Soft Biological Materials Research Articles

Utilizing collagen-coated hydrogels with defined stiffness as calibration standards for AFM experiments on soft biological materials: the case of lung cells and tissue

Abstract Atomic Force Microscopy (AFM) is crucial in mechanobiology for high-resolution imaging and nanomechanical measurements of biological samples, providing insights into their mechanical properties. However, AFM faces challenges such as tip damage and cantilever selection errors, impacting measurement accuracy. This study proposes a methodology using collagen-coated hydrogels with predefined stiffness for calibrating AFM measurements on soft biological materials. By facilitating appropriate cantilever selection, assessing systematic errors, and evaluating tip damage, this approach ensures reliable Young’s modulus measurements. The proof of concept with human lung cells and tissue specimens demonstrates improved accuracy and reliability of AFM-based nanomechanical characterizations, essential for understanding cellular mechanics and disease progression.

Cellular solids and prestressed affine networks as models of the elastic behavior of soft biological structures.

We reviewed two microstructural models, cellular solid models and prestressed affine network models, that have been used previously in studies of elastic behavior of soft biological materials. These models provide simple and mathematically transparent equations that can be used to interpret experimental data and to obtain quantitative predictions of the elastic properties of biological structures. In both models, volumetric density and elastic properties of the microstructure are key determinants of the macroscopic elastic properties. In the prestressed network model, geometrical rearrangement of the microstructure (kinematic stiffness) is also important. As examples of application of these models, we considered the shear behavior of the cytoskeleton of adherent cells, of the collagen network of articular cartilage, and of the lung parenchymal network since their ability to resist shear is important for their normal biological and physiological functions. All three networks carry a pre-existing stress (prestress). We predicted their shear moduli using the microstructural models and compared those predictions with existing experimental data. Prestressed network models of the cytoskeleton and of the lung parenchyma provided a better correspondence to experimental data than cellular solid models. Both cellular solid and prestressed network models of the cartilage collagen network provided reasonable agreements with experimental values. These findings suggested that the kinematic stiffness and material stiffness of microstructural elements were both important determinants of the shear modulus of the cytoskeleton and of the lung parenchyma, whereas elasticity of collagen fibrils had a predominant role in the cartilage shear behavior.

A bi-component model to assess the rheology of soft cellular aggregates probed using the micropipette aspiration technique

The micro-pipette aspiration technique is a classical experiment used to characterize the physical properties of inert fluids and biological soft materials such as cellular aggregates. The physical parameters of the fluid, as viscosity and interfacial tension, are obtained by studying how the fluid enters the pipette when the suction pressure is increased and how it relaxes when the suction pressure is put to zero. A mathematical model representative of the experiment is needed to extrapolate the physical parameters of the fluid-like matter; however, for biological materials as cells or cell aggregates these models are always based on strong starting hypotheses that impact the significance of the identified parameters. In this article, starting from the bi-constituent nature of the cell aggregate, we derive a general mathematical model based of a Cahn-Hilliard-Navier-Stokes set of equations. The model is applied to describe quantitatively the aspiration-retraction dynamics of a cell-aggregate into and out of a pipette. We demonstrate the predictive capability of the model and highlight the impact of the assumptions made on the identified parameters by studying two cases: one with a non-wetting condition between the cells and the wall of the pipette (classical assumption in the literature) and the second one, which is more realistic, with a partial wetting condition (contact angle θs = 150°). Furthermore, our results provide a purely physical explanation to the asymmetry between the aspiration and retraction responses which is alternative to the proposed hypothesis of an mechano-responsive alteration of the surface tension of the cell aggregate. Statement of SignificanceOur study introduces a general mathematical model, based on the Cahn-Hilliard-Navier-Stokes equations, tailored to model micro-pipette aspiration of cell aggregates. The model accounts for the multi-component structure of the cell aggregate and its intrinsic viscoelastic rheology. By challenging prevailing assumptions, particularly regarding perfect non-wetting conditions and the mechano-responsive alteration of cell surface tension, we demonstrate the reliability of the mathematical model and elucidate the mechanisms at play, offering a purely physical explanation for observed asymmetries between the aspiration and retraction stages of the experiment.

