Patterns of flow in the left coronary artery

The purpose of this investigation is to describe our preliminary observations of the overall pattern of flow in a mold of the left coronary artery of a pig. Flow in the coronary mold was visualized by the injection of dye into the sinus of Valsalva. Studies were performed during steady flow at rates of 100, 200, 300, 400, and 500 mL/min. Studies were also performed during pulsatile flow, using a pulse duplicator that simulated the magnitude and phasic pattern of coronary flow at rest and during reactive hyperemia. At conditions that simulated rest, mean coronary flow was adjusted to 121 mL/min of which 24 mL/min (20 percent) was systolic. During simulated reactive hyperemia, mean flow was 440 mL/min. Visualization of flow revealed the absence of disturbances of turbulence during both steady and pulsatile flow in the left anterior descending (LAD) and left circumflex (CIRC) coronary arteries throughout the entire range of flow studied. Prominent spiraling of flow occurred during steady and pulsatile flow. Spiraling of flow was not observed in the LAD at rest during pulsatile flow, but developed during simulated reactive hyperemia. Helical flows were observed in the CIRC both during simulated rest and reactive hyperemia. These observations suggest that helical flows may be characteristic features of flow in the left coronary artery; whereas turbulence may not be a feature of this flow field. Whether the spiraling of flow that we observed related to the spiral distribution of early atheroma reported by others, is undetermined.     

Experimental study of pulsatile and steady flow through a smooth tube and an atherosclerotic coronary artery casting of man

In vitro investigation of pulsatile and steady flows through a smooth, straight circular tube and a diseased human coronary artery cast was conducted with sugar-water solutions simulating the viscosity of blood. Time averaged pressure drops for pulsatile flows measured in the circular tube over a Reynolds number ranging from 50 to 1,000 were found to be identical to those for steady flows in the same tube, both of which were in excellent agreement with the Poiseuille flow prediction. For the polyurethane case (# 124) made from a human main coronary with significant but 'non obstructive' diffuse atherosclerotic disease, pressure drops for steady flows were found to be greater than Poiseuille flow predictions by a factor of 3-8 in the physiological Reynolds number range from about 100 to 400. Pulsatile flows in the same artery cast resulted in additional 30% increases in time averaged pressure drops, and thus flow resistance, compared to the steady flow data. Steady and pulsatile flow data measured in a straight, axisymmetric model of cast # 124 showed considerably smaller increases in flow resistance than those observed in # 124 casting.     

Wall shear stress estimates in coronary artery constrictions.

Wall shear stress estimates from laminar boundary layer theory were found to agree fairly well with the magnitude of shear stress levels along coronary artery constrictions obtained from solutions of the Navier Stokes equations for both steady and pulsatile flow. The relatively simple method can be used for in vivo estimates of wall shear stress in constrictions by using a vessel shape function determined from a coronary angiogram, along with a knowledge of the flow rate.     

Differential effects of pulsatile versus steady flow on coronary endothelial membrane potential

Steady shear stress stimulates transient hyperpolarization coupled to calcium-sensitive potassium (KCa) channels and sustained depolarization linked to chloride-selective channels. Physiological flow is pulsatile not static, and whereas in vivo data suggest phasic shear stress may preferentially activate KCa channels, its differential effects on both currents remain largely unknown. To determine this interaction, coronary endothelial cells were cultured in glass capillary flow tubes, loaded with the voltage-sensitive dye bis-(1,3-dibutylbarbituric acid)trimethine oxonol, and exposed to constant or pulsatile shear stress. The latter was generated by a custom servoperfusion system employing physiological pressure and flow waveforms. Steady shear induced a sustained depolarization inhibited by the Cl- channel blocker DIDS. Even after exposure to steady flow, subsequent transition to pulsatile shear stress further stimulated DIDS-sensitive depolarization. DIDS pretreatment "unmasked" a pulsatile flow-induced hyperpolarization of which magnitude was further enhanced by nifedipine, which augments epoxygenase synthesis. Pulse-shear hyperpolarization was fully blocked by KCa channel inhibition (charybdotoxin + apamin), although these agents had no influence on membrane potential altered by steady flow. Thus KCa-dependent hyperpolarization is preferentially stimulated by pulsatile over steady flow, whereas both can stimulate Cl--dependent depolarization. This supports studies showing greater potency of pulsatile flow for triggering KCa-dependent vasorelaxation.     

