Joris Bols

Variability of Computational Fluid Dynamics Solutions for Pressure and Flow in a Giant Aneurysm: The ASME 2012 Summer Bioengineering Conference CFD Challenge

Stimulated by a recent controversy regarding pressure drops predicted in a giant aneurysm with a proximal stenosis, the present study sought to assess variability in the prediction of pressures and flow by a wide variety of research groups. In phase I, lumen geometry, flow rates, and fluid properties were specified, leaving each research group to choose their solver, discretization, and solution strategies. Variability was assessed by having each group interpolate their results onto a standardized mesh and centerline. For phase II, a physical model of the geometry was constructed, from which pressure and flow rates were measured. Groups repeated their simulations using a geometry reconstructed from a micro-computed tomography (CT) scan of the physical model with the measured flow rates and fluid properties. Phase I results from 25 groups demonstrated remarkable consistency in the pressure patterns, with the majority predicting peak systolic pressure drops within 8% of each other. Aneurysm sac flow patterns were more variable with only a few groups reporting peak systolic flow instabilities owing to their use of high temporal resolutions. Variability for phase II was comparable, and the median predicted pressure drops were within a few millimeters of mercury of the measured values but only after accounting for submillimeter errors in the reconstruction of the life-sized flow model from micro-CT. In summary, pressure can be predicted with consistency by CFD across a wide range of solvers and solution strategies, but this may not hold true for specific flow patterns or derived quantities. Future challenges are needed and should focus on hemodynamic quantities thought to be of clinical interest.

A computational method to assess the in vivo stresses and unloaded configuration of patient-specific blood vessels

In the modelling process of cardiovascular diseases, one often comes across the numerical simulation of the blood vessel wall. When the vessel geometry is patient-specific and is obtained in vivo via medical imaging, the stress distribution throughout the vessel wall is unknown. However, simulating the full physiological pressure load inside the blood vessel without incorporating the in vivo stresses will result in an inaccurate stress distribution and an incorrect deformation of the vessel wall. In this work a computational method is formulated to restore the zero-pressure geometry of patient-specific blood vessels, and to recover the in vivo stress field of the loaded structures at the moment of imaging. The proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations. As only an update of the mesh is required, the formulation of this method allows for a straightforward implementation in combination with existing structural solvers, even if the structural solver is a black box.

The Impact of Simplified Boundary Conditions and Aortic Arch Inclusion on CFD Simulations in the Mouse Aorta: A Comparison With Mouse-specific Reference Data

Computational fluid dynamics (CFD) simulations allow for calculation of a detailed flow field in the mouse aorta and can thus be used to investigate a potential link between local hemodynamics and disease development. To perform these simulations in a murine setting, one often needs to make assumptions (e.g. when mouse-specific boundary conditions are not available), but many of these assumptions have not been validated due to a lack of reference data. In this study, we present such a reference data set by combining high-frequency ultrasound and contrast-enhanced micro-CT to measure (in vivo) the time-dependent volumetric flow waveforms in the complete aorta (including seven major side branches) of 10 male ApoE -/- deficient mice on a C57Bl/6 background. In order to assess the influence of some assumptions that are commonly applied in literature, four different CFD simulations were set up for each animal: (i) imposing the measured volumetric flow waveforms, (ii) imposing the average flow fractions over all 10 animals, presented as a reference data set, (iii) imposing flow fractions calculated by Murrays law, and (iv) restricting the geometrical model to the abdominal aorta (imposing measured flows). We found that - even if there is sometimes significant variation in the flow fractions going to a particular branch - the influence of using average flow fractions on the CFD simulations is limited and often restricted to the side branches. On the other hand, Murrays law underestimates the fraction going to the brachiocephalic trunk and strongly overestimates the fraction going to the distal aorta, influencing the outcome of the CFD results significantly. Changing the exponential factor in Murrays law equation from 3 to 2 (as suggested by several authors in literature) yields results that correspond much better to those obtained imposing the average flow fractions. Restricting the geometrical model to the abdominal aorta did not influence the outcome of the CFD simulations. In conclusion, the presented reference dataset can be used to impose boundary conditions in the mouse aorta in future studies, keeping in mind that they represent a subsample of the total population, i.e., relatively old, non-diseased, male C57Bl/6 ApoE -/- mice.

The aortic reservoir-wave as a paradigm for arterial haemodynamics: insights from three-dimensional fluid–structure interaction simulations in a model of aortic coarctation

Background: The reservoir-wave paradigm considers aortic pressure as the superposition of a ‘reservoir pressure’, directly related to changes in reservoir volume, and an ‘excess’ component ascribed to wave dynamics. The change in reservoir pressure is assumed to be proportional to the difference between aortic inflow and outflow (i.e. aortic volume changes), an assumption that is virtually impossible to validate in vivo. The aim of this study is therefore to apply the reservoir-wave paradigm to aortic pressure and flow waves obtained from three-dimensional fluid-structure interaction simulations in a model of a normal aorta, aortic coarctation (narrowed descending aorta) and stented coarctation (stiff segment in descending aorta). Method and results: We found no unequivocal relation between the intraaortic volume and the reservoir pressure for any of the simulated cases. When plotted in a pressure-volume diagram, hysteresis loops are found that are looped in a clockwise way indicating that the reservoir pressure is lower than the pressure associated with the change in volume. The reservoir-wave analysis leads to very high excess pressures, especially for the coarctation models, but to surprisingly little changes of the reservoir component despite the impediment of the buffer capacity of the aorta. Conclusion: With the observation that reservoir pressure is not related to the volume in the aortic reservoir in systole, an intrinsic assumption in the wave-reservoir concept is invalidated and, consequently, also the assumption that the excess pressure is the component of pressure that can be attributed to wave travel and reflection.

