Soft Biological Materials Research Articles

Adhesive and Cohesive Peel Force Measurement of Human Airway Mucus.

In health, the high-speed airflow associated with cough represents a vital backup mechanism for clearing accumulated mucus from our airways. However, alterations in the mucus layer in cystic fibrosis (CF) and chronic obstructive pulmonary disease (COPD) leads to the mucus layer adhered to the airway surfaces, representing the nidus of chronic lung infection. To understand what is different about diseased mucus and why cough clearance is defective, there is a need for techniques to quantify the strength of the interactions limiting the ability of airflow to strip mucus from the airway surface (i.e., adhesive strength) or tear mucus apart (i.e., cohesive strength). To overcome the issues with measuring these properties in a soft (i.e., low elastic modulus) mucus layer, we present here novel peel-testing technologies capable of quantifying the mucus adhesive strength on cultured airway cells and cohesive strength of excised mucus samples. While this protocol focuses on measurements of airway mucus, this approach can easily be adapted to measuring adhesive/cohesive properties of other soft biological materials.

3D Printed lattice microstructures to mimic soft biological materials

Objective. Our group has developed a method for 3D printing mechanically-realistic soft tissue, as a building block towards developing anatomically realistic 3D-printed biomechanical testbed models. Methods. A Polyjet 3D printer was used to print lattice microstructures, which were tested in compression to evaluate the elastic profile. Lattice properties including element diameter, element spacing (ES), element cross-sectional geometry, element arrangement, and lattice rotation were varied to determine their effect on the stress–strain curve. As a case study, a single 3D printed sample was tuned such that its elastic profile matched plantar fat. Results. Element diameter and ES had the largest effect on the stress–strain profile, and rotating the lattice microstructure tends to linearize the curves. A simple cubic lattice microstructure of cylindrical elements, with 0.5 mm diameter columns and 1.2 mm spacing had a stress–strain curve the was closest to plantar fat. The elastic modulus at 10, 30, and 50% strain was 7.55, 9.50, and 252 kPa respectively. Physiologic plantar fat at the same strain values has moduli values of 1.08, 7.13, and 188 kPa. Significance. We demonstrated that lattice microstructures can decrease the young’s modulus of soft 3D printed materials by three orders of magnitude. By creating a method for fine-tuning the elastic profile of 3D-printed materials to behave like human soft tissue, we provide an attractive alternative to more exotic and time-consuming techniques such as molding and casting.

Nonlinear higher-order shell theory for incompressible biological hyperelastic materials

In the present study, a geometrically nonlinear theory for circular cylindrical shells made of incompressible hyperelastic materials is developed. The 9-parameter theory is higher-order in both shear and thickness deformations. In particular, the four parameters describing the thickness deformation are obtained directly from the incompressibility condition. The hyperelastic law selected is a state-of-the-art material model in biomechanics of soft tissues and takes into account the dispersion of collagen fiber directions. Special cases, obtained from this hyperelastic law setting to zero one or some material coefficients, are the Neo-Hookean material and a soft biological material with two families of collagen fibers perfectly aligned. The proposed model is validated through comparison with the exact solution for axisymmetric cylindrical deformation of a thick cylinder. In particular, the shell theory developed herein is capable to describe, with extreme accuracy, even the post-stability problem of a pre-stretched and inflated Neo-Hookean cylinder until the thickness vanishes. Comparison to the solution of higher-order shear deformation theory, which neglects the thickness deformation and recovers the normal strain from the incompressibility condition, is also presented.

Optical Tweezers Microrheology: From the Basics to Advanced Techniques and Applications.

Over the past few decades, microrheology has emerged as a widely used technique to measure the mechanical properties of soft viscoelastic materials. Optical tweezers offer a powerful platform for performing microrheology measurements and can measure rheological properties at the level of single molecules out to near macroscopic scales. Unlike passive microrheology methods, which use diffusing microspheres to extract rheological properties, optical tweezers can probe the nonlinear viscoelastic response, and measure the space- and time-dependent rheological properties of heterogeneous, nonequilibrium materials. In this Viewpoint, I describe the basic principles underlying optical tweezers microrheology, the instrumentation and material requirements, and key applications to widely studied soft biological materials. I also describe several sophisticated approaches that include coupling optical tweezers to fluorescence microscopy and microfluidics. The described techniques can robustly characterize noncontinuum mechanics, nonlinear mechanical responses, strain-field heterogeneities, stress propagation, force relaxation dynamics, and time-dependent mechanics of active materials.

