Myocardial perfusion, the blood flow to the heart muscle, can be evaluated by tracing the passage of a contrast agent using cardiac magnetic resonance (CMR) imaging. This technique, well-established for diagnosing coronary artery disease, is limited by the necessity for breath-holding, subjective assessment, and low myocardial coverage. In this thesis, we aim to address these limitations of contrast-enhanced myocardial perfusion CMR. We developed a pulse sequence and post-processing pipeline to quantify myocardial perfusion using free-breathing 3D contrast-enhanced CMR. To restrict volume acquisition to the diastolic phase, characterized by minimal cardiac motion, we employed optimal slice oversampling, maximal partial Fourier acquisition, and cartesian undersampling in spatial and temporal domains. To mitigate the effects of breathing, respiratory tracking and image registration were performed. Collaborations for the reconstruction of raw data utilizing deep learning and image registration were established. Validation in healthy volunteers demonstrates that the developed pulse sequence enables isotropic 3D acquisition (3.6 x 3.6 x 3.6 mm^3) of an arterial input function (AIF) and myocardial signal during each cardiac cycle, up to heart rates of 76 bpm. Obtained AIF images exhibit sufficient resolution for extracting the left ventricular blood pool signal and registered myocardial images are of good quality. We investigated and validated a method to convert signal intensity to T1, which is required for MBF quantification. While T1 estimates from the AIF images approximate reference values up to 500 ms well, underestimation was observed from the myocardial images and for high T1 values.

In this thesis, we study the asymptotic behaviour and the dynamics of a one-dimensional active particle model with excluded volume interactions. The model is a version of run-and-tumble motion, where a particle performs both symmetric random walks and active transport. The direction and the speed of the transport are governed by an internal state process. We show that this motion converges to Brownian motion upon diffusive scaling and determine the limiting diffusion coefficient. The internal state converges to a stationary distribution, by which it manifests itself in the diffusion coefficient. Furthermore, we prove that the active particle satisfies the large deviation principle. This allows us to derive an implicit expression for the rate by which the probability of rare events tends to zero. Numerically, we investigate the influence of excluded volume interactions on the diffusion coefficient and the average velocity. We find that the velocity converges exponentially to its theoretical value as the number of particles allowed per position increases. In addition, this exclusion number strongly influences the manner in which the velocity decreases for high particle densities. Predictions for the velocity as a function of particle density based on the model are compared to experimental data of the molecular motor kinesin-II. We find that the model is not adequate for approximating the velocity of molecular motors in crowded environments and extensions in the form of Langmuir kinetics are suggested.