A computational study on the influence of catheter-delivered intravascular probes on blood flow in a coronary artery model

Catheter-delivered intravascular probes are widely used in clinical practice to measure coronary arterial velocity and pressure, but the artefactual effect of the probe on the variables being measured is not well characterised. A coronary artery was simulated with a 180 degrees curved tube 3mm in diameter and the effect of catheters of different diameters was modelled numerically under pulsatile flow conditions. The presence of a catheter increased pressure by 1.3-4.3 mmHg depending on its diameter, and reduced velocity-pressure phase-lag. For an ultrasound sample volume 5mm downstream from the probe tip, the underestimation in velocity measurement attributed to catheter blockage is approximately 15-21% for an average inlet velocity of 0.1m/s. The velocity measurement error is lower at higher mean flow velocity. Accuracy of clinical velocity measurements could be improved by moving the sample volume farther downstream from the probe tip, because the centrifugal pressure gradient intrinsic to the curvature promotes re-development of flow.     

A simple coronary blood flow model to study the collateral flow index

Biomechanics and Modeling in Mechanobiology - In this work, we present a novel modeling framework to investigate the effects of collateral circulation into the coronary blood flow physiology. A...     

Influence of model boundary conditions on blood flow patterns in a patient specific stenotic right coronary artery

Background

In literature, the effect of the inflow boundary condition was investigated by examining the impact of the waveform and the shape of the spatial profile of the inlet velocity on the cardiac hemodynamics. However, not much work has been reported on comparing the effect of the different combinations of the inlet/outlet boundary conditions on the quantification of the pressure field and flow distribution patterns in stenotic right coronary arteries.

Method

Non-Newtonian models were used to simulate blood flow in a patient-specific stenotic right coronary artery and investigate the influence of different boundary conditions on the phasic variation and the spatial distribution patterns of blood flow. The 3D geometry of a diseased artery segment was reconstructed from a series of IVUS slices. Five different combinations of the inlet and the outlet boundary conditions were tested and compared.

Results

The temporal distribution patterns and the magnitudes of the velocity, the wall shear stress (WSS), the pressure, the pressure drop (PD), and the spatial gradient of wall pressure (WPG) were different when boundary conditions were imposed using different pressure/velocity combinations at inlet/outlet. The maximum velocity magnitude in a cardiac cycle at the center of the inlet from models with imposed inlet pressure conditions was about 29% lower than that from models using fully developed inlet velocity data. Due to the fact that models with imposed pressure conditions led to blunt velocity profile, the maximum wall shear stress at inlet in a cardiac cycle from models with imposed inlet pressure conditions was about 29% higher than that from models with imposed inlet velocity boundary conditions. When the inlet boundary was imposed by a velocity waveform, the models with different outlet boundary conditions resulted in different temporal distribution patterns and magnitudes of the phasic variation of pressure. On the other hand, the type of different boundary conditions imposed at the inlet and the outlet did not have significant effect on the spatial distribution patterns of the PD, the WPG and the WSS on the lumen surface, regarding the locations of the maximum and the minimum of each quantity.

Conclusions

The observations from this study indicated that the ways how pressure and velocity boundary conditions are imposed in computational models have considerable impact on flow velocity and shear stress predictions. Accuracy of in vivo measurements of blood pressure and velocity is of great importance for reliable model predictions.

     

Combined effects of pulsatile flow and dynamic curvature on wall shear stress in a coronary artery bifurcation model

A three-dimensional model with simplified geometry for the branched coronary artery is presented. The bifurcation is defined by an analytical intersection of two cylindrical tubes lying on a sphere that represents an idealized heart surface. The model takes into account the repetitive variation of curvature and motion to which the vessel is subject during each cardiac cycle, and also includes the phase difference between arterial motion and blood flowrate, which may be nonzero for patients with pathologies such as aortic regurgitation. An arbitrary Lagrangian Eulerian (ALE) formulation of the unsteady, incompressible, three-dimensional Navier-Stokes equations is employed to solve for the flow field, and numerical simulations are performed using the spectral/hp element method. The results indicate that the combined effect of pulsatile inflow and dynamic geometry depends strongly on the aforementioned phase difference. Specifically, the main findings of this work show that the time-variation of flowrate ratio between the two branches is minimal (less than 5%) for the simulation with phase difference angle equal to 90 degrees, and maximal (51%) for 270 degrees. In two flow pulsatile simulation cases for fixed geometry and dynamic geometry with phase angle 270 degrees, there is a local minimum of the normalized wall shear rate amplitude in the vicinity of the bifurcation, while in other simulations a local maximum is observed.     

