**1. Introduction**

274 Biomaterials – Physics and Chemistry

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Hydroxyapatite and Bioglass® are two well-known biomaterials, belonging to the vast class of ceramic supplies, both highly biocompatible and widely applied in the biomedical field. In spite of a huge research regarding engineering applications of both inorganic materials, still many aspects of their tissue integration mechanism have not been completely cleared at a molecular level. Thus, *in silico* studies play a fundamental role in the prediction and analysis of the main interactions occurring at the surface of these biomaterials in contact with the biological fluid when incorporated in the living tissue (prevalently bones or teeth). Hydroxyapatite [HA, Ca10(PO4)6(OH)2] owes its relevance and use as a biomaterial since it constitutes the majority of the mineral phase of bones and tooth enamel in mammalians (Young & Brown, 1982). For sake of completeness, we mention that hydroxyapatite is also studied as an environmental adsorbent of metals and a catalyst (Matsumura & Moffat, 1996; Toulhat et al., 1996). One of the first applications of HA in biomedicine dates back to 1969, when Levitt *et al.* hot-pressed it in powders for biological experimentations (Levitt et al., 1969). From then on, several commercial forms of HA have appeared on the market. The material has also been utilized for preparing apatitic bioceramic, due to its bioresorbability which can be modulated changing the degree of cristallinity. There are so many examples of applications, from Mg2+-substituted hydroxyapatite (Roveri & Palazzo, 2006) to the synthesis of porous hydroxyapatite materials by colloidal processing (Tadic et al., 2004), starch consolidation (Rodriguez-Lorenzo et al., 2002), gel casting (Padilla et al., 2002) and more. Furthermore, recent applications follow a biologically inspired criterion to combine HA to a collagen matrix aiming at the improvement of mechanical properties and bioactivity (Wahl et al., 2007). However, a complete review of all the practical as well as hypothetical uses of HA in the biomaterial area is outside the scope of this Chapter.

Inside the bone, a highly hierarchical collagen-mineral composite, hydroxyapatite is in the form of nano-sized mineral platelets (Currey, 1998; Fratzl et al., 2004; Weiner & Wagner, 1998) and contains carbonate ions for the 4-8 weight % (Roveri & Palazzo, 2006). In section 2.1 of this Chapter, two aspects of defects which can be encountered in a synthetic or natural HA sample will be presented. The first aspect deals with non-stoichiometric surfaces and

*In Silico* Study of Hydroxyapatite and Bioglass®: How Computational Science Sheds Light on Biomaterials

focusing exclusively on Gaussian type functions.

**2.1 Defects in hydroxyapatite bulk and surfaces** 

2009; Corno et al., 2008).

oxygen atom of the OH-

symmetry equivalent.

computational time. Our calculations are performed either with the pure GGA PBE functional (Perdew et al., 1996) or with the hybrid B3LYP (Becke, 1993), both well-known functionals. Two *ab initio* approaches are possible within DFT and they differ for the type of basis set functions. Indeed, a localized Gaussian basis set can be considered, as in the present case, or a plane waves one, also extremely diffuse. An *excursus* of advantages and disadvantages of these approaches is not useful in this context and will be omitted, by

All the calculations mentioned in this Chapter have been performed using the CRYSTAL code in its latest release (Dovesi et al., 2005a; Dovesi et al., 2005b; Dovesi et al., 2009). This periodic quantum-mechanical software has been developed by the Theoretical Chemistry group of the University of Turin (Italy) together with the Daresbury Laboratory (UK) since 1988. CRYSTAL is capable of computing systems with every dimensionality, from molecules to real infinite crystals and it supports massive parallel calculations. This code uses local Gaussian basis sets and can deal with many electronic structure methods, from Hartree-Fock to Kohn-Sham Hamiltonians. Structural, electrostatic and vibrational properties of the studied materials have been characterized with the program. Another crucial aspect in modeling is the graphical visualization and representation of structures. For all the images displayed in this Chapter, MOLDRAW (Ugliengo et al., 1993), J-ICE (Canepa et al., 2011b) and VMD (Humphrey et al., 1996) programs were used. Further more precise computational details can be read in a number of our recent papers on both HA (Corno et al., 2009; Corno et al., 2006; Corno et al., 2007; Corno et al., 2010) and bioactive glasses (Corno & Pedone,

