Elastic cavitation and fracture via injection

Needle-induced cavitation: A method to probe the local mechanics of brain tissue

Traditional mechanical characterization of extremely soft tissues is challenging given difficulty extracting tissue, satisfying geometric requirements, keeping tissues hydrated, and securing the tissue in an apparatus without slippage. The heterogeneous nature and structural complexity of brain tissues on small length scales makes it especially difficult to characterize. Needle-induced cavitation (NIC) is a technique that overcomes these issues and can mechanically characterize brain tissues at precise, micrometer-scale locations. This small-scale capability is crucial in order to spatially characterize diseased tissue states like fibrosis or cancer. NIC consists of inserting a needle into a tissue and pressurizing a fluid until a deformation occurs at the tip of the needle at a critical pressure. NIC is a convenient, affordable technique to measure mechanical properties, such as modulus and fracture energy, and to assess the performance of soft materials. Experimental parameters such as needle size and fluid flowrate are tunable, so that the end-user can control the length and time scales, making it uniquely capable of measuring local mechanical properties across a wide range of strain rates. The portable nature of NIC and capability to conduct in vivo experiments makes it a particularly appealing characterization technique compared to traditional methods. Despite significant developments in the technique over the last decade, wide implementation in the biological field is still limited. Here, we address the limitations of the NIC technique specifically when working with soft tissues and provide readers with expected results for brain tissue. Our goal is to assist others in conducting reliable and reproducible mechanical characterization of soft biomaterials and tissues.

Effect of Polymer Gel Elasticity on Complex Coacervate Phase Behavior

Gels are key materials in biological systems such as tissues and may control biocondensate formation and structure. To further understand the effects of elastic environments on biomacromolecular assembly, we have investigated the phase behavior and radii of complex coacervate droplets in polyacrylamide (PAM) networks as a function of gel modulus. Poly-l-lysine (PLL) and sodium hyaluronate (HA) complex coacervate phases were prepared in PAM gels with moduli varying from 0.035 to 15.0 kPa. The size of the complex coacervate droplets is reported from bright-field microscopy and confocal fluorescence microscopy. Overall, the complex coacervate droplet volume decreases inversely with the modulus. Fluorescence microscopy is also used to determine the phase behavior and concentration of fluorescently tagged HA in the complex coacervate phases as a function of ionic strength (100-270 mM). We find that the critical ionic strength and complex coacervate stability are nonmonotonic as a function of the network modulus and that the local gel concentration can be used to control phase behavior and complex coacervate droplet size scale. By understanding how elastic environments influence simple electrostatic assembly, we can further understand how biomacromolecules exist in complex, crowded, and elastic cellular environments.

Hydrogel drug delivery systems for minimally invasive local immunotherapy of cancer

Although systemic immunotherapy has achieved durable responses and improved survival for certain patients and cancer types, low response rates and immune system-related systemic toxicities limit its overall impact. Intratumoral (intralesional) delivery of immunotherapy is a promising technique to combat mechanisms of tumor immune suppression within the tumor microenvironment and reduce systemic drug exposure and associated side effects. However, intratumoral injections are prone to variable tumor drug distribution and leakage into surrounding tissues, which can compromise efficacy and contribute to toxicity. Controlled release drug delivery systems such as in situ-forming hydrogels are promising vehicles for addressing these challenges by providing improved spatio-temporal control of locally administered immunotherapies with the goal of promoting systemic tumor-specific immune responses and abscopal effects. In this review we will discuss concepts, applications, and challenges in local delivery of immunotherapy using controlled release drug delivery systems with a focus on intratumorally injected hydrogel-based drug carriers.

