Molecular Dynamics Simulations of Hydroxyapatite Nanopores in Contact with Electrolyte Solutions: The Effect of Nanoconfinement and Solvated Ions on the Surface Reactivity and the Structural, Dynamical, and Vibrational Properties of Water

Effect of Pore Defects on Uniaxial Mechanical Properties of Bulk Hexagonal Hydroxyapatite: A Molecular Dynamics Study

Hydroxyapatite (HAP) is a calcium apatite bioceramic used in various naturally-derived and synthetic forms for bone repair and regeneration. While useful for the regrowth of osseus tissue, the poor load-bearing capacity of this material relative to other biomaterials is worsened by the propensity for pore formation during the synthetic processing of scaffolds, blocks, and granules. Here we use molecular dynamics (MD) simulations to improve the current understanding of the defect-altered uniaxial mechanical response in hexagonal HAP single crystals relative to defect-free structures. The inclusion of a central spherical pore within a repeated lattice was found to reduce both the failure stress and failure strain in uniaxial tension and compression, with up to a 30% reduction in maximum stress at the point of failure compared to a perfect crystalline structure observed when a 30 Å diameter pore was included. The Z axis ([0 0 0 1] crystalline direction) was found to be the least susceptible to pore defects in tension but the most sensitive to pore inclusion in compression. The deformation mechanisms are discussed to explain the observed mechanical responses, for which charge imbalances and geometric stress concentration factor effects caused by pore inclusion play a significant role.

First Steps towards Understanding the Non-Linear Impact of Mg on Calcite Solubility: A Molecular Dynamics Study

Magnesium (Mg2+) is one of the most common impurities in calcite and is known to have a non-linear impact on the solubility of magnesian calcites. Using molecular dynamics (MD), we observed that Mg2+ impacts overall surface energies, local free energy profiles, interfacial water density, structure and dynamics and, at higher concentrations, it also causes crystal surface deformation. Low Mg concentrations did not alter the overall crystal structure, but stabilised Ca2+ locally and tended to increase the etch pit nucleation energy. As a result, Ca-extraction energies over a wide range of 39 kJ/mol were observed. Calcite surfaces with an island were less stable compared to flat surfaces, and the incorporation of Mg2+ destabilised the island surface further, increasing the surface energy and the calcium extraction energies. In general, Ca2+ is less stable in islands of high Mg2+ concentrations. The local variation in free energies depends on the amount and distance to nearest Mg in addition to local disruption of interfacial water and the flexibility of surface carbonate ions to rotate. The result is a complex interplay of these characteristics that cause variability in local dissolution energies. Taken together, these results illustrate molecular scale processes behind the non-linear impact of Mg2+ concentration on the solubility of magnesium-bearing calcites.

A review on hydroxyapatite coatings for the biomedical applications: experimental and theoretical perspectives

The production of hydroxyapatite (HAP) composite coatings has continuously been investigated for bone tissue applications during the last few decades due to their significant bioactivity and osteoconductivity.

Hydrogen-Bond Structure and Low-Frequency Dynamics of Electrolyte Solutions: Hydration Numbers from ab Initio Water Reorientation Dynamics and Dielectric Relaxation Spectroscopy

We present an atomistic simulation scheme for the determination of the hydration number (h) of aqueous electrolyte solutions based on the calculation of the water dipole reorientation dynamics. In this methodology, the time evolution of an aqueous electrolyte solution generated from ab initio molecular dynamics simulations is used to compute the reorientation time of different water subpopulations. The value of h is determined by considering whether the reorientation time of the water subpopulations is retarded with respect to bulk-like behavior. The application of this computational protocol to magnesium chloride (MgCl2 ) solutions at different concentrations (0.6-2.8 mol kg-1 ) gives h values in excellent agreement with experimental hydration numbers obtained using GHz-to-THz dielectric relaxation spectroscopy. This methodology is attractive because it is based on a well-defined criterion for the definition of hydration number and provides a link with the molecular-level processes responsible for affecting bulk solution behavior. Analysis of the ab initio molecular dynamics trajectories using radial distribution functions, hydrogen bonding statistics, vibrational density of states, water-water hydrogen bonding lifetimes, and water dipole reorientation reveals that MgCl2 has a considerable influence on the hydrogen bond network compared with bulk water. These effects have been assigned to the specific strong Mg-water interaction rather than the Cl-water interaction.

