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Risorsa bibliografica facoltativa 

Anno Accademico

2015/2016

Scuola

Scuola di Ingegneria Industriale e dell'Informazione 
Insegnamento

096659  COMPUTATIONAL MODELING IN ELECTRONICS AND BIOMATHEMATICS

Docente 
Sacco Riccardo

Cfu 
8.00

Tipo insegnamento

Monodisciplinare

Corso di Studi 
Codice Piano di Studio preventivamente approvato 
Da (compreso) 
A (escluso) 
Insegnamento 
Ing Ind  Inf (Mag.)(ord. 270)  MI (476) ELECTRONICS ENGINEERING  INGEGNERIA ELETTRONICA  *  A  ZZZZ  096660  NUMERICAL METHODS IN MICROELECTRONICS  Ing Ind  Inf (Mag.)(ord. 270)  MI (487) MATHEMATICAL ENGINEERING  INGEGNERIA MATEMATICA  *  A  ZZZZ  096659  COMPUTATIONAL MODELING IN ELECTRONICS AND BIOMATHEMATICS 
Programma dettagliato e risultati di apprendimento attesi 
COMPUTATIONAL MODELING IN ELECTRONICS AND BIOMATHEMATICS 096659
Objectives and contents of the course
Electronic and biological systems share unexpected structural similarities that make them amenable to a unified mathematical and numerical treatment. As a matter of fact, transmembrane ion flow regulating the functional response of a neuronal or a cardiac cell, as well as the motion of electric charge transporting current in a nanoscalesized transistor, obey the same phenomenological description, the socalled NernstPlanck transport model(in Biology) and the DriftDiffusion transport model (in Electronics). Under this unifying perspective, the course has the objective of providing the common mathematical and computational foundations to modeling and simulation of specific problems in cellular biology and solidstate electronics, the final scope being to couple the two classes of problems in the study of biohybrid devices in which both components (cellular and solidstate) coexist in a dynamically interacting operating mode. This final goal reflects the stateoftheart in modern Neuroscience and represents an original attempt of this course to confront the student with the frontiers of research in Life Sciences of our times.
Description of course topics
Introduction to cellular biology and ion electrodiffusion. ODE models for transmembrane ion flow in cellular physiology. The Kirchhoff current law: capacitive and resistive transmembrane currents. The linear resistor model; the GoldmanHodgkinKatz (GHK) model; the HodgkinHuxley (HH) model. PDE models for transmembrane ion flow in cellular physiology: the PoissonNernstPlanck (PNP) system for M ionic species. Introduction to semiconductor device electronics. Multiscale structure of integrated circuits. Micro/nanoscale view: the Maxwell equation system and the quasistatic approximation. Atomic/macroscale view: charge transport in solids; Ohm's law in metal conductors; the DriftDiffusion (DD) model in semiconductor materials. The PoissonDD (PDD) PDE model for semiconductor device simulation at the micro/nanoscale. Model analogies: PDD = PNP with M=2. Scaling. Functional iterations: Newton's method and Gummel's map. Diffusionadvectionreaction linear model problem (with gradient advective field): wellposedness analysis and numerical approximation with a stabilized Finite Element Method (FEM). Convergence analysis. Conservation properties. Numerical stability of the FEM: continuous and discrete maximum principles. Examples in cellular biology: excitable cells. Nernst potential of a ionic species; cellular homeostatis: the GHK potential. Action potential propagation: the Cable Equation model coupled with the HH ODE system. Simplified treatment of intracellular and extracellular compartments: the electroneutral PNP model. Examples in device electronics: the pn junction. Thermal equilibrium, reverse and forward bias. IV curves and the law of ideal diode. The full depletion approximation: analytical solution of the PDD system. 1D models for the MetalOxideSemiconductor (MOS) transistor. The nMOS capacitor. The n+  n – n+ structure for the nMOS channel. Example of biohybrid devices: interface between cells and a MOS transistor. Celltochip stimulation. Celltocell stimulation. Reducedorder models: areacontact and lumped parameter models.
Organization of the course
The course is organized into class lectures accompanied by laboratory sessions (labs). Seminars will also be scheduled during the course to introduce the students to applications of relevant industrial and/or biological impact. Class lectures provide the theoretical foundations of models and numerical methods. Labs are carried out in a computer room using the Matlab environment and allow the students to verify and compare on simple exercises and more advanced examples the physical accuracy of the models and the numerical performance of the methods.

Note Sulla Modalità di valutazione 
The final examination is divided into two parts: a written exam and an oral exam. The written exam consists of a number of exercises to be solved with the support of the Matlab codes used in the labs. The oral exam consists of the critical discussion of the written exam, plus theoretical questions regarding the topics treated in the class lectures.

Lecture Notes of the PhD Course Multiscale Modeling of Interface Phenomena in Biology http://www1.mate.polimi.it/~ricsac/NotesCMElBioMath.pdf Note:This file contains the lecture notes of the PhD Course Multiscale Modeling of Interface Phenomena in Biology. A substantial part of the material is object of the course.
Notes of the course Computational Electronics http://www1.mate.polimi.it/~ricsac/NotesElComp.pdf Note:This file contains the lecture notes of the course Computational Electronics.
I. Rubinsterin, Electrodiffusion of Ions, Editore: SIAM Philadelphia, Anno edizione: 1990
J. Keener and J. Sneyd, Mathematical Physiology, Editore: SpringerVerlag, Anno edizione: 2009
R. Muller and T. Kamins, Device Electronics for Integrated Circuits, Editore: John Wiley and Sons, Anno edizione: 2003

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Tipo Forma Didattica

Ore didattiche 
lezione

56.0

esercitazione

0.0

laboratorio informatico

28.0

laboratorio sperimentale

0.0

progetto

0.0

laboratorio di progetto

0.0

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Insegnamento erogato in lingua
Inglese

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