Crack propagation and arrests in gelatin hydrogels are linked to tip curvatures

Gelatin hydrogels are attractive scaffold materials for tissue engineering applications as they provide motifs for cell attachment, undergo large deformations, and are tunable. Low toughness and brittle fractures however limit their use in load bearing applications. An investigation of crack tip processes and mechanisms of crack propagation is warranted to link fracture properties with material microstructure. We cross-linked gelatin using glutaraldehyde to obtain low cross-linked control hydrogels and used an additional cross-linker, methylglyoxal, to fabricate MGO hydrogels with higher cross-links. We quantified fractures in the gelatin hydrogels from both groups using pure shear notch tests and characterized strain fields near the crack tip using 2-D digital image correlation. We used a numerical method based on Taylor's series expansion to measure the crack tip curvatures in the hydrogels. This method captures tip curvatures better than the parabolic method routinely used in studies. Results from our study show that cracks in gelatin hydrogels underwent frequent arrests during propagation through the specimen width in both groups. MGO hydrogels had 85% enhanced fracture toughness and a significantly higher number of stalls compared to the control group. Crack initiations following stalls in the sample correlated with low tip curvatures in both hydrogel groups. We also show that mechanical stretching blunts the crack tip before crack propagation; the degree of blunting was independent of the cross-link density and elastic modulus of the gelatin hydrogels. These results show a link between crack growth and the tip curvature in cross-linked gelatin hydrogels, and offer potential insights for the development of tougher hydrogels.

Evaporation-Driven Cellular Patterns in Confined Hyperelastic Hydrogels

When a hyperelastic hydrogel confined between two parallel glass plates begins to dry from a lateral boundary, the volume lost by evaporation is accommodated by an inward displacement of the air-hydrogel interface that induces an elastic deformation of the hydrogel. Once a critical front displacement is reached, we observe intermittent fracture events initiated by a geometric instability resulting in localized bursts at the interface. These bursts relax the stresses and irreversibly form air cavities that lead to cellular networks. We show that the spatial extent of the strain field prior to a burst, influenced by the air-hydrogel interfacial tension and the confinement of the gel, determines the characteristic size of the cavities.

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.

Cavitation Rheology of Model Yield Stress Fluids Based on Carbopol

Measuring the surface tension of yield stress fluids has remained a critical challenge due to limitations of the traditional tensiometry techniques. Here, we overcome those limits and successfully measure the surface tension and mechanical properties of a model yield stress fluid based on Carbopol gels via a needle-induced cavitation (NIC) technique. Our results indicate that the surface tension is approximately 70 ± 3 mN/m, and is independent of the rheology of yield stress fluid over a wide range of yield stress values σ_y = 0.5-120 Pa. In addition, we demonstrate that a Young modulus smaller than E < 1 kPa can be successfully measured for Carbopol gels with NIC method. Finally, we present a time-resolved flow structure around the cavity in a host of yield stress fluids, and assess the impact of fluid rheology on the detailed form of flow around the cavity. Interestingly, prior to the critical point associated with cavitation, the yield stress fluid is weakly deformed suggesting that the measured surface tension data reflect the near equilibrium values. Beyond the critical point, the yield stress fluid experiences a strong flow that is controlled by both the critical pressure and the non-Newtonian rheology of the yield stress fluid.

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.

Experimental Study on the Time-Dependent Characteristics of MLPS Transparent Soil Strength

The time-dependent characteristics of transparent soil strength, composed of magnesium lithium phyllosilicate, is important for applying a thixotropic clay surrogate. The gas injection method was employed to obtain the strength, represented as cracking pressure, which was then correlated to variables including rest time, disturbance time, and recovery time. Three concentrations (3, 4, and 5%) were tested. The results show that the strength was directly proportional to the rest time, recovery time, and concentration while the disturbance time reversed. The calculated limit strengths for 3%, 4%, and 5% transparent soils were 3.831 kPa, 8.849 kPa, and 12.048 kPa, respectively. Experimental data also showed that the residual strength for higher concentration transparent soil was more significant than the lower ones. The elastic property immediately generated partial strength recovery after disturbance, while the viscosity property resulted in a slow recovery stage similar to the rest stage. The strength recovery rate was also sensitive to concentration. Furthermore, the strength with 3%, 4%, and 5% concentrations could regain limit values after sufficient recovery, which were calculated as 4.303 kPa, 8.255 kPa, and 14.884 kPa, respectively.

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.