A Comprehensive Review of Indentation of Gels and Soft Biological Materials

Abstract Indentation measurement has emerged as a widely adapted technique for elucidating the mechanical properties of soft hydrated materials. These materials, encompassing gels, cells, and biological tissues, possess pivotal mechanical characteristics crucial for a myriad of applications across engineering and biological realms. From engineering endeavors to biological processes linked to both normal physiological activity and pathological conditions, understanding the mechanical behavior of soft hydrated materials is paramount. The indentation method is particularly suitable for accessing the mechanical properties of these materials as it offers the ability to conduct assessments in liquid environment across diverse length and time scales with minimal sample preparation. Nonetheless, understanding the physical principles underpinning indentation testing and the corresponding contact mechanics theories, making judicious choices regarding indentation testing methods and associated experimental parameters, and accurately interpreting the experimental results are challenging tasks. In this review, we delve into the methodology and applications of indentation in assessing the mechanical properties of soft hydrated materials, spanning elastic, viscoelastic, poroelastic, coupled viscoporoelastic, and adhesion properties, as well as fracture toughness. Each category is accomplished by the theoretical models elucidating underlying physics, followed by ensuring discussions on experimental setup requirements. Furthermore, we consolidate recent advancements in indentation measurements for soft hydrated materials highlighting its multifaceted applications. Looking forward, we offer insights into the future trajectory of the indentation method on soft hydrated materials and the potential applications. This comprehensive review aims to furnish readers with a profound understanding of indentation techniques and a pragmatic roadmap of characterizing the mechanical properties of soft hydrated materials.

Clots reveal anomalous elastic behavior of fiber networks.

The adaptive mechanical properties of soft and fibrous biological materials are relevant to their functionality. The emergence of the macroscopic response of these materials to external stress and intrinsic cell traction from local deformations of their structural components is not well understood. Here, we investigate the nonlinear elastic behavior of blood clots by combining microscopy, rheology, and an elastic network model that incorporates the stretching, bending, and buckling of constituent fibrin fibers. By inhibiting fibrin cross-linking in blood clots, we observe an anomalous softening regime in the macroscopic shear response as well as a reduction in platelet-induced clot contractility. Our model explains these observations from two independent macroscopic measurements in a unified manner, through a single mechanical parameter, the bending stiffness of individual fibers. Supported by experimental evidence, our mechanics-based model provides a framework for predicting and comprehending the nonlinear elastic behavior of blood clots and other active biopolymer networks in general.

Macro-indentation testing of soft biological materials and assessment of hyper-elastic material models from inverse finite element analysis

Mechanical characterization of hydrogels and ultra-soft tissues is a challenging task both from an experimental and material parameter estimation perspective because they are much softer than many biological materials, ceramics, or polymers. The elastic modulus of such materials is within the 1 - 100 kPa range, behaving as a hyperelastic solid with strain hardening capability at large strains. In the current study, indentation experiments have been performed on agarose hydrogels, bovine liver, and bovine lymph node specimens. This work reports on the reliable determination of the elastic modulus by indentation experiments carried out at the macro-scale (mm) using a spherical indenter. However, parameter identification of the hyperelastic material properties usually requires an inverse finite element analysis due to the lack of an analytical contact model of the indentation test. Hence a comprehensive study on the spherical indentation of hyperelastic soft materials is carried out through robust computational analysis. Neo-Hookean and first-order Ogden hyperelastic material models were found to be most suitable. A case study on known anisotropic hyperelastic material showed the inability of the inverse finite element method to uniquely identify the whole material parameter set.

Force decomposition and toughness estimation from puncture experiments in soft solids.

Several medical applications, like drug delivery and biosensing, are critically preceded by the insertion of needles and microneedles into biological tissue. However, the mechanical process of needle insertions, especially at high velocities, is currently not fully understood. Here, we explore the insertion of hollow needles into transparent silicone samples with an insertion velocity v ranging from 0.1 mm s-1 to 2.3 m s-1 (with needle radius R = 101.5 μm, thus strain rates ∼v/R ranging from 1 s-1 to 2.3 × 104 s-1). We use a double-insertion method, where the needle is inserted and re-inserted at the same location, to estimate the fracture properties of the material. The deflection of the specimen's free surface is found to be different between insertion and re-insertion experiments for identical needle positions, which is associated with different force magnitudes between insertion/reinsertion. This aspect was previously neglected in the original double-insertion method, thus here we develop a method based on imaging, image analyses and force measurements to decompose the measured force into individual force components, including deflection force Fd, frictional and spreading force Ff + Fs, and cutting force Ft. We estimate that the toughness Γ of our silicone samples, calculated using the cutting force Ft and the crack dimensions, increases with needle velocity, and ranges within observed values in previous literature for the same material and for some soft biological materials. In addition to toughness Γ, other parameters, such as critical force Fc and mechanical work Wc, also show strain-rate dependence, suggesting tissue stiffening, due to accumulated strain energy, at high speeds.

