Reaction-diffusion model of the adhesion of osteoblasts on metallic implant using electrical stimulation


The aim of this study is to mathematically model the influence of the electric stimulation on bone cells in case of bone-implant healing process. Previous work has only focused on pure mechanical approaches or biochemical aspects. However the electrical approaches are not well addressed. The idea of this research project is to add the electrical quantities like charge density, electric field and bone electrical properties to the existing mechanobiological models, which describe the reaction and diffusion of bone cells.


  1. Simulating a 3D reaction-diffusion model of bone cells.
  2. Studying the effect of electrical stimulation on bone cells.
  3. Coupling the electrical stimulation with the implemented model.
  4. Conduct experiments in vitro for optimization of the model parameters and also for results validation.


A system of partial differential equations (PDE) is introduced to describe the effect of ES on bone cells. These mathematical formulations are based on the gradient-based models, which assume that the cell has the ability to sense the gradient of its surrounding. Besides, we have constructed an in vitro system, where we exposed the cells to different electric field strengths, in order to estimate the model parameters of the system. The current flow and the electric field strength inside the electro-taxis chamber is simulated. The interactions between the ES and bone cells are currently evaluated.


Reviewed paper important congresses

  • DELENDA, B., BADER, R. and , van RIENEN, U., 2015. Mathematical modelling of the effect of implant-surface micro-topography on bone cells.  5th International Symposium Interface Biology of Implants, Rostock.
  • DELENDA, B., BADER, R. and , van RIENEN, U., 2015. Simulation of bone cells proliferation and migration on rough implant surfaces. Joint ISCA-Inspire workshop on Electrically Active Materials of Medical Devices (EAMMD), Limerick, Ireland.
  • DELENDA, B., BADER, R. and , VAN RIENEN, U., 2015. Modeling and Simulation of Platelet Reaction and Diffusion towards an Electro-Stimulating Dental Implant.  37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Milano, Italy. pp. 2584 - 2587, DOI: 10.1109/EMBC.2015.7318920.