replacement gases. They offer great potential for reducing greenhouse gas emissions from electrical equipment but at the same time involve technical trade-offs. The rumors of one or the other being superior seem premature, in particular because of the lack of dielectric, environmental, and chemical information for these relatively novel compounds and their dissociation products during operation.

The 2018 correlative microscopy techniques roadmap.

Developments in microscopy have been instrumental to progress in the life sciences, and many new techniques have been introduced and led to new discoveries throughout the last century. A wide and diverse range of methodologies is now available, including electron microscopy, atomic force microscopy, magnetic resonance imaging, small-angle x-ray scattering and multiple super-resolution fluorescence techniques, and each of these methods provides valuable read-outs to meet the demands set by the samples under study. Yet, the investigation of cell development requires a multi-parametric approach to address both the structure and spatio-temporal organization of organelles, and also the transduction of chemical signals and forces involved in cell-cell interactions. Although the microscopy technologies for observing each of these characteristics are well developed, none of them can offer read-out of all characteristics simultaneously, which limits the information content of a measurement. For example, while electron microscopy is able to disclose the structural layout of cells and the macromolecular arrangement of proteins, it cannot directly follow dynamics in living cells. The latter can be achieved with fluorescence microscopy which, however, requires labelling and lacks spatial resolution. A remedy is to combine and correlate different readouts from the same specimen, which opens new avenues to understand structure-function relations in biomedical research. At the same time, such correlative approaches pose new challenges concerning sample preparation, instrument stability, region of interest retrieval, and data analysis. Because the field of correlative microscopy is relatively young, the capabilities of the various approaches have yet to be fully explored, and uncertainties remain when considering the best choice of strategy and workflow for the correlative experiment. With this in mind, the Journal of Physics D: Applied Physics presents a special roadmap on the correlative microscopy techniques, giving a comprehensive overview from various leading scientists in this field, via a collection of multiple short viewpoints.

Matrix confinement plays a pivotal role in regulating neutrophil-generated tractions, speed, and integrin utilization.

Neutrophils are capable of switching from integrin-dependent motility on two-dimensional substrata to integrin-independent motion following entry into the confined three-dimensional matrix of an afflicted tissue. However, whether integrins still maintain a regulatory role for cell traction generation and cell locomotion under the physical confinement of the three-dimensional matrix is unknown, and this is challenging to deduce from motility studies alone. Using three-dimensional traction force microscopy and a double hydrogel sandwich system, we determined the three-dimensional spatiotemporal traction forces of motile neutrophils at unprecedented resolution and show, for the first time, that entry into a highly confined space (2.5D) is a sufficient trigger to convert to integrin-independent migration. We find that integrins exert a significant regulatory role in determining the magnitude and spatial distribution of tractions and cell speed on confined cells. We also find that 90% of neutrophil tractions are in the out-of-plane axis, and this may be a fundamental element of neutrophil traction force generation.

Extracting Time-Accurate Acceleration Vectors From Nontrivial Accelerometer Arrangements.

Sports-related concussions are of significant concern in many impact sports, and their detection relies on accurate measurements of the head kinematics during impact. Among the most prevalent recording technologies are videography, and more recently, the use of single-axis accelerometers mounted in a helmet, such as the HIT system. Successful extraction of the linear and angular impact accelerations depends on an accurate analysis methodology governed by the equations of motion. Current algorithms are able to estimate the magnitude of acceleration and hit location, but make assumptions about the hit orientation and are often limited in the position and/or orientation of the accelerometers. The newly formulated algorithm presented in this manuscript accurately extracts the full linear and rotational acceleration vectors from a broad arrangement of six single-axis accelerometers directly from the governing set of kinematic equations. The new formulation linearizes the nonlinear centripetal acceleration term with a finite-difference approximation and provides a fast and accurate solution for all six components of acceleration over long time periods (>250 ms). The approximation of the nonlinear centripetal acceleration term provides an accurate computation of the rotational velocity as a function of time and allows for reconstruction of a multiple-impact signal. Furthermore, the algorithm determines the impact location and orientation and can distinguish between glancing, high rotational velocity impacts, or direct impacts through the center of mass. Results are shown for ten simulated impact locations on a headform geometry computed with three different accelerometer configurations in varying degrees of signal noise. Since the algorithm does not require simplifications of the actual impacted geometry, the impact vector, or a specific arrangement of accelerometer orientations, it can be easily applied to many impact investigations in which accurate kinematics need to be extracted from single-axis accelerometer data.

Differences in Morphology and Traction Generation of Cell Lines Representing Different Stages of Osteogenesis.

