Mechanics and kinematics of soft tissue under indentation are determined by the degree of initial collagen fiber alignment

Effect of matrix properties on transmission and reflectance mode division-of-focal-plane Stokes polarimetry

Significance

Division-of-focal-plane Stokes polarimetry is emerging as a powerful tool for the microstructural characterization of soft tissues. How individual extracellular matrix (ECM) properties influence polarimetric signals in reflectance or transmission modes of quantitative polarized light imaging (QPLI) is not well understood.

Aim

We aimed to investigate how ECM properties affect outcomes obtained from division-of-focal-plane polarimetric imaging in reflectance or transmission modes.

Approach

Tunable collagen gel phantoms were used to modulate ECM properties of anisotropy, collagen density, crosslinking, and absorber density; the effects of degree of linear polarization (DoLP) and angle of polarization (AoP) on polarimetry outcomes were assessed. A model biological tissue (i.e., bovine tendon) was similarly imaged and evaluated using both reflectance and transmission modes.

Results

Reflectance QPLI resulted in decreased DoLP compared with transmission mode. A 90 deg shift in AoP was observed between modes but yielded similar spatial patterns. Collagen density had the largest effect on outcomes besides anisotropy in both imaging modes.

Conclusions

Both imaging modes were sufficiently sensitive to detect structural anisotropy differences in gels of varying fiber alignment. Conclusions drawn from phantom experiments should carry over when interpreting data from more complex tissues and can help provide context for interpretation of other Stokes polarimetry data.

Three-dimensional anisotropic hyperelastic constitutive model describing the mechanical response of human and mouse cervix

The mechanical function of the uterine cervix is critical for a healthy pregnancy. During pregnancy, the cervix undergoes significant softening to allow for a successful delivery. Abnormal cervical remodeling is suspected to contribute to preterm birth. Material constitutive models describing known biological shifts in pregnancy are essential to predict the mechanical integrity of the cervix. In this work, the material response of human cervical tissue under spherical indentation and uniaxial tensile tests loaded along different anatomical directions is experimentally measured. A deep-learning segmentation tool is applied to capture the tissue deformation during the uniaxial tensile tests. A 3-dimensional, equilibrium anisotropic continuous fiber constitutive model is formulated, considering collagen fiber directionality, fiber bundle dispersion, and the entropic nature of wavy cross-linked collagen molecules. Additionally, the universality of the material model is demonstrated by characterizing previously published mouse cervix mechanical data. Overall, the proposed material model captures the tension-compression asymmetric material responses and the remodeling characteristics of both human and mouse cervical tissue. The pregnant (PG) human cervix (mean locking stretch ζ=2.4, mean initial stiffness ξ=12 kPa, mean bulk modulus κ=0.26 kPa, mean dispersion b=1.0) is more compliant compared with the nonpregnant (NP) cervix (mean ζ=1.3, mean ξ=32 kPa, mean κ=1.4 kPa, mean b=1.4). Creating a validated material model, which describes the role of collagen fiber directionality, dispersion, and crosslinking, enables tissue-level biomechanical simulations to determine which material and anatomical factors drive the cervix to open prematurely. STATEMENT OF SIGNIFICANCE: In this study, we report a 3D anisotropic hyperelastic constitutive model based on Langevin statistical mechanics and successfully describe the material behavior of both human and mouse cervical tissue using this model. This model bridges the connection between the extracellular matrix (ECM) microstructure remodeling and the macro mechanical properties change of the cervix during pregnancy via microstructure-associated material parameters. This is the first model, to our knowledge, to connect the the entropic nature of wavy cross-linked collagen molecules with the mechanical behavior of the cervix. Inspired by microstructure, this model provides a foundation to understand further the relationship between abnormal cervical ECM remodeling and preterm birth. Furthermore, with a relatively simple form, the proposed model can be applied to other fibrous tissues in the future.

