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APPLICATIONS OF MATHEMATICS TO MEDICINE

## OVERVIEW

## AIMS AND CONTENT

### LEARNING OUTCOMES

### AIMS AND LEARNING OUTCOMES

### PREREQUISITES

### TEACHING METHODS

### SYLLABUS/CONTENT

### RECOMMENDED READING/BIBLIOGRAPHY

## TEACHERS AND EXAM BOARD

### Exam Board

## LESSONS

### TEACHING METHODS

### LESSONS START

### Class schedule

## EXAMS

### EXAM DESCRIPTION

### Exam schedule

### FURTHER INFORMATION

CODE | 42916 |
---|---|

ACADEMIC YEAR | 2020/2021 |

CREDITS | 7 credits during the 2nd year of 9011 Mathematics (LM-40) GENOVA |

SCIENTIFIC DISCIPLINARY SECTOR | MAT/08 |

LANGUAGE | Italian (English on demand) |

TEACHING LOCATION | GENOVA (Mathematics) |

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: 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.

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.

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

**Office hours:** Office hours by appointment via email

MICHELE PIANA (President)

FEDERICO BENVENUTO

Anna Maria MASSONE (President Substitute)

Traditional lectures + 1 lab

The class will start according to the academic calendar.

Oral Exam

Date | Time | Location | Type | Notes |
---|---|---|---|---|

23/07/2021 | 09:00 | GENOVA | Esame su appuntamento | |

17/09/2021 | 09:00 | GENOVA | Esame su appuntamento | |

11/02/2022 | 09:00 | GENOVA | Esame su appuntamento |

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