Relevance of Indentation Test to Characterize Soft Biological Tissue: Application to Human Skin

This contribution presents a new investigation to identify the viscoelastic parameters of soft biological materials using indentation test. The purpose is to present a new independent method on experimental specificities in order to characterize these materials. The identification was done using inverse analysis based on combining finite element (FE) numerical simulations and experimental indentation tests. By considering soft tissues as an isotropic linear viscoelastic material, we firstly validate our proposed FE model via a comparison between analytic and numerical indentation responses. Secondly, the existence and uniqueness of inverse problem solution based on the comparison of numerical/numerical responses is shown. Finally, we validate the stability of the inverse approach using sensitivity analysis by setting up a design of experiment (DOE) technique which proves the relevance of this proposed method. An application is made on the forearm of human skin and shows performances of this proposed method to identify viscoelastic human skin properties in spherical loading–unloading indentation test. This method can be applied to evaluate other viscoelastic materials.

The quest for mechanically and biologically functional soft biomaterials via soft network composites.

Developing multifunctional soft biomaterials capable of addressing all the requirements of the complex tissue regeneration process is a multifaceted problem. In order to tackle the current challenges, recent research efforts are increasingly being directed towards biomimetic design concepts that can be translated into soft biomaterials via advanced manufacturing technologies. Among those, soft network composites consisting of a continuous hydrogel matrix and a reinforcing fibrous network closely resemble native soft biological materials in terms of design and composition as well as physicochemical properties. This article reviews soft network composite systems with a particular emphasis on the design, biomaterial and fabrication aspects within the context of soft tissue engineering and drug delivery applications.

Mathematical Modeling and Simulations for Large-Strain J-Shaped Diagrams of Soft Biological Materials.

Herein, we study stress–strain diagrams of soft biological materials such as animal skin, muscles, and arteries by Finsler geometry (FG) modeling. The stress–strain diagram of these biological materials is always J-shaped and is composed of toe, heel, linear, and failure regions. In the toe region, the stress is almost zero, and the length of this zero-stress region becomes very large (≃150%) in, for example, certain arteries. In this paper, we study long-toe diagrams using two-dimensional (2D) and 3D FG modeling techniques and Monte Carlo (MC) simulations. We find that, except for the failure region, large-strain J-shaped diagrams are successfully reproduced by the FG models. This implies that the complex J-shaped curves originate from the interaction between the directional and positional degrees of freedom of polymeric molecules, as implemented in the FG model.

Low Dose X-Ray Speckle Visibility Spectroscopy Reveals Nanoscale Dynamics in Radiation Sensitive Ionic Liquids.

X-ray radiation damage provides a serious bottleneck for investigating microsecond to second dynamics on nanometer length scales employing x-ray photon correlation spectroscopy. This limitation hinders the investigation of real time dynamics in most soft matter and biological materials which can tolerate only x-ray doses of kGy and below. Here, we show that this bottleneck can be overcome by low dose x-ray speckle visibility spectroscopy. Employing x-ray doses of 22-438kGy and analyzing the sparse speckle pattern of count rates as low as 6.7×10^{-3} per pixel, we follow the slow nanoscale dynamics of an ionic liquid (IL) at the glass transition. At the prepeak of nanoscale order in the IL, we observe complex dynamics upon approaching the glass transition temperature T_{G} with a freezing in of the alpha relaxation and a multitude of millisecond local relaxations existing well below T_{G}. We identify this fast relaxation as being responsible for the increasing development of nanoscale order observed in ILs at temperatures below T_{G}.