An Animal-Specific FSI Model of the Abdominal Aorta in Anesthetized Mice

Recent research has revealed that angiotensin II-induced abdominal aortic aneurysm in mice can be related to medial ruptures occurring in the vicinity of abdominal side branches. Nevertheless a thorough understanding of the biomechanics near abdominal side branches in mice is lacking. In the current work we present a mouse-specific fluid–structure interaction (FSI) model of the abdominal aorta in ApoE−/− mice that incorporates in vivo stresses. The aortic geometry was based on contrast-enhanced in vivo micro-CT images, while aortic flow boundary conditions and material model parameters were based on in vivo high-frequency ultrasound. Flow waveforms predicted by FSI simulations corresponded better to in vivo measurements than those from CFD simulations. Peak-systolic principal stresses at the inner and outer aortic wall were locally increased caudal to the celiac and left lateral to the celiac and mesenteric arteries. Interestingly, these were also the locations at which a tear in the tunica media had been observed in previous work on angiotensin II-infused mice. Our preliminary results therefore suggest that local biomechanics play an important role in the pathophysiology of branch-related ruptures in angiotensin-II infused mice. More elaborate follow-up research is needed to demonstrate the role of biomechanics and mechanobiology in a longitudinal setting.

Unstructured hexahedral mesh generation of complex vascular trees using a multi-block grid-based approach

The trend towards realistic numerical models of (pathologic) patient-specific vascular structures brings along larger computational domains and more complex geometries, increasing both the computation time and the operator time. Hexahedral grids effectively lower the computational run time and the required computational infrastructure, but at high cost in terms of operator time and minimal cell quality, especially when the computational analyses are targeting complex geometries such as aneurysm necks, severe stenoses and bifurcations. Moreover, such grids generally do not allow local refinements. As an attempt to overcome these limitations, a novel approach to hexahedral meshing is proposed in this paper, which combines the automated generation of multi-block structures with a grid-based method. The robustness of the novel approach is tested on common complex geometries, such as tree-like structures (including trifurcations), stenoses, and aneurysms. Additionally, the performance of the generated grid is assessed using two numerical examples. In the first example, a grid sensitivity analysis is performed for blood flow simulated in an abdominal mouse aorta and compared to tetrahedral grids with a prismatic boundary layer. In the second example, the fluid–structure interaction in a model of an aorta with aortic coarctation is simulated and the effect of local grid refinement is analyzed.

CFD Challenge: Solutions Using the Commercial Finite Volume Solver, Fluent, and a pyFormex-Generated Full Hexahedral Mesh

For many years, there has been a strong intra Ghent University collaboration between the IBiTech-bioMMeda research group, focusing on the application of fluid and structural mechanics for biomedical problems, and the department of Flow, Heat and Combustion Mechanics with a strong background in developing algorithms for numerical fluid mechanics and fluid-structure interaction (FSI) problems. This collaboration joins the strengths of both groups, with ongoing applications in FSI simulations of heart valves, aortic coarctation, aortic aneurysms etc., thereby integrating in vivo (human and (small) animal) hydraulic bench and numerical research.Copyright

Hemodynamics in ascending and abdominal aorta aneurysm formation in the ApoE -/- angiotensin II mouse model

Aortic aneurysm is a pathological dilatation of the aorta that can be life-threatening when it ruptures. Aneurysms occur throughout the entire aorta but there is a predisposition for the ascending and the abdominal aorta, an observation that cannot be fully explained by the current knowledge of the disease pathophysiology. ApoE −/− mice infused with angiotensin II have recently been reported to develop not only abdominal [1], but also ascending aortic aneurysms [2]. These animals thus provide the perfect model to compare aneurysm progression in both aortic locations and to investigate whether disturbed hemodynamics play a role in the initial phase of aneurysm growth. In this study, both imaging and computational biomechanics techniques were used to elucidate the flow field at the location of the aneurysm prior to onset of the disease.Copyright

PREDICTING THE FUNCTIONAL IMPACT OF RESIDUAL AORTIC COARCTATION LESIONS USING FLUID-STRUCTURE INTERACTION SIMULATIONS

Aortic coarctation is a congenital disease, characterized by a narrowing of the upper descending aorta, obstructing the blood flow from the heart towards the lower part of the body. The treatment can be minimally invasive using a stent and/or a balloon catheter to dilate the coarctation zone, or the narrow section can be removed surgically. Even after a successful treatment, a high risk of cardiovascular morbidity and mortality remains. Two aspects contribute to this increased risk: (1) a residual narrowing, leading to an additional resistance in the arterial system and (2) a local stiffening after treatment, disturbing the buffer function of the aorta. Moreover, these residual narrowing and stiffening lead to an impedance mismatch and are a source of wave reflections that reach the heart fast, given the short distance to the heart.Copyright

Structural Simulation of a Mouse-Specific Abdominal Aorta

In the last years there is an increasing interest in patient-specific simulations of the fluid-structure interaction in aortic aneurysms, a.o. to better understand the growth and development of the aneurysm and to support diagnosis through assessment of its rupture potential. In order to verify these simulations, validation is an important and difficult task. Given ethical constraints, the slow time course of the disease in humans and the absence of true baseline data in a healthy aorta, these studies are difficult to perform in humans. This is particularly true for aneurysm rupture research, as rupture will normally be prevented by surgery and access to post-mortem tissue is not always possible. In order to overcome these problems an AAA mouse model can be used [1].© 2011 ASME