An interface tracking finite element methodology is presented for 3D turbulent flow fluid-structure interaction, including full-friction contact and topology changes, with specific focus on heart valve simulations. The methodology is based on a unified continuum fluid-structure interaction model, which is a monolithic approach, where the fundamental conservation laws are formulated for the combined fluid-structure continuum. Contact is modeled by local phase changes in the unified continuum, and computational results show the promise of the approach. The core algorithms are all based on the solution of partial differential equations with standard finite element methods, and hence any general purpose finite element library which can leverage state of the art hardware platforms can be used for the implementation of the methodology.

We present a high performance computing framework for finite element simulation of blood flow in the left ventricle of the human heart. The mathematical model is described together with the discretization method and the parallel implementation in Unicorn which is part of the open source software framework FEniCS-HPC. We show results based on patient-specific data that capture essential features observed with other computational models and imaging techniques, and thus indicate that our framework possesses the potential to provide relevant clinical information for diagnosis and medical treatment. Several other studies have been conducted to simulate the three dimensional blood flow in the left ventricle of the human heart with prescribed wall movement. Our contribution to the field of cardiac research lies in establishing an open source framework modular both in modelling and numerical algorithms.

Due to advances in medical imaging, computational fluid dynamics algorithms and high performance computing, computer simulation is developing into an important tool for understanding the relationship between cardiovascular diseases and intraventricular blood flow. The field of cardiac flow simulation is challenging and highly interdisciplinary. We apply a computational framework for automated solutions of partial differential equations using Finite Element Methods where any mathematical description directly can be translated to code. This allows us to develop a cardiac model where specific properties of the heart such as fluid-structure interaction of the aortic valve can be added in a modular way without extensive efforts. In previous work, we simulated the blood flow in the left ventricle of the heart. In this paper, we extend this model by placing prototypes of both a native and a mechanical aortic valve in the outflow region of the left ventricle. Numerical simulation of the blood flow in the vicinity of the valve offers the possibility to improve the treatment of aortic valve diseases as aortic stenosis (narrowing of the valve opening) or regurgitation (leaking) and to optimize the design of prosthetic heart valves in a controlled and specific way. The fluid-structure interaction and contact problem are formulated in a unified continuum model using the conservation laws for mass and momentum and a phase function. The discretization is based on an Arbitrary Lagrangian-Eulerian space-time finite element method with streamline diffusion stabilization, and it is implemented in the open source software Unicorn which shows near optimal scaling up to thousands of cores. Computational results are presented to demonstrate the capability of our framework.

Echocardiography is the most commonly used image modality in cardiology, assessing several aspects of cardiac viability. The importance of cardiac hemodynamics and 4D blood flow motion has recently been highlighted, however such assessment is still difficult using routine echo-imaging. Instead, combining imaging with computational fluid dynamics (CFD)-simulations has proven valuable, but only a few models have been applied clinically. In the following, patient-specific CFD-simulations from transthoracic dobutamin stress echocardiography have been used to analyze the left ventricular 4D blood flow in three subjects: two with normal and one with reduced left ventricular function. At each stress level, 4D-images were acquired using a GE Vivid E9 (4VD, 1.7MHz/3.3MHz) and velocity fields simulated using a presented pathway involving endocardial segmentation, valve position identification, and solution of the incompressible Navier-Stokes equation. Flow components defined as direct flow, delayed ejection flow, retained inflow, and residual volume were calculated by particle tracing using 4th-order Runge-Kutta integration. Additionally, systolic and diastolic average velocity fields were generated. Results indicated no major changes in average velocity fields for any of the subjects. For the two subjects with normal left ventricular function, increased direct flow, decreased delayed ejection flow, constant retained inflow, and a considerable drop in residual volume was seen at increasing stress. Contrary, for the subject with reduced left ventricular function, the delayed ejection flow increased whilst the retained inflow decreased at increasing stress levels. This feasibility study represents one of the first clinical applications of an echo-based patient-specific CFD-model at elevated stress levels, and highlights the potential of using echo-based models to capture highly transient flow events, as well as the ability of using simulation tools to study clinically complex phenomena. With larger patient studies planned for the future, and with the possibility of adding more anatomical features into the model framework, the current work demonstrates the potential of patient-specific CFD-models as a tool for quantifying 4D blood flow in the heart.

