Precursor cerebral circulation models.
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Blood Flow Velocity↗
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Flow in arteries in the presence of stenosis.
Of concern in the paper is a study of blood flow in an arterial segment having a stenosis. The artery is modelled as an initially stressed orthotropic elastic tube filled with a viscous incompressible fluid. The analysis is based on the assumption of the presence of a mild stenosis in the artery. Blood is treated as a Newtonian fluid. The effect of the surrounding connective tissues on the motion of the wall has been incorporated. Propagation of small amplitude harmonic waves, generated due to the flow of blood where the wave length is large compared to the radius of the arterial segment, is is considered in detail.
Arterial Occlusive Diseases↗
Analysis of blood flow through a model of the human arterial system under periodic body acceleration.
The human system may be subjected to a body acceleration deliberated for example by making subjects lie down on vibrating tables or more frequently unintentionally, for example during travel in water and land or in air and space. The present study is concerned with the effects of externally imposed body accelerations on blood flow in a branched system of arteries. A finite-element model of flow in the arterial system subject to periodic body accelerations is presented. Computational results on the flow rates through selected arteries and the corresponding inlet and outlet pressures under different conditions (magnitude, frequency and direction) of applied acceleration are presented.
Acceleration↗
Turbulent stress measurements downstream of six mechanical aortic valves in a pulsatile flow model.
In a pulsatile flow model aortic Björk-Shiley Standard, Convex-Concave and Monostrut valves were investigated together with the Hall-Kaster (Medtronic-Hall), St Jude Medical and Starr-Edwards Silastic Ball valve using hot-film anemometry. Three-dimensional visualization of average systolic Reynolds normal stresses (RNS) reflected the design of the valves. Mean average RNS were used for comparison of the fluid dynamic performance along with Velocity Energy Ratio (VER100) and Turbulence Energy Ratio (TER) as a relative turbulence intensity for pulsatile flow. Mean average RNS ranged from 13.2 to 37.6 Nm-2 for all the valves with the highest levels for the Björk-Shiley Standard and Starr-Edwards Ball valve and lowest values for the St Jude Medical valve and with the Hall-Kaster (Medtronic-Hall), Björk-Shiley Convex-Concave and Monostrut valves in between.
Aortic Valve↗
Three-dimensional visualization of velocity fields downstream of six mechanical aortic valves in a pulsatile flow model.
Velocity fields downstream of 27 mm Björk-Shiley Standard, Björk-Shiley Convex-Concave, Björk-Shiley Monostrut, Hall-Kaster (Medtronic-Hall), St. Jude Medical and Starr-Edwards Silastic Ball aortic valves were studied in a pulsatile mock circulation. Stroke volume was 70 cm3 and frequency 71 min-1 and 88 min-1. Fluid velocity was measured by a catheter mounted hot-film anemometer probe in a glycerol water mixture one and two diameters downstream of the aortic valve. Velocity fields were dynamically visualized by a three-dimensional technique and revealed qualitative independence of frequency. All profiles were flat in the acceleration phase of systole. From peak systole and throughout the systolic deceleration phase profiles characteristic of the individual valves appeared. The pivoting and tilting disc valves caused a skewed velocity profile with highest velocities downstream of the major orifice and lowest velocities downstream of the minor orifice. The differences between the three investigated Björk-Shiley valves were remarkable. The St. Jude Medical valve generated velocity peaks downstream of the two major orifices and the central slit, and lower velocities in the hinge areas. A rather flat profile with central hollowing was seen downstream of the Starr-Edwards Ball valve. All velocity profiles were more or less dampened two diameters downstream.
Aortic Valve↗
Wall shear stress distribution in the human carotid siphon during pulsatile flow.
Wall shear stress distribution in the carotid siphon, which is a multiple curved segment of the internal carotid artery, is investigated numerically under physiological flow conditions. The computer simulation of flow through the model segment is based on the time-dependent, three-dimensional Navier-Stokes equations, solved numerically with a finite element method. The study shows the behavior of the wall shear stress-vector field and identifies the zones of high and low wall shear stress values during the cardiac cycle.
Blood Flow Velocity↗
In vitro analysis of a model of intracardiac jet: analysis of the central core of axisymmetric jets.