Nanoscale kinetics of amorphous calcium carbonate precipitation in H2O and D2O

Calcium carbonate (CaCO₃) is one of the most well-studied and abundant natural materials on Earth. Crystallisation of CaCO₃ is often observed to proceed via an amorphous calcium carbonate (ACC) phase, as a precursor to more stable crystalline polymorphs such as vaterite and calcite. Despite its importance, the kinetics of ACC formation have proved difficult to study, in part due to rapid precipitation at moderate supersaturations, and the instability of ACC with respect to all other polymorphs. However, ACC can be stabilised under confinement conditions, such as those provided by a nanopipette. This paper demonstrates electrochemical mixing of a Ca²⁺ salt (CaCl₂) and a HCO₃^- salt (NaHCO₃) in a nanopipette to repeatedly and reversibly precipitate nanoparticles of ACC under confined conditions, as confirmed by scanning transmission electron microscopy (STEM). Measuring the current as a function of applied potential across the end of the nanopipette and time provides millisecond-resolved measurements of the induction time for ACC precipitation. We demonstrate that under conditions of electrochemical mixing, ACC precipitation is extremely fast, and highly pH sensitive with an apparent third order dependence on CO₃^2- concentration. Furthermore, the rate is very similar for the equivalent CO₃^2- concentrations in D₂O, suggesting that neither ion dehydration nor HCO₃^- deprotonation represent significant energetic barriers to the formation of ACC. Finite element method simulations of the electrochemical mixing process enable the supersaturation to be estimated for all conditions and accurately predict the location of precipitation.

Density functional theory based molecular dynamics study of solution composition effects on the solvation shell of metal ions

We present an ab initio molecular dynamics study of the alkali metal ions Li+, Na+, K+ and Cs+, and of the alkaline earth metal ions Mg2+ and Ca2+ in both pure water and electrolyte solutions containing the counterions Cl- and SO42-. Simulations were conducted using different density functional theory methods (PBE, BLYP and revPBE), with and without the inclusion of dispersion interactions (-D3). Analysis of the ion-water structure and interaction strength, water exchange between the first and second hydration shell, and hydrogen bond network and low-frequency reorientation dynamics around the metal ions have been used to characterise the influence of solution composition on the ionic solvation shell. Counterions affect the properties of the hydration shell not only when they are directly coordinated to the metal ion, but also when they are at the second coordination shell. Chloride ions reduce the sodium hydration shell and expand the calcium hydration shell by stabilizing under-coordinated hydrated Na(H2O)5+ complexes and over-coordinated Ca(H2O)72+. The same behaviour is observed in CaSO4(aq), where Ca2+ and SO42- form almost exclusively solvent-shared ion pairs. Water exchange between the first and second hydration shell around Ca2+ in CaSO4(aq) is drastically decelerated compared with the simulations of the hydrated metal ion (single Ca2+, no counterions). Velocity autocorrelation function analysis, used to probe the strength of the local ion-water interaction, shows a smoother decay of Mg2+ in MgCl2(aq), which is a clear indication of a looser inter-hexahedral vibration in the presence of chloride ions located in the second coordination shell of Mg2+. The hydrogen bond statistics and orientational dynamics in the ionic solvation shell show that the influence on the water-water network cannot only be ascribed to the specific cation-water interaction, but also to the subtle interplay between the level of hydration of the ions, and the interactions between ions, especially those of opposite charge. As many reactive processes involving solvated metal ions occur in environments that are far from pure water but rich in ions, this computational study shows how the solution composition can result in significant differences in behaviour and function of the ionic solvation shell.

Dual Energy X-ray Methods for the Characterization, Quantification and Imaging of Calcification Minerals and Masses in Breast

Dual energy (DE) technique has been used by numerous studies in order to detect breast cancer in early stages. Although mammography is the gold standard, the dual energy technique offers the advantage of the suppression of the contrast between adipose and glandular tissues and reveals pathogenesis that is not present in conventional mammography. Both dual energy subtraction and dual energy contrast enhanced techniques were used in order to study the potential of dual energy technique to assist in detection or/and visualization of calcification minerals, masses and lesions obscured by overlapping tissue. This article reviews recent developments in this field, regarding: i) simulation studies carried out for the optimizations of the dual energy technique used in order to characterize and quantify calcification minerals or/and visualize suspected findings, and ii) the subsequent experimental verifications, and finally, the adaptation of the dual energy technique in clinical practice.