Osteogenesis is the process by which mesenchymal stem cells differentiate to osteoblasts and form bone. The morphology and root mean squared (RMS) traction of four cell types representing different stages of osteogenesis were quantified. Undifferentiated D1, differentiated D1, MC3T3-E1, and MLO-A5 cell types were evaluated using both automated image analysis of cells stained for F-actin and by traction force microscopy (TFM). Undifferentiated mesenchymal stem cell lines were small, spindly, and exerted low traction, while differentiated osteoblasts were large, had multiple processes, and exerted higher traction. Size, shape, and traction all correlated with the differentiation stage. Thus, cell morphology evolved and RMS traction increased with differentiation. The results provide a foundation for further work with these cell lines to study the mechanobiology of bone formation.

3D Viscoelastic traction force microscopy.

Native cell-material interactions occur on materials differing in their structural composition, chemistry, and physical compliance. While the last two decades have shown the importance of traction forces during cell-material interactions, they have been almost exclusively presented on purely elastic in vitro materials. Yet, most bodily tissue materials exhibit some level of viscoelasticity, which could play an important role in how cells sense and transduce tractions. To expand the realm of cell traction measurements and to encompass all materials from elastic to viscoelastic, this paper presents a general, and comprehensive approach for quantifying 3D cell tractions in viscoelastic materials. This methodology includes the experimental characterization of the time-dependent material properties for any viscoelastic material with the subsequent mathematical implementation of the determined material model into a 3D traction force microscopy (3D TFM) framework. Utilizing this new 3D viscoelastic TFM (3D VTFM) approach, we quantify the influence of viscosity on the overall material traction calculations and quantify the error associated with omitting time-dependent material effects, as is the case for all other TFM formulations. We anticipate that the 3D VTFM technique will open up new avenues of cell-material investigations on even more physiologically relevant time-dependent materials including collagen and fibrin gels.

Estimating Brain Injury Risk from Shipborne Underwater Blasts Using a High-fidelity Finite Element Head Model.

INTRODUCTION: Assessing the survivability of, and potential injury to, a ship's crew from underwater blast is crucial to understanding the operating capability of a military vessel following blast exposure. One form of injury that can occur and affect a crew member's ability to perform tasks is traumatic brain injury (TBI). To evaluate the risk of TBI from underwater blasts, injury metrics based on linear head acceleration have traditionally been used. Although these metrics are popular given their ease of use, they do not provide a direct measure of the tissue-level biomechanical responses that have been shown to cause neuronal injury. Tissue-based metrics of injury, on the other hand, may provide more insight into the potential risk of brain injury. Therefore, in this study, we assess the risk of TBI from underwater blasts using tissue-based measures of injury, such as tissue strain, strain rate, and intracranial pressure, in addition to the more commonly used head acceleration-based injury metrics. MATERIALS AND METHODS: A series of computational simulations were performed using a detailed finite element (FE) head model to study how inertial loading of the head from underwater blast events translates to potential injury in the brain. The head kinematics loading conditions for the simulations were obtained directly from Floating Shock Platform (FSP) tests where 3 Anthropomorphic Test Devices (ATDs) were positioned at 3 shipboard locations (desk, bulkhead, and bench), and the head acceleration was directly measured. The effect of the position and orientation of the ATDs and the distance of the underwater blast from the FSP (20-50 ft) on the risk of brain injury were assessed from the FE analysis. RESULTS: The head accelerations and estimated TBI risk from the underwater blasts highly depend on the positioning of the ATDs on the FSP and decrease in severity as the charge standoff distance is increased. The ATD that was seated at a desk had the largest peak linear head acceleration (77.5 g) and negative intracranial pressure (-51.8 kPa). In contrast, the ATD that was standing at a bulkhead had the largest computed 95th percentile maximum principal strain (19%) and strain rate (25 s-1) in the brain. For all tested conditions, none of the ATDs exceeded the Head Injury Criterion (HIC-15) threshold of 700 for serious or fatal brain injury; however, the predicted tissue strains of the bulkhead ATD at the 20-ft charge standoff distance were within the range of proposed strain thresholds for a 50% risk of concussive injury, which illustrates the added value of considering tissue-level measures in addition to head acceleration when evaluating brain injury risk. CONCLUSIONS: In this work, we assessed the risk of brain injury from underwater blasts using an anatomically detailed subject-specific FE head model. Accurate assessment of the risk of TBI from underwater explosions is important to evaluate the potential injury risk to crew members from underwater blast events, and to guide the development of future injury mitigation strategies to maintain the safety of crew members on military ships.

Beyond symptomatic diagnosis of mild traumatic brain injury.

