Volume-controlled cavity expansion for probing of local elastic properties in soft materials

Elasticity of whole blood clots measured via Volume Controlled Cavity Expansion

Measuring and understanding the mechanical properties of blood clots can provide insights into disease progression and the effectiveness of potential treatments. However, several limitations hinder the use of standard mechanical testing methods to measure the response of soft biological tissues, like blood clots. These tissues can be difficult to mount, and are inhomogeneous, irregular in shape, scarce, and valuable. To remedy this, we employ in this work Volume Controlled Cavity Expansion (VCCE), a technique that was recently developed, to measure local mechanical properties of soft materials in their natural environment. Through highly controlled volume expansion of a water bubble at the tip of an injection needle, paired with simultaneous measurement of the resisting pressure, we obtain a local signature of whole blood clot mechanical response. Comparing this data with predictive theoretical models, we find that a 1-term Ogden model is sufficient to capture the nonlinear elastic response observed in our experiments and produces shear modulus values that are comparable to values reported in the literature. Moreover, we find that bovine whole blood stored at 4 °C for greater than 2 days exhibits a statistically significant shift in the shear modulus from 2.53 ± 0.44 kPa on day 2 (N = 13) to 1.23 ± 0.18 kPa on day 3 (N = 14). In contrast to previously reported results, our samples did not exhibit viscoelastic rate sensitivity within strain rates ranging from 0.22 - 21.1 s-1. By surveying existing data on whole blood clots for comparison, we show that this technique provides highly repeatable and reliable results, hence we propose the more widespread adoption of VCCE as a path forward to building a better understanding of the mechanics of soft biological materials.

Torsion-induced stick-slip phenomena in the delamination of soft adhesives

Soft adhesive contacts are ubiquitous in nature and are increasingly used in synthetic systems, such as flexible electronics and soft robots, due to their advantages over traditional joining techniques. While methods to study the failure of adhesives typically apply tensile loads to the adhesive joint, less is known about the performance of soft adhesives under shear and torsion, which may become important in engineering applications. A major challenge that has hindered the characterization of shear/torsion-induced delamination is imposed by the fact that, even after delamination, contact with the substrate is maintained, thus allowing for frictional sliding and re-adhesion. In this work, we address this gap by studying the controlled delamination of soft cylinders under combined compression and torsion. Our experimental observations expose the nucleation of delamination at an imperfection and its propagation along the circumference of the cylinder. The observed sequence of 'stick-slip' events and the sensitivity of the delamination process to material parameters are explained by a theoretical model that captures axisymmetric delamination patterns, along with the subsequent frictional sliding and re-adhesion. By opening up an avenue for improved characterization of adhesive failure, our experimental approach and theoretical framework can guide the design of adhesives in future applications.

Thermodynamics predicts a stable microdroplet phase in polymer-gel mixtures undergoing elastic phase separation

We study the thermodynamics of binary mixtures with the volume fraction of the minority component less than the amount required to form a flat interface and show that the surface tension dominated equilibrium phase of the mixture forms a single macroscopic droplet. Elastic interactions in gel-polymer mixtures stabilize a phase with multiple droplets. Using a mean-field free energy we compute the droplet size as a function of the interfacial tension, Flory parameter, and elastic moduli of the gel. Our results illustrate the role of elastic interactions in dictating the phase behavior of biopolymers undergoing liquid-liquid phase separation.

Interfacial cavitation

Cavitation has long been recognized as a crucial predictor, or precursor, to the ultimate failure of various materials, ranging from ductile metals to soft and biological materials. Traditionally, cavitation in solids is defined as an unstable expansion of a void or a defect within a material. The critical applied load needed to trigger this instability -- the critical pressure -- is a lengthscale independent material property and has been predicted by numerous theoretical studies for a breadth of constitutive models. While these studies usually assume that cavitation initiates from defects in the bulk of an otherwise homogeneous medium, an alternative and potentially more ubiquitous scenario can occur if the defects are found at interfaces between two distinct media within the body. Such interfaces are becoming increasingly common in modern materials with the use of multimaterial composites and layer-by-layer additive manufacturing methods. However, a criterion to determine the threshold for interfacial failure, in analogy to the bulk cavitation limit, has yet to be reported. In this work, we fill this gap. Our theoretical model captures a lengthscale independent limit for interfacial cavitation, and is shown to agree with our observations at two distinct lengthscales, via two different experimental systems. To further understand the competition between the two cavitation modes (bulk versus interface), we expand our investigation beyond the elastic response to understand the ensuing unstable propagation of delamination at the interface. A phase diagram summarizes these results, showing regimes in which interfacial failure becomes the dominant mechanism.

