3D non-affine finite strains measured in isolated bovine annulus fibrosus tissue samples

Brain tissue mechanics is governed by microscale relations of the tissue constituents

Local mechanical tissue properties are a critical regulator of cell function in the central nervous system (CNS) during development and disorder. However, we still don't fully understand how the mechanical properties of individual tissue constituents, such as cell nuclei or myelin, determine tissue mechanics. Here we developed a model predicting local tissue mechanics, which induces non-affine deformations of the tissue components. Using the mouse hippocampus and cerebellum as model systems, we show that considering individual tissue components alone, as identified by immunohistochemistry, is not sufficient to reproduce the local mechanical properties of CNS tissue. Our results suggest that brain tissue shows a universal response to applied forces that depends not only on the amount and stiffness of the individual tissue constituents but also on the way how they assemble. Our model may unify current incongruences between the mechanics of soft biological tissues and the underlying constituents and facilitate the design of better biomedical materials and engineered tissues. To this end, we provide a freely-available platform to predict local tissue elasticity upon providing immunohistochemistry images and stiffness values for the constituents of the tissue.

Simultaneous Wide-Field Planar Strain-Fiber Orientation Distribution Measurement Using Polarized Spatial Domain Imaging

In the present study, we demonstrate that soft tissue fiber architectural maps captured using polarized spatial frequency domain imaging (pSFDI) can be utilized as an effective texture source for DIC-based planar surface strain analyses. Experimental planar biaxial mechanical studies were conducted using pericardium as the exemplar tissue, with simultaneous pSFDI measurements taken. From these measurements, the collagen fiber preferred direction [Formula: see text] was determined at the pixel level over the entire strain range using established methods ( https://doi.org/10.1007/s10439-019-02233-0 ). We then utilized these pixel-level [Formula: see text] maps as a texture source to quantify the deformation gradient tensor [Formula: see text] as a function of spatial position [Formula: see text] within the specimen at time t. Results indicted that that the pSFDI approach produced accurate deformation maps, as validated using both physical markers and conventional particle based method derived from the DIC analysis of the same specimens. We then extended the pSFDI technique to extract the fiber orientation distribution [Formula: see text] as a function of [Formula: see text] from the pSFDI intensity signal. This was accomplished by developing a calibration procedure to account for the optical behavior of the constituent fibers for the soft tissue being studied. We then demonstrated that the extracted [Formula: see text] was accurately computed in both the referential (i.e. unloaded) and deformed states. Moreover, we noted that the measured [Formula: see text] agreed well with affine kinematic deformation predictions. We also demonstrated this calibration approach could also be effectively used on electrospun biomaterials, underscoring the general utility of the approach. In a final step, using the ability to simultaneously quantify [Formula: see text] and [Formula: see text], we examined the effect of deformation and collagen structural measurements on the measurement region size. For pericardial tissues, we determined a critical length of [Formula: see text] 8 mm wherein the regional variations sufficiently dissipated. This result has immediate potential in the identification of optimal length scales for meso-scale strain measurement in soft tissues and fibrous biomaterials.

A computational framework for biomaterials containing three-dimensional random fiber networks based on the affine kinematics

Understanding the structure-function relationship of biomaterials can provide insights into different diseases and advance numerous biomedical applications. This paper presents a finite element-based computational framework to model biomaterials containing a three-dimensional fiber network at the microscopic scale. The fiber network is synthetically generated by a random walk algorithm, which uses several random variables to control the fiber network topology such as fiber orientations and tortuosity. The geometric information of the generated fiber network is stored in an array-like data structure and incorporated into the nonlinear finite element formulation. The proposed computational framework adopts the affine fiber kinematics, based on which the fiber deformation can be expressed by the nodal displacement and the finite element interpolation functions using the isoparametric relationship. A variational approach is developed to linearize the total strain energy function and derive the nodal force residual and the stiffness matrix required by the finite element procedure. Four numerical examples are provided to demonstrate the capabilities of the proposed computational framework, including a numerical investigation about the relationship between the proposed method and a class of anisotropic material models, a set of synthetic examples to explore the influence of fiber locations on material local and global responses, a thorough mesh-sensitivity analysis about the impact of mesh size on various numerical results, and a detailed case study about the influence of material structures on the performance of eggshell-membrane-hydrogel composites. The proposed computational framework provides an efficient approach to investigate the structure-function relationship for biomaterials that follow the affine fiber kinematics.

