A simple basis for determination of the modulus and hydraulic conductivity of human ocular surface using nano-indentation

Depth profiling via nanoindentation for characterisation of the elastic modulus and hydraulic properties of thin hydrogel layers

The accurate determination of the mechanical properties of hydrogels is of fundamental importance for a range of applications, including in assessing the effect of stiffness on cell behaviour. This is a particular issue when using thin hydrogel layers adherent to stiff substrate supports, as the apparent stiffness can be significantly influenced by the constraint of the underlying impermeable substrate, leading to inaccurate measurements of the elastic modulus and permeability of thin hydrogel layers. This study used depth profiling nanoindentation and a poroelastic model for spherical indentation to identify the elastic moduli and hydraulic conductivity of thin polyacrylamide (PAAm) hydrogel layers (∼27 μm-782 μm thick) on impermeable substrates. The apparent stiffness of thin PAAm layers increased with indentation depth and was significantly greater than those of thicker hydrogels, which showed no influence of indentation depth. The hydraulic conductivity decreased as the geometrical confinement of hydrogels increased, indicating that the fluid became more constrained within the confinement areas. The impact of geometrical confinement on the apparent modulus and hydraulic conductivity of thin PAAm hydrogel layers was then established, and their elastic moduli and intrinsic permeability were determined in relation to this effect. This study offers valuable insights into the mechanical characterisation of thin PAAm hydrogel layers used for the fundamental study of cell mechanobiology.

Deciphering load attenuation mechanisms of the dentin-enamel junction: Insights from a viscoelastic constitutive model

A considerable material discontinuity between the enamel and dentin might jeopardize the tooth's mechanical durability over time without the attenuation of the dentin-enamel junction (DEJ). However, the critical loading transmission mechanism at the DEJ remains understudied. This study aimed to define the extent and effective width of the DEJ, along with its mechanical competence. The presence of DEJ interphase layer was identified using a motif analysis based on the ion beam-transmission electron microscopy coupled with nanoindentation modulus mapping. For each region, nanoindentation load-displacement curves were recorded and mathematically analyzed using an appropriate viscoelastic constitutive model. The time-course of indenter penetration (creep) behavior of the tooth tissues can be mathematically approximated by the Kelvin-Voigt model in series, which determined the visco-contribution to the overall mechanical responses. Therefore, the elastic-plastic contribution can be distinguished from the overall mechanical responses of the tooth after subtracting the visco-contributions. During the loading period, the enamel behavior was dominated by elastic-plastic responses, while both the dentin and DEJ showed pronounced viscoelastic responses. The instantaneous modulus of the DEJ, which was measured by eliminating viscoelastic behavior from the raw load-displacement curve, was almost double that of the dentin. The DEJ was stiffer than the dentin, but it exhibited large viscoelastic motion even at the initial loading stage. This study revealed that the load attenuation competence of the DEJ, which involves extra energy expenditure, is mainly associated with its viscoelasticity. The mathematical analysis proposed here, performed on the nanoindentation creep behavior, could potentially augment the existing knowledge on hard-tissue biomechanics. STATEMENT OF SIGNIFICANCE: In this study, we undertake a rigorous mechanical characterization of the dentin-enamel junction (DEJ) using an advanced nanoindentation technique coupled with a pertinent viscoelastic constitutive model. Our approach unveils the substantial viscoelastic contribution of the DEJ during the initial indentation loading phase and offers an elaborate delineation of the DEJ interphase layer through sophisticated image analysis. These insights significantly augment our understanding of tooth durability. Importantly, our innovative mathematical analysis of creep behavior introduces a novel approach with profound implications for future research in the expansive field of hard-tissue biomechanics. The pioneering methodologies and findings presented in this work hold substantial potential to invigorate progress in biomaterials research and fuel further explorations into the functionality of biological tissues.