Cavitation in a soft porous material

We study the collapse and expansion of a cavitation bubble in a deformable porous medium. We develop a continuum-scale model that couples compressible fluid flow in the pore network with the elastic response of a solid skeleton. Under the assumption of spherical symmetry, our model can be reduced to an ordinary differential equation that extends the Rayleigh-Plesset equation to bubbles in soft porous media. The extended Rayleigh-Plesset equation reveals that finite-size effects lead to the breakdown of the universal scaling relation between bubble radius and time that holds in the infinite-size limit. Our data indicate that the deformability of the porous medium slows down the collapse and expansion processes, a result with important consequences for wide-ranging phenomena, from drug delivery to spore dispersion.

Cavitation induced fracture of intact brain tissue

Nonpenetrating traumatic brain injuries (TBIs) are linked to cavitation. The structural organization of the brain makes it particularly susceptible to tears and fractures from these cavitation events, but limitations in existing characterization methods make it difficult to understand the relationship between fracture and cavitation in this tissue. More broadly, fracture energy is an important, yet often overlooked, mechanical property of all soft tissues. We combined needle-induced cavitation with hydraulic fracture models to induce and quantify fracture in intact brains at precise locations. We report here the first measurements of the fracture energy of intact brain tissue that range from 1.5 to 8.9 J/m2, depending on the location in the brain and the model applied. We observed that fracture consistently occurs along interfaces between regions of brain tissue. These fractures along interfaces allow cavitation-related damage to propagate several millimeters away from the initial injury site. Quantifying the forces necessary to fracture brain and other soft tissues is critical for understanding how impact and blast waves damage tissue in vivo and has implications for the design of protective gear and tissue engineering.

Linking cavitation and fracture to molecular scale structural damage of model networks

Rapid expansion of soft solids subjected to a negative hydrostatic stress can occur through cavitation or fracture. Understanding how these two mechanisms relate to a material's molecular structure is important to applications in materials characterization, adhesive design, and tissue damage. Here, a recently improved needle-induced cavitation (NIC) protocol is applied to a set of model end-linked PEG gels with quantitatively linked elastic and fracture properties. This quantitative link between molecular scale structure and macroscopic properties is exploited to experimentally probe the relationship between cavitation, fracture, and molecular scale damage. This work indicates that rational tuning of the elastofracture length relative to the crack geometry can be used to alter the expansion mechanism from cavitation to fracture during NIC.

Morphogenesis and cell ordering in confined bacterial biofilms

Biofilms are aggregates of bacterial cells surrounded by an extracellular matrix. Much progress has been made in studying biofilm growth on solid substrates; however, little is known about the biophysical mechanisms underlying biofilm development in three-dimensional confined environments in which the biofilm-dwelling cells must push against and even damage the surrounding environment to proliferate. Here, combining single-cell imaging, mutagenesis, and rheological measurement, we reveal the key morphogenesis steps of Vibrio cholerae biofilms embedded in hydrogels as they grow by four orders of magnitude from their initial size. We show that the morphodynamics and cell ordering in embedded biofilms are fundamentally different from those of biofilms on flat surfaces. Treating embedded biofilms as inclusions growing in an elastic medium, we quantitatively show that the stiffness contrast between the biofilm and its environment determines biofilm morphology and internal architecture, selecting between spherical biofilms with no cell ordering and oblate ellipsoidal biofilms with high cell ordering. When embedded in stiff gels, cells self-organize into a bipolar structure that resembles the molecular ordering in nematic liquid crystal droplets. In vitro biomechanical analysis shows that cell ordering arises from stress transmission across the biofilm-environment interface, mediated by specific matrix components. Our imaging technique and theoretical approach are generalizable to other biofilm-forming species and potentially to biofilms embedded in mucus or host tissues as during infection. Our results open an avenue to understand how confined cell communities grow by means of a compromise between their inherent developmental program and the mechanical constraints imposed by the environment.

