Amanpreet K. Bembey

Viscoelastic properties of bone as a function of hydration state determined by nanoindentation

Spherical indentation creep testing was used to examine the effect of hydration state on bone mechanical properties. Analysis of creep data was based on the elastic–viscoelastic correspondence principle and utilized a direct solution for the finite loading-rate experimental conditions. The zero-time shear modulus was computed from the creep compliance function and compared to the indentation modulus obtained via conventional indentation analysis, based on an elastic unloading response. The method was validated using a well-known polymer material under three different loading conditions. The method was applied to bone samples prepared with different water content by partial exchange with ethanol, where 70% ethanol was considered as the baseline condition. A hydration increase was associated with a 43% decrease in stiffness, while a hydration decrease resulted in a 20% increase in bone tissue stiffness.

Composite bounds on the elastic modulus of bone

Advances in diagnosis and treatment of some bone disorders can be made by understanding the linkage between mineral content and mechanical function. Bone is approximately half by volume a hydrated protein network, and the remainder is a biomineral analogue of hydroxyapatite. In the current work, paired measurements of mechanical properties, using nanoindentation, and of bone mineral volume fraction, computed from quantitative back-scattered electron imaging, were made on six different types of normal and outlier bone samples. Local elastic modulus was plotted against mineral fraction and compared with predictions of engineering bounds for a two-phase composite material. Experimental data spanning the composite bounds showed no one-to-one relationship between mechanical stiffness and bone composition, excluding the possibility of any single, simple composites model for bone at nanometer length-scales.

Hydration Effects on the Viscoelastic Properties of Collagen

The manner in which liquid interacts with collagen is unclear, with changes in hydration presenting ambiguity. At present, elastic modulus values for collagen quoted range from MPa to GPa. Dynamic mechanical analysis (DMA) of collagen in isolation provides an insight into the mechanical changes due to altered hydration states. Changes in the viscoelastic properties of collagen were examined as the material was systematically dehydrated in a series of water:solvent mixes to examine effects of dehydration. The effect of solvents with varying polarity was also examined. Tails from 11-week old wild type mice were used. Mouse tail is a tissue with a well-defined, hierarchical organization of type I collagen. The viscoelastic response of collagen was measured using dynamic mechanical analysis (DMA) in fiber extension mode over the frequency range of 1Hz to 10Hz. Samples were sequentially dehydrated in a series of solvent concentrations: 70% ethanol to 100% ethanol to 100% acetone and 70% ethanol to 70% methanol to 100% methanol for at least 1h. Selectively removing and then replacing water from collagen samples provides insight into the role of water in the ultrastructure of the tissue from the corresponding changes in the experimentally determined elastic modulus and viscous energy.

Nanoindentation and finite element analysis of resin-embedded bone samples as a three-phase composite material

The effective elastic modulus of composite materials results from a combination of elastic moduli of the component phases. Recent efforts to understand the mechanical behavior of calcified tissues in bones and teeth require estimates of the component phase properties, which are difficult to establish independently. A three-phase system, based on naturally occurring bone, is therefore examined by a combined nanoindentation and finite element modelling approach to better understand the proportions and properties of the component phases. Bone samples were prepared in four two- or three-phase composite configurations as follows: (1) as a dehydrated mineral-protein composite (with some void space); (2) similarly dehydrated mineral-protein composite but with polymethylmethacrylate (PMMA) resin filling the voids resulting in three solid phases; (3) as a PMMA-mineral composite following protein removal and replacement with PMMA, and (4) as a PMMA-protein composite following mineral removal and replacement with PMMA. Effective component volume fractions and elastic moduli for each phase in each system were computed based on the composite nanoindentation results. Finite element models of the two- and three-phase systems were constructed to explore the structural anisotropy of the composite systems, as demonstrated in the nanoindentation tests, and to examine the sensitivity of the composite results to changes in the assumed component properties.

Elastic Modulus and Mineral Density of Dentine and Enamel in Natural Caries Lesions

