Biorheology

Adherent platelets are an important part of both thrombus formation and in certain stages of atherogenesis. Platelets can be activated by potent chemicals released from adherent platelets and adhere far more readily than unactivated ones. An analytical and numerical model is presented utilising high Peclet number for the activation and adhesion of platelets in shear flows. The model uses a similarity transformation, which characterises the relationship between convective, diffusive transport and the bulk platelet activating reaction mechanism. A first order surface reaction mechanism is used to model platelet adhesion at the wall (cell) surface. The reduced Damköhler number, ℳ, characterises the importance of the bulk reaction and includes both convective and diffusive terms. For a high rate of blood flow (ℳ→0) the activation of platelets can effectively be terminated. In contrast, for (ℳ→∞) an inner layer of activated platelets exists with an infinitesimally thin reaction sheet separating activated and non‐activated platelets. This characterisation by the Damköhler number highlights results found clinically, in that thrombus forms in areas of low shear (high ℳ) and in some cases an increased blood flow (low ℳ) can inhibit the activation of platelets completely. The model shows the critical balance that exists between convection, diffusion and reaction.

The completion of the Human Genome Project and ongoing sequencing of mouse, rat and other genomes has led to an explosion of genetics‐related technologies that are finding their way into all areas of biological research; the field of biorheology is no exception. Here we outline how two disparate modern molecular techniques, microarray analyses of gene expression and real‐time spatial imaging of living cell structures, are being utilized in studies of endothelial mechanotransduction associated with controlled shear stress in vitro and haemodynamics in vivo. We emphasize the value of such techniques as components of an integrated understanding of vascular rheology. In mechanotransduction, a systems approach is recommended that encompasses fluid dynamics, cell biomechanics, live cell imaging, and the biochemical, cell biology and molecular biology methods that now encompass genomics. Microarrays are a useful and powerful tool for such integration by identifying simultaneous changes in the expression of many genes associated with interconnecting mechanoresponsive cellular pathways.

Local haemodynamic forces acting on the endothelium modulate vascular tone through mechanisms that normalize intimal shear stress. This flow‐dependent diameter response contributes to the optimization of circulatory function and is mediated via shear stress‐induced release of NO, vasodilator prostanoids and a putative endothelium‐derived hyperpolarizing factor or EDHF. There is growing evidence that NO/prostanoid independent relaxations involve direct heterocellular signalling between endothelial and smooth muscle cells via gap junctions.

Chronic changes in wall shear stress lead to vascular remodeling, characterized by increased vascular wall diameter and thickness, to restore wall shear stress values to baseline. Release of nitric oxide from endothelial cells exposed to excessive shear is a fundamental step in the remodeling process, and potentially triggers a cascade of events, including growth factor induction and matrix metalloproteinase activation, that together contribute to restructuralization of the vessel wall. Understanding these processes could help explain how changes in blood vessel wall structure occur in the context of atherosclerosis or aortic aneurisms.

Adhesion of monocytes to arterial endothelium may contribute to the asymmetric distribution of atherosclerotic lesions. Possible mechanisms for adhesion in the relatively high shear stress environment found in arteries include greater monocyte deformation and/or more frequent penetration of microvilli through steric and charge barriers. In vivo, secondary flows generate forces acting normal to the endothelial cell surface. These forces may cause compression of the microvilli or enable cells to overcome steric or electrostatic barriers, increasing adhesion. To investigate this, we examined monocyte adhesion to activated endothelium in recirculating flow. Adhesion was characterized by short arrests in a narrow region on either side of the reattachment line. The median arrest time was longer than that observed at comparable shear stresses in a linear shear flow. The lifetimes of adhesion were analyzed using a model for multiple bond formation. For cells adhering near the reattachment line, the bond number per cell was greater than the value found for similar shear stresses under shear flow. Thus, multiple bond formation arising from greater normal forces in recirculating flow permits monocytes to adhere at higher shear stresses.

