Abstract:

The human heart is a masterpiece of the highest complexity coordinating multi-physics aspects on a multi-scale range. Thus, modeling the cardiac function to reproduce physiological characteristics and diseases remains challenging. Especially the complex simulation of the blood's hemodynamics and its interaction with the myocardial tissue requires a high accuracy of the underlying computational models and solvers. These demanding aspects make whole-heart fully-coupled simulations computationally highly expensive and call for simpler but still accurate models. While the mechanical deformation during the heart cycle drives the blood flow, less is known about the feedback of the blood flow onto the myocardial tissue. To solve the fluid-structure interaction problem, we suggest a cycle-to-cycle coupling of the structural deformation and the fluid dynamics. In a first step, the displacement of the endocardial wall in the mechanical simulation serves as a unidirectional boundary condition for the fluid simulation. After a complete heart cycle of fluid simulation, a spatially resolved pressure factor (PF) is extracted and returned to the next iteration of the solid mechanical simulation, closing the loop of the iterative coupling procedure. All simulations were performed on an individualized whole heart geometry. The effect of the sequential coupling was assessed by global measures such as the change in deformation and-as an example of diagnostically relevant information-the particle residence time. The mechanical displacement was up to 2 mm after the first iteration. In the second iteration, the deviation was in the sub-millimeter range, implying that already one iteration of the proposed cycle-to-cycle coupling is sufficient to converge to a coupled limit cycle. Cycle-to-cycle coupling between cardiac mechanics and fluid dynamics can be a promising approach to account for fluid-structure interaction with low computational effort. In an individualized healthy whole-heart model, one iteration sufficed to obtain converged and physiologically plausible results.

Abstract:

Computational models of the fluid dynamics in the human heart are a powerful tool to investigate disease mechanisms and their impact on the blood flow patterns. These models can for example be used to assess alterations occurring in hypertrophic cardiomyopathy, which is a genetic disease that increases the risk of sudden cardiac death. To overcome the challenges of a moving mesh approach, we modeled the movement of the endocardial surface based on an immersed boundary method. The verification on a simple moving 2D geometry proved plausible results. The application to the dis- eased, hypertrophic heart geometry confirmed that the computation of the mesh movement is made possible with this approach.

Abstract:

Individualized computer models of the geometry of the human heart are often based on mag- netic resonance images (MRI) or computed tomography (CT) scans. The stress distribution in the imaged state cannot be measured but needs to be estimated from the segmented geometry, e.g. by an iterative algorithm. As the convergence of this algorithm depends on different geometrical conditions, we system- atically studied their influence. Beside various shape alterations, we investigated the chamber volume, as well as the effect of material parameters. We found a marked influence of passive material parameters: increasing the model stiffness by a factor of ten halved the residual norm in the first iteration. Flat and concave areas led to a reduced robustness and convergence rate of the unloading algorithm. With this study, the geometric effects and modeling aspects governing the unloading algorithm’s convergence are identified and can be used as a basis for further improvement.

Abstract:

Mitral regurgitation alters the flow conditions in the left ventricle. To account for quantitative changes and to investigate the behavior of different flow components, a realistic computational model of the whole human heart was employed in this study. While performing fluid dynamics simulations, a scalar transport equation was solved to analyze vortex formation and ventricular wash-out for different regurgitation severities. Additionally, a particle tracking algorithm was implemented to visualize single components of the blood flow. We confirmed a significantly lowered volume of the direct flow component as well as a higher vorticity in the diseased case.

Abstract:

In order to be used in a clinical context, numerical simulation tools have to strike a balance between accuracy and low computational effort. For re- producing the pumping function of the human heart numerically, the physical domains of cardiac continuum mechanics and fluid dynamics have a significant relevance. In this context, fluid-structure interaction between the heart muscle and the blood flow is particularly important: Myocardial tension development and wall deformation drive the blood flow. However, the degree to which the blood flow has a retrograde effect on the cardiac mechanics in this multi-physics problem remains unclear up to now. To address this question, we implemented a cycle-to-cycle coupling based on a finite element model of a patient-specific whole heart geometry. The deforma- tion of the cardiac wall over one heart cycle was computed using our mechanical simulation framework. A closed loop circulatory system model as part of the simulation delivered the chamber pressures. The displacement of the endo- cardial surfaces and the pressure courses of one cycle were used as boundary conditions for the fluid solver. After solving the Navier-Stokes equations, the relative pressure was extracted for all endocardial wall elements from the three dimensional pressure field. These local pressure deviations were subsequently returned to the next iteration of the continuum mechanical simulation, thus closing the loop of the iterative coupling procedure. Following this sequential coupling approach, we simulated three iterations of mechanic and fluid simulations. To characterize the convergence, we evaluated the time course of the normalized pressure field as well as the euclidean distance between nodes of the mechanic simulation in subsequent iterations. For the left ventricle (LV), the maximal euclidean distance of all endocardial wall nodes was smaller than 2mm between the first and second iteration. The maximal distance between the second and third iteration was 70μm, thus the limit of necessary cycles was already reached after two iterations. In future work, this iterative coupling approach will have to prove its abil- ity to deliver physiologically accurate results also for diseased heart models. Altogether, the sequential coupling approach with its low computational effort delivered promising results for modeling fluid-structure interaction in cardiac simulations.

