Mathematical models on bone cell homeostasis and kinetics in the presence of electric fields: a review

The role of bioelectricity in regulating various physiological processes has attracted increasing scientific interest in implementing exogenous electrical stimulations as a therapeutic approach. In particular, electrical stimuli are used clinically in pre-/post-surgery patient care for the musculoskeletal tissues. The reported potential of electric fields (EF) to regulate bone cell homeostasis and kinetics in vitro has further provoked more studies in this field of research. Various customised apparatuses have been developed, and a range of parameters for the applied EFs have been investigated in vitro with bone cells or mesenchymal stem cells. Additionally, biomaterials with conductive or piezo-electric properties have been designed to complement the enhancing effects of the EF on bone regeneration. Despite much research, there remained a significant gap in knowledge due to the diverse range of EF parameters available. Mathematical models are built to facilitate further understanding and zero in on an effective range of EF parameters in silico. However, the diverse range of EF parameters, experimental conditions, and reported analytical output of different works of literature were reported to possess significant variance, making it challenging to accurately model the field in silico. This review categorises the existing experimental approaches and the parameters used to distinguish the potential variables that apply to mathematical modelling. Furthermore, we will discuss existing modelling approaches and models available in the literature. With this, we will concisely highlight the need to categorise EF parameters, osteogenic differentiation initiators and research output.