Nanoindentation of hydrated materials and tissues

Nanoindentation techniques have recently been adapted for the study of hydrated materials, including biological materials and hydrogels. There are unique challenges associated with handling and testing hydrated samples. For hydrated materials, a poroelastic or poroviscoelastic analysis, which explicitly treats the fluid flow through the porous material, is used to extract material properties from experimental data. Some key results from recent works using nanoindentation to evaluate hydrated materials are reviewed in the context of these challenges. Finally, as these studies represent relatively recent developments in the nanoindentation field, an outlook for the future is presented, in which it is clear that a consensus is emerging for quantitative evaluation of hydrated materials via a modified nanoindentation approach.This is the accepted manuscript. The final version is available at http://www.sciencedirect.com/science/article/pii/S1359028615000236

Indentation across interfaces between stiff and compliant tissues

Abstract Bone–tendon, bone–ligament and bone–cartilage junctions are multi-tissue interfaces that connect materials that differ by two orders of magnitude in mechanical properties, via gradual variations in mineral content and matrix composition. These sites mediate load transfer between highly dissimilar materials and are consequently a primary site of injury during orthopedic failure. Given the large incidence rate and the lack of suitable surgical solutions for their regeneration or repair, characterization of their natural structure and subsequent replication through tissue engineering is important. Here, we evaluate the ability and accuracy of instrumented indentation to characterize the mechanical properties of both biological tissues and engineered scaffolds with interfaces between materials that contain significant changes in mechanical properties. In this study, finite element simulations and reference samples are developed that characterize how accurately indentation measures the modulus of a material as it varies with distance across a continuous interface between dissimilar tissues with multiple orders of magnitude difference in properties. Finite element simulations accurately predicted discrepancies between the modulus function across an interface observed by indentation and the true modulus function of the material and hence allow us to understand the limits of instrumented indentation as a technique for quantifying gradual changes in material properties. It was found that in order to accurately investigate mechanical property variations in tissues with significant modulus heterogeneity the indenter size should be less than 10 percent of the expected length scale of the modulus variations. Statement of Significance The interfaces between stiff and compliant orthopedic tissues such as bone–tendon, bone–ligament and bone–cartilage are frequent sites of failure during both acute and chronic orthopedic injury and as such their replication via tissue engineering is of importance. The characterization and understanding of these tissue interfaces on a mechanical basis is a key component of elucidating the structure-function relationships that allow them to function naturally and hence a core component of efforts to replicate them. This work uses finite element models and exeperiments to outline the ability of instrumented indentation to characterize the elastic modulus variations across tissue interfaces and provides guidelines for investigators seeking to use this method to understand any interface between dissimilar tissues.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) via the Doctoral Training Award, Department of Engineering, University of Cambridge, grant number 1220717

Structural determinants of hydration, mechanics and fluid flow in freeze-dried collagen scaffolds.

UNLABELLED: Freeze-dried scaffolds provide regeneration templates for a wide range of tissues, due to their flexibility in physical and biological properties. Control of structure is crucial for tuning such properties, and therefore scaffold functionality. However, the common approach of modeling these scaffolds as open-cell foams does not fully account for their structural complexity. Here, the validity of the open-cell model is examined across a range of physical characteristics, rigorously linking morphology to hydration and mechanical properties. Collagen scaffolds with systematic changes in relative density were characterized using Scanning Electron Microscopy, X-ray Micro-Computed Tomography and spherical indentation analyzed in a time-dependent poroelastic framework. Morphologically, all scaffolds were mid-way between the open- and closed-cell models, approaching the closed-cell model as relative density increased. Although pore size remained constant, transport pathway diameter decreased. Larger collagen fractions also produced greater volume swelling on hydration, although the change in pore diameter was constant, and relatively small at ∼6%. Mechanically, the dry and hydrated scaffold moduli varied quadratically with relative density, as expected of open-cell materials. However, the increasing pore wall closure was found to determine the time-dependent nature of the hydrated scaffold response, with a decrease in permeability producing increasingly elastic rather than viscoelastic behavior. These results demonstrate that characterizing the deviation from the open-cell model is vital to gain a full understanding of scaffold biophysical properties, and provide a template for structural studies of other freeze-dried biomaterials. STATEMENT OF SIGNIFICANCE: Freeze-dried collagen sponges are three-dimensional microporous scaffolds that have been used for a number of exploratory tissue engineering applications. The characterization of the structure-properties relationships of these scaffolds is necessary to understand their biophysical behavior in vivo. In this work, the relationship between morphology and physical properties in the dry and hydrated states was investigated across a range of solid concentrations in the scaffolds. The quantitative results provided can aid the design of scaffolds with a target trade-off between mechanical properties and structural features important for their biological activity.Engineering and Physical Sciences Research Council CDT in Nanoscience and Nanotechnology (NanoDTC)This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.actbio.2016.05.02

