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.     

Three-dimensional numerical simulations of flow through a stenosed coronary bypass

This work analyzes the flow patterns at the anastomosis of a stenosed coronary bypass. Three-dimensional numerical simulations are performed using a finite elements method. We consider a geometrical model of the host coronary artery with and without a 75% severity stenosis for three different locations from the anastomosis. The flow features - velocity profiles, secondary motions and wall shear stresses - are compared for different configurations of the flow rate and of the distance of the anastomosis from the site of occlusion (called distance of grafting). The combination of the junction flow effects - counter rotating vortices - with the stenosis effects - confined jet flow - is particularly important when the distance of grafting is short. Given that the residual flow issued from the pathologic stenosis being non-negligible after two weeks grafting, models without stenosis cannot predict the evolution of the wall shear stress in the vicinity of the anastomosis.     

Fluid flow structure in arterial bypass anastomosis

The fluid flow through a stenosed artery and its bypass graft in an anastomosis can substantially influence the outcome of bypass surgery. To help improve our understanding of this and related issues, the steady Navier-Stokes flows are computed in an idealized arterial bypass system with partially occluded host artery. Both the residual flow issued from the stenosis--which is potentially important at an earlier stage after grafting--and the complex flow structure induced by the bypass graft are investigated. Seven geometric models, including symmetric and asymmetric stenoses in the host artery, and two major aspects of the bypass system, namely, the effects of area reduction and stenosis asymmetry, are considered. By analyzing the flow characteristics in these configurations, it is found that (1) substantial area reduction leads to flow recirculation in both upstream and downstream of the stenosis and in the host artery near the toe, while diminishes the recirculation zone in the bypass graft near the bifurcation junction, (2) the asymmetry and position of the stenosis can affect the location and size of these recirculation zones, and (3) the curvature of the bypass graft can modify the fluid flow structure in the entire bypass system.     

Numerical and experimental models of post-operative realistic flows in stenosed coronary bypasses.

By means of both experimental and finite element methods, we simulated three-dimensional unsteady flows through coronary bypass anastomosis. The host artery includes a stenosis shape located at two different distances of grafting. The inflow rates are issued from in vivo measurements in patients who had undergone coronary bypass surgery a few days before. We provide a comparison between experimental and numerical velocity profiles coupled with the numerical analysis of spatial and temporal wall shear stress evolution. The interaction between the graft and coronary flows has been demonstrated. The phase inflow difference can partly be responsible for specific flow phenomena: jet deflection towards a preferential wall or feedback phenomenon that causes the flapping of the post-stenotic jet during the cardiac cycle. In conclusion, we showed the sensitivity of these typical flows to distance of grafting, inflows waveforms but also to their phase difference.     

Numerical flow studies in human carotid artery bifurcations: basic discussion of the geometric factor in atherogenesis

In this study fluid dynamic variables are analysed numerically in different human carotid artery bifurcation models in order to clarify the geometric factor in carotid bifurcation atherogenesis. The geometric variations describe healthy human carotid bifurcation anatomy and concern the shape of the carotid sinus and the angle between the branches. The flow conditions remain unchanged. The governing Navier-Stokes equations describing incompressible, pulsatile, three-dimensional viscous flow are approximated using a pressure correction finite element procedure which has been developed for time-consuming, three-dimensional, time-dependent viscous flow problems. The study concentrates on flow velocity, on detailed analysis of flow separation and flow recirculation, and on wall shear stress distribution. The results show that the extension and the location of the recirculation zone in the sinus as well as the duration of separated flow during the pulse cycle are affected by the geometrical variations. In view of the significance of the reversed flow zones and of the accompanied low shear regions in atherogenesis the geometry-dependent flow separation characteristics in the sinus is of substantial interest.     

Haemodynamic assessment of human coronary arteries is affected by degree of freedom of artery movement

Abnormal haemodynamic parameters are associated with atheroma plaque progression and instability in coronary arteries. Flow recirculation, shear stress and pressure gradient are understood to be important pathogenic mediators in coronary disease. The effect of freedom of coronary artery movement on these parameters is still unknown. Fluid–structure interaction (FSI) simulations were carried out in 25 coronary artery models derived from authentic human coronaries in order to investigate the effect of degree of freedom of movement of the coronary arteries on flow recirculation, wall shear stress (WSS) and wall pressure gradient (WPG). Each FSI model had distinctive supports placed upon it. The quantitative and qualitative differences in flow recirculation, maximum wall shear stress (MWSS), areas of low wall shear stress (ALWSS) and maximum wall pressure gradient (MWPG) for each model were determined. The results showed that greater freedom of movement was associated with lower MWSS, smaller ALWSS, smaller flow recirculation zones and lower MWPG. With increasing percentage diameter stenosis (%DS), the effect of degree of freedom on flow recirculation and WSS diminished. Freedom of movement is an important variable to be considered for computational modelling of human coronary arteries, especially in the setting of mild to moderate stenosis.