Dynamical and Structural Properties of Water in Silica Nanoconfinement: Impact of Pore Size, Ion Nature, and Electrolyte Concentration

In this study, we characterized the structure and the dynamics at a picosecond scale of water molecules in aqueous solutions with cations having various kosmotropic properties (XCl₂ where X = Ba²⁺, Ca²⁺, and Mg²⁺) confined in highly ordered mesoporous silica (MCM-41 and grafted MCM-41) by Fourier transform infrared spectroscopy and quasi-elastic neutron scattering. We pinpointed the critical pore size and the electrolyte concentration at which the influence of the ion nature becomes the main factor affecting the water properties. These results suggest that whatever the ions kosmotropic properties, for pore sizes ϕ_p < 2.6 nm and [XCl₂] ≤ 1 M, the water dynamics is mainly slowed down by the size of the confinement. For pore sizes of 6.6 nm, the water dynamics depends on the concentration and kosmotropic properties of the ion more than on the confinement. The water properties within the interfacial layer were also assessed and related to the surface ion excesses obtained by sorption isotherms. We showed that, for pore sizes ϕ_p ≥ 2.6 nm, the surface ion excess at the pore surface is the main driver affecting the structural properties of water molecules and their dynamics within the interfacial layer.

Absolute Luminescence Efficiency of Europium-Doped Calcium Fluoride (CaF2:Eu) Single Crystals under X-ray Excitation

The absolute luminescence efficiency (AE) of a calcium fluoride (CaF2:Eu) single crystal doped with europium was studied using X-ray energies met in general radiography. A CaF2:Eu single crystal with dimensions of 10 × 10 × 10 mm3 was irradiated by X-rays. The emission light photon intensity of the CaF2:Eu sample was evaluated by measuring AE within the X-ray range from 50 to 130 kV. The results of this work were compared with data obtained under similar conditions for the commercially employed medical imaging modalities, Bi4Ge3O12 and Lu2SiO5:Ce single crystals. The compatibility of the light emitted by the CaF2:Eu crystal, with the sensitivity of optical sensors, was also examined. The AE of the 10 × 10 × 10 mm3 CaF2:Eu crystal peaked in the range from 70 to 90 kV (22.22 efficiency units; E.U). The light emitted from CaF2:Eu is compatible with photocathodes, charge coupled devices (CCD), and silicon photomultipliers, which are used as radiation sensors in medical imaging systems. Considering the AE results in the examined energies, as well as the spectral compatibility with various photodetectors, a CaF2:Eu single crystal could be considered for radiographic applications, including the detection of charged particles and soft gamma rays.

A 3D Model of the Effect of Tortuosity and Constrictivity on the Diffusion in Mineralized Collagen Fibril

Bone tissue is a hierarchically structured material composed at the nanoscale by an organic matrix of collagen type I, apatite mineral and water. We considered an idealized 3D geometrical model of the mineralized collagen fibril in order to analyze the influence of structural factors, i.e. tortuosity, constrictivity, on the water effective diffusivity. The average values of the factors investigated in the diffusivity are computed on 5000 iterations by means of the Montecarlo method. The input parameters of the numerical model are the geometrical dimensions of the apatite mineral, collagen fibrils and their spatial orientation obtained with random extractions from Gaussian probability distribution functions. We analyzed the diffusion phenomenon for concentration gradients parallel to three orthogonal directions (Length, Width and Thickness) and for different scenarios, namely low, intermediate and high apatite volume fraction. For each degree of volume fraction, in the thickness direction, the tortuosity assumes greater values, up to two orders of magnitude, in comparison with the tortuous factors computed in the other directions, highlighting the anisotropy of the nanostructure. Furthermore, it was found that the tortuosity is the dominant parameter which control the effective transport properties within the mineralized collagen fibrils.

3D diffusion model within the collagen apatite porosity: An insight to the nanostructure of human trabecular bone

Bone tissue at nanoscale is a composite mainly made of apatite crystals, collagen molecules and water. This work is aimed to study the diffusion within bone nanostructure through Monte-Carlo simulations. To this purpose, an idealized geometric model of the apatite-collagen structure was developed. Gaussian probability distribution functions were employed to design the orientation of the apatite crystals with respect to the axes (length L, width W and thickness T) of a plate-like trabecula. We performed numerical simulations considering the influence of the mineral arrangement on the effective diffusion coefficient of water. To represent the hindrance of the impermeable apatite crystals on the water diffusion process, the effective diffusion coefficient was scaled with the tortuosity, the constrictivity and the porosity factors of the structure. The diffusion phenomenon was investigated in the three main directions of the single trabecula and the introduction of apatite preferential orientation allowed the creation of an anisotropic medium. Thus, different diffusivities values were observed along the axes of the single trabecula. We found good agreement with previous experimental results computed by means of a genetic algorithm.