CODE  42916 

ACADEMIC YEAR  2022/2023 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/08 
TEACHING LOCATION 

SEMESTER  2° Semester 
TEACHING MATERIALS  AULAWEB 
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.
The course intends to describe the mathematical modeling of two very important tomographic problems in the medical field: Xray tomography and microwave tomography. In both cases, the objective of the discussion is twofold: on the one hand, to emphasize how sophisticated mathematical formalisms are indispensable for the understanding of two problems of such great application value; On the other hand, provide students with the numeric tools needed to process the images from these capture modes.
This course aims to describe the mathematical modeling of three medical imaging problems: the Xray tomography, the Positron Emission Tomography and the Magnetic Resonance Imaging. The scope of the course is twofold: 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.
Fondamenti di Calcolo Numerico
Traditional lectures + 1 lab
Part I: Xray 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 (GaussNewton 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
Office hours: By appointment via email.
Office hours: Office hours by appointment via email
MICHELE PIANA (President)
FEDERICO BENVENUTO
Anna Maria MASSONE (President Substitute)
The class will start according to the academic calendar.
Oral Exam
The prerequisites are: Hilbert spaces, continuous linear operators between Hilbert spaces, Fourier analysis