Modeling ramp-hold indentation measurements based on Kelvin–Voigt fractional derivative model

Interpretation of experimental data from micro- and nano-scale indentation testing is highly dependent on the constitutive model selected to relate measurements to mechanical properties. The Kelvin–Voigt fractional derivative model (KVFD) offers a compact set of viscoelastic features appropriate for characterizing soft biological materials. This paper provides a set of KVFD solutions for converting indentation testing data acquired for different geometries and scales into viscoelastic properties of soft materials. These solutions, which are mostly in closed-form, apply to ramp-hold relaxation, load-unload and ramp-load creep-testing protocols. We report on applications of these model solutions to macro- and nano-indentation testing of hydrogels, gastric cancer cells and ex vivo breast tissue samples using an atomic force microscope (AFM). We also applied KVFD models to clinical ultrasonic breast data using a compression plate as required for elasticity imaging. Together the results show that KVFD models fit a broad range of experimental data with a correlation coefficient typically R2 > 0.99. For hydrogel samples, estimation of KVFD model parameters from test data using spherical indentation versus plate compression as well as ramp relaxation versus load-unload compression all agree within one standard deviation. Results from measurements made using macro- and nano-scale indentation agree in trend. For gastric cell and ex vivo breast tissue measurements, KVFD moduli are, respectively, 1/3–1/2 and 1/6 of the elasticity modulus found from the Sneddon model. In vivo breast tissue measurements yield model parameters consistent with literature results. The consistency of results found for a broad range of experimental parameters suggest the KVFD model is a reliable tool for exploring intrinsic features of the cell/tissue microenvironments.

Anti-plane crack solutions in higher-order elasticity

The asymptotic solutions for cracks in a linear elastic medium under plane or anti-plane state were obtained by Williams (1957) nearly sixty years ago. However, solutions for cracks in second-order elasticity are unavailable, in contrast to those based on the neo–Hookean models, e.g., Knowles (1997). This paper addresses the formulation and solution of crack problems under finite anti-plane deformation using higher-order elasticity. It is found that: (1) a combined second- and third-order elasticity is necessary to ensure that full equilibrium is satisfied, (2) the equilibrium equations are non-homogeneous partial differential equations (pde's) with variable coefficients, and (3) exact particular solutions can be obtained while the homogeneous pde's reduce to nonlinear eigenvalue problems that can be solved numerically. The results show that: (1) the displacement or stress dependence on the radial coordinate is generally a function of the elastic constants, (2) the Piola–Kirchhoff stress matrix is fully populated, with induced normal stresses, in-plane as well as out-of-plane shear stresses, (3) singular stresses at the crack tip may exist, depending on the eigenvalues, and (4) normal stresses are predicted on the crack faces, which may lead to anomalous mechanical behavior in soft biological materials.

Biphasic Synergistic Gel Materials with Switchable Mechanics and Self-Healing Capacity.

A fabrication strategy for biphasic gels is reported, which incorporates high-internal-phase emulsions. Closely packed micro-inclusions within the elastic hydrogel matrix greatly improve the mechanical properties of the materials. The materials exhibit excellent switchable mechanics and shape-memory performance because of the switchable micro- inclusions that are incorporated into the hydrogel matrix. The produced materials demonstrated a self-healing capacity that originates from the noncovalent effect of the biphasic heteronetwork. The aforementioned characteristics suggest that the biphasic gels may serve as ideal composite gel materials with validity in a variety of applications, such as soft actuators, flexible devices, and biological materials.

Biphasic Synergistic Gel Materials with Switchable Mechanics and Self‐Healing Capacity

AbstractA fabrication strategy for biphasic gels is reported, which incorporates high‐internal‐phase emulsions. Closely packed micro‐inclusions within the elastic hydrogel matrix greatly improve the mechanical properties of the materials. The materials exhibit excellent switchable mechanics and shape‐memory performance because of the switchable micro‐ inclusions that are incorporated into the hydrogel matrix. The produced materials demonstrated a self‐healing capacity that originates from the noncovalent effect of the biphasic heteronetwork. The aforementioned characteristics suggest that the biphasic gels may serve as ideal composite gel materials with validity in a variety of applications, such as soft actuators, flexible devices, and biological materials.

Efficient isogeometric thin shell formulations for soft biological materials

This paper presents three different constitutive approaches to model thin rotation-free shells based on the Kirchhoff-Love hypothesis. One approach is based on numerical integration through the shell thickness while the other two approaches do not need any numerical integration and so they are computationally more efficient. The formulation is designed for large deformations and allows for geometrical and material nonlinearities, which makes it very suitable for the modeling of soft tissues. Furthermore, six different isotropic and anisotropic material models, which are commonly used to model soft biological materials, are examined for the three proposed constitutive approaches. Following an isogeometric approach, NURBS-based finite elements are used for the discretization of the shell surface. Several numerical examples are investigated to demonstrate the capabilities of the formulation. Those include the contact simulation during balloon angioplasty.