Cavitation nucleation and its ductile-to-brittle shape transition in soft gels under translational mechanical impact

Cavitation bubbles in the human body, when subjected to impact, are being increasingly considered as a possible brain injury mechanism. However, the onset of cavitation and its complex dynamics in biological materials remain unclear. Our experimental results using soft gels as a tissue simulant show that the critical acceleration (a_cr) at cavitation nucleation monotonically increases with increasing stiffness of gelatin A/B, while a_cr for agarose and agar initially increases but is followed by a plateau or even decrease after stiffness reach to ∼100 kPa. Our image analyses of cavitation bubbles and theoretical work reveal that the observed trends in a_cr are directly linked to how bubbles grow in each gel. Gelatin A/B, regardless of their stiffness, form a localized damaged zone (tens of nanometers) at the gel-bubble interface during bubble growth. In contrary, the damaged zone in agar/agarose becomes significantly larger (> 100 times) with increasing shear modulus, which triggers the transition from formation of a small, damaged zone to activation of crack propagation. STATEMENT OF SIGNIFICANCE: We have studied cavitation nucleation and bubble growth in four different types of soft gels (i.e., tissue simulants) under translational impact. The critical linear acceleration for cavitation nucleation has been measured in the simulants by utilizing a recently developed method that mimics acceleration profiles of typical head blunt events. Each gel type exhibits significantly different trends in the critical acceleration and bubble shape (e.g., A gel-specific sphere-to-saucer transition) with increasing gel stiffness. Our theoretical framework, based on the concepts of a damaged zone and crack propagation in each gel, explains underlying mechanisms of the experimental observations. Our in-depth studies shed light on potential links between traumatic brain injuries and cavitation bubbles induced by translational acceleration, the overlooked mechanism in the literature.

Predicting complex nonspherical instability shapes of inertial cavitation bubbles in viscoelastic soft matter

Inertial cavitation in soft matter is an important phenomenon featured in a wide array of biological and engineering processes. Recent advances in experimental, theoretical, and numerical techniques have provided access to a world full of nonlinear physics, yet most of our quantitative understanding to date has been centered on a spherically symmetric description of the cavitation process in water. However, cavitation bubble growth and collapse rarely occur in a perfectly symmetrical fashion, particularly in soft materials. Predicting the onset of dynamically arising, nonspherical instabilities in soft matter has remained a significant, unresolved challenge, in part due to the additional constitutive complexities introduced by the surrounding nonlinear viscoelastic solid. Here, we provide a new theoretical framework capable of accurately predicting the onset of nonspherical instability shapes of a bubble in a soft material by explicitly accounting for all pertinent nonlinear interactions between the cavitation bubble and the solid surroundings. Comparison with high-resolution experimental images from laser-induced cavitation events in a polyacrylamide hydrogel show excellent agreement. Interestingly, and consistent with experimental findings, our model predicts the emergence of various dynamic instability shapes for circumferential bubble stretch ratios greater than 1, in contrast to most quasistatic investigations. Our new theoretical framework not only provides unprecedented insight into the cavitation dynamics in a soft, nonlinear solid, but also provides a quantitative means of interpreting bubble dynamics relevant to a wide array of engineering and medical applications as well as natural phenomena.

Effect of random fiber networks on bubble growth in gelatin hydrogels

In hydrodynamics, the event of dynamic bubble growth in a pure liquid under tensile pressure is known as cavitation. The same event can also be observed in soft materials (e.g., elastomers and hydrogels). However, for soft materials, bubble/cavity growth is either defined as cavitation if the bubble growth is elastic and reversible or as fracture if the cavity growth is by material failure and irreversible. In any way, bubble growth can cause damage to soft materials (e.g., tissue) by inducing high strain and strain-rate deformation. Additionally, a high-strength pressure wave is generated upon the collapse of the bubble. Therefore, it is crucial to identify the critical condition of spontaneous bubble growth in soft materials. Experimental and theoretical observations have agreed that the onset of bubble growth in soft materials requires higher tensile pressure than pure water. The extra tensile pressure is required since the cavitating bubble needs to overcome the elastic and surface energy in soft materials. In this manuscript, we developed two models to study and quantify the extra tensile pressure for different gelatin concentrations. Both the models are then compared with the existing cavitation onset criteria of rubber-like materials. Validation is done with the experimental results of threshold tensile pressure for different gelatin concentrations. Both models can moderately predict the extra tensile pressure within the intermediate range of gelatin concentrations (3-7% [w/v]). For low concentration (∼1%), the network's non-affinity plays a significant role and must be incorporated. On the other hand, for higher concentrations (∼10%), the entropic deformation dominates, and the strain energy formulation is not adequate.