To find out whether concentration polarization of low‐density lipoprotein (LDL) occurs at the surface of a vascular endothelium or not, transport of LDL in flowing blood to an water‐permeable endothelium was studied theoretically by means of CFD. Calculations were carried out for an endothelium exposed to a Couette flow by assuming that the surface geometry of the endothelium could be expressed by a cosine function. Two typical cases were considered for the permeability of endothelium to water; one was uniform permeability everywhere in the endothelium, and the other was uneven permeability which was augmented at the intercellular junction. It was found that, in both cases, the surface concentration of LDL increased in going distally from the entrance, taking locally high and low values at the valleys and hills of the endothelium, respectively, and the variation was larger in the case of endothelium with uneven permeability. These results clearly showed that concentration polarization of LDL which might affect the uptake of LDL by the arterial wall certainly occurs at the surface of the endothelium even if the flow is disturbed microscopically by the uneven surface of the endothelium.

Flow induced shear stress influences vascular cellular biology and pathophysiology in numerous ways. Previous in vitro studies on interactions between flow and endothelial cells using parallel‐plate flow chambers involve two‐dimensional flows, whereas flows in larger vessels are commonly three‐dimensional. We have constructed a parallel plate flow chamber with a backward facing step aligned oblique to the axis of the chamber. Flow visualisation by steady injection of ink through a hypodermic tube reveals swirling flow in the recirculation region downstream of the step. At given angles of the step, θ (to the axis of the chamber), the pitch of the swirl and the width of the separation region, as measured in the direction perpendicular to the step, increase with the Reynolds number (Re). On the other hand, at given values of Re, reduction of θ results in increases in the swirl pitch but decreases in the width of the separation zone. Furthermore, clearance time of ink from the separation region is shorter with an oblique step than a perpendicular one at given Re. Computer simulation confirms the 3D swirling flow created by the oblique step and provides detailed distribution of wall shear stresses in the flow chamber.

The macrocirculation is modelled by incompressible Newtonian flow through a rigid network of pipes for which possible simplifications are discussed. The common assumptions of two‐dimensionality or axisymmetry can be generalised to helical symmetry, and in the first part of the paper, the three‐dimensionality of arterial bends is considered by varying the curvature and torsion of a section of a helical pipe. The torsion is found to impart a preferential twist to the cross‐sectional flow. This loss of symmetry ensures that flow separation is less severe for a helical bend than for a toroidal bend. The effects of variations in body size are examined using allometric scaling laws.

In the second part of the paper, the approach to “fully developed” Dean or Womersley flow is considered in an attempt to quantify the regions of validity of idealised models. A perturbation approach, akin to hydrodynamic stability theory, is used. It is argued that often potential flows are more suitable for describing the rapid interactions between geometry and pulsatility rather than the eventual fully developed state so that, for example, the first 100° of the aortic arch may be considered irrotational. Helical potential flows are found to develop faster than the corresponding toroidal flows, but slower than those in a straight pipe. The presence of vorticity in the core also retards the development of symmetric flows. It is concluded that while idealised flows can occur at some points in the body, in general experimental observation is needed to justify their use. Particular caution is recommended when interpreting calculations with Poiseuille input.

The aim of this study is to examine the interaction between two mild atherosclerotic proliferations spaced apart by a distance S by analyzing their influence on flow structure, pressure drop and stress field in an arterial vessel under pulsatile flow conditions. This has been achieved numerically by employing a time accurate, cell centered finite volume method in solving the Navier–Stokes equations governing the 3D unsteady flow dynamics in a conceptual model of an multiply constricted arterial vessel. In comparison to the pressure drop across a single stenosis, nearly a 50% increase in the late systolic and early diastolic pressure drops has been observed across the two mild constrictions when they are spaced within a distance of S≤4. When S≤4, more than a 25% reduction in the peak systolic wall shear stress (WSS) on the downstream constriction is noted.

This work was motivated by the problems of analysing detailed 3D models of vascular districts with complex anatomy. It suggests an approach to prescribing realistic boundary conditions to use in order to obtain information on local as well as global haemodynamics. A method was developed which simultaneously solves Navier–Stokes equations for local information and a non‐linear system of ordinary differential equations for global information. This is based on the principle that an anatomically detailed 3D model of a cardiovascular district can be achieved by using the finite element method. In turn the finite element method requires a specific boundary condition set. The approach outlined in this work is to include the system of ordinary differential equations in the boundary condition set. Such a multiscale approach was first applied to two controls: (i) a 3D model of a straight tube in a simple hydraulic network and (ii) a 3D model of a straight coronary vessel in a lumped‐parameter model of the cardiovascular system. The results obtained are very close to the solutions available for the pipe geometry. This paper also presents preliminary results from the application of the methodology to a particular haemodynamic problem: namely the fluid dynamics of a systemic‐to‐pulmonary shunt in paediatric cardiac surgery.