A Validation Study of the Repeatability and Accuracy of Atomic Force Microscopy Indentation Using Polyacrylamide Gels and Colloidal Probes.

The elasticity of soft biological materials is a critical property to understand their biomechanical behaviors. Atomic force microscopy (AFM) indentation method has been widely employed to measure the Young's modulus (E) of such materials. Although the accuracy of the method has been recently evaluated based on comparisons with macroscale E measurements, the repeatability of the method has yet to be validated for rigorous biomechanical studies of soft elastic materials. We tested the AFM indentation method using colloidal probes and polyacrylamide (PAAM) gels of E < 20 kPa as a model soft elastic material after having identified optimal trigger force and probe speed. AFM indentations repeated with time intervals show that the method is well repeatable when performed carefully. Compared with the rheometric method and the confocal microscopy indentation method, the AFM indentation method is evaluated to have comparable accuracy and better precision, although these elasticity measurements appear to rely on the compositions of PAAM gels and the length scale of measurement. Therefore, we have confirmed that the AFM indentation method can reliably measure the elasticity of soft elastic materials.

Assembling Enzymatic Cascade Pathways inside Virus-Based Nanocages Using Dual-Tasking Nucleic Acid Tags.

The packaging of proteins into discrete compartments is an essential feature for cellular efficiency. Inspired by Nature, we harness virus-like assemblies as artificial nanocompartments for enzyme-catalyzed cascade reactions. Using the negative charges of nucleic acid tags, we develop a versatile strategy to promote an efficient noncovalent co-encapsulation of enzymes within a single protein cage of cowpea chlorotic mottle virus (CCMV) at neutral pH. The encapsulation results in stable 21–22 nm sized CCMV-like particles, which is characteristic of an icosahedral T = 1 symmetry. Cryo-EM reconstruction was used to demonstrate the structure of T = 1 assemblies templated by biological soft materials as well as the extra-swelling capacity of these T = 1 capsids. Furthermore, the specific sequence of the DNA tag is capable of operating as a secondary biocatalyst as well as bridging two enzymes for co-encapsulation in a single capsid while maintaining their enzymatic activity. Using CCMV-like particles to mimic nanocompartments can provide valuable insight on the role of biological compartments in enhancing metabolic efficiency.

Versatile and inexpensive Hall-Effect force sensor for mechanical characterization of soft biological materials

Mismatch of hierarchical structure and mechanical properties between tissue-engineered implants and native tissue may result in signal cues that negatively impact repair and remodeling. With bottom-up tissue engineering approaches, designing tissue components with proper microscale mechanical properties is crucial to achieve necessary macroscale properties in the final implant. However, characterizing microscale mechanical properties is challenging, and current methods do not provide the versatility and sensitivity required to measure these fragile, soft biological materials. Here, we developed a novel, highly sensitive Hall-Effect based force sensor that is capable of measuring mechanical properties of biological materials over wide force ranges (μN to N), allowing its use at all steps in layer-by-layer fabrication of engineered tissues. The force sensor design can be easily customized to measure specific force ranges, while remaining easy to fabricate using inexpensive, commercial materials. Although we used the force sensor to characterize mechanics of single-layer cell sheets and silk fibers, the design can be easily adapted for different applications spanning larger force ranges (>N). This platform is thus a novel, versatile, and practical tool for mechanically characterizing biological and biomimetic materials.

Edge wrinkling in elastically supported pre-stressed incompressible isotropic plates

The equations governing the appearance of flexural static perturbations at the edge of a semi-infinite thin elastic isotropic plate, subjected to a state of homogeneous bi-axial pre-stress, are derived and solved. The plate is incompressible and supported by a Winkler elastic foundation with, possibly, wavenumber dependence. Small perturbations superposed onto the homogeneous state of pre-stress, within the three-dimensional elasticity theory, are considered. A series expansion of the plate kinematics in the plate thickness provides a consistent expression for the second variation of the potential energy, whose minimization gives the plate governing equations. Consistency considerations supplement a constraint on the scaling of the pre-stress so that the classical Kirchhoff-Love linear theory of pre-stretched elastic plates is retrieved. Moreover, a scaling constraint for the foundation stiffness is also introduced. Edge wrinkling is investigated and compared with body wrinkling. We find that the former always precedes the latter in a state of uni-axial pre-stretch, regardless of the foundation stiffness. By contrast, a general bi-axial pre-stretch state may favour body wrinkling for moderate foundation stiffness. Wavenumber dependence significantly alters the predicted behaviour. The results may be especially relevant to modelling soft biological materials, such as skin or tissues, or stretchable organic thin-films, embedded in a compliant elastic matrix.