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.

Modeling Elastically Mediated Liquid-Liquid Phase Separation

We propose a continuum theory of the liquid-liquid phase separation in an elastic network, where phase-separated microscopic droplets rich in one fluid component can form as an interplay of fluids mixing, droplet nucleation, network deformation, thermodynamic fluctuation, etc. We find that the size of the phase-separated droplets decreases with the shear modulus of the elastic network in the form of ∝[modulus]^{-1/3} and the number density of the droplet increases almost linearly with the shear modulus ∝[modulus], which are verified by the experimental observations. Phase diagrams in the space of (fluid constitution, mixture interaction, network modulus) are provided, which can help to understand similar phase separations in biological cells and also to guide fabrications of synthetic cells with desired phase 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.

Cutting to measure the elasticity and fracture of soft gels

The fracture properties of very soft and/or brittle materials are challenging to measure directly due to the limitations of existing fracture testing methods. To address this issue, we introduce a razorblade-initiated fracture test (RIFT) to measure the mechanical properties related to fracture for soft polymeric gels. We use RIFT to quantify the elasticity, crack initiation energy, and the fracture energy of gellan hydrogels as a function of gellan concentration. Additionally, we use RIFT to study the role of friction in quantifying the fracture properties for poly(styrene-b-ethylene butadiene-b-styrene) gels as a function of test velocity. This new method provides a simple and efficient means to quantify the fracture properties of soft materials.

Seeded laser-induced cavitation for studying high-strain-rate irreversible deformation of soft materials

Characterizing the high-strain-rate and high-strain mechanics of soft materials is critical to understanding the complex behavior of polymers and various dynamic injury mechanisms, including traumatic brain injury. However, their dynamic mechanical deformation under extreme conditions is technically difficult to quantify and often includes irreversible damage. To address such challenges, we investigate an experimental method, which allows quantification of the extreme mechanical properties of soft materials using ultrafast stroboscopic imaging of highly reproducible laser-induced cavitation events. As a reference material, we characterize variably cross-linked polydimethylsiloxane specimens using this method. The consistency of the laser-induced cavitation is achieved through the introduction of laser absorbing seed microspheres. Based on a simplified viscoelastic model, representative high-strain-rate shear moduli and viscosities of the soft specimens are quantified across different degrees of crosslinking. The quantified rheological parameters align well with the time-temperature superposition prediction of dynamic mechanical analysis. The presented method offers significant advantages with regard to quantifying high-strain rate, irreversible mechanical properties of soft materials and tissues, compared to other methods that rely upon the cyclic dynamics of cavitation. These advances are anticipated to aid in the understanding of how damage and injury develop in soft materials and tissues.

Understanding Factors Governing Distribution Volume of Ethyl Cellulose-Ethanol to Optimize Ablative Therapy in the Liver

OBJECTIVE

Ethanol ablation, the injection of ethanol to induce necrosis, was originally used to treat hepatocellular carcinoma, with survival rates comparable to surgery. However, efficacy is limited due to leakage into surrounding tissue. To reduce leakage, we previously reported incorporating ethyl cellulose (EC) with ethanol as this mixture forms a gel when injected into tissue. To further develop EC-ethanol injection as an ablative therapy, the present study evaluates the extent to which salient injection parameters govern the injected fluid distribution.

METHODS

Utilizing ex vivo swine liver, injection parameters (infusion rate, EC%, infusion volume) were examined with fluorescein added to each solution. After injection, tissue samples were frozen, sectioned, and imaged.

RESULTS

While leakage was higher for ethanol and 3%EC-ethanol at a rate of 10 mL/hr compared to 1 mL/hr, leakage remained low for 6%EC-ethanol regardless of infusion rate. The impact of infusion volume and pressure were also investigated first in tissue-mimicking surrogates and then in tissue. Results indicated that there is a critical infusion pressure beyond which crack formation occurs leading to fluid leakage. At a rate of 10 mL/hr, a volume of 50 μL remained below the critical pressure.

