Current Views on Calcium Phosphate Osteogenicity and the Translation into Effective Bone Regeneration Strategies




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НазваниеCurrent Views on Calcium Phosphate Osteogenicity and the Translation into Effective Bone Regeneration Strategies
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(6) Computer Modelling of Bone Regeneration In CaP Scaffolds

Improvements in computer capacity now enable an increased model realism and complexity (e.g. 3D calculations, complex geometries, multi-scale and multi-physics) [151]. As a consequence of this technological revolution, there has been an enormous increase in the use of mathematical models in biology and medicine. These mathematical models can propose and test possible biological mechanisms, contributing to the unravelling of the complex nature of biological systems, like bone regeneration processes inside CaP structures. Moreover, they can be used to design and test possible experimental strategies in silico before they are tested in vitro or in vivo [152-153]. Eventually, all this knowledge can be used to develop clinically relevant CaP-based bone reparative units (figure 4).


Currently, many computational models of bone formation and regeneration in general [154], or even in scaffolds specifically [11] exist. Bohner et al. propose a theoretical approach to determine the effect of geometrical factors on the resorption rate of CaP scaffolds [155]. Their theoretical model was based on five assumptions: (i) the sphericity of the pores, (ii) a face-centered cubic packing of the pores, (iii) surface-controlled resorption, (iv) the resorption requires the presence of blood vessels (50 µm in diameter) and (v) the resorption time is proportional to the net amount of material [156]. The model calculations show that, based on these assumptions, the resorption time of a macroporous block depends on the pore radius which is determined by the size of the bone substitute and interpore distance [156]. Subsequently, the model was used to optimize the pore size of CaP scaffolds and validated with experimental data.


The theoretical model mentioned above looks, however, exclusively at geometrical scaffold properties and does not include biological variables such as cell or matrix densities. Byrne et al. developed a 3D mechanoregulatory model of bone regeneration in a regular scaffold to investigate the effect of porosity, Young’s modulus and dissolution rate on bone regeneration in different loading conditions [157]. They modelled the scaffold as a poroelastic material which resorbs in a linear, load-independent fashion, i.e. the porosity will be increased by a 0%, 0.5%, 1% per iteration for low, intermediate and high dissolution rates respectively [158]. Consequently, the size of all scaffold elements decreases uniformly resulting in an overall volumetric reduction while the scaffold geometry remains unaltered. Their calculations show that as scaffold degradation progresses, the regenerating tissue must take over the mechanical function of the bone-scaffold system, which would otherwise collapse due to a lack of mechanical strength. Moreover, all three variables (i.e. porosity, Young’s modulus and dissolution rate) appear to influence the amount of bone formation in a non-intuitive way, demonstrating the need to optimize scaffolds for site-specific loading requirements. This model was improved by including blood vessel growth thereby establishing a framework to investigate the effect of vascularization on bone formation [159].


Other studies have modeled the bone regeneration process inside biodegradable polymer-based scaffolds. Stops et al. further investigated the influence of mechanical strain and perfusive fluid flow on cell differentiation and proliferation within a collagen-glycosaminoglycan scaffold [160]. Sanz-Herrera et al. presented a multi-scale model of bone regeneration inside a porous scaffold [161]. The degradation mechanism of the biodegradable polymer scaffold was modelled as a hydrolysis process, i.e. the water content in the polymer chemically reacts and breaks down the polymer molecules resulting in biomaterial bulk erosion. The mechanical properties of the polymer were assumed to relate linearly to its molecular weight. The model was used to predict the evolution of the bone formation process in a scaffold implanted in the femoral condyle of a rabbit. They found a good qualitative agreement between the obtained computational and experimental results. Although further validation is necessary, the proposed multi-scale model is a useful tool to investigate the complex phenomena that occur at different length and time scales, i.e. the bone formation and scaffold resorption at the microscopic scale and the change of mechanical properties at the macroscopic scale. Lacroix et al. reviewed the current techniques used for scaffold development: from scaffold optimization of scaffolds by mathematical models (e.g. FEM) to scaffold design using computer aided design (CAD) and scaffold characterization by computed tomography (CT) [162].


