Salta al contenuto principale della pagina

## APPLICATIONS OF MATHEMATICS TO MEDICINE

CODE 42916 2017/2018 7 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA 6 credits during the 2nd year of 9014 Computer Science (LM-18) GENOVA MAT/08 Italian (English on demand) GENOVA (Mathematics) 1° Semester 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

The course intends to describe the mathematical modeling of two very important tomographic problems in the medical field: X-ray 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.

### 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.

### 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.

Professor’s lecture notes

## TEACHERS AND EXAM BOARD

### Exam Board

MICHELE PIANA (President)

FEDERICO BENVENUTO

Anna Maria MASSONE

## LESSONS

### TEACHING METHODS

Traditional lectures. Six lab lessons are planned

### LESSONS START

The class will start according to the academic calendar.

### Class schedule

APPLICATIONS OF MATHEMATICS TO MEDICINE

## EXAMS

Oral Exam

### Exam schedule

Date Time Location Type Notes
16/02/2018 09:00 GENOVA Esame su appuntamento
27/07/2018 09:00 GENOVA Esame su appuntamento
21/09/2018 09:00 GENOVA Esame su appuntamento
28/02/2019 09:00 GENOVA Esame su appuntamento

### FURTHER INFORMATION

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