Abstract:

The human heart is the highly complex core part of the cardiovascular system, permanently, reliably and autonomously keeping up the blood flow. In computational models, the cardiac function is reproduced in silico to deduce simulation studies that deliver deeper insights into underlying phenomena or investigate parameters of interest under perfectly controlled conditions. In light of cardiovascular diseases being the number one cause of death in Western countries, contributing to the early stage diagnosis is of high clinical relevance. In this context, computational fluid dynamics simulations can deliver valuable insights into blood flow dynamics and thus offer the opportunity to investigate a central area of physics of this multi-physics organ. As the deformation of the endocardial surface triggers the blood flow, the effects of elastomechanics have to be considered as boundary conditions for such fluid simulations. However, to be relevant in the clinical context, a balance between computational effort and necessary accuracy has to be met and models need to be both, robust and reliable. Thus, in this thesis the opportunities and challenges of light and therefore less complex coupling strategies are assessed focusing on three key aspects:First, a fluid dynamics solver based on the immersed boundary approach is implemented, as this method attracts with a highly robust representation of moving meshes. Basic func- tionality was verified for various simplified geometries and showed a high accordance with analytical solutions. Comparing the 3D simulation of a realistic left heart geometry to a body-fitted mesh approach, basic global quantities were reproduced. However, variations in the boundary conditions revealed a high influence on the simulation results.The application of the solver to simulate the influence of pathologies on the blood flow patterns showed results in good accordance with literature values. In mitral valve regurgitation simulations, the regurgitation jet was visualized by a particle tracking method. In hypertrophic cardiomyopathy, flow patterns in the left ventricle were assessed by a passive scalar transport to visualize the local concentration of the initial blood volume.As in the just mentioned studies, only a unidirectional flow of information from the elas- tomechanical model to the fluid solver was considered, the retrograde effect of the spatially resolved pressure field resulting from fluid dynamics simulations on the elastomechanics is quantified. A sequential coupling approach is introduced to consider fluid dynamics influences in a cycle-to-cycle coupling structure. The low deviations in the mechanical solver of 2 mm vanished already after one iteration, implicating that the retrograde effect of fluid dynamics in the health heart is limited. Summing up, especially in fluid dynamics simulations, boundary conditions have to be set with caution as due to their high influence the vulnerability of the models is increased. Nevertheless, light coupling strategies showed promising results in reproducing global fluid dynamic quantities while the dependence between the solvers is reduced and computational effort is saved.

Abstract:

Als Verfahren zum Monitoring der Lungenaktivität findet die elektrische Impedanztomographie (EIT) in den vergangenenen Jahren zunehmende Anwendung. Dabei wird vergleichsweise einfach, günstig und portabel mittels Elektrodengurt um die Brust des Patienten ein Messsignal aufgenommen. Daraus kann mit Hilfe mathematischer Rekonstruktionsalgorithmen ein Bild errechnet werden, welches die Ventilationsverhältnisse in der Lunge wiedergibt. Um aus den gemessenen Daten zusätzlich das Ventilations-Perfusions-Verhältnis (VPR) anzugeben, welches als Maß für den Gasaustausch in der Lunge von hohem klinischen Interesse ist, ist zusätzlich die Auswertung der Perfusion nötig. Die Perfusion wurde dabei mittels Blutvolumenänderung, die in einer herzsynchronen Pulsatilität im EIT-Signal resultiert, bestimmt. Ziel dieser Arbeit war es, den Einfluss zu untersuchen, den verschiedene Rekonstruktionsalgorithmen und dieWahl derer Parameter - hinsichtlich dieser herzsynchronen Pulsatilität - auf das resultierende Bild haben. Dazu wurde in einem ersten Schritt ein Simulationsmodell implementiert, die Pulsatilität mittels einer kugelförmigen Impedanzänderung approximiert und anschließend eine Simulation durchgeführt. Um die erzielten Ergebnisse adäquat vergleichen zu können, wurden neben mehreren Simulationsszenarien auch die Auswertungskriterien, anhand derer die Rekonstruktionsergebnisse quantifiziert werden können, entwickelt. Dabei wurde zuerst der statische Fall eingehender betrachtet, mit dem die wichtige Wahl des korrekten Hyperparameters durchgeführt wird. Davon ausgehend wurden die Rekonstruktionseinflüsse im dynamischen Fall untersucht. Sowohl die Variation der Gefäßgröße als auch die Änderung der Leitfähigkeiten eines stark durchbluteten Gebietes, sowie die Einflüsse von anderen Gewebeschichten wurden dazu beleuchtet. Auch das Einbringen von Vorwissen, das genutzt werden kann, um das schlecht gestellte Rekonstruktionsproblem zu verbessern, wurde untersucht. In einem letzten Schritt wurden die untersuchten Rekonstruktionsalgorithmen auf real gemessene Daten angewendet, um den Einsatz in der Praxis zu testen. Zusammenfassend lässt sich festhalten, dass eine Rekonstruktion der herzsynchronen Pulsatilität aus simulierten Daten gut möglich war. Das Vorhandensein einer Impedanzänderung wurde eindeutig erkannt. Auch die Variation verschiedener Einflussfaktoren konnte quantitativ erfasst werden. Die Einflüsse verschiedener Rekonstruktionsalgorithmen waren dabei erkennbar. Abschließend lieferte die Anwendung auf gemessene Daten ein plausibles Rekonstruktionsergebnis. Die rekonstruierte Lungenlage stimmte gut mit dem MRT-Bild überein.