Universal contact stiffness of elastic solids covered with tensed membranes and its application in indentation tests of biological materials

The inherent membrane tension of biological materials could vitally affect their responses to contact loading but is generally ignored in existing indentation analysis. In this paper, the authors theoretically investigate the contact stiffness of axisymmetric indentations of elastic solids covered with thin tensed membranes. When the indentation size decreases to the same order as the ratio of membrane tension to elastic modulus, the contact stiffness accounting for the effect of membrane tension becomes much higher than the prediction of conventional contact theory. An explicit expression is derived for the contact stiffness, which is universal for axisymmetric indentations using indenters of arbitrary convex profiles. On this basis, a simple method of analysis is proposed to estimate the membrane tension and elastic modulus of biological materials from the indentation load-depth data, which is successfully applied to analyze the indentation experiments of cells and lungs. This study might be helpful for the comprehensive assessment of the mechanical properties of soft biological systems. STATEMENT OF SIGNIFICANCE: This paper highlights the crucial effect of the inherent membrane tension on the indentation response of soft biomaterials, which has been generally ignored in existing analysis of experiments. For typical indentation tests on cells and organs, the contact stiffness can be twice or higher than the prediction of conventional contact model. A universal expression of the contact stiffness accounting for the membrane tension effect is derived. On this basis, a simple method of analysis is proposed to abstract the membrane tension of biomaterials from the experimentally recorded indentation load-depth data. With this method, the elasticity of soft biomaterials can be characterized more comprehensively.

Use of Nanoindentation in Determination of Regional Biomechanical Properties of Rabbit Cornea After UVA Cross-Linking

Purpose

To evaluate the regional effects of different corneal cross-linking (CXL) protocols on corneal biomechanical properties.

Methods

The study involved both eyes of 50 rabbits, and the left eyes were randomized to the five intervention groups, which included the standard CXL group (SCXL), which was exposed to 3-mW/cm2 irradiation, and three accelerated CXL groups (ACXL1-3), which were exposed to ultraviolet-A at irradiations of 9 mW/cm2, 18 mW/cm2, and 30 mW/cm2, respectively, but with the same total dose (5.4 J/cm2). A control (CO) group was not exposed to ultraviolet-A. No surgery was done on the contralateral eyes. The corneas of each group were evaluated by the effective elastic modulus (Eeff) and the hydraulic conductivity (K) within a 7.5-mm radius using nanoindentation measurements.

Results

Compared with the CO group, Eeff (in regions with radii of 0-1.5 mm, 1.5-3.0 mm, and 3.0-4.5 mm) significantly increased by 309%, 276%, and 226%, respectively, with SCXL; by 222%, 209%, and 173%, respectively, with ACXL1; by 111%, 109%, and 94%, respectively, with ACXL2; and by 59%, 41%, and 37%, respectively, with ACXL3 (all P < 0.05). K was also significantly reduced by 84%, 81%, and 78%, respectively, with SCXL; by 75%, 74%, and 70%, respectively, with ACXL1; by 64%, 62%, and 61%, respectively, with ACXL2; and by 33%, 36%, and 32%, respectively, with ACXL3 (all P < 0.05). For the other regions(with radii between 4.5 and 7.5 mm), the SCXL and ACXL1 groups (but not the ACXL2 and ACXL3 groups) still showed significant changes in Eeff and K.

Conclusions

CXL had a significant effect on corneal biomechanics in both standard and accelerated procedures that may go beyond the irradiated area. The effect of CXL in stiffening the tissue and reducing permeability consistently decreased with reducing the irradiance duration.

Characterization of the Immediate and Delayed Biomechanical Response to UV-A Crosslinking of Human Corneas

PURPOSE

Keratoconus leads to visual deterioration due to irregular astigmatism and corneal thinning. Riboflavin-based corneal UV-A crosslinking (CXL) induces novel intramolecular and intermolecular links resulting in corneal tissue stiffening, thereby halting disease progression. The purpose of this study was to analyze the immediate and delayed biomechanical responses of human donor corneas to CXL.

METHODS

CXL was performed according to the Dresden protocol to corneas not suitable for transplantation. Biomechanical properties were subsequently monitored by measuring the Young modulus using nanoindentation. The immediate tissue response was determined after 0, 1, 15, and 30 minutes of irradiation. Delayed biomechanical effects were investigated with follow-up measurements immediately and 1, 3, and 7 days after CXL.

RESULTS

Young's modulus indicated a linear trend in direct response to increasing irradiation times (mean values: total 61.31 kPa [SD 25.53], 0 minutes 48.82 kPa [SD 19.73], 1 minute 53.44 kPa [SD 25.95], 15 minutes 63.56 kPa [SD 20.99], and 30 minutes 76.76 kPa [SD 24.92]). The linear mixed model for the elastic response of corneal tissue was 49.82 kPa + (0.91 kPa/min × time [minutes]); P < 0.001. The follow-up measurements showed no significant delayed changes in the Young modulus (mean values: total 55,28 kPa [SD 15.95], immediately after CXL 56,83 kPa [SD 18.74], day 1 50.28 kPa [SD 14.15], day 3 57.08 kPa [SD 14.98], and day 7 56.83 kPa [SD 15.07]).

