A numerical study of blood flow patterns in anatomically realistic and simplified end-to-side anastomoses

PURPOSE

Recently, some numerical and experimental studies of blood flow in large arteries have attempted to accurately replicate in vivo arterial geometries, while others have utilized simplified models. The objective of this study was to determine how much an anatomically realistic geometry can be simplified without the loss of significant hemodynamic information.

METHOD

A human femoral-popliteal bypass graft was used to reconstruct an anatomically faithful finite element model of an end-to-side anastomosis. Nonideal geometric features of the model were removed in sequential steps to produce a series of successively simplified models. Blood flow patterns were numerically computed for each geometry, and the flow and wall shear stress fields were analyzed to determine the significance of each level of geometric simplification.

RESULTS

The removal of small local surface features and out-of-plane curvature did not significantly change the flow and wall shear stress distributions in the end-to-side anastomosis. Local changes in arterial caliber played a more significant role, depending upon the location and extent of the change. The graft-to-host artery diameter ratio was found to be a strong determinant of wall shear stress patterns in regions that are typically associated with disease processes.

CONCLUSIONS

For the specific case of an end-to-side anastomosis, simplified models provide sufficient information for comparing hemodynamics with qualitative or averaged disease locations, provided the "primary" geometric features are well replicated. The ratio of the graft-to-host artery diameter was shown to be the most important geometric feature. "Secondary" geometric features such as local arterial caliber changes, out-of-plane curvature, and small-scale surface topology are less important determinants of the wall shear stress patterns. However, if patient-specific disease information is available for the same arterial geometry, accurate replication of both primary and secondary geometric features is likely required.

Effects of ethacrynic acid on Schlemm's canal inner wall and outflow facility in human eyes

PURPOSE

The role of the inner wall of Schlemm's canal in determining aqueous outflow facility is poorly understood. To quantify the relationship between inner wall pore characteristics and aqueous outflow facility in human eyes, both control eyes and eyes in which facility had been pharmacologically increased by ethacrynic acid (ECA) infusion were studied.

METHODS

Outflow facility was measured in enucleated human eyes before and after delivery of 0.25 mM ECA (one eye of each of 6 pairs) or 2.5 mM ECA (one eye of each of 13 pairs). ECA, and vehicle in contralateral eyes, was delivered into Schlemm's canal by retroperfusion, thereby largely avoiding drug exposure to the trabecular meshwork. After facility measurement, eyes were fixed under conditions of either constant pressure (physiological intraocular pressure, 13 pairs) or "equal flow" (6 pairs) and were microdissected to expose the inner wall of Schlemm's canal. The density and diameter of intercellular and intracellular inner wall pores were measured using scanning electron microscopy.

RESULTS

Retroperfusion with 2.5 mM ECA increased facility by 73% (P < 0.001), whereas 0.25 mM ECA increased facility by 19% (not statistically significant). The density of intercellular pores in the inner wall of Schlemm's canal was increased by 520% in 2.5 mM ECA-retroperfused eyes (P < 0.00004), whereas intracellular pore density remained approximately constant. Large pores (size > or = 1.1 microm) were particularly enhanced in ECA retroperfused eyes. The net change in facility due to ECA was not correlated with changes in pore density or other inner wall pore statistics.

CONCLUSIONS

Our data are most consistent with a model in which pores in the inner wall of Schlemm's canal indirectly influence facility. However, measured changes in facility due to changes in inner wall properties did not agree with quantitative predictions of the pore funneling theory, suggesting that changes in facility may instead be due to gel leakage from the extracellular spaces of the juxtacanalicular tissue. More definitive experiments are required to confirm this hypothesis.

Enthacrynic and acid effects on inner wall pores in living monkeys

PURPOSE

The influence of the inner wall of Schlemm's canal on aqueous outflow facility remains poorly understood. We examined the relationship between inner wall pore characteristics and outflow facility in living primate eyes in which facility had been pharmacologically increased by ethacrynic acid (ECA) infusion and in contralateral control eyes.

METHODS

Outflow facility (two-level constant pressure perfusion) was measured in eight pairs of living monkey eyes before and after administration of a bolus dose of either 0.125 mM ECA or vehicle. After exsanguination, eyes were fixed in situ under constant-pressure conditions (mean fixation pressure approximately 19 mm Hg). The density and diameter of inner wall pores and the number and area of platelet aggregates on the inner wall of Schlemm's canal were measured by scanning electron microscopy.