Combining Unique Planar Biaxial Testing with Full-Field Thickness and Displacement Measurement for Spatial Characterization of Soft Tissues

Soft tissues rely on the incredible complexity of their microstructure for proper function. Local variations in material properties arise as tissues develop and adapt, often in response to changes in loading. A barrier to investigating the heterogeneous nature of soft tissues is the difficulty of developing experimental protocols and analysis tools that can accurately capture spatial variations in mechanical behavior. In this article, we detail protocols enabling mechanical characterizations of anisotropic, heterogeneous soft tissues or tissue analogs. We present a series of mechanical tests designed to maximize inhomogeneous strain fields and in-plane shear forces. A customized, 3D-printable gripping system reduces tissue handling and enhances shear. High-resolution imaging and laser micrometry capture full-field displacement and thickness, respectively. As the equipment necessary to conduct these protocols is commercially available, the experimental methods presented offer an accessible route toward addressing heterogeneity. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: Unique biaxial testing of soft tissues and tissue analogs Basic Protocol 2: Full-field thickness measurement of soft tissues and tissue analogs Support Protocol 1: Creating and speckling cruciform-shaped samples for mechanical testing Support Protocol 2: Creating custom gripping system to minimize sample handling.

Anisotropic Mechanical Properties of the Human Uterus Measured by Spherical Indentation

The mechanical function of the uterus is critical for a successful pregnancy. During gestation, uterine tissue grows and stretches to many times its size to accommodate the growing fetus, and it is hypothesized the magnitude of uterine tissue stretch triggers the onset of contractions. To establish rigorous mechanical testing protocols for the human uterus in hopes of predicting tissue stretch during pregnancy, this study measures the anisotropic mechanical properties of the human uterus using optical coherence tomography (OCT), instrumented spherical indentation, and video extensometry. In this work, we perform spherical indentation and digital image correlation to obtain the tissue's force and deformation response to a ramp-hold loading regimen. We translate previously reported fiber architecture, measured via optical coherence tomography, into a constitutive fiber composite material model to describe the equilibrium material behavior during indentation. We use an inverse finite element method integrated with a genetic algorithm (GA) to fit the material model to our experimental data. We report the mechanical properties of human uterine specimens taken across different anatomical locations and layers from one non-pregnant (NP) and one pregnant (PG) patient; both patients had pathological uterine tissue. Compared to NP uterine tissue, PG tissue has a more dispersed fiber distribution and equivalent stiffness material parameters. In both PG and NP uterine tissue, the mechanical properties differ significantly between anatomical locations.

Anisotropic Material Characterization of Human Cervix Tissue Based on Indentation and Inverse Finite Element Analysis

The cervix is essential to a healthy pregnancy as it must bear the increasing load caused by the growing fetus. Preterm birth is suspected to be caused by the premature softening and mechanical failure of the cervix. The objective of this paper is to measure the anisotropic mechanical properties of human cervical tissue using indentation and video extensometry. The human cervix is a layered structure, where its thick stromal core contains preferentially aligned collagen fibers embedded in a soft ground substance. The fiber composite nature of the tissue provides resistance to the complex three-dimensional loading environment of pregnancy. In this work, we detail an indentation mechanical test to obtain the force and deformation response during loading which closely matches in vivo conditions. We postulate a constitutive material model to describe the equilibrium material behavior to ramp-hold indentation, and we use an inverse finite element method based on genetic algorithm (GA) optimization to determine best-fit material parameters. We report the material properties of human cervical slices taken at different anatomical locations from women of different obstetric backgrounds. In this cohort of patients, the anterior internal os (the area where the cervix meets the uterus) of the cervix is stiffer than the anterior external os (the area closest to the vagina). The anatomic anterior and posterior quadrants of cervical tissue are more anisotropic than the left and right quadrants. There is no significant difference in material properties between samples of different parities (number of pregnancies reaching viable gestation age).

Integrated Biophysical Characterization of Fibrillar Collagen-Based Hydrogels

This paper describes an experimental characterization scheme of the biophysical properties of reconstituted hydrogel matrices based on indentation testing, quantification of transport via microfluidics, and confocal reflectance microscopy analysis. While methods for characterizing hydrogels exist and are widely used, they often do not measure diffusive and convective transport concurrently, determine the relationship between microstructure and transport properties, and decouple matrix mechanics and transport properties. Our integrated approach enabled independent and quantitative measurements of the structural, mechanical, and transport properties of hydrogels in a single study. We used fibrillar type I collagen as the base matrix and investigated the effects of two different matrix modifications: (1) cross-linking with human recombinant tissue transglutaminase II (hrTGII) and (2) supplementation with the nonfibrillar matrix constituent hyaluronic acid (HA). hrTGII modified the matrix structure and transport but not mechanical parameters. Furthermore, changes in the matrix structure due to hrTGII were seen to be dependent on the concentration of collagen. In contrast, supplementation of HA at different collagen concentrations altered the matrix microstructure and mechanical indentation behavior but not transport parameters. These experimental observations reveal the important relationship between extracellular matrix (ECM) composition and biophysical properties. The integrated techniques are versatile, robust, and accessible; and as matrix-cell interactions are instrumental for many biological processes, the methods and findings described here should be broadly applicable for characterizing hydrogel materials used for three-dimensional (3-D) tissue-engineered culture models.

