Soft Biological Materials Research Articles

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures

Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress–strain curves of human skins. The underlying relations between the J-shaped stress–strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress–strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress–strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress–strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress–strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions.

Geometric effects in microfluidics on heterogeneous cell stress using an Eulerian-Lagrangian approach.

The response of individual cells at the micro-scale in cell mechanics is important in understanding how they are affected by changing environments. To control cell stresses, microfluidics can be implemented since there is tremendous control over the geometry of the devices. Designing microfluidic devices to induce and manipulate stress levels on biological cells can be aided by computational modeling approaches. Such approaches serve as an efficient precursor to fabricating various microfluidic geometries that induce predictable levels of stress on biological cells, based on their mechanical properties. Here, a three-dimensional, multiphase computational fluid dynamics (CFD) modeling approach was implemented for soft biological materials. The computational model incorporates the physics of the particle dynamics, fluid dynamics and solid mechanics, which allows us to study how stresses affect the cells. By using an Eulerian-Lagrangian approach to treat the fluid domain as a continuum in the microfluidics, we are conducting studies of the cells' movement and the stresses applied to the cell. As a result of our studies, we were able to determine that a channel with periodically alternating columns of obstacles was capable of stressing cells at the highest rate, and that microfluidic systems can be engineered to impose heterogenous cell stresses through geometric configuring. We found that when using controlled geometries of the microfluidics channels with staggered obstructions, we could increase the maximum cell stress by nearly 200 times over cells flowing through microfluidic channels with no obstructions. Incorporating computational modeling in the design of microfluidic configurations for controllable cell stressing could help in the design of microfludic devices for stressing cells such as cell homogenizers.

Indentation analysis of biphasic viscoelastic hydrogels

Mechanical properties of soft biological materials are dependent on the responses of the two phases of which they are comprised: the solid matrix and interstitial fluid. Indentation techniques are commonly used to measure properties of such materials, but comparisons between different experimental, and analytical techniques can be difficult. Most models relating load, and time during spherical indentation are based on Hertzian contact theory, but the exact limitation of this theory for soft materials are unclear. Here, we examine the response of gelatin hydrogels to shear and indentation loading to quantify combined effects of the solid, and fluid phases. The instantaneous behavior of the hydrogels is different for each test geometry, and loading rate, but the relaxed response, measured by the relaxed modulus, is the same for all tests, within 17%. Additionally, indentation depths from 15% to 25% of the radius of the spherical indenter are found to minimize error in the estimate of relaxed modulus.

Swelling Behavior of Soft and Biological Materials

Injuries or other ailments can cause swelling of tissues in the body, or of ligaments and tendons surrounding the bones. Such inflammation can lead to discomfort, pain, or even serious illness. Knowledge of the biomechanics of soft tissues is essential for correct prognosis and diagnosis. This requires good modeling and simulation of soft skeletal tissues, which cannot be carried out without experimental material characterization. Behavior of organic tissues is quite similar to that of elastomeric materials that swell when immersed in certain fluids. This work investigates the effect of swelling on compression and bulk properties and the polymeric structure of a water-based elastomer. A drastic change in mechanical and structural properties is observed during the initial swelling period. Elastic and shear moduli decrease by nearly 90% within a few days, and then exhibit almost no change. An opposite trend can be observed for Poisson’s ratio; dramatic increase in the beginning, then a near-constant behavior. Variation in bulk modulus is somewhat fluctuating, but the general trend is a decrease due to swelling. After ten days of swelling, value of Poisson’s ratio becomes approximately 0.5. A sharp decrease in the first week of swelling can be observed in chain density, while cross-link average molecular weight shows the opposite trend of an increase with swelling (with minor fluctuations). Results of this study can provide the material input values for modeling and simulation of the behavior of tissues and other soft biological materials. This, in turn, can form a basis for more detailed analytical and computational studies in biomechanics and biomedical engineering.