RESULTS

In ECA-treated eyes, outflow facility increased 63% (P < 0.0001), intracellular pore density decreased 46% (P = 0.0094), intracellular pore size increased 27% (P = 0.049), platelet aggregate density increased 158% (P < 0.0001), and area covered by platelets increased 210% (P = 0.012) relative to contralateral controls. Although the average density and size of intercellular pores were essentially unaffected by ECA, an increased density of large (> or = 1.90 microm) intercellular pores was seen in ECA-treated eyes. The density of intracellular pores increased with the duration of fixative perfusion. Other than a weak negative correlation between outflow facility and intracellular pore density in ECA-treated eyes (P = 0.052), facility was not correlated with inner wall pore features.

CONCLUSIONS

Our data are most consistent with a scenario in which ECA promotes formation of large intercellular pores in the inner wall of Schlemm's canal, which are then masked by platelet aggregates. Masking of intercellular pores, combined with fixation-induced alteration of inner wall pore density, greatly complicates attempts to relate facility to inner wall structure and suggests that in vivo pore density is smaller than in fixed tissue. Additionally, facility-influencing effects of ECA on the juxtacanalicular tissue cannot be excluded.

Accuracy of computational hemodynamics in complex arterial geometries reconstructed from magnetic resonance imaging

PURPOSE

Combining computational blood flow modeling with three-dimensional medical imaging provides a new approach for studying links between hemodynamic factors and arterial disease. Although this provides patient-specific hemodynamic information, it is subject to several potential errors. This study quantifies some of these errors and identifies optimal reconstruction methodologies.

METHODS

A carotid artery bifurcation phantom of known geometry was imaged using a commercial magnetic resonance (MR) imager. Three-dimensional models were reconstructed from the images using several reconstruction techniques, and steady and unsteady blood flow simulations were performed. The carotid bifurcation from a healthy, human volunteer was then imaged in vivo, and geometric models were reconstructed.

RESULTS

Reconstructed models of the phantom showed good agreement with the gold standard geometry, with a mean error of approximately 15% between the computed wall shear stress fields. Reconstructed models of the in vivo carotid bifurcation were unacceptably noisy, unless lumenal profile smoothing and approximating surface splines were used.

CONCLUSIONS

All reconstruction methods gave acceptable results for the phantom model, but in vivo models appear to require smoothing. If proper attention is paid to smoothing and geometric fidelity issues, models reconstructed from MR images appear to be suitable for use in computational studies of in vivo hemodynamics.

Two pore types in the inner-wall endothelium of Schlemm's canal

PURPOSE

It has been reported that fixation conditions significantly influence the apparent pore density in the inner-wall endothelium of Schlemm's canal. In the present study, the manner in which fixation conditions affect the two subtypes of inner-wall pores, intracellular pores and intercellular (or border) pores, was investigated.

METHODS

Outflow facility was measured in enucleated human eyes. Eyes were fixed under constant flow" or constant pressure conditions, microdissected to expose the inner wall of Schlemm's canal, and prepared for scanning electron microscopy. The density and diameter of the two subtypes of pores in the inner wall were measured.

RESULTS

Intracellular pore density decreased with increasing postmortem time (P < 0.001) and increased with increasing volume of fixative passed through the outflow pathway (P < 0.001), whereas border pore density showed no dependence on these parameters (P > 0.25 and P > 0.15, respectively). Border pore density increased with increasing fixation pressure (P < 0.005), even though intracellular pore density showed no such dependence (P > 0.4). No correlation was found between outflow facility and the predictions of Poiseuille's law, Sampson's law, or the funneling theory for the hydraulic conductivity of the intracellular pores (P > 0.35) or the border pores (P > 0.1).

CONCLUSIONS

The intracellular and border pores form two morphologically and functionally distinct populations in the inner wall of Schlemm's canal. The dependence of intracellular pore density on postmortem time and on volume of fixative passed through the outflow pathway suggests that these pores are artifacts of tissue fixation or processing conditions. That border pores do not depend on such conditions and that their presence is correlative with perfusion pressure suggests that this population may be nonartifactual. New histologic techniques for examining the inner wall of Schlemm's canal are necessary to determine the in vivo state of inner-wall pores and how they influence outflow facility.