Saline-polyethylene glycol blends preserve in vitro annulus fibrosus hydration and mechanics: An experimental and finite-element analysis

Precise control of tissue water content is essential for ensuring accurate, repeatable, and physiologically relevant measurements of tissue mechanics and biochemical composition. While previous studies have found that saline and polyethylene glycol (PEG) blends were effective at controlling tendon and ligament hydration levels, this work has yet to be extended to the annulus fibrosus (AF). Thus, the first objective of this study was to determine and validate an optimal buffer solution for targeting and maintaining hydration levels of tissue-level AF specimens in vitro. This was accomplished by measuring the transient swelling behavior of bovine AF specimens in phosphate-buffered saline (PBS) and PEG buffers across a wide range of concentrations. Sub-failure, failure, and post-failure mechanics were measured to determine the relationship between changes in tissue hydration and tensile mechanical response. The effect of each buffer solution on tissue composition was also assessed. The second objective of this study was to assess the feasibility and effectiveness of using multi-phasic finite element models to investigate tissue swelling and mechanical responses in different external buffer solutions. A solution containing 6.25%w/v PBS and 6.25%w/v PEG effectively maintained tissue-level AF specimen hydration at fresh-frozen levels after 18 h in solution. Modulus, failure stress, failure strain, and post-failure toughness of specimens soaked in this solution for 18 h closely matched those of fresh-frozen specimens. In contrast, specimens soaked in 0.9%w/v PBS swelled over 100% after 18 h and exhibited significantly diminished sub-failure and failure properties compared to fresh-frozen controls. The increased cross-sectional area with swelling contributed to but was not sufficient to explain the diminished mechanics of PBS-soaked specimens, suggesting additional sub-tissue scale mechanisms. Computational simulations of these specimens generally agreed with experimental results, highlighting the feasibility and importance of including a fluid-phase description when models aim to provide accurate predictions of biological tissue responses. As numerous previous studies suggest that tissue hydration plays a central role in maintaining proper mechanical and biological function, robust methods for controlling hydration levels are essential as the field advances in probing the relationship between tissue hydration, aging, injury, and disease.

3D virtual reconstruction and quantitative assessment of the human intervertebral disc's annulus fibrosus: a DTI tractography study

The intervertebral disc’s (IVD) annulus fibrosus (AF) retains the hydrostatic pressure of the nucleus pulposus (NP), controls the range of motion, and maintains the integrity of the motion segment. The microstructure of the AF is not yet fully understood and quantitative characterization is lacking, leaving a caveat in modern medicine’s ability to prevent and treat disc failure (e.g., disc herniation). In this study, we show a reconstruction of the 3D microstructure of the fibers that constitute the AF via MRI diffusion tensor imaging (DTI) followed by fiber tracking. A quantitative analysis presents an anisotropic structure with significant architectural differences among the annuli along the width of the fibrous belt. These findings indicate that the outer annuli's construction reinforces the IVD while providing a sufficient degree of motion. Our findings also suggest an increased role of the outer annuli in IVD nourishment.

Interlamellar-induced time-dependent response of intervertebral disc annulus: A microstructure-based chemo-viscoelastic model

