Mathematical modelling of the dynamic response of an implantable enhanced capacitive glaucoma pressure sensor

Glaucoma as an eye disease influences the optic nerve, resulting in progressive vision loss and, thus, blindness. For this disease, the most important risk factor is high intraocular pressure. Therefore, it is important to accurately measure the intraocular pressure. The present work aimes to present a mathematical description of a capacitive pressure sensor based on a Micro-Electro-Mechanical-Systems (MEMS) to measure intraocular pressure (IOP). The relatively high working bias voltage of MEMS capacitive pressure sensors restricts their potential applications as implantable sensors. Hence, Polydimethylsiloxane (PDMS) is employed as a porous elastomeric substance between the deformable and fixed electrodes of the capacitor. With a low young modulus and a higher dielectric constant, it reduces the sensor's working bias voltage. The PDMS's permittivity and young modulus are a function of the porosity volume fraction based on displacement in terms of a power law with fractional power constant. The dynamic equation of the microplate's transversal motion is used in the developed model, taking mid-plane stre-tching into account along with the generated force owing to the PDMS film squeezing. To decompose the governing nonlinear equation, a weak formulation is used with appropriate basis functions, thus integrating the attained ordinary differential equations over time. The sensor response to static pressure and step-wise alteration of the applied pressure is examined by dynamic and static analysis. The results of pull-in voltage reveal that using the PDMS as a dielectric causes a considerable reduction. Additionally, the effect of the PDMS elasticity on the capacitance and displacement was assessed along with the effects of the geometrical parameters on the sensor response.