Elasticity of microscale volumes of viscoelastic soft matter by cavitation rheometry

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.

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.

Microacoustic Metagratings at Ultra-High Frequencies Fabricated by Two-Photon Lithography

The recently proposed bianisotropic acoustic metagratings offer promising opportunities for passive acoustic wavefront manipulation, which is of particular interest in flat acoustic lenses and ultrasound imaging at ultra-high frequency ultrasound. Despite this fact, acoustic metagratings have never been scaled to MHz frequencies that are common in ultrasound imaging. One of the greatest challenges is the production of complex microscopic structures. Owing to two-photon polymerization, a novel fabrication technique from the view of acoustic metamaterials, it is now possible to precisely manufacture sub-wavelength structures in this frequency range. However, shrinking in size poses another challenge; the increasing thermoviscous effects lead to a drop in efficiency and a frequency downshift of the transmission peak and must therefore be taken into account in the design. In this work three microacoustic metagrating designs refracting a normally incident wave toward -35° at 2 MHz are proposed. In order to develop meta-atoms insensitive to thermoviscous effects shape optimization techniques incorporating the linearized Navier-Stokes equations discretized with finite element method are used. The authors report for the first time microscopic acoustic metamaterials manufactured using two-photon polymerization and, subsequently, experimentally verify their effectiveness using an optical microphone as a detector in a range from 1.8 to 2.2 MHz.

Pressurized interfacial failure of soft adhesives

Interfacial separation of soft, often viscoelastic, materials typically cause the onset of instabilities, such as cavitation and fingering. These instabilities complicate the pathways for interfacial separation, and hence hinder the quantitative characterization of bulk and interfacial contributions to soft material adhesion. To overcome these challenges, we developed a method termed pressurized interfacial failure (PIF), in which the interfacial separation is controlled by applying a positive pressure at the contact interface between a rigid, annular probe and a thin adhesive. We conducted experiments on model and commercially-available acrylic adhesives. Surprisingly, all the materials studied here fail by an inside-out growth of an interfacial cavity and show similar trends in the interrelationship between the cavity radius, applied pressure and change of contact force. In contrast, the force-displacement relationships of the same materials measured by conventional tack tests vary significantly. Accordingly, we conclude that the PIF method allows for controlling the interfacial failure mechanism. Furthermore, we have applied a linear elastic fracture mechanics framework and conducted finite element analysis to develop analytical models to calculate the critical energy release rate for interfacial separation, G_c. For model acrylic adhesives and commercially available adhesives, the values of G_c are similar to values determined by sphere-probe tack tests. Collectively, the herein introduced PIF method and analysis work provide a new foundation for quantitatively decoupling the interfacial and bulk contributions to soft polymer adhesion.

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.

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.

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.

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

Cavity expansion can be used to measure the local nonlinear elastic properties in soft materials, regardless of the specific damage or instability mechanism that it may ultimately induce. To that end, we introduce a volume-controlled cavity expansion procedure and an accompanying method that builds on the Cavitation Rheology technique [J. A. Zimberlin et al., Soft Matter, 2007, 3, 763-767], but without relying on the maximum recorded pressure. This is achieved by determining an effective radius of the cavity that is based on the volume measurements, and is further supported by numerical simulations. Applying this method to PDMS samples, we show that it consistently collapses the experimental curves to the theoretical prediction of cavity expansion prior to the occurrence of fracture or cavitation, thus resulting in high precision measurement with less than 5% of scatter and good agreement with results obtained via conventional techniques. Moreover, since it does not require visual tracking of the cavity, this technique can be applied to measure the nonlinear elastic response in opaque samples.

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.

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.

The mechanical properties of individual cell spheroids

The overall physical properties of tissues emerge in a complex manner from the properties of the component cells and other constituent materials from which the tissue is formed, across multiple length scales ranging from nanometres to millimetres. Recent studies have suggested that interfacial tension between cells contributes significantly to the mechanical properties of tissues and that the overall surface tension is determined by the ratio of adhesion tension to cortical tension. Using cavitation rheology (CR), we have measured the interfacial properties and the elastic modulus of spheroids formed from HEK cells. By comparing the work of bubble formation with deformation of the cell spheroid at different length scales, we have estimated the cortical tension for HEK cells. This innovative approach to understanding the fundamental physical properties associated with tissue mechanics may guide new approaches for the generation of materials to replace or regenerate damaged or diseased tissues.

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.

Elastic cavitation and fracture via injection

The cavitation rheology technique extracts soft materials mechanical properties through pressure-monitored fluid injection. Properties are calculated from the system's response at a critical pressure that is governed by either elasticity or fracture (or both); however previous elementary analysis has not been capable of accurately determining which mechanism is dominant. We combine analyses of both mechanisms in order to determine how the full system thermodynamics, including far-field compliance, dictate whether a bubble in an elastomeric solid will grow through either reversible or irreversible deformations. Applying these analyses to experimental data, we demonstrate the sensitivity of cavitation rheology to microstructural variation via a co-dependence between modulus and fracture energy.

Nonlinear elasticity and cavitation of a triblock copolymer gel

Polymer gels are subjected to large-strain deformation during their applications. The gel deformation at large-strain is non-linear and can often lead to failure of the material. Here, we report the large-strain deformation behavior of a physically cross-linked, swollen triblock copolymer gel, which displays unique strain-stiffening response at large-strain. Investigations were performed using large amplitude oscillatory shear (LAOS) and custom developed cavitation rheology techniques. The Gent constitutive equation, which considers finite extensibility of midblock, was fitted with the LAOS data, thereby, linking the estimated parameters from LAOS analysis to the structure of the gel. The pressure responses obtained from the cavitation experiments were modeled using neo-Hookean and Gent constitutive equations. Our results capture the failure behavior of a gel with finite chain extensibility, initiated from a defect within the gel.

Elasticity of microscale volumes of viscoelastic soft matter by cavitation rheometry

Measurement of the elastic modulus of soft, viscoelastic liquids with cavitation rheometry is demonstrated for specimens as small as 1 μl by application of elasticity theory and experiments on semi-dilute polymer solutions. Cavitation rheometry is the extraction of the elastic modulus of a material, E, by measuring the pressure necessary to create a cavity within it [J. A. Zimberlin, N. Sanabria-DeLong, G. N. Tew, and A. J. Crosby, Soft Matter 3, 763-767 (2007)]. This paper extends cavitation rheometry in three ways. First, we show that viscoelastic samples can be approximated with the neo-Hookean model provided that the time scale of the cavity formation is measured. Second, we extend the cavitation rheometry method to accommodate cases in which the sample size is no longer large relative to the cavity dimension. Finally, we implement cavitation rheometry to show that the theory accurately measures the elastic modulus of viscoelastic samples with volumes ranging from 4 ml to as low as 1 μl.