In order to provide physical information supporting the clinical use of flow mapping, an in vitro model was designed to measure the velocity fields in a pulsatile hydraulic turbulent jet. We used a peak velocity ranging from 2.5 to 5.5 m.s-1, an orifice diameter ranging from 5.8 to 11.3 mm and confined the jet in a receiving tube whose diameter ranged from 16 to 30 mm, thus simulating a large variety of valvular leaks. In steady flow conditions, our results agreed with previously reported descriptions. Under pulsatile conditions, the same structure was found at peak velocity and during the beginning of the deceleration. Below a threshold velocity, the length of the central core was independent of the peak velocity and proportional to about six times the orifice diameter. Above the threshold velocity, this relationship was no longer true, the threshold value being related to the ratio of the orifice diameter to the diameter of the receiving tube.
Blood Flow Velocity↗
The constitutive behaviour of passive heart muscle tissue: a quasi-linear viscoelastic formulation.
A quasi-linear viscoelastic law with a continuous relaxation spectrum describing triaxial constitutive behaviour of heart muscle tissue is presented. The elastic response of the viscoelastic law is anisotropic, while the relaxation behaviour is assumed isotropic. The law is designed for a biphasic description (fluid-solid) of the myocardial tissue. Biaxial and uniaxial stress-strain curves from the literature are used to evaluate the parameters of the model. The non-linear elastic response, the difference between fibre and cross-fibre stiffness, the phenomenon of stress relaxation, the stiffening of the stress-strain relationship with increasing strain rate and the weak frequency dependency of the dissipated energy during cyclic loading are fairly well described by the proposed law. However, it is found that the model produces realistic values for the dissipated energy during cyclic loading only when relaxation parameter values are chosen which result in an overestimation of the stress relaxation data by more than 100%. This finding may indicate non-quasi-linearity of viscoelasticity of passive heart muscle tissue.
Biomechanical Phenomena↗
An inverse approach to determining myocardial material properties.
Passive myocardial material properties have been measured previously by subjecting test samples of myocardium to in vitro load-deformation analysis or, in the intact heart, by pressure-volume relationships. A new method for determining passive material properties, described in this paper, couples a p-version finite element model of the heart, a nonlinear optimization algorithm and a dense set of transmural measured strains that could be obtained in the intact heart by magnetic resonance imaging (MRI) radiofrequency tissue tagging. Unknown material parameters for a nonlinear, nonhomogeneous material law are determined by solving an inverse boundary value problem. An objective function relating the least-squares difference of model-predicted and measured strains is minimized with respect to the unknown material parameters using a novel optimization algorithm that utilizes forward finite element solutions to calculate derivatives of model-predicted strains with respect to the material parameters. Test cases incorporating several salient features of the inverse material identification problem for the heart are formulated to test the performance of the inverse algorithm in typical experimental conditions. Known true material parameters can be determined to within a small tolerance and random noise is shown not to affect the stability of the inverse solution appreciably. On the basis of these validation experiments, we conclude that the inverse material identification problem for the heart can be extended to solve for unknown material parameters that describe in vivo myocardial material behavior.
Algorithms↗
The effect of varying degrees of stenosis on the characteristics of turbulent pulsatile flow through heart valves.
Many problems and complications associated with heart valves are related to the dynamic behavior of the valve and the resultant unsteady flow patterns. An accurate depiction of the spatial and temporal velocity and rms distributions imparts better understanding of flow related valve complications, and may be used as a guideline in valve design. While the generalized correlation between increased turbulence level and the severity of the stenosis is well established, few studies addressed the issue of the intermittent nature of turbulence and its timing in the cardiac cycle, and almost none assessed the effect of a progressive stenosis on the flow characteristics through heart valves. In this experimental work we simulated the type of flow which is present in normal and stenosed valves and conducted a comprehensive investigation of valve hemodynamics, valvular turbulence and morphology under varying degrees of stenosis. The characteristics of valves and stenoses were simulated closely, to achieve the flow conditions that initiate turbulent flow conditions. Laser Doppler anemometry (LDA) measurements were carried out in a pulse duplicator system distal to trileaflet polyurethane prosthetic heart valves, installed at mitral and aortic positions. The effect of the degree of the stenosis was comparatively studied through the structure of the turbulent jets emerging from normal and stenotic heart valves. Maximum turbulence level was achieved during the decelerating phase and correlated to the severity of the stenosis, followed by relaminarization of the flow during the acceleration phase. The intermittent nature of the turbulence emphasized the importance of realizing the timing of the turbulence production and its spatial location for optimizing current valve designs. The plug flow through the normal aortic valve prosthesis was replaced by jet like behavior for a 65% stenosis, with the jet becoming narrower and stronger for a 90% stenosis. The morphology of the velocity and turbulence waveforms was found to be governed by the stenosis geometry and the valve position (aortic, mitral).
Aortic Valve↗
The effect of residual strain on the diastolic function of the left ventricle as predicted by a structural model.