It is commonly assumed that there is no brain injury if there are no noticeable symptoms following a head impact. There is growing evidence that traumatic brain injuries can occur with no outward symptoms and that the damage from these injuries can accumulate over time resulting in disease and impairment later in life. It is time to rethink the role that symptoms play in traumatic brain injury and adopt a quantitative understanding of brain health at the cellular level to improve the way we diagnose, prevent, and ultimately heal brain injury.

It is commonly assumed that there is no brain injury if there are no noticeable symptoms following a head impact. There is growing evidence that traumatic brain injuries can occur with no outward symptoms and that the damage from these injuries can accumulate over time resulting in disease and impairment later in life. It is time to rethink the role that symptoms play in traumatic brain injury and adopt a quantitative understanding of brain health at the cellular level to improve the way we diagnose, prevent, and ultimately heal brain injury.

Mechanosensitive traction force generation is regulated by the neutrophil activation state.

The generation of traction forces by neutrophils regulates many crucial effector functions responsible for host defense, such as attachment, spreading, migration, phagocytosis, and NETosis. The activation state of the cell is a strong determinant of the functional efficacy of the neutrophil; however, the effect of activation on traction force production has not yet been determined experimentally. Previously, the mapping of cellular-generated forces produced by human neutrophils via a Traction Force Microscopy (TFM) method has required a three-dimensional imaging modality to capture out-of-plane forces, such as confocal or multiphoton techniques. A method newly developed in our laboratories can capture out-of-plane forces using only a two-dimensional imaging modality. This novel technique-combined with a topology-based single particle tracking algorithm and finite element method calculations-can construct high spatial frequency three-dimensional traction fields, allowing for traction forces in-plane and out-of-plane to the substrate to now be differentially visualized and quantified with a standard epifluorescence microscope. Here we apply this technology to determine the effect of neutrophil activation on force generation. Sepsis is a systemic inflammatory response that causes dysregulated neutrophil activation in vivo. We found that neutrophils from septic patients produced greater total forces than neutrophils from healthy donors and that the majority of this dysregulation occurred in-plane to the substrate. Ex vivo activation of neutrophils from healthy donors showed differential consequences depending on activation stimuli with mechanosensitive force decreases observed in some cases. These findings demonstrate the feasibility of epifluorescence-based microscopy in mapping traction forces to ask biologically significant questions regarding neutrophil function.

Head Impact Modeling to Support a Rotational Combat Helmet Drop Test.

INTRODUCTION: The Advanced Combat Helmet (ACH) military specification (mil-spec) provides blunt impact acceleration criteria that must be met before use by the U.S. warfighter. The specification, which requires a helmeted magnesium Department of Transportation (DOT) headform to be dropped onto a steel hemispherical target, results in a translational headform impact response. Relative to translations, rotations of the head generate higher brain tissue strains. Excessive strain has been implicated as a mechanical stimulus leading to traumatic brain injury (TBI). We hypothesized that the linear constrained drop test method of the ACH specification underreports the potential for TBI. MATERIALS AND METHODS: To establish a baseline of translational acceleration time histories, we conducted linear constrained drop tests based on the ACH specification and then performed simulations of the same to verify agreement between experiment and simulation. We then produced a high-fidelity human head digital twin and verified that biological tissue responses matched experimental results. Next, we altered the ACH experimental configuration to use a helmeted Hybrid III headform, a freefall cradle, and an inclined anvil target. This new, modified configuration allowed both a translational and a rotational headform response. We applied this experimental rotation response to the skull of our human digital twin and compared brain deformation relative to the translational baseline. RESULTS: The modified configuration produced brain strains that were 4.3 times the brain strains from the linear constrained configuration. CONCLUSIONS: We provide a scientific basis to motivate revision of the ACH mil-spec to include a rotational component, which would enhance the test's relevance to TBI arising from severe head impacts.

Optomechanically Actuated Hydrogel Platform for Cell Stimulation with Spatial and Temporal Resolution.

Cells exist in the body in mechanically dynamic environments, yet the vast majority of in vitro cell culture is conducted on static materials such as plastic dishes and gels. To address this limitation, we report an approach to transition widely used hydrogels into mechanically active substrates by doping optomechanical actuator (OMA) nanoparticles within the polymer matrix. OMAs are composed of gold nanorods surrounded by a thermoresponsive polymer shell that rapidly collapses upon near-infrared (NIR) illumination. As a proof of concept, we crosslinked OMAs into laminin-gelatin hydrogels, generating up to 5 µm deformations triggered by NIR pulsing. This response was tunable by NIR intensity and OMA density within the gel and is generalizable to other hydrogel materials. Hydrogel mechanical stimulation enhanced myogenesis in C2C12 myoblasts as evidenced by ERK signaling, myocyte fusion, and sarcomeric myosin expression. We also demonstrate rescued differentiation in a chronic inflammation model as a result of mechanical stimulation. This work establishes OMA-actuated biomaterials as a powerful tool for in vitro mechanical manipulation with broad applications in the field of mechanobiology.