Flow measurements in a highly curved atherosclerotic coronary artery cast of man.

Flow visualization and wall pressure measurements were made in a polyurethane cast of a cadaver coronary artery with a significant "s" shaped reverse curvature. A sucrose solution was used to simulate the kinematic viscosity of blood, with flow rates in the physiologic range. Flow visualization demonstrated significant secondary flow patterns in the wall vicinity, which increased with increasing Reynolds number. Random dye dispersion was observed at a Reynolds number of about 400, but not at 200. Dye filament patterns in the transition between the first and second curved region were predominantly influenced by the second curved region at lower Reynolds numbers, and by the first curved region at higher Re. Local wall pressure measurements demonstrated a significant centrifugal effect with large radial pressure differences across the casting. Flow resistances for the casting were considerably greater than reference Poiseuille flow values, and increased further with pulsatile flow.     

Flow investigations in a model of a three-dimensional human artery with Newtonian and non-Newtonian fluids. Part I

Together with biochemical factors, fluid mechanical factors play a role in atherogenesis and the deposition of blood platelets at bends and bifurcations in human arteries. Hence, flow patterns were investigated in a simplified 3-dimensional model of a human renal artery bifurcation using Newtonian (aqueous glycerol) and non-Newtonian (aqueous solution of polyacrylamide) fluids. Studies were carried out in steady as well as pulsatile flow at inflow Reynolds numbers of 498 and 951 with flow rate ratios main tube V1: right branch V4: left branch V3 of 1: 0.25: 0.25 and 1: 0.18: 0.18 respectively. The velocity distribution proximal and distal to the bifurcations was measured using a laser-Doppler anemometer. In steady flow, zones of flow separation and reverse flow were observed distal to the bifurcations. In pulsatile flow using non-Newtonian fluids, there was a significant enlargement of these zones. Differences between the Newtonian and non-Newtonian fluids occurred especially distal to the bifurcations. Shear stresses along all measuring positions were computed from the velocity gradients.     

Experimental investigation of branch flow ratio, angle, and Reynolds number effects on the pressure and flow fields in arterial branch models

An experimental investigation was carried out to acquire an understanding of local pressure changes and flow along the main lumen of arterial branch models similar to the femoral artery of man with three different branch angles (30, 60, and 90 deg) and side branch to the main lumen diameter ratio of 0.4. Effects of branch to main lumen flow rate ratios and physiological Reynolds numbers were found to be significant on the local pressure changes, while that of branch angle was also found to be important. The flow visualization study revealed that the flow separated in the main lumen near the branch junction when the pressure rise coefficient along the main lumen was above a critical value (i.e., 0.35 - 0.46), which was observed to be a function of the Reynolds number. The critical value of the branch to main lumen flow rate ratio was found to be about 0.38 - 0.44 also depending on the Reynolds number. Time averaged pressure distributions for pulsatile flow were similar in trend to steady flow values although they differed somewhat in detail in the main lumen in the branch region.     

Epicardial coronary blood flow including the presence of stenoses and aorto-coronary bypasses--I: Model and numerical method

A computer model and numerical method for calculating left epicardial coronary blood flow has been developed. This model employs a finite-branching geometry of the coronary vasculature and the one-dimensional, unsteady equations for flow with friction. The epicardial coronary geometry includes the left main and its bifurcation, the left anterior descending and left circumflex coronary arteries, and a selected number of small branches. Each of the latter terminate in an impedance, whose resistive component is related to intramyocardial compression through a linear dependence on left ventricular pressure. The elastic properties of the epicardial arteries are taken to be non-linear and are prescribed by specifying the local small-disturbance wave speed. The model allows for the incorporation of multiple stenoses as well as aorto-coronary bypasses. Calculations using this model predict pressure and flow waveform development and allow for the systematic investigation of the dependence of coronary flow on various parameters, e.g., peripheral resistance, wall properties, and branching pattern, as well as the presence of stenoses and bypass grafts. Reasonable comparison between calculations and earlier experiments in horses has been obtained.     