The unloaded heart is not stress-free. It is subjected to residual stress and strain. Their extent and influence on the global performance of the left ventricle and on local phenomena in the ventricular wall are studied by model simulation. The analysis focuses on the equatorial region of the ventricle, with an approximate thick-walled cylindrical geometry. The in vivo myocardium is considered to be incompressible, consisting of fibers embedded in a fluid matrix, with transmurally varying anisotropic microstructure in accordance with morphological characteristics. The results show that residual strain is transmurally distributed with a pattern and magnitude which agree well with measurements. The calculated residual strains are within mean +/- one standard deviation of the measured ones. Their magnitude was found to increase with increasing opening angle and with increasing wall thickness. The residual strain was found to have several effects on ventricular function: At volumes higher than the reference one it gives rise to more uniform transmural distributions of stress and intramyocardial pressure; it causes about 50% increase in the ventricular compliance at high volumes and doubles the suction of atrial blood at low volumes, thus facilitating the diastolic filling. In addition, residual strains cause bias of in vivo measured strains from their true values. This may significantly affect physiological interpretation of measured ventricular deformations. In conclusion, the present structural analysis predicts that residual strain has favorable effect on left-ventricular diastolic performance, and gives rise to more uniform ventricular stress distribution.
Atrial Function, Left↗
A numerical fluid mechanical study of repaired congenital heart defects. Application to the total cavopulmonary connection.
A computational fluid dynamics study based on the application of the finite element method has been performed to investigate the local hemodynamics of the total cavopulmonary connection. This operation is used to treat congenital malformations of the right heart and consists of a by-pass of the right ventricle. In this paper the adopted methodology is presented, together with some of the preliminary results. A three-dimensional parametric model of the connection and a lumped-parameter mechanical model of the pulmonary circulation have been developed. The three-dimensional model has been used to simulate the local fluid dynamics for different designs of the connection, allowing a quantitative evaluation of the dissipated energy in each of the examined configurations. The pulmonary afterload of the three-dimensional model has been reproduced by coupling it with the pulmonary mechanical model. The results show that, from a comparative point of view, the energetic losses can be greatly reduced if a proper hydraulic design of the connection is adopted, which also allows control of the blood flow distribution into the lungs.
Algorithms↗
On the wave transmission and reflection properties of stenoses.
This study is concerned with the wave reflection properties of arterial stenoses. Two theoretical models have been developed for deriving the reflection coefficient: a linear model resulting from the linearization of the pressure drop-flow equation and an indirect, quasi-nonlinear model, based on the separation of pressure waves into their forward and backward running components proximal and distal to the stenosis. The linear method gave consistently lower values for the reflection coefficient when compared to the quasi-nonlinear model. In vitro experiments in elastic tubes showed that the reflection coefficient is strongly dependent on stenosis severity, mean flowrate, and the elastic properties of the proximal unobstructed artery. For critical stenoses the reflection coefficient is frequency and pulsatility independent. The results suggest that hemodynamically nonsevere stenoses may cause significant wave reflections.
Algorithms↗
The influence of the angle of confluence on the flow in a vertebro-basilar junction model.
In earlier work, it was demonstrated that the flow in models of the vertebro-basilar junction is highly three-dimensional and the geometry exerts a strong influence on the hemodynamics. The morphology of the vertebro-basilar junction is very variable amongst individuals. In a study of 85 human vertebro-basilar junctions, the angle between the vertebral arteries varied between 10 and 160 degrees. To determine how the flow is influenced by this geometrical parameter, the flow is studied both experimentally, with laser Doppler velocimetry, and numerically, with a finite element package. A series of junction models is used with a range of confluence angles (45, 85 and 125 degrees). It appears that the angle of confluence has a strong influence on the structure and strength of the secondary flow field. The secondary velocities persist far downstream. Furthermore, near the apex, a region with low velocities is present. The larger the confluence angle is, the larger this region is, and even backflow may occur. In addition, the occurrence of atherosclerotic plaques in 85 human vertebro-basilar junctions is studied. Only one preferential location was found: the apex, the other plaques seem to be randomly distributed. The magnitude of the confluence angle of junctions with sharp-edged apices has a significant influence (p = 0.006) on the occurrence of a plaque at the apex. Apparently, a large confluence angle is a geometrical risk factor for atherosclerosis.
Arteriosclerosis↗
Effects of wall shear stress and fluid recirculation on the localization of circulating monocytes in a three-dimensional flow model.