Hydroxyapatite (HA) is a mineral which occurs in nature in two polymorphs, a monoclinic form, thermodynamically stable at low temperatures, and an hexagonal form, which can be easily stabilized by substitution of the OH- ions (Suda et al., 1995). These ions are aligned along the c axis (the [001] direction), as highlighted in Fig. 1. The single crystal structure of the hexagonal form of HA is characterized by the *P63/m* space group. The mirror plane,

an intrinsic static disorder of these ions, which can point, with no preference, in one of the two opposite directions ([001] or [00-1]). The result is a fractional occupation of the sites in the solved crystallographic structure (50% probability for each direction). As *ab initio* simulation cannot take into account the structural disorder, we reduced the symmetry to

configuration found, both the OH- ions point in the same direction, as reported in Fig. 1. The

the *ab* plane. Moreover, there are six phosphate ions inside the crystallographic cell, all

The bulk structure of crystalline HA, fully characterized in the literature (Corno et al., 2006), has been considered as a starting point to model the surfaces which are experimentally found to be the most important: (001) in terms of reactivity, and (010) in terms of exposure in the crystal habit (Wierzbicki & Cheung, 2000). Those surfaces have already been fully characterized at an *ab initio* level, and all the structural, geometrical and electronic properties

ion is close to three Ca ions, which form an equilateral triangle in

perpendicular to the [001] direction, is compatible with the column of OH-

*P63*, removing the mirror plane and fixing the directions of the OH-

**2. Hydroxyapatite and Bioglass® as computational case study** 

277

ions because of

ions. In the most stable

their adsorptive behavior towards simple molecules (water and carbon monoxide). The second concerns the inclusion of carbonate ions in the pure HA bulk structure to simulate the apatite bone tissue. These examples of applying sophisticated computational techniques to the investigation of defects in HA represent a very recent progress achieved in our laboratory inside this biomedical research area, which has being carried out since 2003. For the interested reader, a summary of the last years work on simulation of HA in our research group has been recently published (Corno et al., 2010).

As for bioactive glasses, the first synthesis was performed in 1969-71 by Larry Hench in Florida (Hench et al., 1971). He had synthesised a silicate-based material containing calcium and phosphate and had implanted this composition in rats' femurs (Hench, 2006). The result was a complete integration of the inorganic material with the damaged bone. This very first composition was called Bioglass® 45S5 (45SiO2 - 24.5Na2O - 24.5CaO - 6P2O5 in wt. % or 46.1 SiO2, 24.4 Na2O, 26.9 CaO and 2.6 P2O5 in mol %) and has been introduced in clinical use since 1985. The interest has been then to investigate the steps of the bioactivity mechanism leading to the formation of a strong bond between the material and the biological tissue. The most renowned hypothesis is the so-called Hench mechanism and its crucial step resides in the growth of a thin amorphous layer of hydroxy-carbonated apatite (HCA) (Hench, 1998; Hench & Andersson, 1993; Hench et al., 1971). Indeed, on that layer biological growth factors are adsorbed and desorbed to promote the process of stem cells differentiation. Moreover, before the growth of HCA, several other chemical reactions occur, dealing particularly with the exchange of sodium and calcium ions present in the Bioglass® with protons derived from the biological fluid. The influence of the chemical components of the inorganic material on its bioactivity has recently been object of scientific research and discussion. For instance, additives such as fluorine (Christie et al., 2011; Lusvardi et al., 2008a), boron, magnesium (A. Pedone et al., 2008) and zinc (Aina et al., 2011) were considered in a number of systematic studies. In section 2.2 of this Chapter, the role of phosphate concentration inside models with the 45S5 composition will be highlighted, since these changes in content can affect the crucial mechanism of gene activation and modify the local environment of the silicon framework and of Na and Ca sites, as well as the dissolution rate of silica (O'Donnell et al., 2009).

The joint use of experimental and theoretical techniques nowadays has reached a very large diffusion due to the completeness of the derived information. Particularly, in the biological or biochemical field, computational methods are essential to the investigation of interfacial mechanisms at a molecular level. Moreover, very often the interplay between experimental and calculated data allows researchers to improve both methodologies. A huge amount of examples could be reported, but for sake of brevity here we limit to our own experience of collaboration with a number of experimentalists. Indeed, in our research papers, dealing either with HA or with bioactive glasses, there is always a detailed comparison with measured data, for instance by means of NMR (Pedone et al., 2010), IR and Raman spectroscopy and of adsorption microcalorimetry (Corno et al., 2009; Corno et al., 2008). In our computational studies, we refer to quantum-mechanical techniques, which are very accurate but also quite heavy as for the need of resources. Usually, high parallel computing systems are required to run the simulations and we have successfully used the supercomputers of several HPC centers, such as the Barcelona Supercomputing Centre (Spain) or the CINECA Supercomputing Center (Italy).