Pulsatile blood flow in the entire coronary arterial tree: theory and experiment

The pulsatility of coronary circulation can be accurately simulated on the basis of the measured branching pattern, vascular geometry, and material properties of the coronary vasculature. A Womersley-type mathematical model is developed to analyze pulsatile blood flow in diastole in the absence of vessel tone in the entire coronary arterial tree on the basis of previously measured morphometric data. The model incorporates a constitutive equation of pressure and cross-section area relation based on our previous experimental data. The formulation enables the prediction of the impedance, the pressure distribution, and the pulsatile flow distribution throughout the entire coronary arterial tree. The model is validated by experimental measurements in six diastolic arrested, vasodilated porcine hearts. The agreement between theory and experiment is excellent. Furthermore, the present pulse wave results at low frequency agree very well with previously published steady-state model. Finally, the phase angle of flow is seen to decrease along the trunk of the major coronary artery and primary branches toward the capillary vessels. This study represents the first, most extensive validated analysis of Womersley-type pulse wave transmission in the entire coronary arterial tree down to the first segment of capillaries. The present model will serve to quantitatively test various hypotheses in the coronary circulation under pulsatile flow conditions.     

Is arterial wall-strain stiffening an additional process responsible for atherosclerosis in coronary bifurcations?: an in vivo study based on dynamic CT and MRI

Coronary bifurcations represent specific regions of the arterial tree that are susceptible to atherosclerotic lesions. While the effects of vessel compliance, curvature, pulsatile blood flow, and cardiac motion on coronary endothelial shear stress have been widely explored, the effects of myocardial contraction on arterial wall stress/strain (WS/S) and vessel stiffness distributions remain unclear. Local increase of vessel stiffness resulting from wall-strain stiffening phenomenon (a local process due to the nonlinear mechanical properties of the arterial wall) may be critical in the development of atherosclerotic lesions. Therefore, the aim of this study was to quantify WS/S and stiffness in coronary bifurcations and to investigate correlations with plaque sites. Anatomic coronary geometry and cardiac motion were generated based on both computed tomography and MRI examinations of eight patients with minimal coronary disease. Computational structural analyses using the finite element method were subsequently performed, and spatial luminal arterial wall stretch (LW(Stretch)) and stiffness (LW(Stiff)) distributions in the left main coronary bifurcations were calculated. Our results show that all plaque sites were concomitantly subject to high LW(Stretch) and high LW(Stiff), with mean amplitudes of 34.7 ± 1.6% and 442.4 ± 113.0 kPa, respectively. The mean LW(Stiff) amplitude was found slightly greater at the plaque sites on the left main coronary artery (mean value: 482.2 ± 88.1 kPa) compared with those computed on the left anterior descending and left circumflex coronary arteries (416.3 ± 61.5 and 428.7 ± 181.8 kPa, respectively). These findings suggest that local wall stiffness plays a role in the initiation of atherosclerotic lesions.     

Simulation of coronary artery revascularization

Simulation of the commonly constructed geometries of aorto-coronary bypass anastomoses was carried out using especially fabricated distensible tubes and a pulsatile pump. The system pressure was maintained between 80 and 120 mmHg. The total mean flow was set at 250 ml min-1 (Reynolds number of 200) and the pulsatile frequency was varied from 0 to 2 Hz. A water-glycerine mixture having a density and viscosity similar to that of blood was used throughout. A 16 mm film of the front of black dye injected proximal to the anastomosis was made as the dye approached and passed through the anastomosis. Anastomotic geometries consisted of: end to side, parallel, 45 degree angle, and 90 degree angle. Stenoses, located in the tube representing the coronary artery, were simulated using a bevelled insert which represented an 80-85% area reduction. Flow visualization revealed that distensible tubes gave more realistic flow patterns than rigid tubes, a result particularly evident when a stenosis was present. Pulsatile flow demonstrated considerably more mixing than steady flow. The use of pulsatile flow in distensible tubing with a partial stenosis showed retrograde flow through the stenosis which was not evident for either steady flow or for flow in rigid tubing. The flow at the anastomatic site of the graft having an angle of 0 degrees showed a jetting action with a zone of recirculating fluid being present whereas for a 90 degree graft a distinct helical flow was formed distal to the anastomosis.     