Abbreviations: 3D: Three-dimensional; 3DR: Three-dimensional Reconstruction; 3D-QCA: Three-dimensional quantitative coronary angiography; ALWSS: Areas of low wall shear stress; CAD: Coronary artery disease; CFD: Computational fluid dynamics; %DS: Diameter stenosis percentage; EPCS: End point of counter-rotating streamlines; FSI: Fluid–structure interaction; IVUS: Intravascular ultrasound; LAD: Left anterior descending; MWSS: Maximum wall shear stress; SST: Shear stress transport; TAWSS: Time-averaged wall shear stress; WSS: wall shear stress; WPG: Wall pressure gradient; MWPG: Maximum wall pressure gradient; FFR: Fractional flow reserve; iFR: Instantaneous wave-free ratio     

Surgical treatment of impending myocardial infarction: Report of two cases

Two men, aged 29 and 44, presented with clinical and electrocardiographic evidence suggesting impending myocardial infarction. Selective coronary angiography revealed serious obstructive coronary atherosclerosis including gross stenosis of the main left coronary artery in both. Emergency surgical operations were performed, a double aorto-coronary venous bypass in one and a single venous bypass combined with a Vineberg operation in the other. Neither patient sustained myocardial infarction. Both patients are very well more than six months after operation. Clinical, electrocardiographic and angiographic evidence of the effectiveness of these operations is presented.     

Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts

A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the hemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patient-specific medical images to fast parameterized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier–Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parameterization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases.     

Simulation of LV pacemaker lead in marginal vein: potential risk factors for acute dislodgement

Although left ventricular (LV) coronary sinus lead dislodgement remains a problem, the risk factors for dislodgement have not been clearly defined. In order to identify potential risk factors for acute lead dislodgement, we conducted dynamic finite element simulations of pacemaker lead dislodgement in marginal LV vein. We considered factors such as mismatch in lead and vein diameters, velocity of myocardial motion, branch angle between the insertion vein and the coronary sinus, degree of slack, and depth of insertion. The results show that large lead-to-vein diameter mismatch, rapid myocardial motion, and superficial insertion are potential risk factors for lead dislodgement. In addition, the degree of slack presents either a positive or negative effect on dislodgement risk depending on the branch angle. The prevention of acute lead dislodgment can be enforced by inducing as much static friction force as possible at the lead-vein interface, while reducing the external force. If the latter exceeds the former, dislodgement will occur. The present findings underscore the major risk factors for lead dislodgment, which may improve implantation criterion and future lead design.     

Non-Newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses

Non-Newtonian fluid flow in a stenosed coronary bypass is investigated numerically using the Carreau-Yasuda model for the shear thinning behavior of the blood. End-to-side coronary bypass anastomosis is considered in a simplified model geometry where the host coronary artery has a 75% severity stenosis. Different locations of the bypass graft to the stenosis and different flow rates in the graft and in the host artery are studied. Particular attention is given to the non-Newtonian effect of the blood on the primary and secondary flow patterns in the host coronary artery and the wall shear stress (WSS) distribution there. Interaction between the jet flow from the stenosed artery and the flow from the graft is simulated by solving the three-dimensional Navier-Stokes equation coupled with the non-Newtonian constitutive model. Results for the non-Newtonian flow, the Newtonian flow and the rescaled Newtonian flow are presented. Significant differences in axial velocity profiles, secondary flow streamlines and WSS between the non-Newtonian and Newtonian fluid flows are revealed. However, reasonable agreement between the non-Newtonian and the rescaled Newtonian flows is found. Results from this study support the view that the residual flow in a partially occluded coronary artery interacts with flow in the bypass graft and may have significant hemodynamic effects in the host vessel downstream of the graft. Non-Newtonian property of the blood alters the flow pattern and WSS distribution and is an important factor to be considered in simulating hemodynamic effects of blood flow in arterial bypass grafts.     

