Herbert Oertel

MRI-Based CFD analysis of flow in a human left ventricle: Methodology and application to a healthy heart

A three-dimensional computational fluid dynamics (CFD) method has been developed to simulate the flow in a pumping left ventricle. The proposed method uses magnetic resonance imaging (MRI) technology to provide a patient specific, time dependent geometry of the ventricle to be simulated. Standard clinical imaging procedures were used in this study. A two-dimensional time-dependent orifice representation of the heart valves was used. The location and size of the valves is estimated based on additional long axis images through the valves. A semi-automatic grid generator was created to generate the calculation grid. Since the time resolution of the MR scans does not fit the requirements of the CFD calculations a third order bezier approximation scheme was developed to realize a smooth wall boundary and grid movement. The calculation was performed by a Navier–Stokes solver using the arbitrary Lagrange–Euler (ALE) formulation. Results show that during diastole, blood flow through the mitral valve forms an asymmetric jet, leading to an asymmetric development of the initial vortex ring. These flow features are in reasonable agreement with in vivo measurements but also show an extremely high sensitivity to the boundary conditions imposed at the inflow. Changes in the atrial representation severely alter the resulting flow field. These shortcomings will have to be addressed in further studies, possibly by inclusion of the real atrial geometry, and imply additional requirements for the clinical imaging processes.

Partitioned fluid-solid coupling for cardiovascular blood flow: left-ventricular fluid mechanics.

We present a 3D code-coupling approach which has been specialized towards cardiovascular blood flow. For the first time, the prescribed geometry movement of the cardiovascular flow model KaHMo (Karlsruhe Heart Model) has been replaced by a myocardial composite model. Deformation is driven by fluid forces and myocardial response, i.e., both its contractile and constitutive behavior. Whereas the arbitrary Lagrangian–Eulerian formulation (ALE) of the Navier–Stokes equations is discretized by finite volumes (FVM), the solid mechanical finite elasticity equations are discretized by a finite element (FEM) approach. Taking advantage of specialized numerical solution strategies for non-matching fluid and solid domain meshes, an iterative data-exchange guarantees the interface equilibrium of the underlying governing equations. The focus of this work is on left-ventricular fluid–structure interaction based on patient-specific magnetic resonance imaging datasets. Multi-physical phenomena are described by temporal visualization and characteristic FSI numbers. The results gained show flow patterns that are in good agreement with previous observations. A deeper understanding of cavity deformation, blood flow, and their vital interaction can help to improve surgical treatment and clinical therapy planning.

Partitioned fluid-solid coupling for cardiovascular blood flow: validation study of pressure-driven fluid-domain deformation.

The Karlsruhe Heart Model (KaHMo) is a patient-specific simulation tool for a three-dimensional blood flow evaluation inside the human heart. Whereas KaHMo MRT is based on geometry movement identified from MRT data, KaHMo FSI allows the consideration of structural properties and the analysis of FSI. Previous investigations by Oertel etxa0al. have shown the ability of KaHMo to gain insight into different intra-ventricular fluid mechanics of both healthy and diseased hearts. However, the in vivo validation of the highly dynamic cavity flow pattern has been a challenging task in recent years. As a first step, the focus of this study is on an artificial ventricular experiment, derived from real heart anatomy. Fluid domain deformation and intra-ventricular flow dynamics are enforced by an outer surface pressure distribution. The pure geometrical representation of KaHMo MRT can now be complemented by constitutive properties, pressure forces, and interaction effects using KaHMo FSI’s partitioned code-coupling approach. For the first time, fluid domain deformation and intra-ventricular flow of KaHMo FSI has been compared with experimental data. With a good overall agreement, the proof of KaHMo’s validity represents an important step from feasibility study toward patient-specific analysis.

Fluid-structure interaction simulation of an avian flight model.

SUMMARY A three-dimensional numerical avian model was developed to investigate the unsteady and turbulent aerodynamic performance of flapping wings for varying wingbeat frequencies and flow velocities (up to 12 Hz and 9 m s–1), corresponding to a reduced frequency range of k=0.22 to k=1.0 and a Reynolds number range of Re=16,000 to Re=50,000. The wings of the bird-inspired model consist of an elastic membrane. Simplifying the complicated locomotion kinematics to a sinusoidal wing rotation about two axes, the main features of dynamic avian flight were approximated. Numerical simulation techniques of fluid–structure interaction (FSI) providing a fully resolved flow field were applied to calculate the aerodynamic performance of the flapping elastic wings with the Reynolds averaged Navier–Stokes (RANS) approach. The results were used to characterize and describe the macroscopic flow configurations in terms of starting, stopping, trailing and bound vortices. For high reduced frequencies up to k=0.67 it was shown that the wake does not consist of individual vortex rings known as the discrete vortex ring gait. Rather, the wake is dominated by a chain of elliptical vortex rings on each wing. The structures are interlocked at the starting and stopping vortices, which are shed in pairs at the reversal points of the wingbeat cycle. For decreasing reduced frequency, the results indicate a transition to a continuous vortex gait. The upstroke becomes more aerodynamically active, leading to a consistent circulation of the bound vortex on the wing and a continuous spanwise shedding of small scale vortices. The formation of the vortices shed spanwise in pairs at the reversal points is reduced and the wake is dominated by the tip and root vortices, which form long drawn-out vortex structures.