The annulus fibrosus of the intervertebral disc exhibits an unusual transversal behavior for which a constitutive representation that considers as well regional effect, chemical sensitivity and time-dependency has not yet been developed, and it is hence the aim of the present contribution. A physically-based model is proposed by introducing a free energy function that takes into account the actual disc annulus structure in relation with the surrounding biochemical environment. The response is assumed to be dominated by the viscoelastic contribution of the extracellular matrix, the elastic contribution of the oriented collagen fibers and the osmo-induced volumetric contribution of the internal fluid content variation. The regional dependence of the disc annulus response due to variation in fibers content/orientation allows a micromechanical treatment of the soft tissue. A finite element model of the annulus specimen is designed while taking into consideration the 'interlamellar' ground substance zone between lamellae of the layered soft tissue. The kinetics is designed using full-field strain measurements performed on specimens extracted from two disc annulus regions and tested under different osmotic conditions. The time-dependency of the tissue response is reported on stress-free volumetric changes, on hysteretic stress and transversal strains during quasi-static stretching at different strain-rates and on their temporal changes during an interrupted stretching. Considering the effective contributions of the internal fluid transfer and the extracellular matrix viscosity, the microstructure-based chemo-mechanical model is found able to successfully reproduce the significant features of the macro-response and the unusual transversal behavior including the strong regional dependency from inner to outer parts of the disc: Poisson's ratio lesser than 0 (auxetic) in lamellae plane, higher than 0.5 in fibers plane, and their temporal changes towards usual values (between 0 and 0.5) at chemo-mechanical equilibrium. The underlying time-dependent mechanisms occurring in the tissue are analyzed via the local numerical fields and important insights about the effective role of the interlamellar zone are revealed for the different disc localizations. STATEMENT OF SIGNIFICANCE: The structural complexity of the annulus fibrosus has only been appreciated through recent experimental contributions and a constitutive representation that considers as well regional effect, chemical sensitivity and time-dependency of the unusual transversal behavior has not yet been developed. Here, a microstructure-based chemo-viscoelastic model is developed to highlight the interlamellar-induced time-dependent response by means of a two-scale strategy. The model provides important insights about the origin of the time-dependent phenomena in disc annulus along with regional dependency, essential for understanding disc functionality.

Simple and accurate methods for quantifying deformation, disruption, and development in biological tissues

When mechanical factors underlie growth, development, disease or healing, they often function through local regions of tissue where deformation is highly concentrated. Current optical techniques to estimate deformation can lack precision and accuracy in such regions due to challenges in distinguishing a region of concentrated deformation from an error in displacement tracking. Here, we present a simple and general technique for improving the accuracy and precision of strain estimation and an associated technique for distinguishing a concentrated deformation from a tracking error. The strain estimation technique improves accuracy relative to other state-of-the-art algorithms by directly estimating strain fields without first estimating displacements, resulting in a very simple method and low computational cost. The technique for identifying local elevation of strain enables for the first time the successful identification of the onset and consequences of local strain concentrating features such as cracks and tears in a highly strained tissue. We apply these new techniques to demonstrate a novel hypothesis in prenatal wound healing. More generally, the analytical methods we have developed provide a simple tool for quantifying the appearance and magnitude of localized deformation from a series of digital images across a broad range of disciplines.

On the presence of affine fibril and fiber kinematics in the mitral valve anterior leaflet

In this study, we evaluated the hypothesis that the constituent fibers follow an affine deformation kinematic model for planar collagenous tissues. Results from two experimental datasets were utilized, taken at two scales (nanometer and micrometer), using mitral valve anterior leaflet (MVAL) tissues as the representative tissue. We simulated MVAL collagen fiber network as an ensemble of undulated fibers under a generalized two-dimensional deformation state, by representing the collagen fibrils based on a planar sinusoidally shaped geometric model. The proposed approach accounted for collagen fibril amplitude, crimp period, and rotation with applied macroscopic tissue-level deformation. When compared to the small angle x-ray scattering measurements, the model fit the data well, with an r(2) = 0.976. This important finding suggests that, at the homogenized tissue-level scale of ∼1 mm, the collagen fiber network in the MVAL deforms according to an affine kinematics model. Moreover, with respect to understanding its function, affine kinematics suggests that the constituent fibers are largely noninteracting and deform in accordance with the bulk tissue. It also suggests that the collagen fibrils are tightly bounded and deform as a single fiber-level unit. This greatly simplifies the modeling efforts at the tissue and organ levels, because affine kinematics allows a straightforward connection between the macroscopic and local fiber strains. It also suggests that the collagen and elastin fiber networks act independently of each other, with the collagen and elastin forming long fiber networks that allow for free rotations. Such freedom of rotation can greatly facilitate the observed high degree of mechanical anisotropy in the MVAL and other heart valves, which is essential to heart valve function. These apparently novel findings support modeling efforts directed toward improving our fundamental understanding of tissue biomechanics in healthy and diseased conditions.