Although the above models can be used to optimize some (mechanical) properties of scaffolds, e.g. the porosity, the micro-architecture, the Young’s modulus and dissolution rate, they neglect the influence of growth factors and other biochemical signals on the bone formation process. Moreover, the dissolution process is only crudely modeled, neglecting the influence of the degradation products (e.g. Ca2+ and Pi) on the cellular activities and bone formation processes. Carlier et al. developed and implemented an experimentally informed bioregulatory model of the effect of calcium ions released from CaP-based biomaterials on the activity of osteogenic cells and mesenchymal stem cell driven ectopic bone formation [163]. The dissolution kinetics of the CaP scaffold were modeled by a general empirical equation [164], assuming that the dissolution rate is proportional to the driving force (i.e. the difference between the current and the saturated calcium concentration) and that the rate constant is time-independent. The amount of bone formation predicted by the model of Carlier et al. corresponded to the amount measured experimentally under similar conditions. Moreover, experimentally impaired bone formation due to conditions such as insufficient cell seeding and scaffold decalcification, was also retrieved in silico. Subsequently, this model was used to optimise CaP scaffold selection to make their use in combination with cells more clinically relevant.


Although computational models can contribute to the general knowledge on bone formation inside CaP structures and useful to customise the CaP carriers to the patient-specific needs as well as the particular bone application, experimental research is necessary to establish and validate the mathematical models. The most important parameters and their respective parameter values should be experimentally quantified. Consequently, the multidisciplinary problem of optimizing scaffold architecture and seeding protocols for bone tissue engineering strategies requires an integrative approach which was nicely summarized by Bohner et al. [165]: a combination of mathematical modelling to explain a mechanism of biomaterial-cell interactions with experimental research to provide data for the determination of model parameters as well as the validation of the mathematical model. This integrative approach requires a careful design and an extensive characterisation of the scaffold. Moreover, this process is intrinsically iterative: new experimental results can be fed to the model and new research hypotheses can result from thorough model analysis.


(7) Limitations, Future Perspectives and Conclusion

As discussed above, it is clear that the bone induction by CaP biomaterials is influenced by the physicochemical properties of the material and thus the subsequent cellular events of osteogenesis. However, the exact key determinant(s) of CaP osteoinduction, meaning the molecular mechanisms involved and the stem cell-material-host interactions upon implantation is/are still underdetermined. Therefore, further study to decipher the molecular signalling at the cellular level (such as receptor binding of the released Ca2+ and PO43- and the activation of critical intracellular osteogenesis pathway), and to understand the critical biological parameters that are essential for implanted cells to communicate and integrate effectively with the host system are required [166]. Unfortunately, the translation of the complex in vivo osteogenesis environment into an in vitro system is far from trivial, and the predictiveness of in vitro observations often does not correlate well with the in vivo bone formation capability [89]. This is due to some critical issues such as the use of correct cell types for a specific type of CaP-based biomaterial and the selection of the correct culture conditions. Therefore, there is a need for customisation of the CaP-based biomaterial to overcome these limitations. Moreover, other parameters present in vivo, including the compositions and dynamics of body fluids and blood vessel in-growth, are technically challenging to be translated into a simplified in vitro setting. Recently, the reactivity of CaP-based biomaterials in culture medium was revealed to have significant influences on Ca2+ and PO43- dissolution kinetics and the subsequent cellular behaviour, which was not correlated to the ion dissolution behaviour evaluated in simulated body fluid (SBF) or phosphate-buffered saline. This must be carefully considered when evaluating the osteoinductive potential of the material [167]. We propose the standardisation of in vitro dissolution tests to evaluate the ions release kinetics of a CaP-based biomaterial, where the in vitro dissolution experiment should resemble and be customised to the in vivo environment as close as possible [156]. Firstly, the CaP scaffolds should be thoroughly characterised (porosity, pore size distribution, grain size, surface topography and surface area, composition and etc.) before and after the dissolution test. Here, we highlight on the use of non-invasive methods including Raman spectroscopy [158] and micro- or nano-focus X-ray computed tomography to obtain quantitative characterisation of the material properties [168]. Secondly, we propose a dual solution system for the in vitro dissolution testing using simulated body fluid [169] and culture medium (with and without the presence of cells) [170]. This will allow for the characterisation of the intrinsic ionic dissolution behaviour of the biomaterial in a solution having similar ionic composition to the bodily fluid, followed by the understanding on the interactions or the influences of the cells and proteins on the ionic dissolution kinetics. In fact, more and more studies have shown the reduction of Ca2+ in the culture medium, indicating the formation of new CaP crystals onto the existing CaP substrate [128]. Thirdly, the experimental setting should also account for the local in vivo hydrodynamic of the bodily fluid, for instance, at the implantation site. This can be achieved by performing the dissolution test under dynamic condition (e.g. using perfusion system) at physiologically relevant flow rate [118, 127].