Building on previous studies of unsteady flow within model distal bypass grafts we analyse the near wall residence times and shear exposure in a 45 degrees anastomosis under symmetrical and symmetry breaking geometric configurations. We define residence time as the minimum time for a particle to exit a spherical region and shear exposure as a temporal integral of the Huber‐Henky‐von‐Mises criterion along a particle path over a fixed time interval. Decomposing the pulsatile cycle into four equal intervals we find that the interval of peak residence time in the host vessel is from mid‐deceleration to peak diastole and peak diastole to mid‐acceleration. The asymmetric model is shown to have a significantly lower residence time during these intervals. Considering the shear exposure prior to the residence time evaluation we determine that a higher average shear exposure exists in the asymmetric model associated with the upstream geometry modification. Analysis of the regions of high residence time and shear exposure suggests that the “toe” region and the interface between the “heel” and bulk flow are more significant than the bed and heel region. Although the asymmetric model considered in this study reduces residence times in the host artery, the product of the measure of shear exposure and residence time is not found to be preferable. If shear exposure were to be considered as an important factor in particle activation, the findings imply that for junction optimisation, greater consideration needs to be given both to the local junction asymmetry and upstream influence on the shear history.

Theoretical modelling of bending and branching tube flows at medium‐to‐high flow rates is described for current industrial and biomedical projects. This mostly uses slender‐flow modelling. Much pressure loss occurs in bends, with increased swirl, large variations in velocity components and wall shear stress, skewing of the downstream motion and reduced flow rate, but the flow regime which is established shows sensitive dependence on the imposed pressure drop and entrance conditions. A small side‐branch off a mother tube produces most rapid variation in pressure and velocity near the daughter entrance, this variation now being quantifiable. A multiple branching yields large flow rates and nonunique flow patterns, depending on the form of the imposed pressure differences.

A parallel, time‐accurate flow solver is devised to study the human cardio‐vascular system. The solver is capable of dealing with moving boundaries and moving grids. It is designed to handle complex, three‐dimensional vascular systems. The computational domain is divided into multiple block subdomains. At each cross section the plane is divided into twelve sub‐zones to allow flexibility for handling complex geometries and, if needed, appropriate parallel data partitioning. The unsteady, three‐dimensional, incompressible Navier–Stokes equations are solved numerically. A second‐order in time and third‐order upwind finite volume method for solving time‐accurate incompressible flows based on pseudo‐compressibility and dual time‐stepping technique is used. For parallel execution, the flow domain is partitioned. Communication between the subdomains of the flow on Riken's VPP/700E supercomputer is implemented using MPI message‐passing library. A series of numerical simulations of biologically relevant flows is used to validate this code.

We are presenting computational fluid dynamics simulation results for the flow in an anatomically accurate right internal carotid artery, exhibiting two saccular aneurysms close to each other. Our study focuses on the investigation of passage times for blood cells through the two‐aneurysm malformation. We construct residence time maps that exhibit strong non‐uniformity, linked to the entry of fluid in only the first, only the second, or in both aneurysms. An entrance index is computed, showing qualitatively the regions at an arterial section upstream of the aneurysms, where cells following one of these scenarios emanate. The significance of the residence time profiles and entry scenarios obtained is discussed with respect to thrombosis and pharmacokinetics. Preliminary evidence that the inflow–outflow patterns of the two aneurysms may be leading to particularly complex flow and to chaotic mixing is discussed.

A computational fluid dynamics study was conducted using a simplified model of the right coronary artery, which deforms with contraction of the heart. The right coronary artery was modeled using an ordinary helix, whose torsion and curvature changed in time with the contraction and dilatation of the heart which was modeled as a cylinder. In the computational result, the flow in the model right coronary artery was thought to be more affected by the change of the curvature compared to that of the torsion.

