My PhD Project

• Title: Mathematical and computational modeling of metallic biomaterials biodegradation

• Public defense: The recorded version of the public PhD defense, held on 15 June 2023, Leuven, Belgium, can be found here:
  

• (Not so short) summary: Degradable metallic materials are gaining popularity in a wide variety of applications. In the biomedical field, biocompatibility, biodegradability, and positive impact on biological processes are the critical properties that nominate a metal as an applicable option. Taking this into account, magnesium (Mg), iron (Fe), and zinc (Zn) are usually considered as biodegradable metallic (bio)materials. Due to their mechanical properties, metallic biomaterials are appropriate candidates for load-bearing conditions in various bone healing and cardiovascular applications. Biodegradable metals meet the (often temporary) need for mechanical support while avoiding stress-shielding (in orthopedic applications) in the long term and omitting the need for revision surgery as required for permanent materials. Despite the advantages of using biodegradable metals in implant design, their fast degradation and uncontrolled ion release remain a challenge in practical applications. Beside experimental approaches to investigate the properties of biodegradable metallic implants and scaffolds, computational modeling of the biodegradation process and behavior can act as an efficient tool to design the next generation of medical devices and implants. A validated computational model of the degradation process can facilitate tuning of biodegradation properties and optimizing the design for specific applications.
  
  In this study, we have developed a mathematical and computational model to predict the biodegradation behavior of biodegradable metallic biomaterials, focusing on Mg. Our developed model captures the release of metallic ions, changes in pH, the formation of a protective film, the effect of different ions in the environment, and the effect of perfusion of the surrounding fluid, when applicable. This has been accomplished by deriving a system of time-dependent reaction-diffusion-convection partial differential equations (PDEs) from the underlying oxidation-reduction reactions and solving them using the finite element method. The level-set formalism was employed to track the biodegradation interface between the biomaterial and its surroundings. The model was validated by comparing the predicted and experimentally obtained values of global and local pH changes in corrosion tests, for which a good agreement was observed.
  
  Tracking the moving front at the diffusion interface requires high numerical accuracy of the diffusive state variables. Improving the accuracy requires a refined computational mesh, leading to a more computation-intensive simulation. To overcome this challenge and yield interactable simulations in more feasible turnaround times, scalable parallelization techniques were implemented, making the model capable of being run on massively parallel systems to reduce the simulation time. Subsequently, the scaling behavior of the models was evaluated on hundreds to thousands of CPU cores in high-performance computing environments.
  
  Due to the complexity of the derived model, it was most convenient to implement it in an in-house code with full control of the details of the numerical solution and computational implementation. The model was implemented in the open-source domain-specific language FreeFEM, in which a wide range of relevant scientific computing libraries was employed to perform sub-tasks such as mesh generation, mesh refinement, iterative solution of linear systems of equations, and preconditioning the models. In order to yield the highest performance for solving the equations, an iterative approach using parallel iterative solvers and proper preconditioners available via the PETSc library was employed.
  
  Additionally, the core biodegradation model was coupled with fluid flow models to enable capturing the effect of hydrodynamics and perfusion conditions. Finally, the model was employed in a couple of multi-physics use cases as the biodegradation compartment to demonstrate the ability of the model to be integrated into other modeling workflows in biomedical engineering. The biodegradation model was coupled with other models in these case studies to simulate more comprehensive phenomena. The case studies selected to present in this PhD thesis include the biodegradation of personalized printed porous implants, the mechanical integrity of infilled structures during the biodegradation process, and investigating the mechanical loosening of degradable jaw bone plates after implantation.
  
  The computational models and workflows developed as part of this PhD thesis were assembled together in a standalone software called BioDeg, which is available to download from GitHub as an open-source tool for biodegradation simulation of any arbitrary 3D geometry. The software features a graphical user interface and a basic pre-processor, helping non-technical users to take advantage of its functionality in a user-friendly manner. Furthermore, the details and workflow developed for the Bayesian parameter estimation of the developed biodegradation model were separately published as open-source educational material, done in the format of Jupyter notebooks using the open science principles to be used as either tools or educational content for students.
  
  Taken together, this PhD work has developed a broad range of mathematical and computational tools in the field of degradable biomaterials, demonstrating the potential of integrating in silico technologies in the design of patient-specific implants. The research carried out in this PhD thesis lies at the interface of biomedical engineering, chemistry, mechanical engineering, materials science, mathematics, and computational science. The relevant elements of these disciplines were employed in a multidisciplinary manner to deliver a multiphysics model of the biodegradation process. Moreover, by openly sharing the developed computational tools and emphasizing open science principles, this work fosters collaboration and knowledge dissemination within the research community, thereby facilitating further advancements in the design and optimization of novel biomaterial-based implants in biomedical engineering and patient care. As the next step, the model is being further developed by a new PhD candidate in the group to include more variants of the biodegradation process as well as to integrate it into topology optimization routines of personalized implants and biodegradable scaffolds in tissue engineering.

• Glimpse into the results: The following visualization is a typical output of simulations that I perform using the model I have developed (it’s an interactive ParaView Glance session, so you can explore it using your mouse buttons and modify it using the panel on the left).