Every year, thousands of women are diagnosed with breast cancer. To increase their survival chance and improve the treatment plans available, it is important to accurately predict the patient's response to treatment. For HER2+ breast cancer patients, normally a set number of chemotherapy rounds are administered. However, perhaps some patients would benefit from more chemotherapy or conversely, fewer rounds are sufficient. A reaction-diffusion model as well as a mechanically coupled reaction-diffusion model are used to predict the tumour cellularity. Using two magnetic resonance imaging (MRI) scans, a patient-specific model is calibrated to calculate the response for each individual patient. A third MRI scan is used to validate the results. Several preprocessing techniques are used to obtain the necessary information from the MRI scans such as tumour cellularity, segmentation of tissues and breast region.

The model calculations are performed in 2-dimensions and the slice thickness chosen determines how much effect the incorporation of surrounding tissue has. Using thicker slices means that the surrounding tissue has a larger effect on the tumour growth. For patients that respond well to treatment, the models are both able to calculate the downward trend in tumour cellularity. For thin slices (1.6 mm), both models perform similarly. Using thicker slices (6.5 mm), the mechanically coupled model shows better performance. The most important additions to the model are implementation in 3-dimensions so the slice thickness no longer has an effect. Most importantly, the chemotherapy should be incorporated to better obtain a patient-specific prediction of the response to treatment.

In this thesis we look at the most cost-
effective trajectory for power limited rockets, i.e. the trajectory which costs the least amount of propellant. First some background information as well as the differences between thrust limited and power limited rockets will be discussed. Then the optimal trajectory for thrust limited rockets, the Hohmann Transfer Orbit, will be explained. Using Optimal Control Theory, the optimal trajectory for power limited rockets can be found. Three trajectories will be discussed: Low Earth Orbit to Geostationary Earth Orbit, Earth to
Mars and Earth to Saturn. After this we compare the propellant use of the thrust limited rockets for these trajectories with the power limited rockets. Here we made this comparison between a conventional thrust limited rocket with a specic impulse of 455 seconds and the VASIMR rocket for the power limited rocket. Also the initial mass of both rocket types was taken as
5 * 10^5 kg. Lastly, we take a look at a gravity assist. Gravity assists can help reduce propellant use even further. Therefore we will once more look at the trajectory for a power limited rocket
from Earth to Saturn. Only this time we use a gravity assist from Jupiter. Then we can see if the propellant use is indeed even lower when using the gravity assist. We find that the the power limited rocket becomes more fuel-effcient as travel time increases. Also using a gravity assist further reduces propellant consumption.