|SCIENTIFIC DISCIPLINARY SECTOR
|Italian (English on demand)
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
The course intends to describe the mathematical modeling of two very important tomographic problems in biomedical field: X-ray tomography and magnetic resonance. In both cases, the objective is twofold: on the one hand, to emphasize how sophisticated mathematical formalisms are indispensable to fully understand problems of such great application value; On the other hand, to provide students with the numerical tools needed to process the images from these acquisition modes.
AIMS AND LEARNING OUTCOMES
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.
After these lectures, students will know the main mathematical properties of two important medical imaging modalities, some crucial issues concerned with mathematical models of cellular respiration, and the way an in-silico model of the cancer cell can be constructed.
Fondamenti di Calcolo Numerico
Traditional lectures + 1 lab
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.
Professor’s lecture notes
TEACHERS AND EXAM BOARD
Ricevimento: Office hours by appointment via email (firstname.lastname@example.org)
MICHELE PIANA (President)
CRISTINA CAMPI (President Substitute)
The class will start according to the academic calendar.
L'orario di tutti gli insegnamenti è consultabile all'indirizzo EasyAcademy.
Oral exam. We will ask students about topics discussed during the lectures and students will be assessed on the base of their knowledge of the content of the topics described during the course
|Esame su appuntamento
The prerequisites are: Hilbert spaces, continuous linear operators between Hilbert spaces, Fourier analysis