Moreover, the in vitro and in vivo experiments should be designed in such a way that they minimise variability and enable quantification, thus providing the essential data for the determination of model parameters as well as for the model validation. It is of note that as mathematical models predict the dynamics at different scales (e.g. molecular, cellular and tissue) as a function of time and space, temporal and spatial quantitative data are crucial to the success of mathematical models. Clearly, computational modelling plays an essential role to further unravel the complex mechanism of CaP osteoinduction in vivo. Most of the current models look either at mechanoregulatory or bioregulatory stimuli, depending on the specific research question that is being answered. In the future, however, these models could be combined to further improve the predictive capabilities of the model.


The limitations mentioned above underline the importance of an interdisciplinary strategy for the optimisation of CaP scaffolds for bone tissue engineering applications [165]. An essential characteristic of these integrative research efforts is their iterativity: model analysis can lead to new research hypotheses and new experimental findings can be used to improve the predictive capacities of the model.

In conclusion, this review discussed the importance of CaP for physiological bone homeostasis as well as its potential for bone tissue engineering. Although numerous studies have been devoted to unravel the mechanisms of osteoinductivity of CaP scaffolds, many questions still remain unresolved. To overcome this bottleneck, it is therefore essential that experimental and computational research are combined so that the complex in vivo biological process of bone regeneration inside CaP constructs can be deciphered in an effective and systematic manners. This includes computational modelling and correlation analysis between the physicochemical properties of CaP constructs and the influences on in vitro and in vivo biological outcomes, thus identifying the critical parameters and thorough understanding of the underlying biological that govern osteoinductivity of CaP constructs. Only in this way, it will be possible to make CaP a clinically relevant and predictive tissue engineering construct for effective bone defect repair.


Acknowledgements

This work is funded by the KU Leuven IDO project 05/009 – QuEST, Stem Cell Institute of Leuven – KU Leuven, ENDEAVOUR project G.0982.11N. Aurélie Carlier and Johanna Bolander are PhD fellows of the Research Foundation Flanders (FWO Vlaanderen). The work is part of Prometheus, the Leuven Research and Development Division of Skeletal Tissue Engineering of KU Leuven: www.kuleuven.be/Prometheus. The authors declare that they have no potential conflict of interest and they had and will have no financial relationships with companies whose products are relevant to the subject of this study.


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Figure Legends:


Figure 1: (a) Composition and (b) mechanical properties of human bone [Athanasiou KA et al. 2000; Keaveny TM et al. 2001].


Figure 2: Theories of biomineralisation of collagen fibril. (a) Direct nucleation of CaP crystal. (i) CaP clusters form complexes with the functional biopolymer (e.g. polyaspartic acid), and (ii) form stable mineral droplets. (iii) The mineral droplets bind to a distinct region on the collagen fibres and enter the fibril, and (iv) diffuse through the interior of the fibril before solidifying into a disordered (amorphous) phase. (v) This amorphous phase is transformed into oriented apatite crystals directed by the collagen orientation [modified from Colfen H. Nat Mater. 2010]. (b) Matrix vesicle (MV) mediated matrix mineralisation. Schematic showing the three possible mechanisms for the initiation of MV-mediated matrix mineralisation [adapted from Golub E.E. Biochimical et Biophysica Acta. 2009]. PPi, pyrophosphate.


Figure 3: The influence of specific surface area of CaP-based biomaterials on in vivo ectopic bone formation. Each data point represents one type of CaP-implant with specific surface area and its in vivo bone forming capacity. Based on these studies, a threshold level of specific surface area required to induce bone formation, was chosen at around 1.0 m2/g (the cut-off point). [Data are adopted from Habibovic et al. 2005; Li et al. 2008; Yuan et al. 2010].


Figure 4: The concept of integrating manufacturing process, stem cell technology and computational modelling as a novel strategy to design and optimise CaP-based bone reparative unit for effective bone regeneration that can also assist the translation to personalised bone regeneration.

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