Blood flow through arteries represents a very complex, fluid–structure interaction (FSI) problem. Strong coupling between the blood and artery is due to the relatively low stiffness of the artery compared to that of blood. Hence, the pressure exerted by the flowing blood on the artery wall can result in considerable deformations of the artery, and vice‐versa, arterial deformations can in turn affect the blood flow. In the present work, the finite volume method is employed to solve the problem where compressible fluid, representing blood, flows in healthy arteries as well as in unhealthy, i.e., partly stiffened arteries. The stiffening of the arterial wall is assumed to be the first key stage in the development of atherosclerosis. The comparison between various deformation profiles of healthy and unhealthy arteries demonstrates significant and measurable differences, in particular in the radial direction. This is hoped to help toward establishing procedures for early diagnosis of the disease.

Through cardiac looping during embryonic development, human and other vertebrate hearts adopt sinuous curvatures with marked changes in direction of flow at atrial, ventricular and arterial levels. We used magnetic resonance phase velocity mapping to study flow through the hearts of resting volunteers, and Doppler ultrasound to record changes with exercise. We found asymmetric recirculation of blood during filling phases of all four heart cavities, with blood redirected appropriately for onward passage to the next cavity. Doppler traces showed that biphasic ventricular filling became rapid and monophasic on strenuous exercise. We propose that looped curvatures of the heart have fluidic and dynamic advantages. Intra‐cavity flow appears to be asymmetric in a manner that preserves stability, and allows momentum of inflowing streams to be redirected towards rather than away from the next cavity. Direction‐change at ventricular level is such that recoil away from ejected blood is in a direction that can enhance rather than inhibit ventriculo‐atrial coupling. These factors may combine to allow a reciprocating, sling‐like, ‘morphodynamic’ mode of action become effective when heart rate and output increase with exercise. Dynamic efficiency of the looped heart may have favoured evolution of large, complex, active species characteristic of the vertebrate line.

The carotid bifurcation has been a region of particular interest due to its predilection for clinically significant atherosclerosis. It has been shown that the vessel geometry is a major determinant of the local haemodynamic properties which are believed to be associated with the location of atherosclerotic lesions. Current knowledge of the geometry of the carotid bifurcation is insufficient and restricted to basic geometric parameters. To provide some means of quantifying the degree of complexity of the 3D shape of the bifurcation, we made an initial attempt by evaluating the non‐planarity of an arterial bifurcation based upon the singular value decomposition theorem.

In this paper we present our results obtained on the right carotid bifurcations of six normal subjects, each of whom was scanned twice using the 2D time‐of‐flight MR sequence. The acquired 2D cross sectional images were processed by using our in‐house software which comprises 2D segmentation, 3D reconstruction and smoothing. The centroids of each transverse slices were determined and used as input data for the non‐planarity analysis. Our results using the singular value decomposition method have demonstrated discernible differences in non‐planarity among individuals. Comparisons with the planarity definition proposed by other investigators suggest that the singular value decomposition method offers more information about the linearity and planarity of the bifurcation. However, it is also realised that a single measure of non‐planarity can never fully characterise a bifurcation owing to the great variety of geometries.

Physiological correct modelling of blood flow through the human ascending aorta is done by combining computational fluid dynamics (CFD) and magnetic resonance imaging (MRI). This method provides a relatively new approach in the analysis and quantification of the haemodynamic variables. Velocity patterns and wall shear stress distributions occurring in the ascending aorta of an individual subject are examined. Geometrical data and inflow velocity profiles just downstream of the valve were acquired from MRI measurements. Based on the extraction of arterial cross‐sections a computer model of the time‐dependent geometrical vessel wall was generated. After surface creation the arterial lumen was filled with an appropriate 3D finite element mesh. The mathematical description of the blood flow uses the Navier–Stokes equations applying an Arbitrary Lagrangian–Eulerian modification with respect to the time‐varying geometry with externally imposed boundary motion. The numerical approach uses our recently developed finite element solver. The computational results agree very well with the measured data.

Non‐planarity in blood vessels is known to influence arterial flows and wall shear stress. To gain insight, computational fluid dynamics (CFD) has been used to investigate effects of curvature and out‐of‐plane geometry on the distribution of fluid flows and wall shear stresses in a hypothetical non‐planar bifurcation. Three‐dimensional Navier–Stokes equations for a steady state Newtonian fluid were solved numerically using a finite element method. Non‐planarity in one of the two daughter vessels is found to deflect flow from the inner wall of the vessel to the outer wall and to cause changes in the distribution of wall shear stresses. Results from this study agree to experimental observations and CFD simulations in the literature, and support the view that non‐planarity in blood vessels is a factor with important haemodynamic significance and may play a key role in vascular biology and pathophysiology.

