Skip to main content
CODE 42916
ACADEMIC YEAR 2016/2017
CREDITS
SCIENTIFIC DISCIPLINARY SECTOR MAT/08
LANGUAGE Italiano (Inglese a richiesta)
TEACHING LOCATION
SEMESTER 1° Semester
TEACHING MATERIALS AULAWEB

OVERVIEW

The credits for the course Application of Mathematics to Medicine (AMM, code 42916) are 7. The course is held during the first semester of the 1°, 2° LM years. On request of one student, the lectures and teaching activities will be delivered in English, otherwise in Italian.

AIMS AND CONTENT

LEARNING OUTCOMES (FURTHER INFO)

This course aims to describe the mathematical modeling of three medical imaging problems: the X-ray tomography, the Positron Emission Tomography and the Magnetic Resonance Imaging. The scope of the course is two-fold: on one hand, we want to highlight how sophisticated mathematics is needed for the comprehension of problems with high practical significance; on the other hand, we want to equip the students with the numerical analysis tools required for the processing of the data acquired with these three modalities.

TEACHING METHODS

Traditional lectures. Six lab lessons are planned

SYLLABUS/CONTENT

Part I: X-ray tomography (overview); Radon transform, formulas for the inversion of the Radon transform (as back projection and filtered back projection), issues of uniqueness.

Part II: positron emission tomography (overview); on the two inverse problems related to positron emission tomography: an imaging problem (inversion of the Radon transform) and a compartment alone (Gauss-Newton optimization scheme)

Part III: magnetic resonance imaging (overview); models for data acquisition and magnetic field distortion, Fourier transform, inversion of the Fourier transform from undersampled data.

RECOMMENDED READING/BIBLIOGRAPHY

Professor’s lecture notes

TEACHERS AND EXAM BOARD

Exam Board

MICHELE PIANA (President)

CRISTINA CAMPI

Anna Maria MASSONE

LESSONS

LESSONS START

September 26, 2016

EXAMS

EXAM DESCRIPTION

Oral Exam

Exam schedule

Data appello Orario Luogo Degree type Note
05/06/2017 09:00 GENOVA Orale
05/06/2017 09:00 GENOVA Scritto
23/06/2017 09:00 GENOVA Orale
23/06/2017 09:00 GENOVA Scritto
30/06/2017 12:40 GENOVA Orale
12/07/2017 09:00 GENOVA Orale
12/07/2017 09:00 GENOVA Scritto
01/08/2017 09:30 GENOVA Orale
04/09/2017 09:00 GENOVA Orale
04/09/2017 09:00 GENOVA Scritto

FURTHER INFORMATION

The prerequisites are: Hilbert spaces, continuous linear operators between Hilbert spaces, Fourier analysis