Mechanically Induced Cavitation in Biological Systems

Cavitation bubbles form in soft biological systems when subjected to a negative pressure above a critical threshold, and dynamically change their size and shape in a violent manner. The critical threshold and dynamic response of these bubbles are known to be sensitive to the mechanical characteristics of highly compliant biological systems. Several recent studies have demonstrated different biological implications of cavitation events in biological systems, from therapeutic drug delivery and microsurgery to blunt injury mechanisms. Due to the rapidly increasing relevance of cavitation in biological and biomedical communities, it is necessary to review the current state-of-the-art theoretical framework, experimental techniques, and research trends with an emphasis on cavitation behavior in biologically relevant systems (e.g., tissue simulant and organs). In this review, we first introduce several theoretical models that predict bubble response in different types of biological systems and discuss the use of each model with physical interpretations. Then, we review the experimental techniques that allow the characterization of cavitation in biologically relevant systems with in-depth discussions of their unique advantages and disadvantages. Finally, we highlight key biological studies and findings, through the direct use of live cells or organs, for each experimental approach.

3D fluorescent mapping of invisible molecular damage after cavitation in hydrogen exposed elastomers

Elastomers saturated with gas at high pressure suffer from cavity nucleation, inflation, and deflation upon rapid or explosive decompression. Although this process often results in undetectable changes in appearance, it causes internal damage, hampers functionality (e.g., permeability), and shortens lifetime. Here, we tag a model poly(ethyl acrylate) elastomer with π-extended anthracene-maleimide adducts that fluoresce upon network chain scission, and map in 3D the internal damage present after a cycle of gas saturation and rapid decompression. Interestingly, we observe that each cavity observable during decompression results in a damaged region, the shape of which reveals a fracture locus of randomly oriented penny-shape cracks (i.e., with a flower-like morphology) that contain crack arrest lines. Thus, cavity growth likely proceeds discontinuously (i.e., non-steadily) through the stable and unstable fracture of numerous 2D crack planes. This non-destructive methodology to visualize in 3D molecular damage in polymer networks is novel and serves to understand how fracture occurs under complex 3D loads, predict mechanical aging of pristine looking elastomers, and holds potential to optimize cavitation-resistance in soft materials.

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.

Localized characterization of brain tissue mechanical properties by needle induced cavitation rheology and volume controlled cavity expansion

Changes in the elastic properties of brain tissue have been correlated with injury, cancers, and neurodegenerative diseases. However, discrepancies in the reported elastic moduli of brain tissue are persistent, and spatial inhomogeneities complicate the interpretation of macroscale measurements such as rheology. Here we introduce needle induced cavitation rheology (NICR) and volume-controlled cavity expansion (VCCE) as facile methods to measure the apparent Young's modulus E of minimally manipulated brain tissue, at specific tissue locations and with sub-millimeter spatial resolution. For different porcine brain regions and sections analyzed by NICR, we found E to be 3.7 ± 0.7 kPa and 4.8 ± 1.0 kPa for gray matter, and white matter, respectively. For different porcine brain regions and sections analyzed by VCCE, we found E was 0.76 ± 0.02 kPa for gray matter and 0.92 ± 0.01 kPa for white matter. Measurements from VCCE were more similar to those obtained from macroscale shear rheology (0.75 ± 0.06 kPa) and from instrumented microindentation of white matter (0.97 ± 0.40 kPa) and gray matter (0.86 ± 0.20 kPa). We attributed the higher stiffness reported from NICR to that method's assumption of a cavitation instability due to a neo-Hookean constitutive response, which does not capture the strain-stiffening behavior of brain tissue under large strains, and therefore did not provide appropriate measurements. We demonstrate via both analytical modeling of a spherical cavity and finite element modeling of a needle geometry, that this strain stiffening may prevent a cavitation instability. VCCE measurements take this stiffening behavior into account by employing an incompressible one-term Ogden model to find the nonlinear elastic properties of the tissue. Overall, VCCE afforded rapid and facile measurement of nonlinear mechanical properties of intact, healthy mammalian brain tissue, enabling quantitative comparison among brain tissue regions and also between species. Finally, accurate estimation of elastic properties for this strain stiffening tissue requires methods that include appropriate constitutive models of the brain tissue response, which here are represented by inclusion of the Ogden model in VCCE.