Blood flow patterns in the proximal human coronary arteries: relationship to atherosclerotic plaque occurrence

Atherosclerotic plaques in human coronary arteries are focal manifestations of systemic disease, and biomechanical factors have been hypothesized to contribute to plaque genesis and localization. We developed a computational fluid dynamics (CFD) model of the ascending aorta and proximal sections of the right and left coronary arteries of a normal human subject using computed tomography (CT) and magnetic resonance imaging (MRI) and determined the pulsatile flow field. Results demonstrate that flow patterns in the ascending aorta contribute to a pro-atherosclerotic flow environment, specifically through localization of low and oscillatory wall shear stress in the neighborhood of coronary orifices. Furthermore, these patterns differ in their spatial distribution between right and left coronary arteries. Entrance effects of aortic flow diminish within two vessel diameters. We examined relationships between spatial distributions of wall shear stress and reports of plaque occurrence in the literature. Results indicate low wall shear stress is co-located with increased incidence of lesions, and higher wall shear stresses are associated with lesion-resistant areas. This investigation does not consider plaque progression or advanced lesions, inasmuch as the CFD model was developed from a normal individual and the clinical data used for comparisons were obtained from autopsy specimens of subjects who died from non-cardiovascular causes. The data reported are consistent with the hypothesis that low wall shear stress is associated with the localization of atherosclerotic lesions, and the results demonstrate the importance of aortic flow on flow patterns in the proximal segments of the coronary arteries.     

Fluid particle motion and Lagrangian velocities for pulsatile flow through a femoral artery branch model

A flow visualization study using selective dye injection and frame by frame analysis of a movie provided qualitative and quantitative data on the motion of marked fluid particles in a 60 degree artery branch model for simulation of physiological femoral artery flow. Physical flow features observed included jetting of the branch flow into the main lumen during the brief reverse flow period, flow separation along the main lumen wall during the near zero flow phase of diastole when the core flow was in the downstream direction, and inference of flow separation conditions along the wall opposite the branch later in systole at higher branch flow ratios. There were many similarities between dye particle motions in pulsatile flow and the comparative steady flow observations.     

A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree

Using a frequency-domain Womersley-type model, we previously simulated pulsatile blood flow throughout the coronary arterial tree. Although this model represents a good approximation for the smaller vessels, it does not take into account the nonlinear convective energy losses in larger vessels. Here, using Womersley's theory, we present a hybrid model that considers the nonlinear effects for the larger epicardial arteries while simulating the distal vessels (down to the 1st capillary segments) with the use of Womersley's Theory. The main trunk and primary branches were discretized and modeled with one-dimensional Navier-Stokes equations, while the smaller-diameter vessels were treated as Womersley-type vessels. Energy losses associated with vessel bifurcations were incorporated in the present analysis. The formulation enables prediction of impedance and pressure and pulsatile flow distribution throughout the entire coronary arterial tree down to the first capillary segments in the arrested, vasodilated state. We found that the nonlinear convective term is negligible and the loss of energy at a bifurcation is small in the larger epicardial vessels of an arrested heart. Furthermore, we found that the flow waves along the trunk or at the primary branches tend to scale (normalized with respect to their mean values) to a single curve, except for a small phase angle difference. Finally, the model predictions for the inlet pressure and flow waves are in excellent agreement with previously published experimental results. This hybrid one-dimensional/Womersley model is an efficient approach that captures the essence of the hemodynamics of a complex large-scale vascular network. The present model has numerous applications to understanding the dynamics of coronary circulation.     

Pulsatile flow through a constricted tube: effect of stenosis morphology on hemodynamic parameters

In this paper, we investigate pulsatile flow through a constricted tube with the aim of assessing the effect of stenosis morphology on hemodynamic parameters. The fluid-solid interaction of pulsatile flow through a compliant tube with elastic walls was simulated using an arbitrary Lagrangian-Eulerian (ALE) finite-element method. We consider blood flow through various mild stenoses of 25.8% severity in diameter with trapezoidal and bell-like morphologies at a fixed Womersley number of 7.75. The results show that the distribution of the time-averaged wall shear stress (TAWSS), which is the main factor affecting the hemodynamic parameters, strongly depends on the axial stretch of the stenosis; elongation of the stenotic region increases by 41.1% the maximum TAWSS for stenoses of trapezoidal morphology whereas the maximum TAWSS decreases by 14.8% for the corresponding stenoses of bell-like morphology. The present findings indicate that risk factors due to atherosclerosis may vary in a complicated manner as an atheromatous plaque gradually builds up and morphs with time.     

Pulmonary capillaries are recruited during pulsatile flow.