3D computational parametric analysis of eccentric atheroma plaque: influence of axial and circumferential residual stresses

Plaque rupture plays a role in the majority of acute coronary syndromes. Rupture has usually been associated with stress concentrations, which are mainly affected by the plaque geometry and the tissue properties. The aim of this study is to evaluate the influence of morphology on the risk of plaque rupture, including the main geometrical factors, and to assess the role of circumferential and axial residual stresses by means of a parametric 3D finite element model. For this purpose, a 3D parametric finite element model of the coronary artery with eccentric atheroma plaque was developed. Healthy (adventitia and media in areas without atheroma plaque) and diseased (fibrotic and lipidic) tissues were considered in the model. The geometrical parameters used to define and design the idealized coronary plaque anatomy were the lipid core length, the stenosis ratio, the fibrous cap thickness, and the lipid core ratio. Finally, residual stresses in longitudinal and circumferential directions were incorporated into the model to analyse the influence of the important mechanical factors in the vulnerability of the plaque. Viewing the results, we conclude that residual stresses should be considered in the modelling of this kind of problems since they cause a significant alteration of the vulnerable plaque region limits. The obtained results show that the fibrous cap thickness and the lipid core length, in combination with the lipid core width, appear to be the key morphological parameters that play a determinant role in the maximal principal stress (MPS). However, the stenosis ratio is found to not play a significant role in vulnerability related to the MPS. Plaque rupture should therefore be observed as a consequence, not only of the cap thickness, but as a combination of the stenosis ratio, the fibrous cap thickness and the lipid core dimensions.     

Optimization of shunt placement for the Norwood surgery using multi-domain modeling

An idealized systemic-to-pulmonary shunt anatomy is parameterized and coupled to a closed loop, lumped parameter network (LPN) in a multidomain model of the Norwood surgical anatomy. The LPN approach is essential for obtaining information on global changes in cardiac output and oxygen delivery resulting from changes in local geometry and physiology. The LPN is fully coupled to a custom 3D finite element solver using a semi-implicit approach to model the heart and downstream circulation. This closed loop multidomain model is then integrated with a fully automated derivative-free optimization algorithm to obtain optimal shunt geometries with variable parameters of shunt diameter, anastomosis location, and angles. Three objective functions: (1) systemic; (2) coronary; and (3) combined systemic and coronary oxygen deliveries are maximized. Results show that a smaller shunt diameter with a distal shunt-brachiocephalic anastomosis is optimal for systemic oxygen delivery, whereas a more proximal anastomosis is optimal for coronary oxygen delivery and a shunt between these two anatomies is optimal for both systemic and coronary oxygen deliveries. Results are used to quantify the origin of blood flow going through the shunt and its relationship with shunt geometry. Results show that coronary artery flow is directly related to shunt position.     

Pulsatile non-newtonian blood flow in three-dimensional carotid bifurcation models: a numerical study of flow phenomena under different bifurcation angles

Flow and stress patterns in human carotid artery bifurcation models, which differ in the bifurcation angle, are analysed numerically under physiologically relevant flow conditions. The governing Navier-Stokes equations describing pulsatile, three-dimensional flow of an incompressible non-Newtonian fluid are approximated using a pressure correction finite element method, which has been developed recently. The non-Newtonian behaviour of blood is modelled using Casson's relation, based on measured dynamic viscosity. The study concentrates on flow and stress characteristics in the carotid sinus. The results show that the complex flow in the sinus is affected by the angle variation. The magnitude of reversed flow, the extension of the recirculation zone in the outer sinus region and the duration of flow separation during the pulse cycle as well as the resulting wall shear stress are clearly different in the small angle and in the large angle bifurcation. The haemodynamic phenomena, which are important in atherogenesis, are more pronounced in the large angle bifurcation.     

Steady flow through a double converging-diverging tube model for mild coronary stenoses

Velocity profiles and the pressure drop across two mild (62 percent) coronary stenoses in series have been investigated numerically and experimentally in a perspex-tube model. The mean flow rate was varied to correspond to a Reynolds number range of 50-400. The pressure drop across two identical (62 percent) stenoses show that for low Reynolds numbers the total effect of two stenoses equals that of two single stenoses. A reduction of 10 percent is found for the higher Reynolds numbers investigated. Numerical and experimental results obtained for the velocity profiles agree very well. The effect of varying the converging angle of a single mild (62 percent) coronary stenosis on the fluid flow has been determined numerically using a finite element method. Pressure-flow relation, especially with respect to relative short stenoses, is discussed.     

Influence of stenosis on hemodynamic parameters in the realistic left coronary artery under hyperemic conditions

The current study investigates the hyperemic flow effects on heamodynamics parameters such as velocity, wall shear stress in 3D coronary artery models with and without stenosis. The hyperemic flow is used to evaluate the functional significance of stenosis in the current era. Patients CT scan data of having healthy and coronary artery disease was chosen for the reconstruction of 3D coronary artery models. The diseased 3D models of coronary artery shows a narrowing of >50% lumen area. Computational fluid dynamics was performed to simulate the hyperemic flow condition. The results showed that the recirculation zone was observed immediate to the stenosis and highest wall shear stress was observed across the stenosis. The decrease in pressure was found downstream to the stenosis as compared to the coronary artery without stenosis. Our analysis provides an insight into the distribution of wall shear stress and pressure drop, thus improving our understanding of hyperemic flow effect under both conditions.     