Laminar‐to‐turbulent transition in pulsatile flow through a stenosis is studied by means of three‐dimensional numerical simulations. The flow transition is associated with the occurrence of a flow instability initiating in the stenosis region. The instability is manifested by a three‐dimensional symmetry‐breaking and leads to asymmetric separation and intense swirling motion downstream of the stenosis. The above have profound effects on the wall shear stress (WSS). The simulations reveal that the asymmetric separation is extended several radii downstream of the stenosis with substantial WSS fluctuations, in both space and time, occurring in the poststenotic region.

The human carotid artery bifurcation is a complex, three‐dimensional structure exhibiting non‐planarity and both in‐ and out‐of‐plane curvature. The aim of this study was to determine the relative importance of vessel planarity, a potential geometric risk factor for atherogenesis, in determining the local hemodynamics. A combination of computational fluid dynamics and magnetic resonance imaging was used to reconstruct the subject‐specific hemodynamics for three subjects. Planar models were then constructed by translating the centroids of the lumen contours onto a plane defined by the centroids of the vessel branches near the bifurcation apex. A novel “patching” technique was used to convert the continuous arterial surfaces into contiguous but discrete patches according to an objective scheme, making it possible to compare the original and planar models without the need for registration and warping. Results suggest that the planarity of the vessel has a relatively minor effect on the spatial distribution of mean and oscillatory wall shear stress. Out‐of‐plane curvature was, however, found to have a marked influence on the extent and magnitude of these hemodynamic variables. We conclude that vessel curvature – whether in‐ or out‐of‐plane – rather than planarity may deserve further scrutiny as a potential geometric risk for atherogenesis.

This article will review the ability of ultrasound techniques to provide 3D information on arterial geometry, blood flow and tissue motion.

3D systems. 3D datasets can be obtained by sequential acquisition of 2D slices. Ideally a transducer is required in which there is full control of beam steering within a 3D volume. This requires a 2D array consisting of several thousand elements. Prototype 2D arrays have been built which provide several 3D datasets per second.

Blood velocity measurement. Current Doppler systems estimate only the component of velocity in the direction of the Doppler beam. Lack of knowledge of the direction of blood motion and also other effects associated with ‘spectral broadening’ limit the accuracy of velocity measurement. Improved accuracy can be obtained using vector Doppler systems using 2 or 3 beam directions; this approach is referred to as ‘vector Doppler’.

Tissue motion. Doppler techniques can also be used to detect tissue motion (Tissue Doppler Imaging or TDI). Motion of the artery wall can be calculated from the TDI images. It is possible to estimate simultaneously motion for adjacent diameters within the longitudinal plane, and to visualise the relative motion at different parts of the wall.

Clinical evidence suggests that the development of myointimal hyperplasia in prosthetic femorodistal bypass grafts may be reduced by the interposition of a cuff of autologous vein between the graft and the recipient artery. Previous experimental work has shown that some of the benefits may be attributed to the geometry of the cuffed anastomosis. Since the distal anastomosis in vivo is often non‐planar we have carried out a preliminary study in a model where the graft is at an angle of 45° to the anterior–posterior plane of the anastomosis. This out‐of‐plane angulation produces highly asymmetric flow patterns in the anastomosis with significant flow separation on the ipsilateral side of the cuff. In the proximal and distal outflow, however, the velocity vectors show significant helical motion with temporal instability in the distal outflow.

Steady flow of a blood mimicking fluid in a physiologically realistic model of the human carotid bifurcation was studied using both magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) modelling techniques. Quantitative comparisons of the 3D velocity field in the bifurcation phantom were made between phase contrast MRI measurements and CFD predictions. The geometry for the CFD model was reconstructed from T₁ weighted MR imaging of the test phantom. It was found that the predicted velocity fields were in fair agreement with MR measured velocities. In both the internal and external carotid arteries, the agreement between CFD predictions and MRI measurements was better along the inner–outer wall axis with a correlation factor C>0.897 (average 0.939) where the velocity profiles were skewed, than along the anterior–posterior axis (average correlation factor 0.876) where the velocity profiles were in M‐shape.