Chain trajectories, domain shapes, and terminal boundaries in block copolymers

AbstractThe packing geometry of macromolecules in complex mesophases is of key importance to self‐organization in synthetic and biological soft materials. While approximate or heuristic models rely on often‐untested assumptions about how flexible molecules “fit in” to distinct locations of complex assemblies, physical assemblies derive from ensembles of fluctuating conformations, obscuring the connection between mesophase geometry and the underlying arrangements. Here, we present an approach to extract and analyze features of molecular packing in diblock block copolymer (BCP) melts, a prototypical soft matter system, based on the statistical description of chain conformations in self‐consistent field (SCF) theory. We show how average BCP chain trajectories in ordered morphologies can be analyzed from the SCF‐derived orientational order parameter of chain segments. We use these extracted trajectories to analyze the features of local packing geometry, including chain bending and tilt, as well as the terminal boundaries that delineate distinct domains in ordered BCP morphologies. We illustrate this analysis by focusing on measurable features of packing frustration in 2D (columnar) and 3D (spherical and bicontinuous) morphologies, notably establishing an explicit link between chain conformations in complex morphologies and their medial geometry.

Optical Manipulation of Soft Matter.

Optical manipulation has emerged as a pivotal tool in soft matter research, offering superior applicability, spatiotemporal precision, and manipulation capabilities compared to conventional methods. Here, an overview of the optical mechanisms governing the interaction between light and soft matter materials during manipulation is provided. The distinct characteristics exhibited by various soft matter materials, including liquid crystals, polymers, colloids, amphiphiles, thin liquid films, and biological soft materials are highlighted, and elucidate their fundamental response characteristics to optical manipulation techniques. This knowledge serves as a foundation for designing effective strategies for soft matter manipulation. Moreover, the diverse range of applications and future prospects that arise from the synergistic collaboration between optical manipulation and soft matter materials in emerging fields are explored.

On the experimental investigation of silicone-based soft composites under mode I loading using Digital Image Correlation

There is a growing interest in understanding the mechanical behavior of fibrous soft biological materials under several loading conditions. Due to difficulties in manipulating and testing these materials, synthetic composites have already been employed in literature. In this work, a fiber-reinforced soft composite was manufactured and tested to extract its mechanical behavior at two different fiber orientations under mode I loading. The domain J-integral was evaluated by means of DIC using a pure shear (planar) configuration. The coefficients of the fourth-order strain energy function proposed by Luo and Chou were adjusted to describe the mechanical behavior of the considered soft composite and its isolated components (i.e., pure silicone rubber and extensible cotton knit fabric) under tensile loading. The values of the J-integral were validated using a classical formulation for homogeneous rubber-like materials. For the soft composite with fibers oriented at θ0=90°, in which the fiber contribution was not considerable, a satisfactory matching was found between J-integral and classical results in the absence of fiber reinforcement (homogeneous materials), resulting in approximately 13.67% of mean relative error. In fact, the J-integral obtained by DIC and the fourth-order hyperelastic strain energy function can be employed to estimate the energy release rate of fiber-reinforced soft composites.

Dose-efficient scanning Compton X-ray microscopy

The highest resolution of images of soft matter and biological materials is ultimately limited by modification of the structure, induced by the necessarily high energy of short-wavelength radiation. Imaging the inelastically scattered X-rays at a photon energy of 60 keV (0.02 nm wavelength) offers greater signal per energy transferred to the sample than coherent-scattering techniques such as phase-contrast microscopy and projection holography. We present images of dried, unstained, and unfixed biological objects obtained by scanning Compton X-ray microscopy, at a resolution of about 70 nm. This microscope was realised using novel wedged multilayer Laue lenses that were fabricated to sub-ångström precision, a new wavefront measurement scheme for hard X rays, and efficient pixel-array detectors. The doses required to form these images were as little as 0.02% of the tolerable dose and 0.05% of that needed for phase-contrast imaging at similar resolution using 17 keV photon energy. The images obtained provide a quantitative map of the projected mass density in the sample, as confirmed by imaging a silicon wedge. Based on these results, we find that it should be possible to obtain radiation damage-free images of biological samples at a resolution below 10 nm.

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.