An interpenetrating network composite for a regenerative spinal disc application

Severe degeneration of the intervertebral disc has an immensely debilitating effect on quality of life that has become a serious health and economic burden throughout the world. The disc plays an integral role in biomechanical movement and support within the spine. The emergence of tissue engineering endeavours to restore the structural characteristics and functionality of the native tissue. Hydrogels have been widely investigated as a candidate for regeneration of the gelatinous nucleus pulposus due to its architectural resemblance and fluid retention characteristics. However, hydrogels are often limited due to small compressive stiffness and tear resistance, leading to extrusion complications. Reinforcement of the hydrogel network using polymeric scaffolds may address these issues of inadequate mechanical properties and implant instability. This study investigates the potential of a carrageenan gel-infused polycaprolactone scaffold for nucleus pulposus tissue engineering. Mechanical properties were characterised using viscoelastic and poroelastic frameworks via microindentation. The incorporation of polymeric reinforcement within the gels increased material stiffness to that comparable to the native nucleus pulposus, however permeability was significantly greater than native values. A preliminary cell evaluation culturing NIH 3T3s over 21 days suggested the incorporation of polymeric networks also enhanced cellular proliferation compared to gels alone

Mechanical measurements of heterogeneity and length scale effects in PEG-based hydrogels.

Colloidal-probe spherical indentation load-relaxation experiments with a probe radius of 3 μm are conducted on poly(ethylene glycol) (PEG) hydrogel materials to quantify their steady-state mechanical properties and time-dependent transport properties via a single experiment. PEG-based hydrogels are shown to be heterogeneous in both morphology and mechanical stiffness at this scale; a linear-harmonic interpolation of hyperelastic Mooney-Rivlin and Boussinesq flat-punch indentation models was used to describe the steady-state response of the hydrogels and determine upper and lower bounds for indentation moduli. Analysis of the transient load-relaxation response during displacement-controlled hold periods provides a means of extracting two time constants τ1 and τ2, where τ1 and τ2 are assigned to the viscoelastic and poroelastic properties, respectively. Large τ2 values at small indentation depths provide evidence of a non-equilibrium state characterized by a phenomenon that restricts poroelastic fluid flow through the material; for larger indentations, the variability in τ2 values decreases and pore sizes estimated from τ2via indentation approach those measured via macroscopic swelling experiments. The contact probe methodology developed here provides a means of assessing hydrogel heterogeneity, including time-dependent mechanical and transport properties, and has potential implications in hydrogel biomedical and engineering applications.The authors would like to acknowledge funding from the National Institutes of Health.This is the author accepted manuscript. The final version is available from the Royal Society of Chemistry via http://dx.doi.org/10.1039/C5SM01210

On the difference between updating the mixing matrix and updating the separation matrix

Raw data for our paper: "Interrelated chemical-microstructural-nanomechanical variations in the structural units of the cuttlebone of Sepia officinalis" DOI: 10.1063/1.499320

Villous Tree Model with Active Contractions for Estimating Blood Flow Conditions in the Human Placenta

$\textit{Background:}$ In the human placenta, maternal and fetal bloods exchange substances through the surface of the villous trees: the fetal blood circulates in the villous trees, around which the maternal blood circulates. The blood flows directly influence fetal growth. Stem villi, the main supports of the villous tree, have contractile cells along the axes, whose contractions are expected to influence the blood circulations in the placenta. The displacement is neither measurable nor predictable while non-invasive measurements such as umbilical Doppler waveforms are helpful to predict the histological changes of the villous trees and vascularization in the placenta. $\textit{Objective:}$ The displacement caused by the contraction of the villous tree is necessary to predict the blood flows in the placenta. Hence, a computational villous tree model, which actively contracts, was developed in this study. $\textit{Method:}$ The villous tree model was based on the previous reports: shear moduli of the human placenta; branching patterns in the stem villi. The displacement pattern in the placenta was estimated by the computational model when the shear elastic moduli were changed. $\textit{Results:}$ The results show that the displacement caused by the contraction was influenced by the shear elastic moduli, but kept useful for the blood flows in the placenta. The characteristics agreed with the robustness of the blood flows in the placenta. $\textit{Conclusion:}$ The villous tree model, which actively contracts, was developed in this study. The combination of this computational model and noninvasive measurements will be useful to evaluate the condition of the placenta

