Streamline pattern and velocity components of flow in a model of a branching coronary vessel--possible functional implication for the development of localized platelet deposition in vitro

Formation of Vortices in Idealised Branching Vessels: A CFD Benchmark Study

PURPOSE

Atherosclerosis preferentially occurs near the junction of branching vessels, where blood recirculation tends to occur (Malek et al. in J Am Med Assoc 282(21):2035-2042, 1999, https://doi.org/10.1001/jama.282.21.2035 ). For decades, CFD has been used to predict flow patterns such as separation and recirculation zones in hemodynamic models, but those predictions have rarely been validated with experimental data. In the context of verification and validation (V&V), we first conduct a CFD benchmark calculation that reproduces the vortex detection experiments of Karino and Goldsmith (1980) with idealised branching blood vessels (Karino and Goldsmith in Trans. Am. Soc. Artif. Internal Organs 26:500-506, 1980). The critical conditions for the formation of recirculation vortices, the so-called critical Reynolds numbers, are the main parameters for comparison with the experimental data to demonstrate the credibility of the CFD workflow. We then characterise the wall shear stresses and develop a surrogate model for the size of formed vortices.

METHODS

An automated parametric study generating more than 12,000 CFD simulations was performed, sweeping the geometries and flow conditions found in the experiments by Karino and Goldsmith. The flow conditions were restricted to steady-state laminar flow, with a range of inflow Reynolds numbers up to 350, with various flow ratios between the main branch outlet and side branch outlet. The side branch diameter was scaled relative to the main branch diameter, ranging from 1.05/3 to 3/3; and the branching angles ranged in size from [Formula: see text] to [Formula: see text]. Recirculation vortices were detected by the inversion of the velocity vector at certain locations, as well as by the inversion of the wall shear stress (WSS) vector.

RESULTS

The CFD simulations demonstrated good agreement with the experimental data on the critical Reynolds numbers. The spatial distributions of WSS on each branch were analysed to identify potential regions of disease. Once a vortex is formed, the size of the vortex increases by the square root of the Reynolds number. The CFD data was fitted to a surrogate model that accurately predicts the vortex size without the need to run computationally more expensive CFD simulations.

CONCLUSIONS

This benchmark study validates the CFD simulation of vortex detection in idealised branching vessels under comprehensive flow conditions. This work also proposes a surrogate model for the size of the vortex, which could reduce the computational requirements in the studies related to branching vessels and complex vascular systems.

CFD modeling of blood flow following coil embolization of aneurysms

In case of coil embolization of a giant or a multilobular aneurysm, it is difficult to fill an aneurysm sac completely with coils, therefore, partial blocking of an aneurysm sac is inevitable. Blood flow characteristics, which may influence embolization process of an aneurysm, are affected by the locations of coils for partially blocked aneurysms. Blood flow fields inside an aneurysm are also influenced by the geometry of a parent vessel. In order to suggest the coil locations effective for aneurysm embolization, the blood flow fields of lateral aneurysm models were analyzed for different coil locations and parent vessel geometries. Flow rate into an aneurysm sac from a parent vessel (inflow rate) and wall shear stress were also calculated. Inflow rates were smaller and low wall shear regions were larger in the distal neck blocked model comparing to the dome blocked models. In the distal neck blocked model, inflow volume was smaller by 31% (straight parent vessel model) and 34% (curved parent vessel model) comparing to other models. The time averaged values of normalized low wall shear regions were 4% and 12% greater in the distal neck blocked models with a straight and a curved parent vessel, respectively. Since smaller inflow and low wall shear stress provide hemodynamic environment promoting thrombus embolization, distal neck should be the effective coil location for aneurysm embolization.

Is primary haemostasis controlled by a 'platelet delay time'? Formulation of a new hypothesis

A simple physical model is able to adequately describe platelet thrombus formation during primary haemostasis ex vivo, under the assumption of a 'platelet delay time' (Pdel), which is defined as the difference between the moment of platelet adhesion (to collagen or to another adherent platelet) and the time when the newly adherent platelet allows another platelet to adhere. Pdel was estimated with an ex vivo model of primary haemostasis (modified PFA-100, Dade Behring, Marburg). ADP and epinephrine test cartridges were perfused with human anticoagulated blood of control persons using a pressure/flow clamp technique (Kretschmer V, et al. Platelets 2001; 12: 462-9). Platelets gradually occluded the aperture in the test system. Pressure (p) across and flow (Q) through the aperture were measured versus time. The change of the aperture radius versus time (dr/dt) was calculated from p and Q using the Law of Hagen-Poiseuille. The surprising result was a constant decay of dr/dt (Rsqu approximately 0.996), in spite of a 5-fold increase in the shear- and transport-rates of platelets. This can be explained by postulating the existence of a Pdel, which was estimated as 2.89 s for collagen/ADP and 4.62 s in collagen/epinephrine test cartridges. This new hypothesis explains for the first time the relative independence of in vivo and ex vivo bleeding time on blood platelet concentrations, a well known observation at platelet counts higher than 40,000/microl. If the described physical model is correct, platelet thrombus growth rate is strongly decreased as a consequence of Pdel in extreme arterial flow conditions. A preliminary report of these experiments has been published (Kratzer MAA, Platelets 2002; 13: 344).