Study of regional deformation of the optic nerve head using scanning laser tomography

PURPOSE

Previous studies have suggested that IOP-induced deformation of the optic nerve head (ONH) at the level of the lamina cribrosa may contribute to axonal damage in glaucomatous optic neuropathy. Our purpose was to introduce a novel enucleated eye model for characterizing acute IOP-induced changes in ONH topography, and to develop improved analytical methods for detection of regional topographic change in the ONH.

METHODS

Using a specially designed experimental apparatus, enucleated human eyes were progressively pressurized to 5, 15, 30, and 50 mmHg. Seven topographic images of the optic disc were taken at each pressure by a scanning laser tomographer (Heidelberg Retina Tomograph-HRT). The dependence of ONH topography on IOP was quantified for the entire nerve using standard HRT indices of ONH topographic change. The supero-inferior and nasal-temporal hemifields were also analyzed. A new method of analysis was developed which computes the location of the point of maximum slope within a 10 degrees sector of the ONH, as well as the magnitude of this slope. This method, termed "Inflection Point Analysis," was designed to be robust to the potential artefacts of image translation, reference plane location, and the subjective determination of ONH limits.

RESULTS

The results of three eyes are presented to illustrate the techniques. In our enucleated eye model, average ONH depth progressively increased with IOP, showing a maximum average posterior displacement of 36 microm as IOP was changed from 5 to 50 mmHg. Significant regional variability in ONH displacement was observed, which both Inflection Point Analysis and standard HRT parameters were able to detect. Inflection point analysis showed several advantages over standard HRT parameters: it was insensitive to artefacts due to tilt, was able to objectively delineate the boundary between the optic cup and neuroretinal rim, and was able to sensitively track changes in the location of this margin.

CONCLUSIONS

Scanning laser tomography is capable of detecting regional variation in the deformation of the ONH in response to acute changes in IOP. Our enucleated eye model and Inflection Point Analysis are promising tools for basic studies of ONH deformation in response to IOP. More extensive studies of both enucleated and in vivo eyes are required to determine the potential of Inflection Point Analysis for studying and tracking the progression of glaucomatous optic neuropathy.

Flow waveform effects on end-to-side anastomotic flow patterns

PURPOSE

Restenosis due to distal anastomotic intimal hyperplasia, a leading cause of arterial bypass graft failure, is thought to be promoted by hemodynamic effects, specifically 'abnormal' wall shear stress patterns. The purpose of this study was to quantify the effects of flow waveform on peri-anastomotic flow and wall shear stress patterns.

METHODS

Blood flow and wall shear stress patterns were numerically computed in a representative three-dimensional anastomosis using femoral, iliac and coronary flow waveforms suitable for humans at rest. Numerical results were validated against experimental data.

RESULTS

Peri-anastomotic wall shear stress patterns were influenced by a complex interplay between secondary flow effects and unsteadiness. Peripheral flow waveforms (iliac, femoral) produced large temporal and spatial wall shear stress gradients on the host artery bed. In comparison, the coronary flow waveform produced normalized bed wall shear stress gradients that were a factor of 2-3 less than for the peripheral waveforms, even though average bed wall shear stress magnitudes were similar for the two waveforms.

CONCLUSIONS

If anastomotic intimal hyperplasia is promoted by large spatial and/or temporal gradients of wall shear stress, as has been proposed, this study predicts that there will be markedly less intimal hyperplasia on the host artery bed of coronary bypass grafts than for peripheral bypass grafts. This information, in conjunction with a comparative histopathologic study of intimal hyperplasia distribution, could help determine specific wall shear stress factors promoting intimal hyperplasia.