A simulated dye method for flow visualization with a computational model for blood flow

A numerical dye method for the visualization of unsteady three-dimensional flow calculations is introduced by coupling the unsteady convection-diffusion equation to the Navier-Stokes equation for mass and momentum. This system of equations is descretized using a finite volume projection-like algorithm with generalized coordinates and overset grids. A powerful pressure prediction method is used to accelerate the convergence of the Pressure Poisson equation. To demonstrate the visualization technique, blood flow through the aortic arch region and the three main arterial branches is computed using various Womersley numbers. In this technique, parcels of fluid are followed in time as a function of the cardiac cycle without having to track individual particles, which in turn aids us to better understand some important aspects of the three-dimensionality of the developing unsteady flow. Using this numerical dye method we analyze the strength of the cross flow during the cardiac cycle, the relationship between the penetration of blood into the aortic branches from its relative position in the ascending aortic region and the effects of the Womersley parameter. This technique can be very useful in the design and development of stents where the topology of the device would require understanding where the blood emanating from the heart ends up at the end of the cardiac cycle. Moreover, this method could be useful in investigating the influence of flow and geometry on the local introduction of medication.     

Effects of cyclooxygenase inhibition on canine coronary artery blood flow and thrombosis

This study was designed to determine the effect of inhibitors of cyclooxygenase (COX)-1, COX-2, and the nonselective COX inhibitor naproxen on coronary vasoactivity and thrombogenicity under baseline and lipopolysaccharide (LPS)-induced inflammatory conditions. We hypothesize that endothelial COX-1 is the primary COX isoform in the canine normal coronary artery, which mediates arachidonic acid (AA)-induced vasodilatation. However, COX-2 can be induced and overexpressed by inflammatory mediators and becomes the major local COX isoform responsible for the production of antithrombotic prostaglandins during systemic inflammation. The interventions included the selective COX-1 inhibitor SC-560 (0.3 mg/kg iv), the selective COX-2 inhibitor nimesulide (5 mg/kg iv), or the nonselective COX inhibitor naproxen (3 mg/kg iv). The selective prostacyclin (IP) receptor antagonist RO-3244794 (RO) was used as an investigational tool to delineate the role of prostacyclin (PGI(2)) in modulating vascular reactivity. AA-induced vasodilatation of the left circumflex coronary artery was suppressed to a similar extent by each of the COX inhibitors and RO. The data suggest that AA-induced vasodilatation in the normal coronary artery is mediated by a single COX isoform, the constitutive endothelial COX-1, which is reported to be susceptible to COX-2 inhibitors. The effect of the COX inhibitors on thrombus formation was evaluated in a model of carotid artery thrombosis secondary to electrolytic-induced vessel wall injury. Pretreatment with LPS (0.5 mg/kg iv) induced a systemic inflammatory response and prolonged the time-to-occlusive thrombus formation, which was reduced in the LPS-treated animals by the administration of nimesulide. In contrast, neither SC-560 nor naproxen influenced the time to thrombosis in the animals pretreated with LPS. The data are of significance in view of reported adverse cardiovascular events observed in clinical trials involving the use of selective COX-2 inhibitors, thereby suggesting that the endothelial constitutive COX-1 and the inducible vascular COX-2 serve important functions in maintaining vascular homeostasis.     

A simple model for the two dimensional blood flow in the collapse of veins

Veins in the cardiovascular system may collapse if the internal pressure is less than the external pressure. Such collapse or buckling will have important consequence in terms of the rate of blood flow. Here a steady, parallel unidirectional flow as an exact solution of the continuity and the Navier Stokes equations is constructed. Various stages of the deformation process of the elastic tube (before contact of opposite sides occurring), from an ellipse to a `strongly buckled' configuration, are obtained in analytical forms as a by-product of the calculations. The pressure – area and the pressure – flow rate diagrams computed numerically from the model agree with the trends measured experimentally. Partial Financial Support has been provided by the Research Grants Council Contract HKU 7184/04E.     