Leukocyte recruitment from blood to the endothelium plays an important role in atherosclerotic plaque formation. Cells show a primary and secondary adhesive process with primary bonds responsible for capture and rolling and secondary bonds for arrest. Our objective was to investigate the role played by this process on the adhesion of leukocytes in complex flow. Cells were modelled as rigid spheres with spring like adhesion molecules which formed bonds with endothelial receptors. Models of bond kinetics and Newton's laws of motion were solved numerically to determine cell motion. Fluid force was obtained from the local shear rate obtained from a CFD simulation of the flow over a backward facing step.

In stagnation point flow the shear rate near the stagnation point has a large gradient such that adherent cells in this region roll to a high shear region preventing permanent adhesion. This is enhanced if a small time dependent perturbation is imposed upon the stagnation point. For lower shear rates the cell rolling velocity may be such that secondary bonds have time to form. These bonds resist the lower fluid forces and consequently there is a relatively large permanent adhesion region.

The blood flow immediately adjacent to the wall of a blood vessel or an artificial surface is of great interest. This flow defines the shear stress at the wall and is known to have a great physiological importance. The use of models is a viable method to investigate this flow. However, even in models the shear stress at the wall is difficult to assess. A new optical method is based on transparent models and uses particles in the model fluid, which are only visible near the wall. This is achieved with a model fluid having a defined opacity. This fluid obscures particles in the center of the models, but permits the observation and recording of particles close to the wall. The method has been applied for Hagen–Poiseuille flow and for the likewise well researched flow in a tube with a sudden expansion.

Coronary artery bypass graft surgery (CABG) is widely used for the treatment of atheromatous stenosis of coronary arteries. However, as many as 50% of grafts fail within 10 years after CABG due to neointima (NI) formation, a process involving the proliferation and migration of vascular smooth muscle cells (VSMCs). Superimposed on neointima formation is accelerated atherogenesis which ultimately results in late vein graft failure. To date no therapeutic intervention has proved successful in treating late vein graft failure and as such is a matter of some urgency. However, in recent years, several diverse approaches aimed at preventing neointimal formation have been devised which have yielded promising results. These include the use of external stents, gene therapy as well as conventional pharmacological interventions. The objective of this article, therefore, is to review these recent approaches and their potential clinical applications in the treatment of vein graft disease.

Patient‐to‐patient variations in artery geometry may determine their susceptibility to stenosis formation. These geometrical variations can be linked to variations in flow characteristics such as wall shear stress through stents, which increases the risk of restenosis. This paper considers computer models of stents in non‐symmetric flows and their effects on flow characteristics at the wall. This is a fresh approach from the point of view of identifying a stent design whose performance is insensitive to asymmetric flow. Measures of dissipated energy and power are introduced in order to discriminate between competing designs of stents.

The long‐term success of arterial bypass grafting with autologous saphenous veins is limited by neointimal hyperplasia (NIH), which seemingly develops preferentially at sites where hydrodynamic wall shear is low. Placement of a loose‐fitting, porous stent around end‐to‐end, or end‐to‐side, autologous saphenous vein grafts on the porcine common carotid artery has been found significantly to reduce NIH, but the mechanism is unclear. In a preliminary study, we implanted autologous saphenous vein grafts bilaterally on the common carotid arteries of pigs, placing a stent around one graft and leaving the contralateral graft unstented. At sacrifice 1 month post implantation, the grafts were pressure fixed in situ and resin casts were made. Unstented graft geometry was highly irregular, with non‐uniform dilatation, substantial axial lengthening, curvature, kinking, and possible long‐pitch helical distortion. In contrast, stented grafts showed no major dilatation, lengthening or curvature, but there was commonly fine corrugation, occasional slight kinking or narrowing of segments, and possible long‐pitch helical distortion. Axial growth of grafts against effectively tethered anastomoses could account for these changes. CFD studies are planned, using 3D MR reconstructions, on the effects of graft geometry on the flow. Abnormality of the flow could favour the development of vascular pathology, including NIH.