Multiscale model of fatigue of collagen gels

Fatigue as a mode of failure becomes increasingly relevant with age in tissues that experience repeated fluctuations in loading. While there has been a growing focus on the mechanics of networks of collagen fibers, which are recognized as the predominant mechanical components of soft tissues, the network's fatigue behavior has received less attention. Specifically, it must be asked (1) how the fatigue of networks differs from that of its component fibers, and (2) whether this difference in fatigue behaviors is affected by changes in the network's architecture. In the present study, we simulated cyclic uniaxial loading of Voronoi networks to model fatigue experiments performed on reconstituted collagen gels. Collagen gels were cast into dog-bone shape molds and were tested on a uniaxial machine under a tension-tension cyclic loading protocol. Simulations were performed on networks modeled as trusses of, on average, 600 nonlinear elastic fibers connected at freely rotating pin-joints. We also simulated fatigue failure of Delaunay, and Erdős-Rényi networks, in addition to Voronoi networks, to compare fatigue behavior among different architectures. The uneven distribution of stresses within the fibers of the unstructured networks resulted in all three network geometries being more endurant than a single fiber or a regular lattice under cyclic loading. Among the different network geometries, for low to moderate external loads, the Delaunay networks showed the best fatigue behavior, while at higher loads, the Voronoi networks performed better.

Biphasic analysis of rat brain slices under creep indentation shows nonlinear tension-compression behavior

Biphasic theory can provide a mechanistic description of deformation and transport phenomena in soft tissues, and has been used to model surgery and drug delivery in the brain for decades. Knowledge of corresponding mechanical properties of the brain is needed to accurately predict tissue deformation and flow transport in these applications. Previously in our group, creep indentation tests were conducted for multiple anatomical regions in acute rat brain tissue slices. In the current study, a biphasic finite element model of creep indentation was developed with which to compare these data. Considering the soft tissue structure of brain, the solid matrix was assumed to be composed of a neo-Hookean ground matrix reinforced by continuously distributed fibers that exhibits tension-compression nonlinearity during deformation. By fixing Poisson's ratio of the ground matrix, Young's modulus, fiber modulus and hydraulic permeability were estimated. Hydraulic permeability was found to be nearly independent of the properties of the solid matrix. Estimated modulus (40 Pa to 1.1 kPa for the ground matrix, 3.2-18.2 kPa for fibers) and hydraulic permeability (1.2-5.5×10^-13m⁴/N s) fell within an acceptable range compared with those in previous studies. Instantaneous indentation depth was dominated by tension provided by fibers, while the tissue response at equilibrium was sensitive to Poisson's ratio. Results of sensitivity analysis also point to the necessity of considering tension-compression nonlinearity in the solid phase when the biphasic material undergoes large creep deformation.

Collagen organization regulates stretch-initiated pain-related neuronal signals in vitro: Implications for structure-function relationships in innervated ligaments

Injury to the spinal facet capsule, an innervated ligament with heterogeneous collagen organization, produces pain. Although mechanical facet joint trauma activates embedded afferents, it is unclear if, and how, the varied extracellular microstructure of its ligament affects sensory transduction for pain from mechanical inputs. To investigate the effects of macroscopic deformations on afferents in collagen matrices with different organizations, an in vitro neuron-collagen construct (NCC) model was used. NCCs with either randomly organized or parallel aligned collagen fibers were used to mimic the varied microstructure in the facet capsular ligament. Embryonic rat dorsal root ganglia (DRG) were encapsulated in the NCCs; axonal outgrowth was uniform and in all directions in random NCCs, but parallel in aligned NCCs. NCCs underwent uniaxial stretch (0.25 ± 0.06 strain) corresponding to sub-failure facet capsule strains that induce pain. Macroscopic NCC mechanics were measured and axonal expression of phosphorylated extracellular signal-regulated kinase (pERK) and the neurotransmitter substance P (SP) was assayed at 1 day to assess neuronal activation and nociception. Stretch significantly upregulated pERK expression in both random and aligned gels (p < 0.001), with the increase in pERK being significantly higher (p = 0.013) in aligned than in random NCCs. That increase likely relates to the higher peak force (p = 0.025) and stronger axon alignment (p < 0.001) with stretch direction in the aligned NCCs. In contrast, SP expression was greater in stretched NCCs (p < 0.001) regardless of collagen organization. These findings suggest that collagen organization differentially modulates pain-related neuronal signaling and support structural heterogeneity of ligament tissue as mediating sensory function. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:770-777, 2018.

