The main function of the heart is to pump blood throughout the cardiovascular system by generating pressure differences created through volume changes. Although the main purpose of the heart and vessels is to lead the flowing blood throughout the body, clinical assessments of cardiac function are usually based on morphology, approximating the flow features by viewing the motion of the myocardium and vessels. Measurement of three-directional, three-dimensional and time-resolved velocity (4D Flow) data is feasible using magnetic resonance (MR). The focus of this thesis is the development and application of methods that facilitate the analysis of larger groups of data in order to increase our understanding of intracardiac flow patterns and take the 4D flow technique closer to the clinical setting. In the first studies underlying this thesis, a pathline based method for analysis of intra ventricular blood flow patterns has been implemented and applied. A pathline is integrated from the velocity data and shows the path an imaginary massless particle would take through the data volume. This method separates the end-diastolic volume (EDV) into four functional components, based on the position for each individual pathline at end-diastole (ED) and end-systole (ES). This approach enables tracking of the full EDV over one cardiac cycle and facilitates calculation of parameters such as e.g. volumes and kinetic energy (KE). Besides blood flow, pressure plays an important role in the cardiac dynamics. In order to study this parameter in the left ventricle, the relative pressure field was computed using the pressure Poisson equation. A comprehensive presentation of the pressure data was obtained dividing the LV blood pool into 17 pie-shaped segments based on a modification of the standard seventeen segment model. Further insight into intracardiac blood flow dynamics was obtained by studying the turbulent kinetic energy (TKE) in the LV. The methods were applied to data from a group of healthy subjects and patients with dilated cardiomyopathy (DCM). DCM is a pathological state where the cardiac function is impaired and the left ventricle or both ventricles are dilated. The validation study of the flow analysis method showed that a reliable user friendly tool for intra ventricular blood flow analysis was obtained. The application of this tool also showed that roughly one third of the blood that enters the LV, directly leaves the LV again in the same heart beat. The distribution of the four LV EDV components was altered in the DCM group as compared to the healthy group; the component that enters and leaves the LV during one cardiac cycle (Direct Flow) was significantly larger in the healthy subjects. Furthermore, when the kinetic energy was normalized by the volume for each component, at time of ED, the Direct Flow had the highest values in the healthy subjects. In the DCM group, however, the Retained Inflow and Delayed Ejection Flow had higher values. The relative pressure field showed to be highly heterogeneous, in the healthy heart. During diastole the predominate pressure differences in the LV occur along the long axis from base to apex. The distribution and variability of 3D pressure fields differ between early and late diastolic filling phases, but common to both phases is a relatively lower pressure in the outflow segment. In the normal LV, TKE values are low. The highest TKE values can be seen during early diastole and are regionally distributed near the basal LV regions. In contrast, in a heterogeneous group of DCM patients, total diastolic and late diastolic TKE values are higher than in normals, and increase with the LV volume. In conclusion, in this thesis, methods for analysis of multidirectional intra cardiac velocity data have been obtained. These methods allow assessment of data quality, intra cardiac blood flow patterns, relative pressure fields, and TKE. Using these methods, new insights have been obtained in intra cardiac blood flow dynamics in health and disease. The work underlying this thesis facilitates assessment of data from a larger population of healthy subjects and patients, thus bringing the 4D Flow MRI technique closer to the clinical setting.

In this project, the inverse problem of determining regional pressure variations from measured blood velocity data in the contect of a cardiovascular setting has been approached. A common esimator, the pressure poisson estimator (PPE) has been implemented in a non-variational setting and evaluated for clinically relevant synthetic flow cases, over dynamically varying domains, mimicking or directly representing the intra-cardiac space: A synthetic dynamic domain benchmark problem and a patient specific model of the left ventricle. The results obtained show under ideal condition the capability of the approach to tackle complex domains successfully and to obtain regional pressure fields to a high degree of accuracy when compared to a locally provided state of the art estimator, the stokes estimator (STE). Under noise, results obtained suggest that divergence may occur with finer temporal resolution. Spatially convergence in a setting mimicking an image scenario is observed with minor exceptions though to stem from the specific composition of the flow field between discretizations. The implementation at hand avoids common problems in the non-variational approaches of this estimator stemming from domain complexity and leads to a simple application of the pure neumann boundary conditions required to compute the relative pressure field while avoiding the need to estimate boundary normals or use an embedded approach. The resulting linear system has desirable properties such as symmetry and compliance with the discrete compatibility condition by construction. / Syftet med följande projekt har varit att undersöka metoder för uppskattning av regionala tryckvariationer från uppmätta flödeshastigheter, med direkt tillämpning för förbättrad kardiovaskulär diagnostik. Mer specifikt har en tillgänglig gold-standardmetod; Pressure Poisson Estimatorn (PPE); implementerats i en icke-variationell miljö och utvärderats över en samling testfall med ökande komplexitet och med ökande relevans för det kliniska problemet med kardiovaskulär tryckmätning i det dynamiskt varierande hjärtutrymmet: ett syntetiskt referensproblem med varierande dynamisk rörelse, och en patientspecifik modell av vänster kammare. De erhållna resultaten visar att den icke-variationella implementeringen av PPE framgångsrikt kan hantera komplexa domäner och erhålla regionala tryckfält med hög noggrannhet. PPE-metoden påvisar också konkurrenskraftig noggrannhet i jamförelse med alternativa referensmetoder så som den s.k. Stokes-estimators (STE). Resultat visar också på tillfredställande beteende under realistiska signal-till-brus-förhallanden, likväl som spatiotemporell konvergens vid upplösningar som motsvarar vad som kan förväntas vid klinisk bildgivning. I summering visar våra resultat att vår implementering av PPE undviker vanliga problem i alterantiva icke-variationella implementeringar som annars kan uppkomma vid analys av komplexa flödesdomaner, och att en förenklad men likväl korrekt implementering av de rena Neumann-gränsvillkor som krävs för att beräkna det relativa tryckfältet kan uppnås utan behovet av att uppskatta icke-triviala gränsnormaler. Utöver detta påvisar det resulterande linjära systemet även önskvarda egenskaper såsom numerisk symmetri och överenstämmelse med diskreta kompatibilitetsvillkor.