Relation between regional function and coronary blood flow reserve in multivessel coronary artery stenosis

In the setting of chronic coronary stenoses, percent wall thickening (%WT) both at rest and during catecholamine stimulation can be abnormal despite normal resting myocardial blood flow (MBF). We hypothesized that this phenomenon is related to abnormal MBF reserve. Accordingly, 15 dogs were studied between 7 and 10 days after placement of Ameroid constrictors around the proximal coronary arteries and their major branches, at a time when collateral development had not yet occurred. %WT and MBF were measured at rest, after 0.56 mg/kg of dipyridamole, and at incremental doses of dobutamine (5-40 microgram. kg(-1). min(-1)). Resting %WT and MBF were normal in all four sham dogs. Resting transmural MBF was normal in all segments in the 11 study dogs, despite reduced (-2 SD of normal) %WT (<30%) in 40 of 82 segments. MBF reserve was reduced (<3) in segments with reduced %WT, and a close coupling was noted between resting %WT and MBF reserve. All segments showed an increase in %WT with dobutamine up to a dose of 20 microgram. kg(-1). min(-1), above which those with abnormal endocardial MBF reserve showed a "biphasic" response. It is concluded that, in the presence of chronic coronary stenoses, abnormalities in resting %WT as well as inducible reduction in %WT during pharmacological stress are related to the degree of abnormal MBF reserve.     

Effect of neurokinin A on human temporal muscle blood flow

The effect of neurokinin A on human temporal muscle blood flow was compared to saline when injected into the muscle in six normal subjects. The 133-Xenon washout technique was used and the test solutions administered in a double-blind, cross-over manner. Neurokinin A (0.02 ml, 10(-5)M) caused a blood flow increase of 193%, while saline caused an increase of 23%. The difference between neurokinin A and saline was significant (p less than 0.05). It is suggested that a possible pathophysiological role of neurokinin A in migraine must involve modulation of vascular response as well as of primary nociception.     

Effect of statins on coronary blood flow after percutaneous coronary intervention in patients with stable coronary artery disease

Aims

Statins have favourable effects on the vascular system. However, few data are available regarding the effect of these drugs on patients undergoing percutaneous coronary intervention (PCI). We sought to determine the impact of prior statin use on coronary blood flow after PCI in patients with stable coronary artery disease (CAD) by using the corrected thrombolysis in myocardial infarction (TIMI) frame count (CTFC).

Methods

A total of 80 consecutive eligible patients (mean age: 60 ± 7 years, 65?% male) with the diagnosis of stable CAD who were hospitalised for elective PCI were retrospectively enrolled in our study. The study population was divided into two groups according to statin use at least 6 months before PCI. Group 1 comprised of 51 patients (67?% male; mean age: 58 ± 4 years) taking statins and group 2 comprised of 29 patients (62?% male; mean age: 60 ± 3 years) not taking statins. PCI was applied to de novo type A lesions. CTFC was calculated for the treated vessels at baseline and after PCI.

Results

The two groups had similar characteristics in terms of age, sex, concomitant medications, lesion characteristics, pre-procedural CTFC, lipid parameters, and risk factors for CAD. Post-PCI CTFC (16 ± 3 vs. 22 ± 5, p = 0.01) and hs-CRP (2.1 ± 0.7 mg/l vs. 6.1 ± 2 mg/l, p = 0.01) in patients receiving statins before PCI were significantly lower than in patients without statin therapy. Multiple logistic regression analysis showed that statin pre-treatment (OR 2.5, 95?% CI 1.2 to 3.8, p < 0.001) and hs-CRP level (OR 1.8, 95?% CI 1.2 to 2.4, p = 0.001) were independent predictors of post-PCI CTFC.

Conclusions

In patients with stable CAD undergoing PCI, receipt of long-term statin therapy was associated with improvement in epicardial perfusion after PCI.

     

A numerical calculation of flow in a curved tube model of the left main coronary artery

The flow pattern in the left main coronary artery has been calculated using an idealized geometry and by numerically solving the full Navier-Stokes equations for a Newtonian fluid. Two different forms for the entrance velocity profile were used, one a time-varying, flat profile and the other a time-varying, less flat velocity profile. The results obtained demonstrate the presence of secondary motions for conditions simulating flow in the left main coronary artery, with maximum secondary flow velocities being on the order of three to four percent of the maximum axial velocity. This secondary flow phenomenon has an important influence on the wall shear stress distribution, in spite of the fact that there is virtually no alteration in the axial velocity profile. The maximum ratio of the outer wall shear stress to that on the inner wall is 1.4 at a Reynolds number of Re = 270, and it increases with increasing Reynolds number, reaching a value of 1.7 at Re = 810. Although there are significant differences in the results in the immediate vicinity of the inlet for the two different forms of the entrance velocity profile used, this difference does not persist far into the tube. Independent of the choice of the entrance velocity profile, it appears that there will be significant secondary flow effects on the wall shear stress.     