Computational blood flow modelling: errors associated with reconstructing finite element models from magnetic resonance images

Construction of computational blood flow models from magnetic resonance (MR) scans of real arteries is a powerful tool for studying arterial hemodynamics. In this report we experimentally determine a lower bound for errors associated with such an approach, and present techniques for minimizing such errors. A known, simple three-dimensional geometry (cylindrical tube) was imaged using a commercial MR scanner, and the resulting images were used to construct finite element flow models. Computed wall-shear stresses were compared to known values and peak errors of 40-60% were found. These errors can be attributed to limited spatial resolution, image segmentation and model construction. A simple smoothing technique markedly reduced these peak errors. We conclude that smoothing is required in the construction of arterial models from in vivo MR images. If used appropriately, such images can be used to construct acceptably accurate computational models of realistic arterial geometries.

Oxygen mass transfer calculations in large arteries

The purpose of this study was to model the transport of oxygen in large arteries, including the physiologically important effects of oxygen transport by hemoglobin, coupling of transport between oxygen in the blood and in wall tissue, and metabolic consumption of oxygen by the wall. Numerical calculations were carried out in an 89 percent area reduction axisymmetric stenosis model for several wall thicknesses. The effects of different boundary conditions, different schemes for linearizing the oxyhemoglobin saturation curve, and different Schmidt numbers were all examined by comparing results against a reference solution obtained from solving the full nonlinear governing equations with physiologic values of Schmidt number. Our results showed that for parameters typical of oxygen mass transfer in the large arteries, oxygen transport was primarily determined by wall-side effects, specifically oxygen consumption by wall tissue and wall-side mass transfer resistance. Hemodynamic factors played a secondary role, producing maximum local variations in intimal oxygen tension on the order of only 5-6 mmHg. For purposes of modeling blood-side oxygen transport only, accurate results were obtained through use of a computationally efficient linearized form of the convection-diffusion equation, so long as blood-side oxygen tensions remained in the physiologic range for large arteries. Neglect of oxygen binding by hemoglobin led to large errors, while arbitrary reduction of the Schmidt number led to more modest errors. We conclude that further studies of oxygen transport in large arteries must couple blood-side oxygen mass transport to transport in the wall, and accurately model local oxygen consumption within the wall.

Factors affecting the pores of the inner wall endothelium of Schlemm's canal

PURPOSE

A linear relationship between the density of pores in the inner wall of Schlemm's canal and aqueous outflow facility has been reported previously in a study in which investigators examined only eyes fixed at constant pressure, so that fixative flow rates differed from eye to eye. Because pores may form as a function of flow rate, the purpose in the current study was to verify the previous findings, using constant flow perfusions.

METHODS

Outflow facility was measured in enucleated human eyes. Eyes were fixed under either constant flow or constant pressure conditions, microdissected to expose the inner wall of Schlemm's canal, and prepared for scanning electron microscopy. The density and diameter of pores in the inner wall were measured.

RESULTS

Statistical analysis showed no correlation between outflow facility and either the density or the diameter of pores. Pore density decreased significantly during the hours after death. Examining only eyes for which experimentation was started within 20 hours of death, we found that pore density increased significantly with the volume of fixative that had been perfused through the outflow pathway.

CONCLUSIONS

The correlation found by Allingham et al between outflow facility and pore density in the inner wall endothelium was not confirmed. However, the relationship between pore density and volume of fixative perfused is consistent with and may be responsible for the finding in the previous study. Because fixation conditions can influence the apparent pore density in the inner wall endothelium significantly, the conclusion reached previously, that pores contribute only 10% of the aqueous outflow resistance, may require reevaluation.

Combined analysis of spatial and velocity displacement artifacts in phase contrast measurements of complex flows

MR phase contrast (PC) velocity imaging is a promising tool for quantifying blood flow velocity in vivo. PC velocity imaging is, however, susceptible to artifacts that result from the displacement of spins during the finite duration pulse sequences. Such displacement artifacts can lead to errors in velocity measurements, especially in the presence of oblique and accelerating flows, which are common throughout the cardiovascular system. By tracking particles (representing spins) through a computed velocity field, and assuming that spatial and velocity encodings occur at discrete times during the pulse sequence, we simulate the separate and combined effects of oblique and acceleration artifacts on PC velocity images. We demonstrate, both by simulation and MR measurement, the errors associated with such artifacts in PC velocity measurements in a representative flow geometry. Using example particle trajectories, we provide a fluid dynamic basis for characteristic phase-velocity image distortions that can arise when imaging complex, physiologically relevant flows.

