In silico modeling of bone formation under the influence of calcium phosphate-based biomaterials and osteochondrogenic growth factors

Bone regeneration is a complex process that involves regulation of different cell types by multiple biochemical, physical and mechanical factors. Unlike other biological tissues, bone can heal scarlessly and recover its original shape, size and strength. However, about 5% of bone defects result in non-unions. To tackle these non-unions, tissue engineering (TE) aims to develop bone substitutes or intelligent TE constructs to replace damaged, diseased or aging tissue. These bone substitutes/TE constructs are designed to support the chemotaxis, proliferation and differentiation of bone progenitor cells as well as being a biochemical agent delivery system. However, these delivery systems have a few limitations such as structural weakness of the carrier, high doses of biochemical agents being delivered due to burst release, unknown optimal concentrations of implanted cells and their high cost. Another drawback of these systems is the limited understanding on the relationship between biochemical agent dose, implanted cells, carrier volume, carrier material type and resultant bone formation. Given their significant medical potential, there is an increasing demand to design and develop improved bone substitutes/TE constructs. This PhD work fits in the long-term vision that mathematical models can be used as a part of design and manufacturing processes to develop improved treatment strategies and ultimately save experimental time and costs. In the first part of this work, a novel computational model was developed to predict the in vitro release of Ca2+ ions from calcium phosphate (CaP)-based scaffolds. The developed model was based on the Noyes-Whitney equation, the Fick’s second law of diffusion equation and the level-set method (LSM). The model was dependent on biophysicochemical phenomena such as dissolution, diffusion and degradation along with specific scaffold characteristics such as composition, size and shape. The predictions of the model were compared to dedicated experimental results. In the second part of this work, we investigated the use of a previously reported oxygen-dependent fracture healing model to elucidate the in vivo bone formation capacity of bone morphogenetic protein-2 (BMP-2) delivery systems in an ectopic environment. Specific attention was paid to the influence of BMP-2 dose and carrier volume on ectopic bone formation. The performance of this mathematical model was corroborated by comparison with experimental results published in the literature. Finally, the model was applied to investigate the influence of different BMP-2 release profiles on ectopic bone formation. In the third part of this work, we developed a novel computational model to predict the CaP and BMP-dependent ectopic bone formation in nude mice with and without incorporation of donor cells. The model specifically investigated the influence of BMP-2 dose, donor cell concentrations and calcium ion release on ectopic bone formation. The performance of this mathematical model was compared to the results of dedicated in-house experiments. The model was able to capture essential elements of the experimental results yet at the same time, a number of points for further improvement were identified. In the final part of this work, we investigated the application of the aforementioned CaP and BMP-dependent bone formation model to an orthotopic setting in sheep. The performance of the mathematical model was corroborated by comparing the model predictions with experimental results published in the literature. Subsequently, the model was applied to investigate the influence of different CaP-BMP-cell combinations on orthotopic bone formation, simulating in-house ongoing experiments. In conclusion, this PhD work illustrates a computational step taken towards enhancing the understanding on the role of CaP and BMPs in healing large bone defects

Computational modelling of local calcium ions release from calcium phosphate-based scaffolds

A variety of natural or synthetic calcium phosphate (CaP)-based scaffolds are currently produced for dental and orthopaedic applications. These scaffolds have been shown to stimulate bone formation due to their biocompatibility, osteoconductivity and osteoinductivity. The release of the [Formula: see text] ions from these scaffolds is of great interest in light of the aforementioned properties. It can depend on a number of biophysicochemical phenomena such as dissolution, diffusion and degradation, which in turn depend on specific scaffold characteristics such as composition and morphology. Achieving an optimal release profile can be challenging when relying on traditional experimental work alone. Mathematical modelling can complement experimentation. In this study, the in vitro dissolution behaviour of four CaP-based scaffold types was investigated experimentally. Subsequently, a mechanistic finite element method model based on biophysicochemical phenomena and specific scaffold characteristics was developed to predict the experimentally observed behaviour. Before the model could be used for local [Formula: see text] ions release predictions, certain parameters such as dissolution constant ([Formula: see text]) and degradation constant ([Formula: see text]) for each type of scaffold were determined by calibrating the model to the in vitro dissolution data. The resulting model showed to yield release characteristics in satisfactory agreement with those observed experimentally. This suggests that the mathematical model can be used to investigate the local [Formula: see text] ions release from CaP-based scaffolds