We present a framework for coupled multiphysics in computational fluid dynamics, targeting massively parallel systems. Our strategy is based on general problem formulations in the form of partial differential equations and the finite element method, which open for automation, and optimization of a set of fundamental algorithms. We describe these algorithms, including finite element matrix assembly, adaptive mesh refinement and mesh smoothing; and multiphysics coupling methodologies such as unified continuum fluid-structure interaction (FSI), and aeroacoustics by coupled acoustic analogies. The framework is implemented as FEniCS open source software components, optimized for massively parallel computing. Examples of applications are presented, including simulation of aeroacoustic noise generated by an airplane landing gear, simulation of the blood flow in the human heart, and simulation of the human voice organ.

Heart disease is the leading cause of death in the world. Therefore, numerous studies are undertaken to identify indicators which can be applied to discover cardiac dysfunctions at an early age. Among others, the fluid dynamics of the blood flow (hemodymanics) is considered to contain relevant information related to abnormal performance of the heart.This thesis presents a robust framework for numerical simulation of the fluid dynamics of the blood flow in the left ventricle of a human heart and the fluid-structure interaction of the blood and the aortic leaflets.We first describe a patient-specific model for simulating the intraventricular blood flow. The motion of the endocardial wall is extracted from data acquired with medical imaging and we use the incompressible Navier-Stokes equations to model the hemodynamics within the chamber. We set boundary conditions to model the opening and closing of the mitral and aortic valves respectively, and we apply a stabilized Arbitrary Lagrangian-Eulerian (ALE) space-time finite element method to simulate the blood flow. Even though it is difficult to collect in-vivo data for validation, the available data and results from other simulation models indicate that our approach possesses the potential and capability to provide relevant information about the intraventricular blood flow.To further demonstrate the robustness and clinical feasibility of our model, a semi-automatic pathway from 4D cardiac ultrasound imaging to patient-specific simulation of the blood flow in the left ventricle is developed. The outcome is promising and further simulations and analysis of large data sets are planned.In order to enhance our solver by introducing additional features, the fluid solver is extended by embedding different geometrical prototypes of both a native and a mechanical aortic valve in the outflow area of the left ventricle.Both, the contact as well as the fluid-structure interaction, are modeled as a unified continuum problem using conservation laws for mass and momentum. To use this ansatz for simulating the valvular dynamics is unique and has the expedient properties that the whole problem can be described with partial different equations and the same numerical methods for discretization are applicable.All algorithms are implemented in the high performance computing branch of Unicorn, which is part of the open source software framework FEniCS-HPC. The strong advantage of implementing the solvers in an open source software is the accessibility and reproducibility of the results which enhance the prospects of developing a method with clinical relevance.

The combination of medical imaging with computational fluid dynamics (CFD) has enabled the study of 3D blood flow on a patient-specificlevel. However, with models based on gated high-resolution data, the study of transient flows, and any model implementation into routine cardiac care, is challenging. The present paper presents a novel pathway for patient-specific CFD modelling of the left ventricle (LV), using 4D transthoracic echocardiography (TTE) as input modality. To evaluate the clinical usability, two sub-studies were performed. First, a robustness evaluation was performed where repeated models with alternating input variables were generated for 6 subjects and changes in simulated output quantified. Second, a validation study was carried out where the pathway accuracy was evaluated against pulsed-wave Doppler (100 subjects), and 2D through-plane phase-contrast magnetic resonance imaging measurements over 7 intraventricular planes (6 subjects). The robustness evaluation indicated a model deviation of <12%, with highest regional and temporal deviations at apical segments and at peak systole, respectively. The validation study showed an error of < 11% (velocities < 10 cm/s) for all subjects, with no significant regional or temporal differences observed. With the patient-specific pathway shown to provide robust output with high accuracy, and with the pathway dependent only on 4DTTE, the method has a high potential to be used within future clinical studies on 3D intraventricular flowpatterns. To this, future model developments in the form of e.g. anatomically accurate LV valves may further enhance the clinical value of the simulations.