Systematic mechanical evaluation of electrospun gelatin meshes

Electrospinning is a simple and efficient process for producing sub-micron fibres. However, the process has many variables, and their effects on the non-woven mesh of fibres is complex. In particular, the effects on the mechanical properties of the fibre meshes are poorly understood. This paper conducts a parametric study, where the concentration and bloom strength of the gelatin solutions are varied, while all electrospinning process parameters are held constant. The effects on the fibrous meshes are monitored using scanning electron microscopy and mechanical testing under uniaxial tension. Mesh mechanical properties are relatively consistent, despite changes to the solutions, demonstrating the robustness of electrospinning. The gel strength of the solution is shown to have a statistically significant effect on the morphology, stiffness and strength of the meshes, while the fibre diameter has surprisingly little influence on the stiffness of the meshes. This experimental finding is supported by finite element analysis, demonstrating that the stiffness of the meshes is controlled by the volume fraction, rather than fibre diameter. Our results demonstrate the importance of understanding how electrospinning parameters influence the pore size of the meshes, as controlling fibre diameter alone is insufficient for consistent mechanical properties.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) via the Doctoral Training Award, Department of Engineering, University of Cambridge, grant number 1354760

Insight into differences in nanoindentation properties of bone

Nanoindentation provides the ideal framework to determine mechanical properties of bone at the tissue scale without being affected by the size, shape, and porosity of the bone. However, the values of tissue level mechanical properties vary significantly between studies. Since the differences in the bone sample, hydration state, and test parameters complicate direct comparisons across the various studies, these discrepancies in values cannot be compared directly. The objective of the current study is to evaluate and compare mechanical properties of the same bones using a broad range of testing parameters. Wild type C56BL6 mice tibiae were embedded following different processes and tested in dry and rehydrated conditions. Spherical and Berkovich indenter probes were used, and data analysis was considered within the elasto-plastic (Oliver-Pharr), viscoelastic and visco-elastic-plastic frameworks. The mean values of plane strain modulus varied significantly depending on the hydration state, probe geometry and analysis method. Indentations in dry bone analyzed using a visco-elastic-plastic approach gave values of 34 GPa. After rehydrating the same bones and indenting them with a spherical tip and utilizing a viscoelastic analysis, the mean modulus value was 4 GPa, nearly an order of magnitude smaller. Results suggest that the hydration state, probe geometry and the limitations and assumptions of each analysis method influence significantly the measured mechanical properties. This is the first time that such a systematic study has been carried out and it has been concluded that the discrepancies in the mechanical properties of bone measured by nanoindentation found in the literature should not be attributed only to the differences between the bones themselves, but also to the testing and analysis protocols

Age-related changes in mouse bone permeability

The determination of lacunar-canalicular permeability is essential for understanding local fluid flow in bone, which may indicate how bone senses changes in the mechanical environment to regulate mechano-adaptation. The estimates of lacunar-canalicular permeability found in the literature vary by up to eight orders of magnitude, and age-related permeability changes have not been measured in non-osteonal mouse bone. The objective of this study is to use a poroelastic approach based on nanoindentation data to characterize lacunar-canalicular permeability in murine bone as a function of age. Nine wild type C57BL/6 mice of different ages (2, 7 and 12 months) were used. Three tibiae from each age group were embedded in epoxy resin, cut in half and indented in the longitudinal direction in the mid-cortex using two spherical fluid indenter tips (R=238 μm and 500 μm). Results suggest that the lacunar-canalicular intrinsic permeability of mouse bone decreases from 2 to 7 months, with no significant changes from 7 to 12 months. The large indenter tip imposed larger contact sizes and sampled larger ranges of permeabilities, particularly for the old bone. This age-related difference in the distribution was not seen for indents with the smaller radius tip. We conclude that the small tip effectively measured lacunar-canalicular permeability, while larger tip indents were influenced by vascular permeability. Exploring the age-related changes in permeability of bone measured by nanoindentation will lead to a better understanding of the role of fluid flow in mechano-transduction. This understanding may help indicate alterations in bone adaptation and remodeling