CONCLUSIONS

Although increasing the infusion rate increases stress on the tissue and the risk of crack formation, injections of 6%EC-ethanol were localized regardless of infusion rate. To further limit leakage, multiple low-volume infusions may be employed.

SIGNIFICANCE

These results, and the experimental framework developed to obtain them, can inform optimizing EC-ethanol to treat a range of medical conditions.

Modeling of surface mechanical behaviors of soft elastic solids: theory and examples

Surfaces of soft solids can have significant surface stress, extensional modulus and bending stiffness. Previous theoretical studies have usually examined cases in which both the surface stress and bending stiffness are constant, assuming small deformation. In this work we consider a general formulation in which the surface can support large deformation and carry both surface stresses and surface bending moments. We demonstrate that the large deformation theory can be reduced to the classical linear theory (Shuttleworth equation). We obtain exact solutions for problems of an inflated cylindrical shell and bending of a plate with a finite thickness. Our analysis illustrates the different manners in which surface stiffening and surface bending stabilize these structures. We discuss how the complex surface constitutive behaviors affect the stress field of the bulk. Our calculation provides insights into effects of strain-dependent surface stress and surface bending in the large deformation regime, and can be used as a model to implement surface finite elements to study large deformation of complex structures.

Elastic stresses reverse Ostwald ripening

When liquid droplets nucleate and grow in a polymer network, compressive stresses can significantly increase their internal pressure, reaching values that far exceed the Laplace pressure. When droplets have grown in a polymer network with a stiffness gradient, droplets in relatively stiff regions of the network tend to dissolve, favoring growth of droplets in softer regions. Here, we show that this elastic ripening can be strong enough to reverse the direction of Ostwald ripening: large droplets can shrink to feed the growth of smaller ones. To numerically model these experiments, we generalize the theory of elastic ripening to account for gradients in solubility alongside gradients in mechanical stiffness.

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.

Extreme cavity expansion in soft solids: Damage without fracture

Cavitation is a common damage mechanism in soft solids. Here, we study this using a phase separation technique in stretched, elastic solids to controllably nucleate and grow small cavities by several orders of magnitude. The ability to make stable cavities of different sizes, as well as the huge range of accessible strains, allows us to systematically study the early stages of cavity expansion. Cavities grow in a scale-free manner, accompanied by irreversible bond breakage that is distributed around the growing cavity rather than being localized to a crack tip. Furthermore, cavities appear to grow at constant driving pressure. This has strong analogies with the plasticity that occurs surrounding a growing void in ductile metals. In particular, we find that, although elastomers are normally considered as brittle materials, small-scale cavity expansion is more like a ductile process. Our results have broad implications for understanding and controlling failure in soft solids.

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.

Quantitative relationship between cavitation and shear rheology

Cavitation rheology is a powerful, simple, and inexpensive technique to study the moduli of polymer gels, however its use has not yet become widespread because few studies to date have directly compared this technique to traditional oscillatory shear rheology. Herein, we report a quantitative relationship between the gel modulus determined using cavitation and shear rheology for three series of model gels whose networks are composed of (1) permanently covalent, (2) dynamic-covalent, and (3) physical hydrogen-bond crosslinks. We determine a simple proportionality constant that allows for conversion of the moduli obtained from both types of experiments and is highly dependent on the bond energy responsible for gelation. This study provides a framework for researchers in a broad range of disciplines who can exploit the ease of cavitation rheology and place their results in the context of traditional oscillatory shear rheology.

Acceleration-induced pressure gradients and cavitation in soft biomaterials

The transient, dynamic response of soft materials to mechanical impact has become increasingly relevant due to the emergence of numerous biomedical applications, e.g., accurate assessment of blunt injuries to the human body. Despite these important implications, acceleration-induced pressure gradients in soft materials during impact and the corresponding material response, from small deformations to sudden bubble bursts, are not fully understood. Both through experiments and theoretical analyses, we empirically show, using collagen and agarose model systems, that the local pressure in a soft sample is proportional to the square of the sample depth in the impact direction. The critical acceleration that corresponds to bubble bursts increases with increasing gel stiffness. Bubble bursts are also highly sensitive to the initial bubble size, e.g., bubble bursts can occur only when the initial bubble diameter is smaller than a critical size (≈10 μm). Our study gives fundamental insight into the physics of injury mechanisms, from blunt trauma to cavitation-induced brain injury.