The mechanical properties of plant cell walls soft material at the subcellular scale: the implications of water and of the intercellular boundaries

Subcellular mechanical characterization of the cell wall can provide important insights into the cell wall’s functional organization, especially if the characterization is not confounded by extracellular factors and intercellular boundaries. However, due to the technical challenges associated with the microscale mechanical characterization of soft biological materials, subcellular investigations of the plant cell wall under tensile loading have yet to be properly performed. This study reports the mechanical characterization of primary onion epidermal cell wall profiles using a novel cryosection-based sample preparation method and a microelectromechanical system-based tensile testing protocol. At the subcellular scale, the cell wall showed biphasic behavior similar to tissue samples. However, instead of a transition zone between the linear elastic or viscoelastic and linear plastic zones, the subcellular-scale samples showed a plateau-like trend with a sharp drop in the modulus value. The critical ranges of stress (20–40 MPa) and strain (5–12 %) of the plateau zone were identified. A strain energy of 1.3 MJ m−3 was calculated at the midpoint of the critical stress–strain range; this value was in accordance with the previously estimated hydrogen bond energy of the cell wall. Subcellular-scale samples showed very large lateral/axial deformations (0.8 ± 0.13) at fracturing. In addition, investigating the cell wall’s mechanical properties at three different water states showed that water is critical for the flow-like behavior of cell wall matrix polymers. These results at subcellular scale provide new insights into biological materials that possess a structural hierarchy at different length scales; which cannot be obtained from tissue-scale experiments.

Biomechanical properties and microstructure of human ventricular myocardium

In the multidisciplinary field of heart research it is of utmost importance to identify accurate myocardium material properties for the description of phenomena such as mechano-electric feedback or heart wall thickening. A rationally-based material model is required to understand the highly nonlinear mechanics of complex structures such as the passive myocardium under different loading conditions. Unfortunately, to date there are no experimental data of human heart tissues available to estimate material parameters and to develop adequate material models. This study aimed to determine biaxial extension and triaxial shear properties and the underlying microstructure of the passive human ventricular myocardium. Using new state-of-the-art equipment, planar biaxial extension tests were performed to determine the biaxial extension properties of the passive ventricular human myocardium. Shear properties of the myocardium were examined by triaxial simple shear tests performed on small cubic specimens excised from an adjacent region of the biaxial extension specimens. The three-dimensional microstructure was investigated through second-harmonic generation (SHG) microscopy on optically cleared tissues, which emphasized the 3D orientation and dispersion of the myofibers and adjacent collagen fabrics. The results suggest that the passive human LV myocardium under quasi-static and dynamic multiaxial loadings is a nonlinear, anisotropic (orthotropic), viscoelastic and history-dependent soft biological material undergoing large deformations. Material properties of the tissue components along local microstructural axes drive the nonlinear and orthotropic features of the myocardium. SHG microscopy investigation revealed detailed information about the myocardial microstructure due to its high resolution. It enabled the identification of structural parameters such as the fiber and the sheet orientations and corresponding dispersions. With this complete set of material data, a sophisticated material model and associated material parameters can be defined for a better description of the biomechanical response of the ventricular myocardium in humans. Such a model will lead to more accurate computational simulations to better understand the fundamental underlying ventricular mechanics, a step needed in the improvement of medical treatment of heart diseases. Statement of SignificanceUnfortunately, to date there are no experimental data of human heart tissues available for material parameter estimation and the development of adequate material models. In this manuscript novel biaxial tensile and shear test data at different specimen orientations are presented, which allowed to adequately capture the direction-dependent material response. With these complete sets of mechanical data, combined with their underlying microstructural data (also presented herein), sophisticated material models and associated material parameters can be defined for the description of the mechanical behavior of the ventricular myocardium in humans. Such models will lead to accurate computational simulations to better understand the fundamental underlying ventricular mechanics, a step needed in the improvement of medical treatment of heart diseases.

Biaxial mechanical response of graft material derived from human skin

Soft biological materials (skin, muscle) constituting the face are known to have complex mechanical properties. The characterization of their mechanical properties in different testing configuratio...

