CODE 42916 ACADEMIC YEAR 2018/2019 CREDITS 7 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA 7 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 2 COMPUTER SCIENCE 10852 (LM-18) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/08 LANGUAGE Italian (English on demand) TEACHING LOCATION GENOVA SEMESTER 2° 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 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. RECOMMENDED READING/BIBLIOGRAPHY Professor’s lecture notes TEACHERS AND EXAM BOARD MICHELE PIANA Ricevimento: Office hours by appointment via email FEDERICO BENVENUTO Exam Board MICHELE PIANA (President) FEDERICO BENVENUTO Anna Maria MASSONE LESSONS LESSONS START The class will start according to the academic calendar. Class schedule APPLICATIONS OF MATHEMATICS TO MEDICINE EXAMS EXAM DESCRIPTION Oral Exam Exam schedule Data appello Orario Luogo Degree type Note 15/02/2019 09:00 GENOVA Esame su appuntamento 26/07/2019 09:00 GENOVA Esame su appuntamento 20/09/2019 09:00 GENOVA Esame su appuntamento 14/02/2020 09:00 GENOVA Esame su appuntamento FURTHER INFORMATION The prerequisites are: Hilbert spaces, continuous linear operators between Hilbert spaces, Fourier analysis
