In this talk we formulate and numerically investigate a model of the process of retinal neuron depolarization driven by a retinal prosthesis made of organic polymer nanoparticles (NP). The model consists of a nonlinearly coupled system of elliptic partial differential equations for the electric potential, the number densities of charge carriers photogenerated in the NP bulk and the molar densities of ions moving by electrodiffusion in the aqueous solution surrounding the NP. The nonlinear coupling among the dependent variables throughout the computational domain is mathematically expressed by nonlinear transmission conditions across the interfaces separating the aqueous solution from NP and retinal neuron. In particular, the model accounts for the reactions occurring at the NP/aqueous interface, which lead to the production of O2- anions. The proposed model is solved in stationary conditions and in one spatial dimension by means of a solution map which is a modification of the Gummel Decoupled algorithm conventionally used in inorganic semiconductor simulation. System discretization is conducted using the Finite Element Method, with stabilization terms to prevent spurious unphysical oscillations in the electric potential and ensure positivity of carrier and ion concentrations. Simulations reproduce faithfully the high resistive nature of the interstitial cleft separating the NP from the neuron and suggest the importance of the superoxide O2- in inducing neuron depolarization and eventually triggering neuron firing. Model predictions may shed light on the controversial working mechanisms of organic NPs and support the design and optimization of retinal prostehes.
This is joint work between Riccardo Sacco, Department or Mathematics, Politecnico di Milano, Milano, Italy, Greta Chiaravallii and Guglielmo Lanzani, Center for Nanoscience and Technology, Istituto Italiano di Tecnologia, Milano, Italy, Department of Physics, Politecnico di Milano, Milano, Italy
BIO: Dr. Sacco received a MS in Electronic Engineering from Politecnico di Milano (PoliMi), Italy in 1989, and a PhD in Applied Mathematics from Universita’ degli Studi di Milano, Italy in 1992. In 1995, Dr. Sacco obtained the position of Assistant Professor in Numerical Analysis (NA) at PoliMi, in 2001 the position of Associate Professor in NA at PoliMi and in 2017 the National Habilitation to the role of Full Professor in NA. Dr. Sacco has published 6 books nandmore than 80 research articles in SCI(E) journals. His scientific interests concern with the development, analysis and implementation of models and solution algorithms in Biology, Medicine, Computational Mechanics and Nanoelectronics.