There is a correlation between the location of early atherosclerotic lesions and the hemodynamic characteristics at those sites. Circulating monocytes are key cells in the pathogenesis of atherosclerotic plaques and localize at sites of atherogenesis. The hypothesis that the distribution of monocyte adhesion to the vascular wall is determined in part by hemodynamic factors was addressed by studying monocyte adhesion in an in vitro flow model in the absence of any biological activity in the model wall. Suspensions of U937 cells were perfused (Re = 200) through an axisymmetric silicone flow model with a stenosis followed by a reverse step. The model provided spatially varying wall shear stress, flow separation and reattachment, and a three-dimensional flow pattern. The cell rolling velocity and adhesion rates were determined by analysis of videomicrographs. Wall shear stress was obtained by numerical solution of the equations of fluid motion. Cell adhesion patterns were also studied in the presence of chemotactic peptide gradients. The cell rolling velocity varied linearly with wall shear stress. The adhesion rate tended to decrease with increasing local wall shear stress, but was also affected by the radial component of velocity and the dynamics of the recirculation region and flow reattachment. Adhesion was increased in the vicinity of chemotactic peptide sources downstream of the expansion site. Results with human monocytes were qualitatively similar to the U937 experiments. Differences in the adhesion rates of U937 cells occurring solely as a function of the fluid dynamic properties of the flow field were clearly demonstrated in the absence of any biological activity in the model wall.
Arterial Occlusive Diseases↗
A three-dimensional, time-dependent analysis of flow through a bileaflet mechanical heart valve: comparison of experimental and numerical results.
The flow through a bileaflet mechanical heart valve during the first half of systole was predicted using computational fluid dynamics (CFD). A three-dimensional model of the geometry of the ventricle, valve, sinus and aorta was developed. Flow through the valve was assumed to be Newtonian and laminar. The peak systolic Reynolds number was 1500 based on the aortic radius and the mean aortic velocity. Flow visualisation and laser Doppler anemometry (LDA) experiments were performed and the results were compared to the CFD model. Good agreement between the LDA measurements and CFD predictions was found in the jets through the major orifices of the valve. The global flow fields predicted by the CFD showed reasonable agreement with the flow visualisation. A starting vortex was shed from the valve leaflets of the CarboMedics valve and the prototype valve. As systole progressed the two major orifice jets were directed towards the aortic wall and a weaker central jet was seen in both the experimental and CFD models. Large vortices were present on either side of the central orifice jet in the sinus area of both models. The three-dimensional time-dependent CFD model was considered to give a reasonable indication of the dominant flow patterns downstream of the bileaflet heart valve and has the potential to be an extremely useful tool to analyse the different designs of existing and future bileaflet valves.
Aorta↗
A personal computer-based arrhythmia generator based on mathematical models of cardiac arrhythmia.
A personal computer-based arrhythmia generator has been developed based upon mathematical models of modulated parasystole and the related equations. A system of nonlinear difference equations is used to generate the time series of RR intervals of ECG that contain normal as well as ectopic QRS waves. The ECG waveform is synthesized according to the computed RR interval and the type of QRS wave and output via DA converter in a real-time base. Various types of ECGs with ventricular ectopic beats and those with very long periods were generated by selecting values for a small number of model parameters. This method requires neither large RAM nor external memory for storing a library of arrhythmic ECGs. The theory, hardware design, software implementation on a personal computer, and experimental reconstruction of clinical ECGs based on the model are discussed.
Arrhythmias, Cardiac↗
Mechanisms of atypical atrioventricular Wenckebach periodicity. A theoretical model derived from the concepts of inhomogeneous excitability and electrotonically mediated conduction.
To explain the mechanisms of atypical atrioventricular (AV) Wenckebach periodicity, a model of the AV node was theoretically derived from the concepts of "inhomogeneous excitability" and "electrotonically mediated conduction." The theoretical model of the AV node has the following characteristics: (1) increased vagal tone depresses excitability in the AV node, (2) depressed excitability in the AV node is inhomogeneous in both transverse and longitudinal directions, and (3) electrotonically mediated conduction occurs across inexcitable gaps in the AV node. Many features in atypical AV Wenckebach periodicity are explained by the use of this model. Delayed AV conduction is caused mostly by electrotonically mediated conduction across a much-depressed region in the AV node, and thereafter AV conduction is blocked at the same region, resulting in the occurrence of an AV Wenckebach period with gradual lengthening of PR intervals. Occasionally, longitudinal dissociaton and concealed reentry in the AV node occur in the part below (distal to) the above depressed region, resulting in the occurrence of an AV Wenckebach period with sudden marked lengthening of a PR interval. The sinus impulse following such suddenly delayed AV conduction is usually blocked in the AV node as the result of concealed reentry of the preceding impulse.
Arrhythmias, Cardiac↗