The use of radiation in cancer therapy dates back to the end of 19th century. Shortly after the discovery of X-rays in 1895, researchers used them for diagnostic and therapeutic treatment of cancer. Since then, radiation in the form of highenergy beams of electrons, photons (X-ray), protons, neutrons and other particles have been used for the same purposes.
Early attempts at radiation were far from optimal and were marked by inaccuracy and failure. Gradually, as medicine took advantage of new advances in different scientific and technological fields, radiation therapy become much more sophisticated. Among the advances, we cite, the availability of new and better computer controlled accelerators for clinical work, the substantial understanding of the underlying physics, the emerging of computational algorithms, the development of Computerized Tomography (CT), Magnetic Resonance Imaging (MRI) and computer graphics software.
The major goal of radiation cancer therapy has been ”to maximise the probability of local tumor control with minimal damage in the neighboring healthy tissue”. This is an optimisation problem which is solved by determining a set of beams while providing the necessary dose to each point in the tumor, minimises the risk of complication to the neighboring tissue. this problem is solved iteratively by a sequence of dose calculations obtained through a series of computed transport calculations that simulate the effects of beams penetrating the human tissue.
Clinical dose calculation algorithms for electron beams are usually based on a mathematical model, originally formulated by Fermi. Fermi derived the model in his research concerning cosmic rays . The objective of this project is two-fold:
- Theory: To derive the Fermi pencil beam equation from the linear particle transport equation, see .
- Computations: To construct and implement finite element and Fast Fourier Transform (FFT) algorithms for some related available (clinical?) data for the Fermi model and compare their behavior in different cases.
 E. Fermi, Cosmic Ray theory, Rev. Mod. Phy. 13 (1941) pp. 240–.
 M. Asadzadeh and A. Sopasakis, On the Stability of Characteristic Schemes for the Fermi Equation, Computer Methods in Applied Mechanics and Engineering 191, (2002), 4641-4659.
Gruppstorlek 3-4 studenter
Målgrupp GU- och Chalmersstudenter. För GU-studenter räknas projektet som ett projekt i Tillämpad matematik (MMG900/MMG920).
Projektspecifika förkunskapskrav Fourieranalys och differentialekvationer
Se respektive kursplan för allmänna förkunskapskrav. Utöver de allmänna förkunskapskraven i MVEX01 ska Chalmersstudenter ha avklarat kurser i en- och flervariabelanalys, linjär algebra och matematisk statistik.
Handledare Mohammad Asadzadeh
Examinator Maria Roginskaya, Ulla Dinger
Institution Matematiska vetenskaper