Particle volumetric residence time calculations in arterial geometries

The quantification of particle (platelet) residence times in arterial geometries is relevant to the pathogenesis of several arterial diseases. In this manuscript, the concept of "volumetric residence time" (VRT) is introduced. The VRT takes into account where particles accumulate and how long they remain there, and is well-suited to characterizing particle distributions in the complex geometries typical of the cardiovascular system. A technique for the calculation of volumetric residence time is described, which assumes that platelets are neutrally buoyant passive tracer particles, and which tracks small Lagrangian fluid elements containing a uniform concentration of platelets. This approach is used to quantify particle (platelet) residence times in the region of a modeled stenosis with a 45 percent area reduction. Residence time distributions are computed for a representative population of platelets, and for a subpopulation assumed to be "activated" by exposure to shear stresses above a threshold value. For activated platelets, high particle residence times were observed just distal to the apex of the stenosis throat, which can be explained by the presence of high shear stresses and low velocities in the throat immediately adjacent to the vessel wall. Interestingly, the separation zone distal to the stenosis showed only modestly elevated residence times, due to its highly mobile and transient nature. This calculation demonstrates the utility of the VRT concept for cardiovascular studies, particularly if a subpopulation of all particles is to be tracked. We conclude that the volumetric residence time is a useful tool.

MR measurement and numerical simulation of steady flow in an end-to-side anastomosis model

Magnetic resonance phase contrast velocity imaging ('MR PC velocimetry') is a powerful tool for measuring blood velocity. While it has been demonstrated that MR PC velocimetry can accurately measure velocity profiles in simple, unidirectional flows, errors can arise when measuring the more complex, multidirectional flows of clinical importance. In this work, we have compared MR PC velocity measurements with numerical simulations of steady flow in a physiologically relevant model of an end-to-side anastomosis, which produces many of the complex flow features expected in vivo. MR PC velocity profiles, measured using both 2D and 3D pulse sequences, showed very good agreement with numerically computed profiles, although at 2D PC data showed slightly larger errors than the 3D PC data in regions of high accelerations and oblique flow, likely due to displacement artifacts. We conclude that, under ideal conditions, MR phase contrast velocimetry can measure complex flow patterns to within 15% accuracy, but that care should be taken when using 2D pulse sequences to measure such complex flows.

Schlemm's canal and primary open angle glaucoma: correlation between Schlemm's canal dimensions and outflow facility

The purpose of the study was to examine the correlation between outflow facility and morphometric measurements of Schlemm's canal (SC) in normal and glaucomatous human eyes. Outflow facility was measured in ten normal and five glaucomatous (POAG) human eyes prior to perfusion-fixation at a pressure of 15 mmHg. Two separate sections per quadrant (eight sections per eye) were analysed using a morphometric analysis system. SC cross sectional area, perimeter, and inner wall length were measured. Inner wall endothelial nuclei were counted. When pooled data were examined, a statistically significant correlation was found between facility and SC area (P < or = 0.01). Most importantly, POAG eyes had a significantly smaller SC cross-sectional area, SC perimeter and SC inner wall length compared to normal eyes. If examined as a reduction in SC filtering area, this decrease in SC inner wall length alone could account for approximately 41-55% of the difference in outflow facility observed between normal and POAG eyes. The dimensions of Schlemm's canal in glaucomatous human eyes were significantly smaller than those in normal eyes. This reduction in SC dimensions may account for approximately half of the decrease in outflow facility observed in POAG eyes.

Retroperfusion studies of the aqueous outflow system. Part 2: Studies in human eyes

PURPOSE

To extend the retroperfusion technique to allow the delivery of drugs into Schlemm's canal in enucleated human eyes and to use this technique to gain insights into the function of the inner wall of Schlemm's canal.

METHODS

Using our previously developed retroperfusion technique, the anterior chamber of enucleated human eyes was held at a small negative pressure (-0.75 mm Hg), and fluid was allowed to flow retrograde from the limbal vessels, through the collector channels, and into Schlemm's canal. In this manner, the sulfhydryl agent N-ethyl maleimide (NEM) or the fixative agent glutaraldehyde was delivered to the inner wall of Schlemm's canal in normal and glaucomatous human eyes. Facility changes caused by retroperfusion were measured and correlated with histologic studies of the inner wall of Schlemm's canal.