Cavitation in soft matter

Cavitation is the sudden, unstable expansion of a void or bubble within a liquid or solid subjected to a negative hydrostatic stress. Cavitation rheology is a field emerging from the development of a suite of materials characterization, damage quantification, and therapeutic techniques that exploit the physical principles of cavitation. Cavitation rheology is inherently complex and broad in scope with wide-ranging applications in the biology, chemistry, materials, and mechanics communities. This perspective aims to drive collaboration among these communities and guide discussion by defining a common core of high-priority goals while highlighting emerging opportunities in the field of cavitation rheology. A brief overview of the mechanics and dynamics of cavitation in soft matter is presented. This overview is followed by a discussion of the overarching goals of cavitation rheology and an overview of common experimental techniques. The larger unmet needs and challenges of cavitation in soft matter are then presented alongside specific opportunities for researchers from different disciplines to contribute to the field.

Residual strain effects in needle-induced cavitation

Needle-induced cavitation (NIC) locally probes the elastic and fracture properties of soft materials, such as gels and biological tissues. Current NIC protocols tend to overestimate properties when compared to traditional techniques. New NIC methods are needed in order to address this issue. NIC measurements consist of two distinct processes, namely (1) the needle insertion process and (2) the cavitation process. The cavitation process is hypothesized to be highly dependent on the initial needle insertion process due to the influence of residual strain below the needle. Retracting the needle before pressurization to a state in which a cylindrical, tube-like fracture is left below the needle tip is experimentally demonstrated to reduce the impact of residual strain on NIC. Verification of the critical cavitation pressure equation in this new geometry is necessary before implementing this retraction NIC protocol. Complementary modeling shows that the change in initial geometry has little effect on the critical cavitation pressure. Together, these measurements demonstrate that needle retraction is a viable experimental protocol for reducing the influence of residual strain, thus enabling the confident measurement of local elastic and fracture properties in soft gels and tissues.

Using cavitation rheology to understand dipeptide-based low molecular weight gels

The study of dipeptide-based hydrogels has been the focus of significant effort recently due to their potential for use in a variety of biomedical and biotechnological applications. It is essential to study the mechanical properties in order to fully characterise and understand this type of soft materials. In terms of mechanical properties, the linear elastic modulus is normally measured using traditional shear rheometry. This technique requires millilitre sample volumes, which can be difficult when only small amounts of gel are available, and can present difficulties when loading the sample into the machine. Here, we describe the use of cavitation rheology, an easy and efficient technique, to characterise the linear elastic modulus of a range of hydrogels. Unlike traditional shear rheometry, this technique can be used on hydrogels in their native environment, and small sample volumes are required. We describe our set-up and show how it can be used to probe and understand different types of gels. Gels can be formed by different triggers from the same gelator and this leads to different microstructures. We show that the data from the cavitational rheometer correlates with the underlying microstructure in the gels, which allows a greater degree of understanding of the gels than can be obtained from the bulk measurements.

The intimate relationship between cavitation and fracture

Nearly three decades ago, the field of mechanics was cautioned of the obscure nature of cavitation processes in soft materials [A. Gent, Cavitation in rubber: a cautionary tale, Rubber Chem. Technol., 1990, 63, 49-53]. Since then, the debate on the mechanisms that drive this failure process is ongoing. Using a high precision volume controlled cavity expansion procedure, this paper reveals the intimate relationship between cavitation and fracture. Combining a Griffith inspired formulation for crack propagation, and a Gent inspired formulation for cavity expansion, we show that despite the apparent complexity of the fracture patterns, the pressure-volume response follows a predictable path. In contrast to available studies, both the model and our experiments are able to track the entire process including the unstable branch, by controlling the volume of the cavity. Moreover, this minimal theoretical framework is able to explain the ambiguity in previous experiments by revealing the presence of metastable states that can lead to first order transitions at onset of fracture. The agreement between the simple theory and all of the experimental results conducted in PDMS samples with shear moduli in the range of 25-246 [kPa] confirms that cavitation and fracture work together in driving the expansion process. Through this study we also determine the fracture energy of PDMS and show its significant dependence on strain stiffening.