Applied Mathematics and Mathematical Medicine and Biology

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​​

The usual time and day for this seminar series will be10:10-10:55 a.m. on Fridays on the dates listed below in the fall semester. Talks will be announced in the departmental weekly calendar and willhave both in-person and zoom components.​

Contact Prof. Richard Braun, rjbraun@udel.edu​, for​ details and Zoom passcodes​.

 

 

Riccardo Sacco, Dipartimento di Matematica, Politecnico Milano, Italy140Riccardo Sacco, Dipartimento di Matematica, Politecnico Milano, ItalyZoom<p><strong>​Mode:</strong> Virtual (<a href="https://udel.zoom.us/j/98758622578" target="_blank">Zoom​</a>)<br><strong></strong></p><b>Speaker: </b>Riccardo Sacco, Dipartimento di Matematica, Politecnico Milano, Italy (riccardo.sacco@polimi.it)<br><br><b>Title: </b>Modeling and Simulation of Retinal Neuron Depolarization Using Organic Polymer Nanoparticles<br><br><b>Abstract: </b>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).<br>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.<br><br><div>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. 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.<br>Model predictions suggest that the combined effect of NP polarization and resistivity of the NP-neuron interface results in neuron depolarization and supports the efficacy of organic NPs in the design and development of retinal prostheses.</div><div><br></div><div>This work is in collaboration with Greta Chiaravallii (<a href="mailto:greta.chiaravalli@polimi.it">greta.chiaravalli@polimi.it</a>) and Guglielmo Lanzani (<a href="mailto:Guglielmo.lanzani@iit.it">guglielmo.lanzani@iit.it</a>), Center for Nanoscience and Technology, Istituto Italiano di Tecnologia, Milano, Italy, and Department of Physics, Politecnico di Milano, Milano, Italy.<br></div>12/10/2021 3:10:00 PM12/10/2021 3:55:00 PM

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