Geometric parameters and features vary within the vasculature. Furthermore, at any given anatomic site, there are substantial variations in geometry among individuals. These variations can contribute to a corresponding variability in the hemodynamic environment and, to the extent that hemodynamics affects the atherosclerotic process, the progress of vascular disease. Measurements of the geometry and wall morphometry of post‐mortem human coronary arteries demonstrate a relationship between these variables that supports the notion that geometric variations can contribute to a corresponding variability in the local rate of progression of arterial disease. The dynamic geometry of the coronary arteries also varies from site to site and among individuals, and this variability too may play a role in the epidemiology of coronary artery disease.

The influence of blood flow on the depositions and development of atherosclerotic lesions have been observed and described since the 19th century. Observations have shown that depositions correlate with regions of low wall shear stress. However, the exact correlations between depositions, vessel geometry and flow parameters are not yet known. The purpose of this study was the quantification of atherosclerosis risk factors in carotid bifurcation. This artery has attracted particular interest because lesions are often found in this bifurcation. Post mortem, the arteries are excised and vessel casts are produced. Afterwards, the arteries are analyzed morphometrically. The vessel casts are used for the assessment of some geometrical parameters. 31 carotid bifurcations were analyzed in this study. Eight vessel casts were digitized and rendered three‐dimensional mathematical models of the arteries. These data were imported by the computational fluid dynamics program FLUENT. Further, the blood flow was reconstructed in a computer model based on the individual vessel geometry. The flow parameters, such as velocity, pressure and wall shear stress were computed. At the same time the geometrical parameters and wall alterations are known. This permits the comparison of the anatomical shape and its flow with the distribution and level of the wall alterations.

We report methods for (a) transforming a three‐dimensional geometry acquired by magnetic resonance angiography (MRA) in vivo, or by imaging a model cast, into a computational surface representation, (b) use of this to construct a three dimensional numerical grid for computational fluid dynamic (CFD) studies, and (c) use of the surface representation to produce a stereo‐lithographic replica of the real detailed geometry, at a scale convenient for detailed magnetic resonance imaging (MRI) flow studies. This is applied to assess the local flow field in realistic geometry arterial bypass grafts. Results from a parallel numerical simulation and MRI measurement of flow in an aorto‐coronary bypass graft with various inlet flow conditions demonstrate the strong influence of the graft inlet waveform on the perianastomotic flow field. A sinusoidal and a multi harmonic coronary flow waveform both with a mean Reynolds number (Re) of 100 and a Womersley parameter of 2.7 were applied at the graft inlet. A weak axial flow separation region just distal to the toe was found in sinusoidal flow near end deceleration (Re = 25). At the same location and approximately the same point in the cycle (Re = 30) but in coronary flow, the axial flow separation was stronger and more spatially pronounced. No axial flow separation occurred in steady flow for Re = 100. Numerical predictions indicate a region in the vicinity of the suture line (where there is a local narrowing of the graft) with a wall shear magnitude in excess of five times that associated with fully developed flow at the graft inlet.

The distribution of lesions around arterial branch points is complex and changes with age. Four distinct patterns – here termed the arrowhead pattern, the lateral pattern, the upstream streak and the volcano – have been reported around the origins of intercostal arteries in the human aorta at different ages. The first two patterns also occur in young and old rabbits, the third in minipigs, and the fourth in apolipoprotein E/LDL receptor knockout mice. It is unclear how all four patterns can depend solely on flow; a particular problem is that the prevalence of lipid deposition remains highly nonuniform for several branch diameters upstream of the ostium. Variations in the prevalence of fatty streaks may originate near the branch and then spread by the migration of activated endothelial cells towards the heart. The pattern of raised lesions may reflect a different aetiology.

This paper is presented as a summary and synthesis of the presentations at the conference entitled “Breaking Symmetry in Haemodynamics”. As the accompanying papers will attest, there has been enormous progress in understanding the effects of fluid flow on the arterial endothelium and the consequential effects on the vessel wall. It is now clearly understood that the focal lesions found in atherosclerotic arteries are the product of asymmetrical flow and the resulting disturbed flow that occurs near arterial bifurcations and other selected points around the human vasculature. The flow in large vessels can now be determined accurately with MR and in vitro cast models. Although theory allows arterial flow to be characterized by asymmetry in time and space, our understanding of the processes that act to translate this asymmetry into pathology is becoming much more symmetric, or complete. The new frontiers of research in arterial flow are now translating to smaller scales, at the cellular level and below.