Frederick J. Walburn

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.

TURBULENT STRESSES IN THE REGION OF AORTIC AND PULMONARY VALVES.

The specific features of turbulent flow that are likely to be damaging to the blood cells and platelets are the stresses which are intrinsic to turbulence, known as Reynolds stresses. These include normal stresses as well as shear stresses. The purpose of this study is to determine the magnitude of the turbulent stresses that may occur during ejection in the vicinity of normal and diseased aortic valves near normal pulmonary valves. Both Reynolds normal stresses and Reynolds shear stresses were calculated from velocities obtained in vitro with a laser Doppler anemometer in the region of two severely stenotic and regurgitant human aortic valves. Reynolds normal stresses were also calculated from velocities obtained with a hot-film anemometer in 21 patients in the region of normal and diseased aortic valves. In seven of these patients, it was calculated in the region of the normal pulmonary valve. The Reynolds normal stress in patients with combined aortic stenosis and insufficiency was prominently higher than in patients with normal valves. In the former, the Reynolds normal stress during ejection transiently reached 18,000 dynes/cm2. This was in the range of the Reynolds normal stress observed in vitro. The Reynolds shear stress measured in vitro transiently reached 11,900 dynes/cm2 during ejection. Because the Reynolds normal stresses in the presence of the severely stenotic and regurgitant valves were comparable in vitro and in patients, it is likely that the Reynolds shear stress in patients is also comparable to values measured in vitro. These values were well above the stresses which, when sustained, have been shown to have a damaging effect upon blood cells and platelets.

Flow Visualization in a Mold of an Atherosclerotic Human Abdominal Aorta

Flow in a mold of an atherosclerotic human abdominal aorta and common iliac arteries was studied by flow visualization at a mean Reynolds number of 500 during both pulsatile and steady flow. Flow separation and transient flow reversals were found distal to atherosclerotic plaques during pulsatile flow; whereas flow separation resulting in regions of permanent eddies were observed distal to plaques only during steady flow.

Wall shear stress during pulsatile flow distal to a normal porcine aortic valve

The shear stress at the wall has been of interest as one of the possible fluid dynamic factors that may be damaging in the region of prosthetic valves. The purpose of this study was to measure the axial wall shear stresses in the region of a 29 mm tissue annulus diameter porcine stent mounted prosthetic aortic valve (Hancock, Model 242). Studies were performed in an in vitro pulse duplicating system. The axial wall shear stress was calculated from velocities obtained near the wall with a laser Doppler anemometer. The largest axial wall shear stress was 29 dyn cm-2 and it occurred at the highest stroke volume used (80 ml). At a stroke volume of 50 ml, the largest axial wall shear stress was 17 dyn cm-2 and at a stroke volume of 35 ml, it was 15 dyn cm-2. Stresses of these magnitudes are far below those reported to be damaging to the endothelial surface. These stresses may be high enough, however, to affect platelet function.

Turbulent Stresses in the Region of a Hancock Porcine Bioprosthetic Aortic Valve

The purpose of this study was to measure stresses associated with turbulence (Reynolds stresses), in the region of a 29-mm-dia porcine bioprosthetic valve (Hancock, Model 242). Studies were performed in an in vitro pulse duplicating system with the valve mounted in the aortic position. The Reynolds stresses were calculated from velocities obtained with a two channel laser Doppler anemometer. The largest Reynolds shear stress and normal stress occurred at the highest stroke volume used (80 mL). Averaged over ejection they were 38 dynes/cm2 and 380 dynes/cm2, respectively. The maximal instantaneous Reynolds shear stress was 2500 dynes/cm2 and the maximal instantaneous Reynolds normal stress was 6800 dynes/cm2. Stresses of these magnitudes are in the range reported to damage platelets.

The shear rate at the wall in a symmetrically branched tube simulating the aortic bifurcation

The purpose of this study was to determine the shear rate at the wall in a symmetrically branched tube with a branch-to-trunk area ratio and angle of branching that were comparable to the human abdominal aorta. Velocity profiles were measured with a laser Doppler anemometer during steady and pulsatile flow in which the mean Reynolds numbers were 500, 1000, and 1500. During both steady and pulsatile flow, as the Reynolds numbers increased, the shear rates at the inner wall of the branch increased. Only slight increments of the shear rates occurred along the outer wall of the branch, however, as the Reynolds number increased. No reversals of flow were observed at any Reynolds number during steady flow. Transient reversals of flow (causing negative shear rates) occurred along the outer wall of the branch at a Reynolds number of 500; but such transient flow reversals were not observed at the higher Reynolds numbers during pulsatile flow.

Effect of Vessel Tapering on the Transition to Turbulent Flow: Implications in the Cardiovascular System

The purpose of this study is to explore the effect of tapering upon the tendency of flow to become turbulent in straight symmetric tubes. Velocity was measured with a flow to become turbulent in straight symmetric tubes. Velocity was measured with a laser Doppler anemometer in plexiglass tubes which tapered 0.5 deg, 1.5 deg, and 2.5 deg measured from the centerline to the wall. These angles were comparable to the angles of tapering observed in the abdominal aorta of normal subjects, 1.5 deg +/- 0.2 deg (mean +/- SEM) (range 0 deg to 3 deg). The transition Reynolds number (based on the diameter of the tube at the point of measurement) increased as the angle of tapering increased. When the angle of tapering was constant, the transition Reynolds number increased with increasing distance into the tapered section. These observations suggest that tapering of the abdominal aorta tends to promote laminar flow.

Estimation of Reynolds shear stresses during pulsatile flow in the region of aortic valves.

Some investigators have attempted to estimate the Reynolds shear stress on the basis of a single component of velocity. The purpose of this investigation is to determine the validity of such estimates in a complex flow field, such as occurs in the cardiovascular system in the region of the aortic valve. Turbulent velocities were obtained in an in vitro pulse duplicating system with a two-channel laser Doppler anemometer. Velocities were measured in the region of two stenotic natural aortic valves and a normal stent mounted porcine bioprosthetic valve. Constants of proportionality between the Reynolds shear stress, averaged over ejection, and the Reynolds normal stress were determined. The constants of proportionality depended uppn the local conditions, namely, whether the valves were stenotic or normal bioprosthetic. There was wide scatter of data. This suggests that any estimate of the Reynolds shear stress, based upon a single axial velocity in a complex flow field, such as occurs in the cardiovascular system, is likely to be inaccurate.

Construction of Molds of Complex Arterial Segments

Molds of arterial segments would be advantageous for in-vitro assessments of arterial flow dynamics. Previous techniques have been limited because of their technical difficulty or because they were limited to short planar segments. This paper presents a method, based on the lost wax technique, that is readily accomplished, and permits the fabrication of a mold of any arterial bed, irrespective of its complexity.

Flow characteristics in symmetrically branched tubes simulating the human aortic bifurcation.

The purpose of this study was to investigate the characteristics of flow in a symmetrically branched tube that had an area ratio (0.8) and angle of branching (70 deg) that were comparable to the human descending aorta. Velocity profiles were measured in steady and pulsatile flow with a laser Doppler anemometer. A region of transient flow reversal was found along the outer wall during minimal flow in the pulsatile cycle. Flow separation did not occur. For both steady and pulsatile flow, the shear rates were higher along the inner wall and lower along the outer wall in the region of the vertex of the bifurcation.