Boundary Conditions by Schwarz-Christoffel Mapping in Anatomically Accurate Hemodynamics

Appropriate velocity boundary conditions are a prerequisite in computational hemodynamics. A method for mapping analytical or experimental velocity profiles on anatomically realistic boundary cross-sections is presented. Interpolation is required because the computational and experimental domains are seldom aligned. In the absence of velocity information one alternative is the adaptation of analytical profiles based on volumetric flux constraints. The presented algorithms are based on the Schwarz-Christoffel (S-C) mapping of singly or doubly connected polygons to the unit circle or an annulus with unary external radius. S-C transformations are combined to construct a one-to-one invertible map between the target surface and the measurement domain or the support of the source analytical profile. The proposed technique permits us to segment each space separately and map one onto the other in its entirety. Tests are performed with normal velocity boundary conditions for computational simulations of blood flow in the ascending aorta and cerebrospinal fluid flow in the spinal cavity. Mappings of axisymmetric velocity profiles of the Womersley type through a simply connected circular pipe as well as through a doubly connected circular annulus, and interpolations from in-vivo phase-contrast magnetic resonance imaging velocity measurements under instantaneous volumetric flux constraints are considere

Simulation des Blutflusses in der abdominellen Aorta: Die numerische Simulation des Blutflusses in abdominellen Aortenaneurysmen vor und nach Intervention

Zusammenfassung: Das Ziel der numerischen Simulation des Blutflusses in der Aorta ist, die Mechanik der Entstehung von Aortenaneurysmen im Hinblick auf das Rupturrisiko zu untersuchen und die Wirkungen interventioneller Maßnahmen zu beschreiben. Die Grundlage der numerischen Simulation sind virtuelle Modelle von Gefäßen und die physikalischen Eigenschaften der Gefäßbestandteile, des Blutes und der Strömung. Basierend auf diesen Angaben werden mit Hilfe numerischer Methoden die strömungsmechanischen Probleme des Blutflusses näherungsweise gelöst. Die Ergebnisse können dann quantitativ und qualitativ dargestellt werden. Die Ergebnisse der numerischen Flusssimulation zeigen, dass in abdominellen Aortenaneurysmen die Höhe des Wanddrucks, der von entscheidender Bedeutung für das Rupturrisiko ist, von verschiedenen Faktoren, wie z.B. der Lage des Wandthrombus, abhängt. In Modellen mit Stentgrafts wurden mit Hilfe der numerischen Simulation Faktoren, welche die Stentgraftmigration beeinflussen, untersucht. Obwohl die numerische Simulation des Blutflusses noch einige Limitationen aufweist, zeigen aktuelle Studien, dass die Methode das Potenzial hat, um in Zukunft eine dedizierte Beurteilung des Rupturrisikos von Aortenaneurysmen vorzunehme

In-vivo flow simulation in coronary arteries based on computed tomography datasets: feasibility and initial results

The purpose of this paper was to non-invasively assess hemodynamic parameters such as mass flow, wall shear stress (WSS), and wall pressure with computational fluid dynamics (CFD) in coronary arteries using patient-specific data from computed tomography (CT) angiography. Five patients (two without atherosclerosis, three with atherosclerosis) underwent retrospectively electrocardiogram (ECG) gated 16-detector row CT using ECG-pulsing and geometric models of coronary arteries were reconstructed for CFD analysis. Blood flow was considered laminar, incompressible, Newtonian, and pulsatile. The mass flow, WSS, and wall pressure were quantified and flow patterns were visualized. The wall pressure continuously decreased towards distal segments and showed pressure drops in stenotic segments. In coronary segments without atherosclerotic wall changes, WSS remained low, even during phases of high flow velocity, whereas in atherosclerotic vessels, the WSS was elevated already at low flow velocities. Stenoses and post-stenotic dilatations led to flow acceleration and rapid deceleration, respectively, including a distortion of flow. Areas of high WSS and high flow velocities were found adjacent to plaques, with values correlating with the degree of stenosis. CFD provided detailed mass flow measurements. CFD analysis is feasible in normal and atherosclerotic coronary arteries and provides the rationale for further investigation of the links between hemodynamic parameters and the significance of coronary stenose

Flow and wall shear stress in end-to-side and side-to-side anastomosis of venous coronary artery bypass grafts