CONCLUSIONS

This study suggests a linear increase of corneal Young modulus as a function of CXL timing. No significant short-term delayed biomechanical changes posttreatment were observed.

[Keratoconus: biomechanics ex vivo]

BACKGROUND

Keratoconus is associated with an impairment in corneal biomechanics. Using nanoindentation, spatially resolved measurement of biomechanical properties can be performed on corneal tissue. The aim of this study is to assess the biomechanical properties of corneas with keratoconus in comparison to healthy controls.

METHODS

17 corneas with keratoconus and 10 healthy corneas unsuitable for transplantation were included in the study. After explantation, corneas were kept in culture medium containing 15% dextran for at least 24 h. Nanoindentation was then performed to a depth of 25 µm at a force increase of 300 µN/min.

RESULTS

A total of 2328 individual indentations were performed for this study. In the keratoconus group; the mean modulus of elasticity was 23.2 kPa (± 15.0 kPa) for a total of 1802 indentations. In the control group, the mean modulus of elasticity was 48.7 kPa (± 20.5 kPa) with a total of 526 indentations. The Wilcoxon test showed that the differences were statistically significant.

CONCLUSION

Using nanoindentation, a significantly lower elastic modulus was found in corneas with keratoconus compared to corneas without keratoconus. Further studies are needed to gain a better understanding of how keratoconus affects corneal biomechanics.

Influence of water and protein content on the creep behavior in dental enamel

The creep behavior of untreated and deproteinized dental enamel in dry and wet state was analyzed by nanoindentation with a spherical tip. Additionally, the influence of the loading rate was investigated. Dry untreated and deproteinized dental enamel only showed minor creep over 100 s and deproteinization did not affect the dry enamel's behavior significantly. With slower loading rates some creep already occurs during the loading period, such that the creep displacement during load hold is less than with faster loading rates. Wet untreated and deproteinized enamel showed significantly more creep compared to the dry samples. The differences between the untreated and deproteinized enamel were only minor but significant, revealing that water affects the creep behavior of biological materials such as enamel significantly. The proposed deformation mechanism of naturally porous enamel under compression is compaction of the HAP crystallites and fluid displacement within material underneath the indented area. STATEMENT OF SIGNIFICANCE: This study investigates the creep behavior of untreated and deproteinized dental enamel in dry and wet conditions. It is shown that while the protein content does not affect enamel's behavior significantly, the wet conditions lead to an increased creep in enamel. The proposed deformation mechanism of naturally porous enamel under compression is compaction of the HAP crystallites and fluid displacement within material underneath the indented area. Based on this observation a simple analytical model has been developed, aiming to deepen our understanding of the deformation behavior of biological materials.

Norepinephrine as an Enhancer Promoting Corneal Penetration of Riboflavin for Transepithelial Corneal Crosslinking

Purpose

Previously, we found norepinephrine (NE) could affect the corneal epithelial integrity, herein we investigated the feasibility and safety of NE serving as a chemical enhancer to promote corneal penetration of riboflavin during transepithelial corneal crosslinking (CXL).

Methods

The dosage of NE that could promote riboflavin diffusion through the healthy epithelial barrier without inducing epithelial damage in C57BL/6 mice was determined. The safety of NE treatment was confirmed by morphological and histological examinations of the whole cornea. The efficacy of NE in promoting riboflavin penetration was verified by slit lamp and scanning electron microscope (SEM), and corneal biomechanical measurement after CXL. To better fit the clinical scenario, increased NE dosage and shortened riboflavin infiltration time were further evaluated.

Results

The lowest dosage of NE (1 mg/mL) that facilitated transepithelial riboflavin permeation was 2 µL. No visible corneal structure alteration was observed after NE treatment. SEM indicated dissociation of intercellular junctions among corneal epithelial cells. Homogenous distribution of riboflavin throughout corneal stroma was observed. NE-treated corneas reached comparable biomechanical properties after CXL, including stress-relaxation curve and elastic modulus, with corneas treated with the commercially available transepithelial drug Peschke TE. To better fit the clinical scenario, increasing NE up to 5.5 µL helped riboflavin infiltrate the corneal stroma within 30 minutes. After CXL with 9 mW/cm2 ultraviolet-A (UVA) for 2.5 minutes, the cornea showed significantly enhanced corneal biomechanical properties with undisturbed corneal endothelium.

