Mathematical modeling of bone regeneration during fracture healing and implant osseointegration

Despite the extensive body of literature on bone regeneration, many questions
remain on e.g. the regulatory mechanisms and potential treatment strategies
of pathological regeneration cases. The hypothesis underlying this work states
that mathematical models of bone regeneration can make a substantial contribution
to this domain by proposing pathological regeneration mechanisms and designing therapies, which can subsequently be tested experimentally. In the first part of this work, existing mechanoregulatory and bioregulatory models of bone regeneration are implemented and applied to both implant osseointegration and fracture healing set-ups. A quantitative comparison with experimental results is performed. Thorough sensitivity analyses are carried out to assess the influence of various modelling aspects on the simulation outcome. Shortcomings of these models are identified and suggestions for improvements are made. In the second part of this work, a novel bioregulatory model of bone regeneration is developed in which several of the previously defined shortcomings are addressed. This model includes key aspects of the regeneration process such as intramembranous and endochondral ossification, angiogenesis and directed cell motion. The results obtained with this novel model are corroborated both qualitatively and quantitatively by comparison with experimental data for normal fracture healing. Cases of pathological fracture healing are simulated and experimentally testable therapeutic strategies are implemented. The last part of this work describes the establishment of a mathematical framework, based on the previously developed bioregulatory model, in which the regulatory influence of both biological and mechanical factors is combined.
This is the first model of bone regeneration in which the coupling between mechanical loading and angiogenesis is made in an explicit and mechanistic manner. Several examples are given to illustrate the added value of this approach in simulating normal and pathological bone regeneration. In summary, this work demonstrates the potential of mathematical models in advancing the knowledge on bone regeneration and designing treatment strategies for pathological healing cases.