<p>Abstract</p> <p>Purpose</p> <p>Coronary artery bypass graft (CABG) surgery represents the standard treatment of advanced coronary artery disease. Two major types of anastomosis exist to connect the graft to the coronary artery, i.e., by using an end-to-side or a side-to-side anastomosis. There is still controversy because of the differences in the patency rates of the two types of anastomosis. The purpose of this paper is to non-invasively quantify hemodynamic parameters, such as mass flow and wall shear stress (WSS), in end-to-side and side-to-side anastomoses of patients with CABG using computational fluid dynamics (CFD).</p> <p>Methods</p> <p>One patient with saphenous CABG and end-to-side anastomosis and one patient with saphenous CABG and side-to-side anastomosis underwent 16-detector row computed tomography (CT). Geometric models of coronary arteries and bypasses were reconstructed for CFD analysis. Blood flow was considered pulsatile, laminar, incompressible and Newtonian. Peri-anastomotic mass flow and WSS were quantified and flow patterns visualized.</p> <p>Results</p> <p>CFD analysis based on in-vivo CT coronary angiography data was feasible in both patients. For both types of CABG, flow patterns were characterized by a retrograde flow into the native coronary artery. WSS variations were found in both anastomoses types, with highest WSS values at the heel and lowest WSS values at the floor of the end-to-side anastomosis. In contrast, the highest WSS values of the side-to-side anastomosis configuration were found in stenotic vessel segments and not in the close vicinity of the anastomosis. Flow stagnation zones were found in end-to-side but not in side-to-side anastomosis, the latter also demonstrating a smoother stream division throughout the cardiac cycle.</p> <p>Conclusion</p> <p>CFD analysis of venous CABG based on in-vivo CT datasets in patients was feasible producing qualitative and quantitative information on mass flow and WSS. Differences were found between the two types of anastomosis warranting further systematic application of the presented methodology on multiple patient datasets.</p

Computational simulation of intracoronary flow based on real coronary geometry

Objective: To assess the feasibility of computationally simulating intracoronary blood flow based on real coronary artery geometry and to graphically depict various mechanical characteristics of this flow. Methods: Explanted fresh pig hearts were fixed using a continuous perfusion of 4% formaldehyde at physiological pressures. Omnipaque dye added to lead rubber solution was titrated to an optimum proportion of 1:25, to cast the coronary arterial tree. The heart was stabilized in a phantom model so as to suspend the base and the apex without causing external deformation. High resolution computerized tomography scans of this model were utilized to reconstruct the three-dimensional coronary artery geometry, which in turn was used to generate several volumetric tetrahedral meshes of sufficient density needed for numerical accuracy. The transient equations of momentum and mass conservation were numerically solved by employing methods of computational fluid dynamics under realistic pulsatile inflow boundary conditions. Results: The simulations have yielded graphic distributions of intracoronary flow stream lines, static pressure drop, wall shear stress, bifurcation mass flow ratios and velocity profiles. The variability of these quantities within the cardiac cycle has been investigated at a temporal resolution of 1/100th of a second and a spatial resolution of about 10 μm. The areas of amplified variations in wall shear stress, mostly evident in the neighborhoods of arterial branching, seem to correlate well with clinically observed increased atherogenesis. The intracoronary flow lines showed stasis and extreme vorticity during the phase of minimum coronary flow in contrast to streamlined undisturbed flow during the phase of maximum flow. Conclusions: Computational tools of this kind along with a state-of-the-art multislice computerized tomography or magnetic resonance-based non-invasive coronary imaging, could enable realistic, repetitive, non-invasive and multidimensional quantifications of the effects of stenosis on distal hemodynamics, and thus help in precise surgical/interventional planning. It could also add insights into coronary and bypass graft atherogenesi

Derivation of flow related risk indices for stenosed left anterior descending coronary arteries with the use of computer simulations

The geometry of the coronary vessel network is believed to play a decisive role in the initiation, progression and outcome of coronary artery disease (CAD) and the occurrence of acute coronary syndromes (ACS). It also determines the flow field in the coronary artery which can be linked to CAD evolution. In this work geometric 3D models of left anterior descending (LAD) coronary arteries associated with either myocardial infarction (MI) or stable (STA) CAD were constructed. Transient numerical simulations of the flow for each model showed that specific flow patterns develop in different extent in the different groups examined. Recirculation zones, present distal the stenosis in all models, had larger extent and duration in MI cases. For mild stenosis (up to 50%) areas with low time averaged wall shear stress TAWSS (3 Pa) appeared only in MI models; in moderate and severe stenosis (>50%) these areas were present in all models but were significantly larger for MI than STA models. These differentiations were expressed via numerical indices based on TAWSS, oscillating shear index (OSI) and relative residence time (RRT). Additionally we introduced the coagulation activation index (CAI), based on the threshold behaviour of coagulation initiation, which exceeded the suggested threshold only for MI models with intermediate stenosis (up to 50%). These results show that numerical simulations of flow can produce arithmetic indices linked with the risk of CAD complications

Expert recommendations on the assessment of wall shear stress in human coronary arteries : existing methodologies, technical considerations, and clinical applications

The aim of this manuscript is to provide guidelines for appropriate use of CFD to obtain reproducible and reliable wall shear stress maps in native and instrumented human coronary arteries. The outcome of CFD heavily depends on the quality of the input data, which include vessel geometrical data, proper boundary conditions, and material models. Available methodologies to reconstruct coronary artery anatomy are discussed in ‘Imaging coronary arteries: a brief review’ section. Computational procedures implemented to simulate blood flow in native coronary arteries are presented in ‘Wall shear stress in native arteries’ section. The effect of including different geometrical scales due to the presence of stent struts in instrumented arteries is highlighted in ‘Wall shear stress in stents’ section. The clinical implications are discussed in ‘Clinical applications’ section, and concluding remarks are presented in ‘Concluding remarks’ section

Boundary Conditions by Schwarz-Christoffel Mapping in Anatomically Accurate Hemodynamics

ISSN:1573-9686ISSN:0191-5649ISSN:0090-696