Flow and wall shear stress in end-to-side and side-to-side anastomosis of venous coronary artery bypass grafts

Purpose  

Coronary artery bypass graft (CABG) surgery represents the standard treatment of advanced coronary artery disease. Two major types of anastomosis exist to connect the graft to the coronary artery, i.e., by using an end-to-side or a side-to-side anastomosis. There is still controversy because of the differences in the patency rates of the two types of anastomosis. The purpose of this paper is to non-invasively quantify hemodynamic parameters, such as mass flow and wall shear stress (WSS), in end-to-side and side-to-side anastomoses of patients with CABG using computational fluid dynamics (CFD).     

Which diameter and angle rule provides optimal flow patterns in a coronary bifurcation?

The branching angle and diameter ratio in epicardial coronary artery bifurcations are two important determinants of atherogenesis. Murray's cubed diameter law and bifurcation angle have been assumed to yield optimal flows through a bifurcation. In contrast, we have recently shown a 7/3 diameter law (HK diameter model), based on minimum energy hypothesis in an entire tree structure. Here, we derive a bifurcation angle rule corresponding to the HK diameter model and critically evaluate the streamline flow through HK and Murray-type bifurcations. The bifurcations from coronary casts were found to obey the HK diameter model and angle rule much more than Murray's model. A finite element model was used to investigate flow patterns for coronary artery bifurcations of various types. The inlet velocity and pressure boundary conditions were measured by ComboWire. Y-bifurcation of Murray type decreased wall shear stress-WSS (10%-40%) and created an increased oscillatory shear index-OSI in atherosclerosis-prone regions as compared with HK-type bifurcations. The HK-type bifurcations were found to have more optimal flow patterns (i.e., higher WSS and lower OSI) than Murray-type bifurcations which have been traditionally believed to be optimized. This study has implications for changes in bifurcation angles and diameters in percutaneous coronary intervention.     

Serum activity of angiotensin converting enzyme during extracorporeal circulation in man

Serum activity of angiotensin converting enzyme (ACE) were measured during extra-corporeal circulation in five patients undergoing aorto-coronary bypass surgery. We observed a significant decrease of serum ACE levels in the absence of pulmonary circulation, suggesting that in man the lungs were the major source of circulating ACE. An effective extra-pulmonary liberation of ACE could take place during cardiopulmonary bypass. The levels of serum ACE increased with pulmonary recirculation, but preoperative levels were not reached 24 h later.     

Helical flow as fluid dynamic signature for atherogenesis risk in aortocoronary bypass. A numeric study

The main purpose of the study was to verify if helical flow, widely observed in several vessels, might be a signature of the blood dynamics of vein graft anastomosis. We investigated the existence of a relationship between helical flow structures and vascular wall indexes of atherogenesis in aortocoronary bypass models with different geometric features. In particular, we checked for the existence of a relationship between the degree of helical motion and the magnitude of oscillating shear stress in conventional hand-sewn proximal anastomosis. The study is based on the numerical evaluation of four bypass geometries that are attached to a simplified computer representation of the ascending aorta with different angulations relative to aortic outflow. The finite volume technique was used to simulate realistic graft fluid dynamics, including aortic compliance and proper aortic and graft flow rates. A quantitative method was applied to evaluate the level of helicity in the flow field associated with the four bypass models under investigation. A linear inverse relationship (R = -0.97) was found between the oscillating shear index and the helical flow index for the models under investigation. The results obtained support the hypothesis that an arrangement of the flow field in helical patterns may elicit damping in wall shear stress temporal gradients at the proximal graft. Accordingly, helical flow might play a significant role in preventing plaque deposition or in tuning the mechanotransduction pathways of cells. Therefore, results confirm that helical flow constitutes an important flow signature in vessels, and its strength as a fluid dynamic index (for instance in combination with magnetic resonance imaging flow visualization techniques) for risk stratification, in the activation of both mechanical and biological pathways leading to fibrointimal hyperplasia.     

Haemodynamics of coronary artery - saphenous vein bypass

The velocity distribution of a suspension of red blood cell ghosts in an idealized model of the coronary artery-saphenous vein bypass has been investigated with the aid of laser Doppler anemometry. Pulsatile flow simulated pressure variations in the ascending aorta and ghost cell velocities were determined by the Doppler shift of scattered laser light. Using four different model bypasses it was demonstrated that turbulent flow at the graft-coronary intersection can be delayed by decreasing the discontinuity in diameter between the bypass vein and coronary artery, and also by reducing the bypass vein and host coronary artery intersection angle.