Colorful protein-based fluorescent probes for collagen imaging

Real-time visualization of collagen is important in studies on tissue formation and remodeling in the research fields of developmental biology and tissue engineering. Our group has previously reported on a fluorescent probe for the specific imaging of collagen in live tissue in situ, consisting of the native collagen binding protein CNA35 labeled with fluorescent dye Oregon Green 488 (CNA35-OG488). The CNA35-OG488 probe has become widely used for collagen imaging. To allow for the use of CNA35-based probes in a broader range of applications, we here present a toolbox of six genetically-encoded collagen probes which are fusions of CNA35 to fluorescent proteins that span the visible spectrum: mTurquoise2, EGFP, mAmetrine, LSSmOrange, tdTomato and mCherry. While CNA35-OG488 requires a chemical conjugation step for labeling with the fluorescent dye, these protein-based probes can be easily produced in high yields by expression in E. coli and purified in one step using Ni2+-affinity chromatography. The probes all bind specifically to collagen, both in vitro and in porcine pericardial tissue. Some first applications of the probes are shown in multicolor imaging of engineered tissue and two-photon imaging of collagen in human skin. The fully-genetic encoding of the new probes makes them easily accessible to all scientists interested in collagen formation and remodeling.

DTAF dye concentrations commonly used to measure microscale deformations in biological tissues alter tissue mechanics

Identification of the deformation mechanisms and specific components underlying the mechanical function of biological tissues requires mechanical testing at multiple levels within the tissue hierarchical structure. Dichlorotriazinylaminofluorescein (DTAF) is a fluorescent dye that is used to visualize microscale deformations of the extracellular matrix in soft collagenous tissues. However, the DTAF concentrations commonly employed in previous multiscale experiments (≥2000 µg/ml) may alter tissue mechanics. The objective of this study was to determine whether DTAF affects tendon fascicle mechanics and if a concentration threshold exists below which any observed effects are negligible. This information is valuable for guiding the continued use of this fluorescent dye in future experiments and for interpreting the results of previous work. Incremental strain testing demonstrated that high DTAF concentrations (≥100 µg/ml) increase the quasi-static modulus and yield strength of rat tail tendon fascicles while reducing their viscoelastic behavior. Subsequent multiscale testing and modeling suggests that these effects are due to a stiffening of the collagen fibrils and strengthening of the interfibrillar matrix. Despite these changes in tissue behavior, the fundamental deformation mechanisms underlying fascicle mechanics appear to remain intact, which suggests that conclusions from previous multiscale investigations of strain transfer are still valid. The effects of lower DTAF concentrations (≤10 µg/ml) on tendon mechanics were substantially smaller and potentially negligible; nevertheless, no concentration was found that did not at least slightly alter the tissue behavior. Therefore, future studies should either reduce DTAF concentrations as much as possible or use other dyes/techniques for measuring microscale deformations.

Non-affine deformations in polymer hydrogels

Most theories of soft matter elasticity assume that the local strain in a sample after deformation is identical everywhere and equal to the macroscopic strain, or equivalently that the deformation is affine. We discuss the elasticity of hydrogels of crosslinked polymers with special attention to affine and non-affine theories of elasticity. Experimental procedures to measure non-affine deformations are also described. Entropic theories, which account for gel elasticity based on stretching out individual polymer chains, predict affine deformations. In contrast, simulations of network deformation that result in bending of the stiff constituent filaments generally predict non-affine behavior. Results from experiments show significant non-affine deformation in hydrogels even when they are formed by flexible polymers for which bending would appear to be negligible compared to stretching. However, this finding is not necessarily an experimental proof of the non-affine model for elasticity. We emphasize the insights gained from experiments using confocal rheoscope and show that, in addition to filament bending, sample micro-inhomogeneity can be a significant alternative source of non-affine deformation.