The most used theoretical framework in the last decade's literature is the Density Functional Theory, which grants a good compromise in terms of accuracy of the representation and

their adsorptive behavior towards simple molecules (water and carbon monoxide). The second concerns the inclusion of carbonate ions in the pure HA bulk structure to simulate the apatite bone tissue. These examples of applying sophisticated computational techniques to the investigation of defects in HA represent a very recent progress achieved in our laboratory inside this biomedical research area, which has being carried out since 2003. For the interested reader, a summary of the last years work on simulation of HA in our research

As for bioactive glasses, the first synthesis was performed in 1969-71 by Larry Hench in Florida (Hench et al., 1971). He had synthesised a silicate-based material containing calcium and phosphate and had implanted this composition in rats' femurs (Hench, 2006). The result was a complete integration of the inorganic material with the damaged bone. This very first composition was called Bioglass® 45S5 (45SiO2 - 24.5Na2O - 24.5CaO - 6P2O5 in wt. % or 46.1 SiO2, 24.4 Na2O, 26.9 CaO and 2.6 P2O5 in mol %) and has been introduced in clinical use since 1985. The interest has been then to investigate the steps of the bioactivity mechanism leading to the formation of a strong bond between the material and the biological tissue. The most renowned hypothesis is the so-called Hench mechanism and its crucial step resides in the growth of a thin amorphous layer of hydroxy-carbonated apatite (HCA) (Hench, 1998; Hench & Andersson, 1993; Hench et al., 1971). Indeed, on that layer biological growth factors are adsorbed and desorbed to promote the process of stem cells differentiation. Moreover, before the growth of HCA, several other chemical reactions occur, dealing particularly with the exchange of sodium and calcium ions present in the Bioglass® with protons derived from the biological fluid. The influence of the chemical components of the inorganic material on its bioactivity has recently been object of scientific research and discussion. For instance, additives such as fluorine (Christie et al., 2011; Lusvardi et al., 2008a), boron, magnesium (A. Pedone et al., 2008) and zinc (Aina et al., 2011) were considered in a number of systematic studies. In section 2.2 of this Chapter, the role of phosphate concentration inside models with the 45S5 composition will be highlighted, since these changes in content can affect the crucial mechanism of gene activation and modify the local environment of the silicon framework and of Na and Ca sites, as well as the dissolution

The joint use of experimental and theoretical techniques nowadays has reached a very large diffusion due to the completeness of the derived information. Particularly, in the biological or biochemical field, computational methods are essential to the investigation of interfacial mechanisms at a molecular level. Moreover, very often the interplay between experimental and calculated data allows researchers to improve both methodologies. A huge amount of examples could be reported, but for sake of brevity here we limit to our own experience of collaboration with a number of experimentalists. Indeed, in our research papers, dealing either with HA or with bioactive glasses, there is always a detailed comparison with measured data, for instance by means of NMR (Pedone et al., 2010), IR and Raman spectroscopy and of adsorption microcalorimetry (Corno et al., 2009; Corno et al., 2008). In our computational studies, we refer to quantum-mechanical techniques, which are very accurate but also quite heavy as for the need of resources. Usually, high parallel computing systems are required to run the simulations and we have successfully used the supercomputers of several HPC centers, such as the Barcelona Supercomputing Centre

The most used theoretical framework in the last decade's literature is the Density Functional Theory, which grants a good compromise in terms of accuracy of the representation and

group has been recently published (Corno et al., 2010).

rate of silica (O'Donnell et al., 2009).

(Spain) or the CINECA Supercomputing Center (Italy).

computational time. Our calculations are performed either with the pure GGA PBE functional (Perdew et al., 1996) or with the hybrid B3LYP (Becke, 1993), both well-known functionals. Two *ab initio* approaches are possible within DFT and they differ for the type of basis set functions. Indeed, a localized Gaussian basis set can be considered, as in the present case, or a plane waves one, also extremely diffuse. An *excursus* of advantages and disadvantages of these approaches is not useful in this context and will be omitted, by focusing exclusively on Gaussian type functions.