Monocytes use protrusive forces to generate migration paths in viscoelastic collagen-based extracellular matrices.

Circulating monocytes are recruited to the tumor microenvironment, where they can differentiate into macrophages that mediate tumor progression. To reach the tumor microenvironment, monocytes must first extravasate and migrate through the type-1 collagen rich stromal matrix. The viscoelastic stromal matrix around tumors not only stiffens relative to normal stromal matrix, but often exhibits enhanced viscous characteristics, as indicated by a higher loss tangent or faster stress relaxation rate. Here, we studied how changes in matrix stiffness and viscoelasticity, impact the three-dimensional migration of monocytes through stromal-like matrices. Interpenetrating networks of type-1 collagen and alginate, which enable independent tunability of stiffness and stress relaxation over physiologically relevant ranges, were used as confining matrices for three-dimensional culture of monocytes. Increased stiffness and faster stress relaxation independently enhanced the 3D migration of monocytes. Migrating monocytes have an ellipsoidal or rounded wedge-like morphology, reminiscent of amoeboid migration, with accumulation of actin at the trailing edge. Matrix adhesions and Rho-mediated contractility were dispensable for monocyte migration in 3D, but migration did require actin polymerization and myosin contractility. Mechanistic studies indicate that actin polymerization at the leading edge generates protrusive forces that open a path for the monocytes to migrate through in the confining viscoelastic matrices. Taken together, our findings implicate matrix stiffness and stress relaxation as key mediators of monocyte migration and reveal how monocytes use pushing forces at the leading edge mediated by actin polymerization to generate migration paths in confining viscoelastic matrices. Significance Statement: Cell migration is essential for numerous biological processes in health and disease, including for immune cell trafficking. Monocyte immune cells migrate through extracellular matrix to the tumor microenvironment where they can play a role in regulating cancer progression. Increased extracellular matrix (ECM) stiffness and viscoelasticity have been implicated in cancer progression, but the impact of these changes in the ECM on monocyte migration remains unknown. Here, we find that increased ECM stiffness and viscoelasticity promote monocyte migration. Interestingly, we reveal a previously undescribed adhesion-independent mode of migration whereby monocytes generate a path to migrate through pushing forces at the leading edge. These findings help elucidate how changes in the tumor microenvironment impact monocyte trafficking and thereby disease progression.

Quantifying cellular traction forces in three dimensions.

Cells engage in mechanical force exchange with their extracellular environment through tension generated by the cytoskeleton. A method combining laser scanning confocal microscopy (LSCM) and digital volume correlation (DVC) enables tracking and quantification of cell-mediated deformation of the extracellular matrix in all three spatial dimensions. Time-lapse confocal imaging of migrating 3T3 fibroblasts on fibronectin (FN)-modified polyacrylamide gels of varying thickness reveals significant in-plane (x, y) and normal (z) displacements, and illustrates the extent to which cells, even in nominally two-dimensional (2-D) environments, explore their surroundings in all three dimensions. The magnitudes of the measured displacements are independent of the elastic moduli of the gels. Analysis of the normal displacement profiles suggests that normal forces play important roles even in 2-D cell migration.

Adhesive peptide and polymer density modulate 3D cell traction forces within synthetic hydrogels.

Cell-extracellular matrix forces provide pivotal signals regulating diverse physiological and pathological processes. Although mechanobiology has been widely studied in two-dimensional configurations, limited research has been conducted in three-dimensional (3D) systems due to the complex nature of mechanics and cellular behaviors. In this study, we established a platform integrating a well-defined synthetic hydrogel system (PEG-4MAL) with 3D traction force microscopy (TFM) methodologies to evaluate deformation and force responses within synthetic microenvironments, providing insights that are not tractable using biological matrices because of the interdependence of biochemical and biophysical properties and complex mechanics. We dissected the contributions of adhesive peptide density and polymer density, which determines hydrogel stiffness, to 3D force generation for fibroblasts. A critical threshold of adhesive peptide density at a constant matrix elasticity is required for cells to generate 3D forces. Furthermore, matrix displacements and strains decreased with matrix stiffness whereas stresses, and tractions increased with matrix stiffness until reaching constant values at higher stiffness values. Finally, Rho-kinase-dependent contractility and vinculin expression are required to generate significant 3D forces in both collagen and synthetic hydrogels. This research establishes a tunable platform for the study of mechanobiology and provides new insights into how cells sense and transmit forces in 3D.