Analysis of amplitude modulation atomic force microscopy in aqueous salt solutions

We present a numerical analysis of amplitude modulation atomic force microscopy in aqueous salt solutions, by considering the interaction of the microscope tip with a model sample surface consisting of a hard substrate and soft biological material through Hertz and electrostatic double layer forces. Despite the significant improvements reported in the literature concerning contact-mode atomic force microscopy measurements of biological material due to electrostatic interactions in aqueous solutions, our results reveal that only modest gains of ∼15% in imaging contrast at high amplitude setpoints are expected under typical experimental conditions for amplitude modulation atomic force microscopy, together with relatively unaffected sample indentation and maximum tip–sample interaction values.

Metal-coordination: Using one of nature's tricks to control soft material mechanics.

Growing evidence supports a critical role of dynamic metal-coordination crosslinking in soft biological material properties such as self-healing and underwater adhesion1. Using bio-inspired metal-coordinating polymers, initial efforts to mimic these properties have shown promise2. Here we demonstrate how bio-inspired aqueous polymer network mechanics can be easily controlled via metal-coordination crosslink dynamics; metal ion-based crosslink stability control allows aqueous polymer network relaxation times to be finely tuned over several orders of magnitude. In addition to further biological material insights, our demonstration of this compositional scaling mechanism should provide inspiration for new polymer material property-control designs.

(2+1)-Dimensional manipulation of soft biological materials by opto-thermal diffusiophoresis

In a temperature gradient built by infrared laser heating, polyethylene glycol (PEG) of large concentration moves away from the hot region. The resulting concentration gradient of PEG creates entropic potential well and traps another solute of small concentration due to diffusiophoresis. Here we develop this method to work in two dimensional spaces and time. The steering of laser traps colloids, DNA, and living cells in designed two-dimensional patterns. By modulating laser intensity with time, the protein concentration is periodically controlled in tens of mHz. This method could be useful for a directed assembly of biological materials.

Design and Construction of Low Temperature Attachment for Commercial AFM

With the rapid advancements in the field of nanoscience and nanotechnology, scanning probe microscopy has become an integral part of a typical R&D lab. Atomic force microscope (AFM) has become a familiar name in this category. The AFM measures the forces acting between a fine tip and a sample. The tip is attached to the free end of a cantilever and is brought very close to a surface. Attractive or repulsive forces resulting from interactions between the tip and the surface will cause a positive or negative bending of the cantilever. The bending is detected by means of a laser beam, which is reflected from the backside of the cantilever. Atomic force microscopy is currently applied to various environments (air, liquid, vacuum) and types of materials such as metal semiconductors, soft biological samples, conductive and non-conductive materials. With this technique size measurements or even manipulations of nano-objects may be performed. An experimental setup has been designed and built such that a commercially available Atomic Force Microscope (AFM) (Nanosurf AG, Easyscan 2) can be operated at cryogenic temperature under vacuum and in a vibration-free environment. The design also takes care of portability and flexibility of AFM i.e. it is very small, light weight and AFM can be used in both ambient and cryogenic conditions. The whole set up was assembled in-house at a fairly low cost. It is used to study the surface structure of nanomaterials. Important perovskite manganite Pr0.7Ca0.3MnO3thin films were studied and results such as morphology, RMS area and line roughness as well as the particle size have been estimated at cryogenic temperature.

Piezoelectric tuning fork probe for atomic force microscopy imaging and specific recognition force spectroscopy of an enzyme and its ligand

Piezoelectric quartz tuning fork has drawn the attention of many researchers for the development of new atomic force microscopy (AFM) self-sensing probes. However, only few works have been done for soft biological materials imaging in air or aqueous conditions. The aim of this work was to demonstrate the efficiency of the AFM tuning fork probe to perform high-resolution imaging of proteins and to study the specific interaction between a ligand and its receptor in aqueous media. Thus, a new kind of self-sensing AFM sensor was introduced to realize imaging and biochemical specific recognition spectroscopy of glucose oxidase enzyme using a new chemical functionalization procedure of the metallic tips based on the electrochemical reduction of diazonium salt. This scanning probe as well as the functionalization strategy proved to be efficient respectively for the topography and force spectroscopy of soft biological materials in buffer conditions.

Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery

A preoperative simulation of soft tissue deformations during plastic and reconstructive surgery is desirable to support the surgeon’s planning and to improve surgical outcomes. The current development of constitutive adipose tissue models, for the implementation in multilayer computational frameworks for the simulation of human soft tissue deformations, has proved difficult because knowledge of the required mechanical parameters of fat tissue is limited. Therefore, for the first time, human abdominal adipose tissues were mechanically investigated by biaxial tensile and triaxial shear tests. The results of this study suggest that human abdominal adipose tissues under quasi-static and dynamic multiaxial loadings can be characterized as a nonlinear, anisotropic and viscoelastic soft biological material. The nonlinear and anisotropic features are consequences of the material’s collagenous microstructure. The aligned collagenous septa observed in histological investigations causes the anisotropy of the tissue. A hyperelastic model used in this study was appropriate to represent the quasi-static multiaxial mechanical behavior of fat tissue. The constitutive parameters are intended to serve as a basis for soft tissue simulations using the finite element method, which is an apparent method for obtaining promising results in the field of plastic and reconstructive surgery.

Estimating the Mechanical Properties of Retinal Tissue Using Contact Angle Measurements of a Spreading Droplet

When a drop of liquid is placed on the surface of a soft material, the surface deformation and the rate of spreading of the triple contact point is dependent on the mechanical properties of the substrate. This study seeks to use drop spreading behavior to infer the mechanical properties of soft biological materials. As an illustration of the value of this technique we have compared the spreading behavior of a liquid droplet on two viscoelastic, soft materials, namely, an elastomer and a low concentration agar gel. The ratio of the mechanical properties of these soft materials obtained in this way is confirmed by atomic force microscopy (AFM) nanoindentation. By comparing the spreading behavior of a liquid on the retina with that of the same liquid on each of two viscoelastic materials, we can then estimate the elastic moduli of the retina: an estimate that is extremely difficult to carry out using AFM.

Unexpected strain-stiffening in crystalline solids

Strain-stiffening--an increase in material stiffness at large strains--is a vital mechanism by which many soft biological materials thwart excessive deformation to protect tissue integrity. Understanding the fundamental science of strain-stiffening and incorporating this concept into the design of metals and ceramics for advanced applications is an attractive prospect. Using cementite (Fe3C) and aluminium borocarbide (Al3BC3) as prototypes, here we show via quantum-mechanical calculations that strain-stiffening also occurs, surprisingly, in simple inorganic crystalline solids and confers exceptionally high strengths to these two solids, which have anomalously low resistance to deformation near equilibrium. For Fe3C and Al3BC3, their ideal shear strength to shear modulus ratios attain remarkably high values of 1.14 and 1.34 along the (010)[001] and slip systems, respectively. These values are more than seven times larger than the original Frenkel value of 1/2π (refs 4, 5) and are the highest yet reported for crystalline solids. The extraordinary stiffening of Fe3C arises from the strain-induced reversible 'cross-linking' between weakly coupled edge- and corner-sharing Fe6C slabs. This new bond formation creates a strong, three-dimensional covalent bond network that resists large shear deformation. Unlike Fe3C, no new bond forms in Al3BC3 but stiffening still occurs because strong repulsion between Al and B in a compressed Al-B bond unsettles the existing covalent bond network. These discoveries challenge the conventional wisdom that large shear modulus is a reliable predictor of hardness and strength of materials, and provide new lessons for materials selection and design.

Far-field free tapping-mode tip-enhanced Raman microscopy

A tip-enhanced Raman scattering (TERS) microscope has been developed, which is based on the tapping-mode operation of atomic force microscopy. By synchronizing a multichannel detector with tapping oscillation of the metallic nanotip, one can measure a tip-sample separation dependent TERS spectrum and dynamically obtain both near- and far-field Raman signals during the periodic oscillation of the tip. This facilitates TERS imaging with in situ point-by-point removal of far-field background, resulting in higher contrast in TERS imaging. Furthermore, we can obtain an extremely high spatial resolution of 8 nm. Also, tapping mode operation of tip has an added advantage of low sample damage, which could be important for future application of TERS to soft biological materials. Our TERS imaging technique enables us to construct far-field-free high-contrast near-field image at faster imaging speed with extremely high spatial resolution.