RESULTS

Retroperfusion effectively delivers fluid from the scleral surface into the lumen of Schlemm's canal. Retroperfusion with vehicle alone does not alter facility or change outflow pathway morphology. Retroperfusion with NEM causes an approximately 35% facility increase and concomitant inner wall openings. Retroperfusion with glutaraldehyde in normal eyes and eyes with primary open-angle glaucoma causes a facility decrease of 53% and 64%, respectively, and localized fixation of the inner wall of Schlemm's canal. The magnitude of the facility changes caused by retroperfusion were similar to those seen using conventional forward perfusion of NEM and glutaraldehyde.

CONCLUSIONS

Retroperfusion is a viable technique for the delivery of drugs or other agents into Schlemm's canal in enucleated human eyes. Retroperfusion-induced changes in outflow facility are correlated strongly with morphologically observed alterations in inner wall structure. The majority of outflow resistance is localized to the inner wall of Schlemm's canal or the immediately adjacent 10-microns region of the juxtacanalicular tissue in normal eyes and in eyes with primary open-angle glaucoma. Inner wall giant vacuoles and pores likely persist for sometime, even after fixation at zero or negative pressure.

Accuracy of MR phase contrast velocity measurements for unsteady flow

The accuracy of MR phase contrast (PC) velocity measurements for unsteady flow has been quantitatively assessed. Spatially resolved velocity fields were measured in a long straight tube using a gated PC technique, and the resulting MR PC velocity data were compared with velocities derived from the analytic Womersley solution to the Navier-Stokes equations governing fluid flow. The overall root-mean-square (rms) difference between the measured and analytic velocities was 1.6 cm s-1 for nominally sinusoidal flow waveforms with peak velocities ranging from 51.6 cm s-1 to 59.8 cm s-1. This rms difference corresponded to 7.5% of the mean fluid velocity, which is similar to the cited accuracy of approximately 5% for MR PC velocimetry for steady flows. Linear regression between the PC velocity measurements and the velocities obtained using the analytic expression was highly significant (r2 = 0.997) and yielded a slope of 0.998, close to the expected value of 1. We conclude that the gated MR PC velocity measurements in unsteady flow are accurate.

Simulation of non-Newtonian blood flow in an end-to-side anastomosis

In order to quantify the importance of non-Newtonian blood rheology on anastomotic flow patterns, the characteristics of Newtonian and non-Newtonian blood flows were compared in a 2-D, 45 degree end-to-side anastomosis model under both steady and unsteady flow conditions. All flows were assumed to be two-dimensional, and were simulated numerically using parameters consistent with blood flow in the femoral artery. A novel, purely viscous constitutive relation, based on a generalized form of the power law relation, was developed to model the non-Newtonian rheology of blood. The resulting wall shear stress patterns indicate that for the parameter values under consideration, non-Newtonian blood rheology has a significant effect on steady flow wall shear stresses, but no significant effect on unsteady flow wall shear stresses. Based on these and other simulations, a parameter is formulated that gives an indication of the importance of non-Newtonian blood rheology under a given set of flow conditions. In addition, an argument is presented for allowing the conclusions from this two-dimensional study to be extended to three-dimensional blood flow.

Deformation of the lamina cribrosa by elevated intraocular pressure

The purpose of this study was to determine the mechanical response of the lamina cribrosa (LC) to elevated intraocular pressure (IOP) so as to identify possible mechanisms of optic nerve damage in early glaucoma. Ten pairs of normal human eyes were fixed after 24 hours' exposure to 50 mm Hg pressure (experimental eyes) or 5 mm Hg pressure (contralateral control eyes). Photomicrographs of the central region of the optic nerve head (ONH) were taken to examine the LC morphologically and to measure the dimensions of the LC. It was found that elevated IOP caused the LC to deflect posteriorly without affecting its thickness. The majority of the posterior displacement in the LC occurred near the periphery of the ONH. This shape change is consistent with a model of force distribution within the LC in which shear stresses are dominant; such stresses are maximal at the periphery and minimal at the centre of the ONH. These findings support a model in which mechanical forces, specifically shearing stresses within the peripheral lamina, play a direct role in the pathology of glaucomatous optic neuropathy.