Platelet deposition in stagnation point flow: an analytical and computational simulation

A mathematical and numerical model is developed for the adhesion of platelets in stagnation point flow. The model provides for a correct representation of the axi-symmetric flow and explicitly uses shear rate to characterise not only the convective transport but also the simple surface reaction mechanism used to model platelet adhesion at the wall surface. Excellent agreement exists between the analytical solution and that obtained by the numerical integration of the full Navier--Stokes equations and decoupled conservation of species equations. It has been shown that for a constant wall reaction rate modelling platelet adhesion the maximum platelet flux occurs at the stagnation point streamline. This is in direct contrast to that found in experiment where the maximum platelet deposition occurs at some distance downstream of the stagnation point. However, if the wall reaction rate is chosen to be dependent on the wall shear stress then the analysis shows that the maximum platelet flux occurs downstream of the stagnation point, providing a more realistic model of experimental evidence. The analytical formulation is applicable to a large number of two-dimensional and axi-symmetrical surface reaction flows where the wall shear stress is known a priori.

Experimental analysis of flow calculations based on HRCT imaging of individual bifurcations

Flow simulations in airways and arteries allow the non-invasive study of transport and deposition processes in these vessel systems. Individual vessel geometries as input for such simulations are highly desirable. Computed tomography (CT) permits the acquisition of binary data to reconstruct such geometries. To prove the suitability of this reconstruction method, we compared measured with simulated velocities within model bifurcations. Particle image velocimetry was applied to measure flow velocities. Numerical simulations of these velocities were carried out by using the CT data of the same models as input to flow calculations (CFD). Within the resolution limits good agreement between measured and simulated velocities was found. For the smallest bifurcation (tube diameter: 2 mm) the agreement was less, indicating a methodical limitation by the actual resolution of the CT-scan technique. The study showed that a combination of CT and CFD can be considered as an appropriate step towards realistic simulations of particle transportation and deposition in individual geometries of the respiratory or cardiovascular systems.

Flow mediated fibrin thrombus formation in an endothelium-lined model of arterial branching

In vivo arterial thrombosis occurs preferentially at curvatures and branchings, i.e. regions of flow separation and recirculation where blood is retained orders of magnitude longer than within straight vessel sections. To examine the effect of such disturbed flow on endothelial thromboresistance glass T-branchings lined with endothelial cells from human umbilical cord veins (HUVEC) were perfused with buffered fibrinogen solution (3mg/ml). The flow was adjusted to form a large recirculation zone and flow conditions were determined beforehand by means of flow visualization via dye injection as well as by laser ultramicroscope anemometry. Thrombus formation, which was registered on-line by video and evaluated planimetrically, was induced by injection of thrombin at concentrations ranging from 0.3 to 2.0 units/ml. Fibrin thrombus growth always began within the flow niche at the point of flow separation and extended downstream along the wall and into the vessel lumen finally occluding up to 80% of the lumen. Light and electron microscopy revealed that overall thrombus form as well as the orientation of single fibrin fibers were correlated strictly to the prevailing streamlines. Despite the integrity of the endothelial lining fibrin thrombus formation occurred. The fibrin fibers closely contacted the endothelial surface. These results indicate that recirculation zones promote fibrin thrombus formation sufficient to obstruct the vessel lumen and that intact endothelium alone is insufficient in preventing adhesion of fibrin to its surface.

A method for quantitative determination of flow induced human platelet adhesion and aggregation

Adhesivity and aggregability of blood platelets may reflect normal and diseased states. A quantitative assessment of such reactivity should thus provide further insight into disease mechanism. The well defined conditions of stagnation point flow using platelet-rich-plasma (PRP) as fluid permit quantitative treatment of the formation of platelet microthrombi on the stagnation plate. By measuring the growth kinetics (photometry) and corresponding morphology (light- and electron microscopy) of the microthrombus, platelet adhesion as well as aggregation could be analyzed separately by means of a quantitative procedure. Parameters are evaluated for PRP samples obtained from patients exhibiting deep venous thrombosis, arterial angiopathy or myocardial infarction, respectively. The results obtained demonstrate the usefulness of the proposed method for quantifying platelet reactivity as reflected by type and degree of flow induced platelet deposition. This, in turn, provides a basis for correlating the in vitro findings with the disease state.