Frequency dependence of dynamic curvature effects on flow through coronary arteries

The flow through a curved tube model of a coronary artery was investigated computationally to determine the importance of time-varying curvature on flow patterns that have been associated with the development of atherosclerosis. The entry to the tube was fixed while the radius of curvature varied sinusoidally in time at a frequency of 1 or 5 Hz. Angiographic data from other studies suggest that the radius of curvature waveform contains significant spectral content up to 6 Hz. The overall flow patterns were similar to those observed in stationary curved tubes; velocity profile skewed toward the outer wall, secondary flow patterns, etc. The effects of time-varying curvature on the changes in wall shear rate were expressed by normalizing the wall shear rate amplitude with the shear rate calculated at the static mean radius of curvature. It was found that the wall shear rate varied as much as 94 percent of the mean wall shear rate at the mid wall of curvature for a mean curvature ratio of 0.08 and a 50 percent change in radius of curvature. The effects of 5 Hz deformation were not well predicted by a quasi-static approach. The maximum values of the normalized inner wall shear rate amplitude were found to scale well with a dimensionless parameter equivalent to the product of the mean curvature ratio (delta), normalized change in radius of curvature (epsilon), and a Womersley parameter (alpha). This parameter was less successful at predicting the amplitudes elsewhere in the tube, thus additional studies are necessary. The mean wall shear rate was well predicted with a static geometry. These results indicate that dynamic curvature plays an important role in determining the inner wall shear rates in coronary arteries that are subjected to deformation levels of epsilon delta alpha > 0.05. The effects were not always predictable with a quasi-static approach. These results provide guidelines for constructing more realistic models of coronary artery flow for atherogenesis research.     

A CORF computational model of a simple cell that relies on LGN input outperforms the Gabor function model

Simple cells in primary visual cortex are believed to extract local contour information from a visual scene. The 2D Gabor function (GF) model has gained particular popularity as a computational model of a simple cell. However, it short-cuts the LGN, it cannot reproduce a number of properties of real simple cells, and its effectiveness in contour detection tasks has never been compared with the effectiveness of alternative models. We propose a computational model that uses as afferent inputs the responses of model LGN cells with center–surround receptive fields (RFs) and we refer to it as a Combination of Receptive Fields (CORF) model. We use shifted gratings as test stimuli and simulated reverse correlation to explore the nature of the proposed model. We study its behavior regarding the effect of contrast on its response and orientation bandwidth as well as the effect of an orthogonal mask on the response to an optimally oriented stimulus. We also evaluate and compare the performances of the CORF and GF models regarding contour detection, using two public data sets of images of natural scenes with associated contour ground truths. The RF map of the proposed CORF model, determined with simulated reverse correlation, can be divided in elongated excitatory and inhibitory regions typical of simple cells. The modulated response to shifted gratings that this model shows is also characteristic of a simple cell. Furthermore, the CORF model exhibits cross orientation suppression, contrast invariant orientation tuning and response saturation. These properties are observed in real simple cells, but are not possessed by the GF model. The proposed CORF model outperforms the GF model in contour detection with high statistical confidence (RuG data set: p < 10⁻⁴, and Berkeley data set: p < 10⁻⁴). The proposed CORF model is more realistic than the GF model and is more effective in contour detection, which is assumed to be the primary biological role of simple cells.     

The influence of artery wall curvature on the anatomical assessment of stenosis severity derived from fractional flow reserve: a computational fluid dynamics study

This study aims to investigate the influence of artery wall curvature on the anatomical assessment of stenosis severity and to identify a region of misinterpretation in the assessment of per cent area stenosis (AS) for functionally significant stenosis using fractional flow reserve (FFR) as standard. Five artery models of different per cent AS severity (70, 75, 80, 85 and 90%) were considered. For each per cent AS severity, the angle of curvature of the arterial wall varied from straight to an increasingly curved model (0°, 30°, 60°, 90° and 120°). Computational fluid dynamics was performed under transient physiologic hyperemic flow conditions to investigate the influence of artery wall curvature on the pressure drop and the FFR. The findings in this study may be useful in in vitro anatomical assessment of functionally significant stenosis. The FFR decreased with increasing stenosis severity for a given curvature of the artery wall. Moreover, a significant decrease in FFR was found between straight and curved models discussed for a given severity condition. These findings indicate that the curvature effect was included in the FFR assessment in contrast to minimum lumen area (MLA) or per cent AS assessment. The MLA or per cent AS assessment may lead to underestimation of stenosis severity. From this numerical study, an uncertainty region could be evaluated using the clinical FFR cutoff value of 0.8. This value was observed at 81.98 and 79.10% AS for arteries with curvature angles of 0° and 120° respectively. In conclusion, the curvature of the artery should not be neglected in in vitro anatomical assessment.