Conclusions

NE serves as an effective enhancer in increasing riboflavin diffusion with limited impairment on corneal epithelium and has great potential for clinical application.

Translation Relevance

NE serves as an effective enhancer for riboflavin penetration and clinical transepithelial CXL.

Measuring the elastic modulus of soft biomaterials using nanoindentation

The measurement of the elastic modulus of soft biomaterials via nanoindentation relies on the accurate determination of the zero-point of the tip-sample interaction on which the depth of penetration into the sample is based. Non-cantilever based nanoindentation systems were originally designed for hard materials, and therefore monitoring the zero-point contact presents a significant challenge for the characterisation of very soft biomaterials. This study investigates the ability of non-cantilever based nanoindentation to differentiate between hydrogels with elastic moduli on the order of single kiloPascals (kPa) using a bespoke soft contact protocol and low flexural stiffness of instrument. Polyethylene glycol (PEG) hydrogels were fabricated as a model system with a range of elastic moduli by varying the polymer concentration and degree of crosslinking. Elastic modulus values were calculated using the Oliver-Pharr method, Hertzian contact model, as well as a viscoelastic model to account for the time-dependent behaviour of the gels. The stiffness measurements were validated by measuring cantilever beams with the equivalent flexural stiffness to that of the PEG hydrogels being tested. The results demonstrated a high repeatability of the measurements, enabling differentiation between hydrogels with elastic moduli in the single kPa to hundreds of kPa range.

Indentation of the cornea: A Bi-layer contact problem

Histological observations of the cornea have identified the presence of multiple layers with differing thickness and function. The composition of the cornea consists primarily of collagen fibrils held together with proteoglycans but with an aqueous interstitial component being dominant. Indentation provides a means to quantify the spatial variation of the mechanical properties of the cornea, however the role of the different layers on the indentation response has barely been addressed. In addition, the response of the fluid content and its displacement during indentation has not been adequately considered. In this study indentation of the cornea with a relatively large spherical tipped indenter (R = 500 μm) is considered. It was observed that the initial phase of loading did not fit a classic Hertz elastic response but showed an initial steeper slope that gradually declines with increasing force and displacement. A relatively simple approach is developed that initially considers the cornea as a poro-elastic bi-layer contact problem, that is the presence of an outer thin stiffer Bowman's layer overlaying the thicker less stiff stroma.

Transient viscous response of the human cornea probed with the Surface Force Apparatus

Knowledge of the biomechanical properties of the human cornea is crucial for understanding the development of corneal diseases and impact of surgical treatments (e.g., corneal laser surgery, corneal cross-linking). Using a Surface Force Apparatus we investigated the transient viscous response of the anterior cornea from donor human eyes compressed between macroscopic crossed cylinders. Corneal biomechanics was analyzed using linear viscoelastic theory and interpreted in the framework of a biphasic model of soft hydrated porous tissues, including a significant contribution from the pressurization and viscous flow of fluid within the corneal tissue. Time-resolved measurements of tissue deformation and careful determination of the relaxation time provided an elastic modulus in the range between 0.17 and 1.43 MPa, and fluid permeability of the order of 10⁻¹³ m⁴/(N∙s). The permeability decreased as the deformation was increased above a strain level of about 10%, indicating that the interstitial space between fibrils of the corneal stromal matrix was reduced under the effect of strong compression. This effect may play a major role in determining the observed rate-dependent non-linear stress-strain response of the anterior cornea, which underlies the shape and optical properties of the tissue.

Zone-dependent mechanical properties of human articular cartilage obtained by indentation measurements

Emerging 3D printing technology permits innovative approaches to manufacture cartilage scaffolds associated with layer-by-layer mechanical property adaptation. However, information about gradients of mechanical properties in human articular cartilage is limited. In this study, we quantified a zone-dependent change of local elastic modulus of human femoral condyle cartilage by using an instrumented indentation technique. From the cartilage superficial zone towards the calcified layer, a gradient of elastic modulus values between 0.020 ± 0.003 MPa and 6.44 ± 1.02 MPa was measured. To validate the tissue quality, the histological tissue composition was visualized by glycosaminoglycan and collagen staining. This work aims to introduce a new protocol to investigate the zone-dependent mechanical properties of graded structures, such as human articular cartilage. From this knowledge, better cartilage repair strategies could be tailored in the future.