The influence of medium elasticity on the prediction of histotripsy-induced bubble expansion and erythrocyte viability

Histotripsy is a form of therapeutic ultrasound that liquefies tissue mechanically via acoustic cavitation. Bubble expansion is paramount in the efficacy of histotripsy therapy, and the cavitation dynamics are strongly influenced by the medium elasticity. In this study, an analytic model to predict histotripsy-induced bubble expansion in a fluid was extended to include the effects of medium elasticity. Good agreement was observed between the predictions of the analytic model and numerical computations utilizing highly nonlinear excitations (shock-scattering histotripsy) and purely tensile pulses (microtripsy). No bubble expansion was computed for either form of histotripsy when the elastic modulus was greater than 20 MPa and the peak negative pressure was less than 50 MPa. Strain in the medium due to the expansion of a single bubble was also tabulated. The viability of red blood cells was calculated as a function of distance from the bubble wall based on empirical data of impulsive stretching of erythrocytes. Red blood cells remained viable at distances further than 44 µm from the bubble wall. As the medium elasticity increased, the distance over which bubble expansion-induced strain influenced red blood cells was found to decrease sigmoidally. These results highlight the relationship between tissue elasticity and the efficacy of histotripsy. In addition, an upper medium elasticity limit was identified, above which histotripsy may not be effective for tissue liquefaction.

Cavitation nucleation in gelatin: Experiment and mechanism

Dynamic cavitation in soft materials is becoming increasingly relevant due to emerging medical implications such as the potential of cavitation-induced brain injury or cavitation created by therapeutic medical devices. However, the current understanding of dynamic cavitation in soft materials is still very limited, mainly due to lack of robust experimental techniques. To experimentally characterize cavitation nucleation under dynamic loading, we utilize a recently developed experimental instrument, the integrated drop tower system. This technique allows quantitative measurements of the critical acceleration (a_cr) that corresponds to cavitation nucleation while concurrently visualizing time evolution of cavitation. Our experimental results reveal that a_cr increases with increasing concentration of gelatin in pure water. Interestingly, we have observed the distinctive transition from a sharp increase (pure water to 1% gelatin) to a much slower rate of increase (∼10× slower) between 1% and 7.5% gelatin. Theoretical cavitation criterion predicts the general trend of increasing a_cr, but fails to explain the transition rates. As a likely mechanism, we consider concentration-dependent material properties and non-spherical cavitation nucleation sites, represented by pre-existing bubbles in gels, due to possible interplay between gelatin molecules and nucleation sites. This analysis shows that cavitation nucleation is very sensitive to the initial configuration of a bubble, i.e., a non-spherical bubble can significantly increase a_cr. This conclusion matches well with the experimentally observed liquid-to-gel transition in the critical acceleration for cavitation nucleation.

STATEMENT OF SIGNIFICANCE

From a medical standpoint, understanding dynamic cavitation within soft materials, i.e., tissues, is important as there are both potential injury implications (blast-induced cavitation within the brain) as well as treatments utilizing the phenomena (lithotripsy). In this regard, the main results of the present work are (1) quantitative characterization of cavitation nucleation in gelatin samples as a function of gel concentration utilizing well-controlled mechanical impacts and (2) mechanistic understanding of complex coupling between cavitation and liquid-/solid-like material properties of gel. The new capabilities of testing soft gels, which can be tuned to mimic material properties of target organs, at high loading rate conditions and accurately predicting their cavitation behavior are an important step towards developing reliable cavitation criteria in the scope of their biomedical applications.

Cavitation to fracture transition in a soft solid

When a soft solid such as rubber, gel and soft tissue is subject to hydrostatic tension, a small cavity inside the solid expands. For a neo-Hookean solid, when the hydrostatic tension approaches a critical value: 2.5 times its shear modulus, the initially small cavity can expand unboundedly. Such a phenomenon is usually referred to as cavitation instability in soft solids. Several recent experiments have shown that fractures may occur in the material when the hydrostatic tension is far below the critical value. In this article, we study a spherical cavity with a ring crack on its wall and inside a neo-Hookean elastomer subject to hydrostatic tension. We compute the energy release rate associated with the extension of the ring crack, for both pressure-control and (cavity) volume-control loading modes. We find that for the pressure-control mode, the energy release rate increases with the increase of the crack size as well as the magnitude of pressure; for the (cavity) volume-control mode, with a fixed cavity volume, the energy release rate increases with the increase of the crack size when the crack is short; the energy release rate maximizes for an intermediate crack size, and decreases with the increase of crack size when the crack is long. The results obtained in this article may be helpful for understanding cavitation-to-fracture transition in soft solids subject to different loading conditions.