The effect of wall distensibility on flow in a two-dimensional end-to-side anastomosis

The development of intimal hyperplasia at the distal anastomosis is the major cause of long-term bypass graft failure. To evaluate the suspected role of hemodynamic factors in the pathogenesis of distal intimal hyperplasia, an understanding of anastomotic flow patterns is essential. Due to the complexity of arterial flow, model studies typically make simplifying assumptions, such as treating the artery and graft walls as rigid. In the present study this restriction is relaxed to consider the effects of vessel wall distensibility on anastomotic flow patterns. Flow was simulated in an idealized 2-D distensible end-to-side anastomosis model, using parameters appropriate for the distal circulation and assuming a purely elastic artery wall. A novel numerical approach was developed in which the wall velocities are solved simultaneously with the fluid and pressure fields, while the wall displacements are treated via an iterative update. Both the rigid and distensible cases indicated the presence of elevated temporal variations and low average magnitudes of wall shear stress at sites known to be susceptible to the development of intimal hyperplasia. At these same sites, large spatial gradients of wall shear stress were also noted. Comparison between distensible-walled and corresponding rigid-walled simulations showed moderate changes in wall shear stress at isolated locations, primarily the bed, toe and heel. For example, in the case of a distensible geometry and a physiologic pressure waveform, the heel experienced a 38 percent increase in cycle-averaged shear stress, with a corresponding 15 percent reduction in shear stress variability, both relative to the corresponding values in the rigid-walled case.(ABSTRACT TRUNCATED AT 250 WORDS)

An improved ocular perfusion system

We describe the design, construction and testing of an improved ocular perfusion system for outflow facility measurement. The essential feature of the system is the measurement of a differential pressure across a calibrated length of tubing, which provides a stable and accurate reading of facility and hence also of flowrate. Perfusion of calibrated lengths of tubing showed excellent accuracy, while perfusions of enucleated eyes showed very low noise levels. The system is relatively inexpensive, easy to construct and maintain, insensitive to vibrations and other noise, and accurate. It is therefore felt to be superior to conventional "hanging bucket" ocular perfusion systems.

A numerical simulation of flow in a two-dimensional end-to-side anastomosis model

In order to understand the possible role that hemodynamic factors may play in the pathogenesis of distal anastomotic intimal hyperplasia, we carried out numerical simulations of the flow field within a two-dimensional 45 degree rigid-walled end-to-side model anastomosis. The numerical code was tested and compared with experimental (photochromic dye tracer) studies using steady and near-sinusoidal waveforms, and agreement was generally very good. Using a normal human superficial femoral artery waveform, numerical simulations indicated elevated instantaneous wall shear stress magnitudes at the toe and heel of the graft-host junction and along the host artery bed. These sites also experienced highly variable wall shear stress behavior over the cardiac cycle, as well as elevated spatial gradients of wall shear stress. These observations provide additional evidence that intimal hyperplasia may be correlated to wall shear stresses over the cardiac cycle, high wall shear stress gradients, or a combination of the three. The limitations of the present work (especially in regard to the two-dimensional nature of the flow simulations) are discussed, and results are compared to previous observations about distal anastomotic intimal hyperplasia.

Retroperfusion studies of the aqueous outflow system. Part I: Evaluation of technique using N-ethyl maleimide

PURPOSE

The goal of this study was to develop a new technique to deliver drugs or other agents to the lumen of the angular aqueous plexus/Schlemm's canal (AAP/SC) while bypassing the trabecular meshwork, thereby gaining insight into AAP/SC inner wall function.

METHODS

The anterior chamber is held at a small negative pressure and fluid is allowed to flow retrograde from the limbal vessels, through the collector channels, and into the AAP/SC ("retroperfusion"). Facility measurements are combined with histologic and tracer studies in bovine eyes.

RESULTS

(1) Retroperfusion with a saline solution does not alter facility or change outflow pathway morphology; (2) fluid is able to move retrograde from the scleral surface and enter the lumen of the AAP; and (3) retroperfusion with N-ethyl maleimide causes a dose-dependent increase in washout rate and concomitant inner wall breaks.

CONCLUSIONS

It is hypothesized that the observed increase in washout is due to leakage of extracellular materials through breaks in the inner wall.