Progress in medical imaging, computational fluid dynamics and high performance computing (HPC) enables computer simulations to emerge as a significant tool to enhance our understanding of the relationship between cardiac diseases and hemodynamics. The field of cardiac modelling is diverse, covering different aspects on microscopic and macroscopic level. In our research, we develop a cardiac model which is embedded in a computational environment where specific properties of the heart such as fluid-structure interaction of the aortic valve can be modeled, or numerical and computational algorithms as parallel computing or adaptivity can be added in a modular way without extensive efforts. In this paper, we present a patient-specific Arbitrary Lagrangian-Eulerian (ALE) finite element framework for simulating the blood flow in the left ventricle of a human heart using HPC, which forms the core of our cardiac model. The mathematical model is described together with the discretization method, mesh smoothing algorithms, and the parallel implementation in Unicorn which is part of the open source software framework FEniCS-HPC. The parallel performance is demonstrated, a convergence study is conducted and intraventricular flow patterns are visualized. The results capture essential features observed with other computational models and imaging techniques, and thus indicate that our framework possesses the potential to provide relevant clinical information for diagnosis and medical treatment. Several studies have been conducted to simulate the three dimensional blood flow in the left ventricle of the human heart with prescribed wall movement. Our contribution to the field of cardiac research lies in establishing an open source framework modular both in modelling and numerical algorithms.

In recent years, computational fluid dynamics (CFD) simulations on in-silico models of the heart have provided a valuable insight into cardiac hemodynamic behaviour. However, so far most models have been either based on simplified geometries or on imaging acquisitions with relatively low temporal resolution. It has been suggested that models based entirely on subject-specific ultrasonic images should be used to capture transient flow changes. Therefore, the aim of this study is to present a pathway from routine 4D echocardiography to a patient-specific flow simulation of the left ventricle (LV), evaluating the model robustness and clinical feasibility. The created pathway consisted of initial LV segmentation and mitral/aortic valve positioning, being subsequently used as input for the CFD simulations (based on solving the Navier-Stokes equation using an Arbitrary Lagrangian-Eulerian approach). The output consisted of 4D blood flow velocities and relative pressures in the entire LV. On five subjects, the model robustness was evaluated with regards to variations in singular boundary conditions. The clinical feasibility of the output was compared to clinical PW Doppler measurements and, as a proof-of-concept, synthetic contrast enhanced ultrasound images were simulated on the flow field using the COLE-method. Results indicated a relatively robust model, with variations in regional flow of approximately 5.1/6.2% and 9.7/7.0% for healthy and pathological subject respectively (end diastole/end systole). Furthermore, showing similar behaviour to clinical Doppler measurements the technique serves as a promising tool for future clinical investigations. Additionally, the ability of simulating synthetic ultrasound images further underlines the applicability of the pathway, being potentially useful in studies on improved echocardiographic image analysis.

In this paper we present a new adaptive finite element method directly using the a posteriori error representation as a local error  indicator, and representing the primal and dual solutions in the same finite element space (here piecewise continuous linear functions on the same mesh). Since this approach gives a global a posteriori error estimate that is zero (due to Galerkin orthogonality), the error representation has traditionally been thought to contain no information about the error. However, we show the opposite, that locally, the orthogonal error representation behaves very similar to the non-orthogonal error representation using a higher order approximation of the dual,  which is a standard approach to overcome the problem of a zero error estimate. We present evidence of this both in the  form of an a priori estimate for the local error indicator for an elliptic model problem  and a detailed computational investigation showing that the two methods exhibit very similar behavior and performance, and thus confirming the theoretical prediction. We also present computational results using a stabilized version of the method for non-elliptic partial differential equations where the error representation is no longer orthogonal, and where both the local error indicator and global error estimate behave similar to the error representation using a higher order approximation of the dual. The benefits of this adaptive method are generality and simplicity in formulation, sharpness, and efficiency since high order approximation of the dual and computation of additional constructs such as jump terms over interior facets or local problems are avoided.