A Tutorial on the Stability and Bifurcation Analysis of the Electromechanical Behaviour of Soft Materials

AbstractSoft materials, such as liquids, polymers, foams, gels, colloids, granular materials, and most soft biological materials, play an important role in our daily lives. From a mechanical viewpoint, soft materials can easily achieve large deformations due to their low elastic moduli; meanwhile, surface instabilities, including wrinkles, creases, folds, and ridges, among others, are often observed. In particular, soft dielectrics subject to electrical stimuli can achieve significantly large deformations that are often accompanied by instabilities. While instabilities are often thought to cause failures in the engineering context and carry a negative connotation, they can also be harnessed for various applications such as surface patterning, giant actuation strain, and energy harvesting. In the biological world, instability and bifurcation phenomena often precede important events such as endocytosis, and cell fusion, among others. Stability and bifurcation analysis (especially for soft materials) is challenging and often present a formidable barrier to entry in this important field. A multidisciplinary audience may lack the background in one or more areas that are needed to carry out the requisite modeling or even understand papers in the literature. Furthermore, combining electrostatics together with large deformations brings its own challenges. In this article, we provide a tutorial on the basics of stability and bifurcation analysis in the context of soft electromechanical materials. The aim of the article is to use simple examples and “gently” lead a reader, unfamiliar with either stability analysis or electrostatics of deformable media, to develop the ability to understand the pertinent literature that already exists and position them to embark on state-of-the-art research on this topic.

Prediction of Mechanical Responses of a Uniaxially Stretched Neural Fiber Bundle: Theoretical Approach for a Traumatic Loading Condition

Abstract Viscoelasticity of the spinal nerve roots may play a significant role in predicting nerve root damage caused by overall spinal motion. However, only a few studies have investigated the complex mechanical behavior of this tissue. The current study presents a theoretical protocol for predicting mechanical responses of soft biological materials, and this method was used to a uniaxially stretched neural fiber bundle isolated from porcine spinal nerve roots with various loading configurations. Stress relaxation tests were performed to systematically determine a set of parameters dictating the stress decaying process, i.e., a set of relaxation moduli and the corresponding time constants. Based on the obtained experimental and numerical test data, it was confirmed that the proposed method is effective even for the prediction of mechanical response to a cyclic stretch immediately after the ramp-hold test. In addition, an elastic response, i.e., a stress–strain relationship under a high-rate loading regime, was determined analytically. The results demonstrated that instantaneous mechanical responses of neural fiber bundles can be stiffened against very rapid stretch (>10 s−1); however, the fibers are relatively insensitive to moderate loading rates (<1 s−1). The ultimate tensile strength was estimated to be approximately 8 MPa at the structural failure strain (15%). This information will enable the computational assessment of traumatic nerve root injuries sustained during traffic accidents and contact sports.

Microstructure-based engineering of soft biological materials

Aortic disease (AoD) is a leading cause of mortality in developed countries. Two of the most common forms of AoD are aneurysm (widening) and dissection (tear in inner wall). Aneurysm and dissection often associate with bicuspid aortic valve (BAV) instead of the normal tricuspid aortic valve, and BAV aneurysms of ascending thoracic aorta have the tendency to bulge asymmetrically towards the greater curvature of aorta. Multiphoton microscopy can help us image collagen and elastin fibres, which are considered as main load-bearing constituents of the aortic wall, in order to investigate potential role of fibre microstructure in ascending thoracic aortic aneurysm or dissection. Regional differences in fibre microstructure may be driven by distinct mechanisms of vascular remodelling, and, combined with mechanical tests, could improve our understanding of the biomechanical mechanisms of aortic aneurysm and dissection potential. Should we wish to investigate the effect of microstructure in soft tissue formation and organ development, we would have to consider a rapidly growing process. In that process, the cells are the main load-bearing components, which cooperate to produce tissue-level forces that shape tissue formation. Our understanding of this phenomenon, called mechanotransduction, has advanced significantly over the past years, to the point where it is now clear that nearly every biological process is modulated by how these forces are decoded intracellularly. It is therefore important to create our own fluorescently-labeled matrix that could integrate into the tissue and enable tracking of these forces in-vivo. A new 3D optical nanomechanical biosensor (NMBS) based on fluorescent fibronectin fibres was developed based on integrated photolithography and micro-contact printing technology. NMBS was successfully validated under uniaxial tensile test of biologically relevant materials for microscopic vs. macroscopic mechanical strains. In the future, biomimetic 3D scaffolds could be fabricated by assembly of 2D fibre constructs based on the NMBS technology, in order to analyse the effect of selected set of load-bearing microstructural components on both mechanical and functional response of soft biological materials.

