Mathematical modelling of magnetic field and nanoparticle effects on calcium signalling in malignant esophageal cells

<i>Purpose.</i>This study aimed to develop a mathematical model investigating how low-frequency magnetic fields and magnetic nanoparticles theoretically affect calcium signalling in esophageal squamous cell carcinoma (ESCC) cells through mechanosensitive channel activation.<i>Methods.</i>We modified the Chang model to incorporate magnetic field-induced membrane shear stress mechanisms, simulating intracellular calcium dynamics using ordinary differential equations in Python and Julia. The model examined rotating magnetic fields at 25 mT across frequencies from 0 to 1.7<i>π</i>mHz, analyzing calcium oscillation patterns and their potential effects on mitogen-activated protein kinase (MAPK) signalling pathways.<i>Results.</i>Simulations demonstrated that low-frequency rotating magnetic fields at 1.7<i>π</i>mHz and lower frequencies disrupted normal calcium oscillations, creating inter-burst periods of at least 588.2 seconds. This minimum period exceeds the sensitivity threshold of MAPK signalling (1.7-17 mHz), suggesting potential inhibition of proliferation pathways dependent on calcium oscillation frequency. The model predicted reduced oscillation magnitude and altered temporal dynamics compared to control conditions.<i>Conclusions.</i>The mathematical framework provides theoretical foundation for magnetic field interactions with cellular calcium dynamics through mechanosensitive channels, offering conceptual basis for potential therapeutic applications. All findings require comprehensive experimental validation before any clinical implications can be considered.