Microneedle-based minimally-invasive measurement of puncture resistance and fracture toughness of sclera.

The sclera provides the structural support of the eye and protects the intraocular contents. Since it covers a large portion of the eye surface and has relatively high permeability for most drugs, the sclera has been used as a major pathway for drug administration. Recently, microneedle (MN) technology has shown the possibility of highly local and minimally-invasive drug delivery to the eye by MN insertion through the sclera or the suprachoroidal space. Although ocular MN needs to be inserted through the sclera, there has been no systematic study to understand the mechanical properties of the sclera, which are important to design ocular MNs. In this study, we investigated a MN-based method to measure the puncture resistance and fracture toughness of the sclera. To reflect the conditions of MN insertion into the sclera, force-displacement curves obtained from MN-insertion tests were used to estimate the puncture resistance and fracture toughness of sclera tissue. To understand the effect of the insertion conditions, dependency of the mechanical properties on insertion speeds, pre-strain of the sclera, and MN sizes were analyzed and discussed. Measurement of mechanical property of soft biological tissue is challenging due to variations between tissue samples or lack of well-defined measurement techniques. Although non-invasive measurement techniques such as nano/micro indentation were employed to locally measure the elastic modulus of soft biological materials, mechanical properties such as puncture resistance or fracture toughness, which requires "invasive" measurement and is important for the application of "microneedles or hypodermic needles", has not been well studied. In this work, we report minimally-invasive measurement of puncture resistance and fracture toughness of sclera using a double MN insertion method. Parametric studies showed that use of MN proved to be advantageous because of minimally-invasive insertion into tissue as well as higher sensitivity to sub-tissue architecture during the measurement.

Finite element simulation for the mechanical characterization of soft biological materials by atomic force microscopy

The characterization of the mechanical properties of soft materials has been traditionally performed through uniaxial tensile tests. Nevertheless, this method cannot be applied to certain extremely soft materials, such as biological tissues or cells that cannot be properly subjected to these tests. Alternative non-destructive tests have been designed in recent years to determine the mechanical properties of soft biological tissues. One of these techniques is based on the use of atomic force microscopy (AFM) to perform nanoindentation tests. In this work, we investigated the mechanical response of soft biological materials to nanoindentation with spherical indenters using finite element simulations. We studied the responses of three different material constitutive laws (elastic, isotropic hyperelastic and anisotropic hyperelastic) under the same process and analyzed the differences thereof. Whereas linear elastic and isotropic hyperelastic materials can be studied using an axisymmetric simplification, anisotropic hyperelastic materials require three-dimensional analyses. Moreover, we established the limiting sample size required to determine the mechanical properties of soft materials while avoiding boundary effects. Finally, we compared the results obtained by simulation with an estimate obtained from Hertz theory. Hertz theory does not distinguish between the different material constitutive laws, and thus, we proposed corrections to improve the quantitative measurement of specific material properties by nanoindentation experiments.

Invivo Pattern Recognition and Digital Image Analysis Shear Stress Distribution in Human Eye

Human eye is made of a number of structural components to deliver vision, and cornea is the front window of the eye. Human cornea is made of soft biological materials. It is unfriendly for exposures to the common energy levels of X-ray scans for repeated probing of its structural architecture. Here we study an alternative imaging methodology by using a normal white-light source. By exploiting the natural birefringent property of cornea, the shear stress distribution pattern and its directional characteristics on the surface of cornea is recognized in vivo. Digital image processing of corneal retardation helps us to locate the stress concentration zones on its surface and to study their features along preferential directions. Such digital image outputs could be used in future to bench mark the health standard of cornea as well as a potential identity signature of people’s eyes.