Collagen Organization in Facet Capsular Ligaments Varies With Spinal Region and With Ligament Deformation

The spinal facet capsular ligament (FCL) is primarily comprised of heterogeneous arrangements of collagen fibers. This complex fibrous structure and its evolution under loading play a critical role in determining the mechanical behavior of the FCL. A lack of analytical tools to characterize the spatial anisotropy and heterogeneity of the FCL's microstructure has limited the current understanding of its structure-function relationships. Here, the collagen organization was characterized using spatial correlation analysis of the FCL's optically obtained fiber orientation field. FCLs from the cervical and lumbar spinal regions were characterized in terms of their structure, as was the reorganization of collagen in stretched cervical FCLs. Higher degrees of intra- and intersample heterogeneity were found in cervical FCLs than in lumbar specimens. In the cervical FCLs, heterogeneity was manifested in the form of curvy patterns formed by collections of collagen fibers or fiber bundles. Tensile stretch, a common injury mechanism for the cervical FCL, significantly increased the spatial correlation length in the stretch direction, indicating an elongation of the observed structural features. Finally, an affine estimation for the change of correlation length under loading was performed which gave predictions very similar to the actual values. These findings provide structural insights for multiscale mechanical analyses of the FCLs from various spinal regions and also suggest methods for quantitative characterization of complex tissue patterns.

Microstructural and Mechanical Properties of the Posterior Cruciate Ligament: A Comparison of the Anterolateral and Posteromedial Bundles

BACKGROUND

The microstructural organization (collagen fiber alignment) of the posterior cruciate ligament (PCL), which likely corresponds with its functional properties, has only been described qualitatively in the literature, to our knowledge. The goal of this study was to quantify the tensile mechanical and microstructural properties of the PCL and compare these qualities between the anterolateral and posteromedial bundles.

METHODS

Twenty-two knee specimens from 13 donors (8 male and 5 female; mean age [and standard deviation] at the time of death, 43.0 ± 4.1 years; mean body mass index, 30.0 ± 6.7 kg/m²) were dissected to isolate the PCL, and each bundle was split into 3 regions. Mechanical testing of each regional sample consisted of preconditioning followed by a ramp-and-hold stress-relaxation test and a quasi-static ramp-to-failure test. Microstructural analysis was performed with use of a high-resolution, division-of-focal-plane polarization camera to evaluate the average direction of collagen orientation and the degree to which the collagen fibers were aligned in that direction. Results were compared between the anterolateral and posteromedial bundles and across the regions of each bundle.

RESULTS

The anterolateral and posteromedial bundles demonstrated largely equivalent mechanical and microstructural properties. Elastic moduli in the toe and linear regions were not different; however, the posteromedial bundle did show significantly more stress relaxation (p = 0.004). There were also few differences in microstructural properties between bundles, which again were seen only in stress relaxation. Comparing regions within each bundle, several mechanical and microstructural parameters showed significant relationships across the posteromedial bundle, following a gradient of decreasing strength and alignment from anterior to posterior.

CONCLUSIONS

The PCL has relatively homogenous microstructural and mechanical properties, with few differences between the anterolateral and posteromedial bundles. This finding suggests that distinct functions of the PCL bundles result primarily from size and anatomical location rather than from differences in these properties.

CLINICAL RELEVANCE

These properties of the PCL can be used to assess the utility of graft choices and operative techniques for PCL reconstruction and may partly explain limited differences in the outcomes of single-bundle compared with double-bundle reconstruction techniques for the PCL.