Dental tissues have been reported to show a considerable decrease in both their mineral content and mechanical properties in carious lesions. The changed properties of dentine and enamel have been shown to be dependent on crystal size and not only mineral content [1], although the connectivity between the mineral crystals has been overlooked. Teeth with carious lesions were sectioned, embedded in polymethylmethacrylate (PMMA) and diamond polished. Nanoindentation and quantitative backscattered electron imaging were used to determine relationships between the elastic modulus and mineral density of sound and carious regions within dentine and enamel. The changes in elastic modulus with decreased mineralization for dentine and enamel could not be explained by simple composite mechanics expressions relating elastic modulus and mineral volume fraction. Finite element modeling of dentine and enamel as a two-phase composite material at the ultrastructure level were used to demonstrate how changes in the mineral phase connectivity can produce changes in the elastic modulus. Tissue models for enamel, in which the mineral phase is both the major component of the structure (∼ 85% by volume) and highly interconnected, were consistent with the modulus of sound enamel. The drastic change in enamel modulus with a relatively small change in mineral volume fraction could be modeled as a decrease in mineral phase connectivity at nearly constant volume fraction. The more gradual trend in the dentine data was also consistent with a structure that is initially highly connected in the mineral phase, consistent with the known structure of dentine, and for which the change in modulus is more directly related to changes in mineral content than mineral connectivity.

Poroelastic indentation analysis for hydrated biological tissues

Indentation techniques are employed for the measurement of mechanical properties of a wide range of materials. In particular, techniques focused at small length-scales, such as nanoindentation and AFM indentation, allow for local characterization of material properties in heterogeneous materials including natural tissues and biomimetic materials. Typical elastic analysis for spherical indentation is applicable in the absence of time-dependent deformation, but is inappropriate for materials with time-dependent responses. Recent analyses for the viscoelastic indentation problem, based on elastic-viscoelastic correspondence, have begun to address the issue of time-dependent deformation during an indentation test. The viscoelastic analysis has been shown to fit experimental indentation data well, and has been demonstrated as useful for characterization of viscoelasticity in polymeric materials and in hydrated mineralized tissues. However, a viscoelastic analysis is not necessarily sufficient for multi-phase materials with fluid flow. In the current work, a poroelastic analysis-based on fluid motion through a porous elastic network-is used to examine spherical indentation creep responses of hydrated biological materials. Both analytical and finite element approaches are considered for the poroelastic Hertzian indentation problem. Modeling results are compared with experimental data from nanoindentation of hydrated bone immersed in water and polar solvents (ethanol, methanol, acetone). Baseline (water-immersed) bone responses are characterized using the poroelastic model and numerical results are compared with altered hydration states due to polar solvents.

Effect of water on mechanical properties of mineralized tissue composites

In the current study, the effects of polar solvents on tissue volume and mechanical properties are considered. Area shrinkage measurements are conducted for mineralized bone tissue samples soaked in polar solvents. Area shrinkage is used to calculate approximate linear and volume shrinkage. Results are compared with viscoelastic mechanical parameters for bone in the same solvents (as measured previously) and with both shrinkage measurements and mechanical data for nonmineralized tissues, as taken from the existing literature. As expected, the shrinkage of mineralized tissues is minimal when compared with shrinkage of nonmineralized tissues immersed in the same polar solvents. The mechanical changes in bone are also substantially less than in nonmineralized tissues. The largest stiffness values are found in shrunken bone samples (immersed in acetone and ethanol). The mineral phase in bone thus resists tissue shrinkage that would otherwise occur in the pure soft tissue phase.

Nanoindentation Measurements of Bone Viscoelasticity as a Function of Hydration State

Bone is an anisotropic material, and its mechanical properties are determined by its microstructure as well as its composition. Mechanical properties of bone are a consequence of the proportions of, and the interactions between, mineral, collagen and water. Water plays an important role in maintaining the mechanical integrity of the composite, but the manner in which water interacts within the ultrastructure is unclear. Dentine being an isotropic two-dimensional structure presents a homogenous composite to examine the dehydration effects. Nanoindentation methods for determining the viscoelastic properties have recently been developed and are a subject of great interest. Here, one method based on elastic-viscoelastic correspondence for ‘ramp and hold’ creep testing (Oyen, J. Mater. Res., 2005) has been used to analyze viscoelastic behavior of polymeric and biological materials. The method of ‘ramp and hold’ allows the shear modulus at time zero to be determined from fitting of the displacement during the maximum load hold. Changes in the viscoelastic properties of bone and dentine were examined as the material was systematically dehydrated in a series of water:solvent mixes. Samples of equine dentine were sectioned and cryo-polished. Shear modulus was obtained by nanoindentation using spherical indenters with a maximum load hold of 120s. Samples were tested in different solvent concentrations sequentially, 70% ethanol to 50% ethanol, 70 % ethanol to 100% ethanol, 70% ethanol to 70% methanol to 100% methanol, and 70% ethanol to 100% acetone, after storage in each condition for 24h. By selectively removing and then replacing water from the composite, insights in to the ultrastructure of the tissue can be gained from the corresponding changes in the experimentally determined moduli, as well as an understanding of the complete reversibility of the dehydration process.