Probing Gelation and Rheological Behavior of a Self-Assembled Molecular Gel

Molecular gels have been investigated over the last few decades; however, mechanical behavior of these self-assembled gels is not well understood, particularly how these materials fail at large strain. Here, we report the gelation and rheological behavior of a molecular gel formed by self-assembly of a low molecular weight gelator (LMWG), di-Fmoc-l-lysine, in 1-propanol/water mixture. Gels were prepared by solvent-triggered technique, and gelation was tracked using Fourier transform infrared (FTIR) spectroscopy and shear rheology. FTIR spectroscopy captures the formation of hydrogen bonding between the gelator molecules, and the change in IR spectra during the gelation process correlates with the gelation kinetics results captured by rheology. Self-assembly of gelator molecules leads to a fiber-like structure, and these long fibers topologically interact to form a gel-like material. Stretched-exponential function can capture the stress-relaxation data. Stress-relaxation time for these gels have been found to be long owing to long fiber dimensions, and the stretching exponent value of 1/3 indicates polydispersity in fiber dimensions. Cavitation rheology captures fracture-like behavior of these gels, and critical energy release rate has been estimated to be of the order 0.1 J/m². Our results provide new understanding of the rheological behavior of molecular gels and their structural origin.

Cavitation-induced damage of soft materials by focused ultrasound bursts: A fracture-based bubble dynamics model

A generalized Rayleigh-Plesset-type bubble dynamics model with a damage mechanism is developed for cavitation and damage of soft materials by focused ultrasound bursts. This study is linked to recent experimental observations in tissue-mimicking polyacrylamide and agar gel phantoms subjected to bursts of a kind being considered specifically for lithotripsy. These show bubble activation at multiple sites during the initial pulses. More cavities appear continuously through the course of the observations, similar to what is deduced in pig kidney tissues in shock-wave lithotripsy. Two different material models are used to represent the distinct properties of the two gel materials. The polyacrylamide gel is represented with a neo-Hookean elastic model and damaged based upon a maximum-strain criterion; the agar gel is represented with a strain-hardening Fung model and damaged according to the strain-energy-based Griffith's fracture criterion. Estimates based upon independently determined elasticity and viscosity of the two gel materials suggest that bubble confinement should be sufficient to prevent damage in the gels, and presumably injury in some tissues. Damage accumulation is therefore proposed to occur via a material fatigue, which is shown to be consistent with observed delays in widespread cavitation activity.

Solvent effects on modulus of poly(propylene oxide)-based organogels as measured by cavitation rheology

A series of novel organogels were synthesized from poly(propylene oxide) (PPO) functionalized with main chain urea moieties which provided rapid gelation and high moduli in a variety of solvents. Three different molecular weight PPOs were used in this study: 430, 2000, and 4000 g mol(-1), each with α,ω-amino-end groups. Four urea groups were introduced into the main chain by reaction with hexamethylene diisocyanate followed by subsequent reaction with a monofunctional alkyl or aromatic amine. This PPO/urea gelator was found to form gels in carbon tetrachloride, chloroform, dichloromethane, toluene, ethyl acetate, and tetrahydrofuran. Among these, carbon tetrachloride and toluene were found to be the best solvents for this system, resulting in perfectly clear gels with high moduli at low mass fraction for PPO-2000 systems. Flory-Huggins polymer-solvent interaction parameter, χ, was found to be a useful indicator of gel quality for these systems, with χCCl4/PPO-2000 < 0.5 and χtoluene/PPO-2000≈ 0.5. Systems with χ parameters >0.5 were found to form low moduli gels, indicating that for these systems, polymer-solvent interaction parameters can be a useful predictor of gel quality in different solvent systems.