Material energy balance at articular cartilage: Bio-tribology

The synergy of heterogeneous macromolecules at the cartilage-cartilage tribological interface prevents friction under quasi-static mechanical loading. Viscoelastic rheology of soft biological membrane materials, hydration lubrication, and biomechanical diffusion integrate boundary lubrication at the superficial zone. Synchronization of mechanical efficiency is viable in alignment with mechanical work, energy expenditure, and reducing oxidative stress of environmental load in urban areas. Carbon nanoparticle’s evolution from anthropogenic activities inversely influence the quality of fuel oxidation. Anisotropic fibrous honeycomb structure panel is included for trapping random environmental carbon nanoparticles/particulate matter for favourable environmental indicators.

EXPANSE: A time-of-flight EXPanded Angle Neutron Spin Echo spectrometer at the Second Target Station of the Spallation Neutron Source

EXPANSE, an EXPanded Angle Neutron Spin Echo instrument, has been proposed and selected as one of the first suite of instruments to be built at the Second Target Station of the Spallation Neutron Source at the Oak Ridge National Laboratory. This instrument is designed to address scientific problems that involve high-energy resolution (neV-μeV) of dynamic processes in a wide range of materials. The wide-angle detector banks of EXPANSE provide coverage of nearly two orders of magnitude in scattering wavenumbers, and the wide wavelength band affords approximately four orders of magnitude in Fourier times. This instrument will offer unique capabilities that are not available in the currently existing neutron scattering instruments in the United States. Specifically, EXPANSE will enable direct measurements of slow dynamics in the time domain over wide Q-ranges simultaneously and will also enable time-resolved spectroscopic studies. The instrument is expected to contribute to a diverse range of science areas, including soft matter, polymers, biological materials, liquids and glasses, energy materials, unconventional magnets, and quantum materials.

Femtosecond Laser Densification of Hydrogels to Generate Customized Volume Diffractive Gratings.

Inspired by nature’s ability to shape soft biological materials to exhibit a range of optical functionalities, we report femtosecond (fs) laser-induced densification as a new method to generate volume or subsurface diffractive gratings within ordinary hydrogel materials. We characterize the processing range in terms of fs laser power, speed, and penetration depths for achieving densification within poly(ethylene glycol) diacrylate (PEGDA) hydrogel and characterize the associated change in local refractive index (RI). The RI change facilitates the fabrication of custom volume gratings (parallel line, grid, square, and ring gratings) within PEGDA. To demonstrate this method’s broad applicability, fs laser densification was used to generate line gratings within the phenylboronic acid (PBA) hydrogel, which is known to be responsive to changes in pH. In the future, this technique can be used to convert ordinary hydrogels into multicomponent biophotonic systems.

Parallel-plate compression test for soft materials: confocal microscopy-assisted ferrule-top nanoindentation.

The parallel-plate compression test is one of the simplest ways to measure the mechanical properties of a material. In this test, the Young's modulus ( ) and the Poisson's ratio ( ) of the material are determined directly without applying any additional modelling and parameter fitting in the post-processing. This is, however, limited when dealing soft biological materials due to their inherent properties such as being inhomogeneous, microscopic, and overly compliant. By combining an interferometry-assisted parallel-plate compression system and a confocal microscope, we were able to overcome these limitations and measure the (315 52 Pa) and (0.210 0.043) of fixated and permeabilized bovine oocytes.

Analysis of surgical needle insertion modeling and viscoelastic tissue material interaction for minimally invasive surgery (MIS)

Soft tissue modeling of surgical events is essential for both considering tissue reactions to surgical instrumentation, in addition, to conducting the design of the surgical instrument. Mainly with observes to surgical needle insertion for minimally invasive surgery (MIS) into soft biological tissue, one of the regularly performed surgical events, many works have been prepared in references to modeling how surgical needles insert the soft biological tissue material as they pass through in the direction of objects deep inside the living body. Deformation of biological soft tissue is one of the important issues, which impacts the surgical needle insert inside the living soft viscoelastic tissue. A needle insertion model is presented to calculate the insertion forces and tissue deformation phenomenon. The experimentations are done on the tissue mimic gel specimens, and the surgical needle insertion-based model for the deformation phenomenon is analyzed to investigate the force model, frictional stress and deflection phenomenon. This study can help to investigate the needle insertion process for analyzing the effect of the surgical needle insertion, which could advance the enactment of several surgical needle insertion-based procedures such as minimally invasive surgery (MIS) and brachytherapy.