We study inverse treatment planning approaches for stereotactic radiosurgery using Leksell Gamma Knife Perfexion (PFX, Elekta, Stockholm, Sweden) to treat brain cancer and tumour patients. PFX is a dedicated head-and-neck radiation delivery device that is commonly used in clinics. In a PFX treatment, the patient lies on a couch and the radiation beams are emitted from eight banks of radioactive sources around the patient's head that are focused at a single spot, called an isocentre. The radiation delivery in PFX follows a step-and-shoot manner, i.e., the couch is stationary while the radiation is delivered at an isocentre location, and only moves when no beam is being emitted. To find a set of well-positioned isocentres in tumour volumes, we explore fast geometry-based algorithms, including skeletonization and hybrid grassfire and sphere-packing approaches. For the selected set of isocentres, the optimal beam durations to deliver a high prescription dose to the tumour are later found using a penalty-based optimization model. We next extend our grassfire and sphere-packing isocentre selection method to treatments with homogenous dose distributions. Dose homogeneity is required in multi-session plans where a larger volume is treated to account for daily setup errors, and thus large overlaps with surrounding healthy tissue may exist. For multi-session plans, we explicitly consider the healthy tissue overlaps in our algorithms and strategically select many isocentres in adjacent volumes to avoid hotspots. There is also interest in treating patients with continuous couch motion to decrease the total treatment session and increase plan quality. We therefore investigate continuous dose delivery treatment plans for PFX. We present various path selection methods along which the dose is delivered using Hamiltonian paths techniques, and develop mixed-integer and linear approximation models to determine the configuration and duration of the radiation time along the paths. We consider several criteria in our optimization models, including machine speed constraints and movement accuracy, preference for single or multiple paths, and smoothness of movement. Our plans in all proposed approaches are tested on seven clinical cases and can meet or exceed clinical guidelines and usually outperform clinical treatments.

This project deals with the issue of simulation of dose irradiation. This principle is used in a radiotherapeutic device known as a Leksell Gamma Knife for the treatment of intracranial tumours. With regard to the theoretical observations obtained by studying this device, the project suggests the use of analytical geometry for the creation of a mathematical model for calculation of the intensity in the rayed area. A demonstration program Leksell_xvecer08 has been created for this model in a MatLab software background, which enables the user to change various input arguments and simulate a picture of the dosage spread in the target scanned areas.

The Gamma Knife is a non-invasive stereotactic radiosurgery system used for treatments of deep targets in the brain. Accurate patient positioning is needed for precise radiation delivery to the target. The two latest versions of the Gamma Knife allow fractionated treatment by co-registering Cone-beam computed tomography (CBCT) images of the patient's position in the Gamma Knife with a diagnostic magnetic resonance (MR) image used for treatment planning. However, CBCT images often suffer from artifacts that degrade image quality, which may result in less accurate co-registration. This thesis project investigates the potential of a new reconstruction framework developed by Elekta, which incorporates scattering correction and noise filters, for the reconstruction of Gamma Knife CBCT images. The performance of the new reconstruction framework, along with its noise filter and scatter correction, is quantified using image quality metrics of phantoms, including contrast, uniformity, spatial resolution, and CT-number accuracy. Additionally, brain CBCT images of five patients are co-registered with their diagnostic MR images, and the mean target registration error is measured. The results indicate that the new reconstruction framework, without using scatter correction and noise filtering, performs equally well as the current framework in reconstructing Gamma Knife CBCT images, as it achieved similar image quality and co-registration accuracy. However, when the scatter correction was used, there were improvements in image uniformity and CT-number accuracy without compromising spatial resolution. Additionally, the introduction of a noise filter resulted in an improved contrast-to-noise ratio and low contrast visibility with minimal compromise of spatial resolution. Despite these image quality enhancements, there were no consistent improvements in co-registration accuracy, indicating that the co-registration is not sensitive to scatter or noise artefacts. / Gammakniven är en medicinteknisk apparat som används för icke-invasiv stereotaktisk strålkirurgi vid behandling av djupa mål i hjärnan. För att uppnå precision i strålbehandlingen krävs noggrann patientpositionering. De två senaste versionerna av Gammakniven tillåter fraktionerad behandling genom att co-registrera cone-beam computed tomography (CBCT)-bilder av patientens position i Gammakniven med en diagnostisk magnetresonans (MR)-bild som används för behandlingsplanering. Tyvärr lider CBCT-bilder ofta av artefakter som kan försämra bildkvaliteten och därmed minska precisionen i co-registreringen. Detta examensarbete undersöker ett nytt rekonstruktionsramverk som utvecklats av Elekta. Det nya rekonstruktionsramverket och dess tillhörande brusfilter och spridningskorrigering utvärderas för rekonstruktion av Gammaknivens CBCT bilder med hjälp av bildkvalitetsmått för fantomer, såsom kontrast, uniformitet, spatial upplösning och noggrannhet i CT-nummer. Dessutom co-registreras CBCT-bilder från fem patienter med deras diagnostiska MR-bilder, och det genomsnittliga registreringsfelet mäts. Resultaten visar att det nya rekonstruktionsramverket, utan användning av spridningskorrigering och brusfiltrering, presterar lika bra som det nuvarande ramverket för rekonstruktion av CBCT-bilder från Gammakniven. Båda ramverken ger liknande bildkvalitet och noggrannhet i co-registreringen av bilderna. Vid användning av spridningskorrigering observerades förbättringar i uniformiteten och noggrannheten i CT-nummer utan att den spatiala upplösningen försämrades. Införandet av brusfilter resulterade i ett förbättrat kontrast-brus-förhållande och synlighet av svaga kontrastskillnader med endast lite avkall på den spatiala upplösningen. Trots dessa förbättringar i bildkvaliteten observerades ingen konsekvent förbättring av noggrannheten i co-registreringen av bilderna, vilket tyder på att co-registreringen inte påverkas av spridnings- eller brusartefakter i stor utsträckning.