Capillaries recruit when pulmonary arterial pressure rises. The duration of increased pressure imposed in such experiments is usually on the order of minutes, although recent work shows that the recruitment response can occur in <4 s. In the present study, we investigate whether the brief pressure rise during cardiac systole can also cause recruitment and whether the recruitment is maintained during diastole. To study these basic aspects of pulmonary capillary hemodynamics, isolated dog lungs were pump perfused alternately by steady flow and pulsatile flow with the mean arterial and left atrial pressures held constant. Several direct measurements of capillary recruitment were made with videomicroscopy. The total number and total length of perfused capillaries increased significantly during pulsatile flow by 94 and 105%, respectively. Of the newly recruited capillaries, 92% were perfused by red blood cells throughout the pulsatile cycle. These data provide the first direct account of how the pulmonary capillaries respond to pulsatile flow by showing that capillaries are recruited during the systolic pulse and that, once open, the capillaries remain open throughout the pulsatile cycle.     

Effects of diagnostic guidewire catheter presence on translesional hemodynamic measurements across significant coronary artery stenoses

This study gains insight on the nature of flow blockage effects of small guidewire catheter sensors in measuring mean trans-stenotic pressure gradients Deltap across significant coronary artery stenoses. Detailed pulsatile hemodynamic computations were made in conjunction with previously reported clinical data in a group of patients with clinically significant coronary lesions before angioplasty. Results of this study ascertain changes in hemodynamic conditions due to the insertion of a guidewire catheter (di=0.46 mm) across the lesions used to directly determine the mean pressure gradient (Deltap) and fall in distal mean coronary pressure (pr). For the 32 patient group of Wilson et al. [1988] (minimal lesion diameter dm=0.95 mm; 90% mean area stenosis; proximal measured coronary flow reserve (CFR) of 2.3 in the abnormal range) the diameter ratio of guidewire catheter to minimal lesion was 0.48, causing a tighter "artifactual" mean area stenosis of 92.1%. The results of the computations indicated a significant shift in the Deltap-Q relation due to guidewire induced increases in flow resistances (R=Deltap/Q) of 110% for hyperemic flow, a 35% blockage in hyperemic flow (Qh) and a phase shift of the coronary flow waveform to systolic predominance. These alterations in flow resulted in a fall in distal mean coronary pressure (at lower mean flow rates) below the patho-physiological range of prh approximately 55 mmHg, which is known to cause ischemia in the subendocardium (Brown et al. [1984]) and coincides with symptomatic angina. Transient wall shear stress levels in the narrow throat region (with flow blockage) were of the order of levels during hyperemic conditions for patho-physiological flow. In the separated flow region along the distal vessel wall, vortical flow cells formed periodically during the systolic phase when instantaneous Reynolds numbers Ree(t) exceeded about 110. For patho-physiological flow without the presence of the guidewire these vortical flow cells were much stronger than in the more viscous flow regime with the guidewire present. The non-dimensional pressure data given in tabular form may be useful in interpretation of guidewire measurements done clinically for lesions of similar geometry and severity.     

Effects of gradual expansign on arterial stenosis

The blood flow through an arterial stenosis can theoretically be increased by gradual expansion of the stenosis. This hypothesis was tested by comparing the flow through abruptly expanding and gradually expanding stenosed plastic conduits. The conduits were tested in non-pulsatile flow with water and bank blood and in pulsatile flow in dog's descending aorta. It was found that:

1. (a)
   The pressure drop in arterial stenoses is larger than that predicted by non-pulsatile theory.     
   
   

In-vitro pulsatile flow visualization studies in a pulmonary artery model

In-vitro pulsatile flow visualization studies were conducted in an adult-sized pulmonary artery model to observe the effects of valvular pulmonic stenosis on the flow fields of the main, left and right pulmonary arteries. The flow patterns revealed that as the degree of stenosis increased, the jet-type flow created by the valve became narrower, and it impinged on the far (distal) wall of the left pulmonary artery further downstream from the junction of the bifurcation. This in turn led to larger regions of disturbed turbulent flow, as well as helical-type secondary flow motions in the left pulmonary artery, compared to the right pulmonary artery. The flow field in the main pulmonary artery also became more disturbed and turbulent, especially during peak systole and the deceleration phase. The flow visualization observations have been valuable in helping to conduct further quantitative studies such as pressure and velocity field mapping. Such studies are important to understanding the fluid mechanics characteristics of the main pulmonary artery and its two major branches.