Quantitative model for the change of optical resonance in neural activity detection systems based on surface plasmon resonance

The mechanism of neural activity detection using the surface plasmon resonance (SPR) phenomenon was theoretically explored in this paper. Investigating the mechanism of SPR neural recordings has been difficult due to the complex relationship between different physiological and physical processes such as excitation of a nerve fiber and coherent charge fluctuations on the metal surface. This paper examines how these different processes may be connected by introducing a set of compartmental theoretical models that deal with the molecular scale phenomena; Poisson-Boltzmann (PB) equation, which was used to describe the ion concentration change under the time varying electrostatic potential, Drude-Lorentz electron model, which was used to describe electron dynamics under the time varying external forces, and a Fresnel's three-layered model, which expresses the reflectivity of the SPR system in terms of the dielectric constants. Each physical theoretical model was numerically analyzed using the finite element method (FEM) formulated for the PB equation and the Green's method formulated for the Drude-Lorentz electron equation. The model predicts that the ionic thermal force originating from the opening of the K⁺ ion channel is fundamental for modifying the dipole moment of the gold's free electron; thus, the reflectivity is changed in the SPR system. The discussion was done also on important attributes of the SPR signal such as biphasic fluctuation and the electrical noise-free characteristics.