The Karlsruhe Heart Model KaHMo: A modular framework for numerical simulation of cardiac hemodynamics

Numerical methods are rapidly gaining importance for answering medical questions. One field in which these answer are especially valuable is cardiology. The understanding of the cardiac function on a detailed, physical level can help to improve diagnostics, prognosis and therapy for a large number of pathologies.

Multi-physical simulation of left-ventricular blood flow based on patient-specific MRI data

Statistically, heart disease has been the major cause of death in the recent past, which emphasizes the need for computational heart models. In this context, the so-called KaHMo (Karlsruhe Heart Model) is specialized on the innerventricular blood flow and its influence on the overall heart conditions. Both healthy and diseased hearts are simulated in order to analyze characteristic flow patterns and pressure losses. The patient-specific fluid domain movement is realized by time-dependent geometries out of MRI data.

Biofluidmechanics of Avian Flight: Recent Numerical and Experimental Investigations

A three dimensional mechanical and numerical avian model with identical geometry was developed to investigate the aerodynamic performance of flapping flight for varying flow velocities and wing beat frequencies. The corresponding reduced frequencies range from k=0.22 to k=1.0 providing turbulent and unsteady flow. The model consists of a rigid body and elastic wings. Its shape was inspired by birds, but restricted by manufacturing and numerical specifications. Using a sinusoidal flapping about an off-centre axis parallel to the body axis and a phase-shifted pitching about the moving lateral wing axis the wing beat motion was realized. Wind tunnel tests with Particle Image Velocimetry (PIV) were performed to capture the velocity field around and behind the mechanical model for different reduced frequencies. Furthermore, simulations for the corresponding numerical model have been conducted by means of fluid-structure-interaction (FSI) simulation techniques providing a fully resolved flow field. The results were used to analyze the flow configurations and to validate the numerical and experimental setup for further investigations. The results of the numerical simulations and wind tunnel experiments are in good agreement and facilitate a reconstruction of the three dimensional vortex structures in the wake. The results show, that for all reduced frequencies, the wakes consist of a chain of interlocked vortex rings behind each wing. For high reduced frequencies, a shedding of small-scale vortices composing vortex sheets generates oppositely rotating upstroke (UVS) and downstroke (DVS) vortex structures which contain starting, stopping, tip and root vortices. For decreasing reduced frequencies, the upstroke becomes more aerodynamically active leading to a diffusion of the upstroke vortex structures.

Hemodynamics and Fluid-Structure-Interaction in a Virtual Heart

Abstract Modeling the function of the human heart is of growing importance in a time when surgical treatment becomes the predominant therapy option. The hemodynamics of ventricular and vascular flow is closely linked to other disciplines like structural mechanics of myocardial and vascular tissue, electro-dynamical excitation, etc. A multi-disciplinary approach is therefore needed to describe it. While a monolithic solution of the underlying differential equations in one set is thinkable, a partitioned approach can take into account the specifics of the single disciplines and profit from specialized models and algorithms. We show how by coupling specialized solvers for fluid and solid mechanics a coupled model of ventricular flow can be created that gives insight into the hemodynamics in a way that is more than the sum of its parts. Zusammenfassung In einer Zeit, in der der chirurgische Eingriff die häufigste Therapie darstellt, gewinnt eine Modellbeschreibung der menschlichen Herzfunktion zunehmend an Bedeutung. Die Hämodynamik der Herz- und Gefäßströmung ist mit anderen Disziplinen – wie der Strukturmechanik des Myokards und der Gefäßwand, der elekrodynamischen Reizausbreitung, usw. — eng verzahnt. Ein überdisziplinärer Ansatz ist also gefragt, um sie zu beschreiben. Während eine monolithische Lösung der zugrundeliegenden Differentialgleichungen in einem Gleichungssystem denkbar ist, kann ein partitionierter Ansatz die speziellen Anforderungen der einzelnen Disziplinen berücksichtigen und von spezialisierten Modellen und Algorithmen profitieren. Es wird gezeigt, wie durch Kopplung spezialisierter Löser für die Strömungs- und Strukturmechanik ein gekoppeltes Modell der Ventrikelströmung realisiert werden kann, das einen breiteren Einblick in die Hämodynamik erlaubt, als die Einzelmodelle alleine.