Ing Ind - Inf (Mag.)(ord. 270) - MI (471) BIOMEDICAL ENGINEERING - INGEGNERIA BIOMEDICA

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050492 - COMPUTATIONAL MODELING IN ELECTRONICS AND BIOMATHEMATICS

Ing Ind - Inf (Mag.)(ord. 270) - MI (476) ELECTRONICS ENGINEERING - INGEGNERIA ELETTRONICA

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096660 - NUMERICAL METHODS IN MICROELECTRONICS

Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA

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096659 - COMPUTATIONAL MODELING IN ELECTRONICS AND BIOMATHEMATICS

Obiettivi dell'insegnamento

The course in object has a size of 8 CFUs and is associated with the following other two courses, each sized 5 CFUs:

050492 - COMPUTATIONAL MODELING IN ELECTRONICS AND BIOMATHEMATICS

096660 - NUMERICAL METHODS IN MICROELECTRONICS

The present document defines objectives, programme and expected learning outcomes for all the above mentioned courses.Electronic and biological systems share significant structural similarities. Transmembrane ion flow regulating the functional response of a neuronal or cardiac cell, as well as the motion of electric charge transporting current in a nanoscale-sized transistor, obey the same phenomenological description, well known in Biology as the Nernst-Planck model and in Electronics as the Drift-Diffusion model. The goal of the course is threefold and consists of providing the students:

a unified framework for the mathematical modeling of:

1.a: cellular biology and

1.b: solid-state electronics;

the numerical methods for the simulation of:

2.a: specific cellular systems and

2.b: specific electronic devices;

a critical know-how to perform the design of complex systems in:

3.a: Life Sciences and

3.b: Electronics.

For students of the course coded 050492: goals 1.a, 2.a and 3.a.

For students of the course coded 096660: goals 1.b, 2.b and 3.b.

Risultati di apprendimento attesi

Class lectures and laboratories:

will provide students the theoretical foundations of models and numerical methods;

will allow students verify in a quantitative manner the physical accuracy of the models and the numerical performance of the methods through the solution of exercises of increasing level of difficulty;

will enable students gain acquaintance with the critical analysis and design of a complex system in Life Sciences and Electronics through the combined use of theoretical modeling tools and a flexible computational environment such as Matlab.

For students of the course coded 050492: the course will allow gain acquantaince with the critical analysis and design of a complex system in Life Sciences through the combined use of theoretical modeling tools and a flexible computational environment such as Matlab.

For students of the course coded 096660: the course will allow gain acquantaince with the critical analysis and design of a complex system in Electronics through the combined use of theoretical modeling tools and a flexible computational environment such as Matlab.

Seminars held by experts in clinical research and visits to semiconductor electronics companies:

will introduce the students to realistic contexts of excellence in both national and international environments;

will allow students confront the adequacy (and possible limitations) of theoretical tools, models and methods treated in the class lectures and laboratories against applications of relevant biophysical and industrial impact.

Argomenti trattati

1. Balance laws in local form. The diffusion-advection-reaction linear model problem: well-posedness 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.

2. Introduction to cellular biology and ion electrodynamics. ODE models for transmembrane ion flow in cellular physiology. The Kirchhoff current law: capacitive and resistive transmembrane currents. The linear resistor model; the Goldman-Hodgkin-Katz (GHK) model; the Hodgkin-Huxley (HH) model. PDE models for transmembrane ion flow in cellular physiology: the velocity-extended Poisson-Nernst-Planck (VE-PNP) system for M ionic species. Examples in cellular biology: excitable cells. Nernst potential of an 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 one-dimensional PNP model for a protein channel.

3. Multiscale structure of integrated circuits. Micro/nanoscale view: the Maxwell equation system and the quasi-static approximation. Atomic/macroscale view: charge transport in solids; Ohm's law in metal conductors; the Drift-Diffusion (DD) model in semiconductor materials. The Poisson-DD (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. Examples in device electronics: the p-n junction. Thermal equilibrium, reverse and forward bias. I-V curves and the law of ideal diode. The full depletion approximation: analytical solution of the PDD system. 1D models for the Metal-Oxide-Semiconductor (MOS) transistor. The n-MOS capacitor. The n+ - n - n+ structure for the n-MOS channel.

For students of the course coded 050492: topics 1. and 2.

For students of the course coded 096660: topics 1. and 3.

Prerequisiti

Students are required to know the principles and methods of Calculus, Physics and Linear Algebra.

Modalità di valutazione

The exam consists of a written assignment in which the student has to solve three exercises, each one pertaining to one of the three main topics treated during the classes and the laboratories, namely: Elements of Numerical Approximation of Balance Laws in Local Form, Elements of Cellular Biology and Elements of Solid-State Electronics. Each exercise is divided into two parts. The first part is of theoretical nature whereas the second part is of computational nature and requires the use of the numerical software (run in the Matlab computing environment) that has been introduced during the laboratories.

To successfully get through finals the student has to demonstrate to:

have acquired the advanced mathematical modeling tools and the computational techniques for the analytical and numerical study of:

1.a: a balance law in local form;

1.b: a complex system in biology and

1.c: a complex system in electronics,

by providing detailed answers to specific theoretical questions;

For students of the course coded 050492: questions on topics 1.a and 1.b.

For students of the course coded 096660: questions on topics 1.a and 1.c.

be able to handle and critically use the appropriate modeling tools and numerical methods for the analysis of the complex system at hand, by providing quantitative answers to specific computational questions;

be able to compare the quantitative results obtained at point 2. with theoretical predictions or with data (if available), by providing motivated conclusions and remarks based on the knowledge acquired at point 1.;

be able to provide an adequate comment to quantitative conclusions by making appropriate use of graphical tools and to elaborate with a detailed written presentation the required answers to the theoretical questions.

Bibliografia

Lecture Notes of the Coursehttp://www1.mate.polimi.it/~ricsac/LectureNotesCMEBM.pdfJ. Keener and J. Sneyd, Mathematical Physiology, Editore: Springer-Verlag, Anno edizione: 2009
R. Muller and T. Kamins, Device Electronics for Integrated Circuits, Editore: John Wiley and Sons, Anno edizione: 2003
I. Rubinsterin, Electrodiffusion of Ions, Editore: SIAM Philadelphia, Anno edizione: 1990

Forme didattiche

Tipo Forma Didattica

Ore di attività svolte in aula

(hh:mm)

Ore di studio autonome

(hh:mm)

Lezione

52:00

78:00

Esercitazione

28:00

42:00

Laboratorio Informatico

0:00

0:00

Laboratorio Sperimentale

0:00

0:00

Laboratorio Di Progetto

0:00

0:00

Totale

80:00

120:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione

Insegnamento erogato in lingua
Inglese

Disponibilità di materiale didattico/slides in lingua inglese

Disponibilità di libri di testo/bibliografia in lingua inglese

Possibilità di sostenere l'esame in lingua inglese

Disponibilità di supporto didattico in lingua inglese