Experimental validation of a flat punch indentation methodology calibrated against unconfined compression tests for determination of soft tissue biomechanics

Mechanical characterisation of soft biological tissues using standard compression or tensile testing presents a significant challenge due to specimen geometrical irregularities, difficulties in cutting intact and appropriately sized test samples, and issues with slippage or damage at the grips. Indentation can overcome these problems but requires fitting a model to the resulting load-displacement data in order to calculate moduli. Despite the widespread use of this technique, few studies experimentally validate their chosen model or compensate for boundary effects. In this study, viscoelastic hydrogels of different concentrations and dimensions were used to calibrate an indentation technique performed at large specimen-strain deformation (20%) and analysed with a range of routinely used mathematical models. A rigid, flat-ended cylindrical indenter was applied to each specimen from which 'indentation moduli' and relaxation properties were calculated and compared against values obtained from unconfined compression. Only one indentation model showed good agreement (<10% difference) with all moduli values obtained from compression. A sample thickness to indenter diameter ratio ≥1:1 and sample diameter to indenter diameter ratio ≥4:1 was necessary to achieve the greatest accuracy. However, it is not always possible to use biological samples within these limits, therefore we developed a series of correction factors. The approach was validated using human diseased omentum and bovine articular cartilage resulting in mechanical properties closely matching compression values. We therefore present a widely useable indentation analysis method to allow more accurate calculation of material mechanics which is important in the study of soft tissue development, ageing, health and disease.

Crack Propagation Versus Fiber Alignment in Collagen Gels: Experiments and Multiscale Simulation

It is well known that the organization of the fibers constituting a collagenous tissue can affect its failure behavior. Less clear is how that effect can be described computationally so as to predict the failure of a native or engineered tissue under the complex loading conditions that can occur in vivo. Toward the goal of a general predictive strategy, we applied our multiscale model of collagen gel mechanics to the failure of a double-notched gel under tension, comparing the results for aligned and isotropic samples. In both computational and laboratory experiments, we found that the aligned gels were more likely to fail by connecting the two notches than the isotropic gels. For example, when the initial notches were 30% of the sample width (normalized tip-to-edge distance = 0.7), the normalized tip-to-tip distance at which the transition occurred from between-notch failure to across-sample failure shifted from 0.6 to 1.0. When the model predictions for the type of failure event (between the two notches versus across the sample width) were compared to the experimental results, the two were found to be strongly covariant by Fisher's exact test (p < 0.05) for both the aligned and isotropic gels with no fitting parameters. Although the double-notch system is idealized, and the collagen gel system is simpler than a true tissue, it presents a simple model system for studying failure of anisotropic tissues in a controlled setting. The success of the computational model suggests that the multiscale approach, in which the structural complexity is incorporated via changes in the model networks rather than via changes to a constitutive equation, has the potential to predict tissue failure under a wide range of conditions.

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.

Differences in the microstructural properties of the anteromedial and posterolateral bundles of the anterior cruciate ligament

BACKGROUND

Tissue properties of the anteromedial (AM) and posterolateral (PL) bundles of the anterior cruciate ligament (ACL) have not been previously characterized with real-time dynamic testing. The current study used a novel polarized light technique to measure the material and microstructural properties of the ACL.

HYPOTHESIS

The AM and PL bundles of the ACL have similar material and microstructural properties.

STUDY DESIGN

Controlled laboratory study.

METHODS

The AM and PL bundles were isolated from 16 human cadaveric ACLs (11 male, 5 female; average age, 41 years [range, 24-53 years]). Three samples from each bundle were loaded in uniaxial tension, and a custom-built polarized light imaging camera was used to quantify collagen fiber alignment in real time. A bilinear curve fit was applied to the stress-strain data of a quasistatic ramp-to-failure to quantify the moduli in the toe and linear regions. Fiber alignment was quantified at zero strain, the transition point of the bilinear fit, and in the linear portion of the stress-strain curve by computing the degree of linear polarization (DoLP) and angle of polarization (AoP), which are measures of the strength and direction of collagen alignment, respectively. Data were compared using t tests.

RESULTS

The AM bundle exhibited significantly larger toe-region (AM 7.2 MPa vs. PL 4.2 MPa; P < .001) and linear-region moduli (AM 27.0 MPa vs. PL 16.1 MPa; P = .017) compared with the PL bundle. Average DoLP values were similar at low strain but were significantly larger (ie, more uniform alignment) for the AM bundle in the linear region of the stress-strain curve (AM 0.22 vs. PL 0.19; P = .036) compared with the PL bundle. The standard deviation AoP values was larger for the PL bundle at both transition (P = .041) and linear-region strain (P = .014), indicating more disperse orientation.

CONCLUSION

Material and microstructural properties of the AM and PL bundles of the ACL differ during loading. The AM bundle possessed higher tissue modulus and failure stress, as well as more uniform fiber alignment under load.

CLINICAL RELEVANCE

These insights into native ligament microstructure can be used to assess graft options for ACL reconstruction and optimize surgical reconstruction techniques.