Novel Application of Neutron Radiography to Forced Convective Drying of Fruit Tissue

Neutron imaging is a promising technique to study drying processes in food engineering as it is a non-intrusive, non-destructive technique, which provides quasi-real-time quantitative information of the water loss during drying and of the internal water distribution, at a high spatial and dynamic resolution. Particularly, the high sensitivity to water is its main advantage for drying studies, despite the limited accessibility to reactor facilities, which produce neutrons. This technique was used to investigate forced convective drying of fruit tissue (pear and apple), placed in a small wind tunnel. Water loss, water distribution in the sample and sample shrinkage were evaluated as a function of time. The water loss, determined quantitatively from neutron radiographs, was underestimated slightly compared to gravimetrical measurements. The overall drying behaviour agreed well with control measurements performed in a climatic chamber and was very similar for both fruit tissues. The corresponding shrinkage behaviour of both tissues was also similar. The large shrinkage, which is characteristic for soft biological materials such as food products, however, hindered post-processing to some extent. From the internal water distribution, the water gradients within the sample, induced by drying, were visualised and were found to predominantly occur at the air–material interface, indicating that the water transport inside the tissue dominated the water loss, instead of the convective exchange with the air flow. Neutron imaging was shown to exhibit unique benefits for studying drying processes of food.

Biomechanical modeling of surface wrinkling of soft tissues with growth-dependent mechanical properties

This paper explores growth induced morphological instabilities in biological soft materials. In view of that the growth of a living tissue not only changes its geometry but also can alter its mechanical properties, we suggest a refined volumetric growth model incorporating the effects of growth on the mechanical properties of materials. Analogy between this volumetric growth model and the conventional thermal stress model is addressed for both small and finite deformation problems, which brings great ease for the finite element analysis based on the suggested model. Examples of growth induced surface wrinkling behavior in soft composites, including core-shell soft cylinders and three-layered soft tissues, are explored. The results and discussions foresee possible applications of the model in understanding the correlation between the morphogenesis and growth of soft biological tissues (e.g. skins and tumors), as well as in evaluating the deformation and surface instability behavior of soft artificial materials induced by swelling/shrinkage.

Probing structure in colloidal gels of thermoreversible rodlike virus particles: Rheology and scattering

Aggregated suspensions of rodlike particles are commonly encountered in soft biological materials and their solidlike response at extremely low volume fractions is also exploited technologically. Understanding the link between the physicochemical parameters such as size, aspect ratio, volume fraction, and interparticle forces with the resulting microstructure and the subsequent rheological response remains challenging. In the present work, suspensions of monodisperse rodlike virus particles, whose surface is modified by grafting with a thermoreversible polymer poly(N-isopropylacrylamide), are used as a model system. The repulsive and attractive contributions to the total interaction potential can be changed independently by varying the ionic strength and the temperature. The effects of these changes on the strength and structure of gels have been studied near the gel transition using a combination of rheological and scattering measurements. Rheological measurements of the near critical gel properties as a function of concentration and ionic strength proved to be more sensitive compared to scattering in resolving the structural differences. A percolating structure can be formed at very low volume fractions, which show a weak dependence on the ionic strength with the anisotropy of the repulsive interactions playing the main role in creating more “open” structures. The intrinsic stiffness of the rodlike particles does not affect the moduli of the gel states very strongly.

Macrocompression and Nanoindentation of Soft Viscoelastic Biological Materials

The study of the mechanical behavior of soft biological materials presents many challenges due to the materials' time-dependent mechanical response as well as inherent size and shape limitations. In this study, by using agar as a surrogate material for soft tissues, the effects of these limitations upon standardized macroscale dynamic compression protocols are compared to dynamic nanoindentation procedures. Both techniques are then applied to dynamically test porcine sclera tissue, showing a significant difference in recorded loss and storage modulus values between the two methodologies. Additionally, the tissues of the porcine eye wall are characterized with macrocompression in their layered in vivo arrangement. The overall constraints of standardized macroscale tests for dynamic mechanical characterization of thin and soft biological tissues are discussed.