Effect of turbulent models on left ventricle diastolic flow patterns simulation

Abstract

Vortex structures, as one of the most important features of cardiac flow, have a crucial impact on the left ventricle function and pathological conditions. These swirling flows are closely related to the presence of turbulence in left ventricle which is investigated in the current study. Using an extended model of the left heart, including a fluid-structure interaction (FSI) model of the mitral valve with a realistic geometry, the effect of using two numerical turbulent models, k-ε and Spalart-Allmaras (SA), on diastolic flow patterns is studied and compared with results from laminar flow model. As a result of the higher dissipation rate in turbulent models (k-ε and SA), vortices are larger and stronger in the laminar flow model. Comparing E/A ratio in the three models (Laminar, k-ε, and SA) with experimental data from healthy subjects, it is concluded that the results from k-ε model are more accurate.     

The functional status of the left ventricle in normal conditions. Results of multiphase x-ray contrast left ventriculography]

The main functional characteristics of the left ventricle (LV) were defined using a method of multiphase radiopaque left ventriculography. Three groups of indices of LV function (energetic LV indices, indices of chamber diastolic function, and indices of local motion of the LV walls in the course of a complete cardiocycle) were standardized in healthy persons. An original algorithm of analysis of local LV myocardial contractility was used. A combined approach to interpretation of results of this method was worked out. A standard set of indices, reflecting LV function, was defined. Standardized values of these indices, necessary for an effective use of this method, were obtained.     

Myofiber angle distributions in the ovine left ventricle do not conform to computationally optimized predictions

Recent computational models of optimized left ventricular (LV) myofiber geometry that minimize the spatial variance in sarcomere length, stress, and ATP consumption have predicted that a midwall myofiber angle of 20 degrees and transmural myofiber angle gradient of 140 degrees from epicardium to endocardium is a functionally optimal LV myofiber geometry. In order to test the extent to which actual fiber angle distributions conform to this prediction, we measured local myofiber angles at an average of nine transmural depths in each of 32 sites (4 short-axis levels, 8 circumferentially distributed blocks in each level) in five normal ovine LVs. We found: (1) a mean midwall myofiber angle of -7 degrees (SD 9), but with spatial heterogeneity (averaging 0 degrees in the posterolateral and anterolateral wall near the papillary muscles, and -9 degrees in all other regions); and (2) an average transmural gradient of 93 degrees (SD 21), but with spatial heterogeneity (averaging a low of 51 degrees in the basal posterior sector and a high of 130 degrees in the mid-equatorial anterolateral sector). We conclude that midwall myofiber angles and transmural myofiber angle gradients in the ovine heart are regionally non-uniform and differ significantly from the predictions of present-day computationally optimized LV myofiber models. Myofiber geometry in the ovine heart may differ from other species, but model assumptions also underlie the discrepancy between experimental and computational results. To test the predictive capability of the current computational model would we propose using an ovine specific LV geometry and comparing the computed myofiber orientations to those we report herein.     

The influence of boundary conditions on wall shear stress distribution in patients specific coronary trees

Patient specific geometrical data on human coronary arteries can be reliably obtained multislice computer tomography (MSCT) imaging. MSCT cannot provide hemodynamic variables, and the outflow through the side branches must be estimated. The impact of two different models to determine flow through the side branches on the wall shear stress (WSS) distribution in patient specific geometries is evaluated. Murray's law predicts that the flow ratio through the side branches scales with the ratio of the diameter of the side branches to the third power. The empirical model is based on flow measurements performed by Doriot et al. (2000) in angiographically normal coronary arteries. The fit based on these measurements showed that the flow ratio through the side branches can best be described with a power of 2.27. The experimental data imply that Murray's law underestimates the flow through the side branches. We applied the two models to study the WSS distribution in 6 coronary artery trees. Under steady flow conditions, the average WSS between the side branches differed significantly for the two models: the average WSS was 8% higher for Murray's law and the relative difference ranged from -5% to +27%. These differences scale with the difference in flow rate. Near the bifurcations, the differences in WSS were more pronounced: the size of the low WSS regions was significantly larger when applying the empirical model (13%), ranging from -12% to +68%. Predicting outflow based on Murray's law underestimates the flow through the side branches. Especially near side branches, the regions where atherosclerotic plaques preferentially develop, the differences are significant and application of Murray's law underestimates the size of the low WSS region.     

The left ventricle as confocal prolate spheroids

A model of left ventricle is described which takes into account the physiologic variations of thickness, a function of time and distance prior to and during ejection, by assuming that the prolate spheroids are confocal at a given instant. The hyperbolic segment of arc between innermost and outermost spheroids, confocal with the latter, defines a so-called functional thickness, for which a derivation is given. Results show that this model operates in a range of eccentricity wherein thickness change per unit internal volume change are greatest.     

Experimental evaluation of flow patterns in interposition vein cuff anastomosis. The influence of non-planarity of the inflow

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 degrees 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.     

The motion of the left ventricle. I

The complex arrangement of the muscle fibers in the ventricular wall and the nonsymmetric contraction and expansion of the ventricle preclude the writing of a differential equation of motion for the ventricle as a whole. We can, however, describe the motion of the ventricle by describing the motion of the dimensional parameters length and diameter; the radius, circumference, cross-sectional area, and volume following naturally from these. The ventricle is assumed to be an ellipsoid of revolution and the dimensional parameters to be periodic functions of time. Each of the parameters is expressed as a Fourier series.     

The motion of the left ventricle: II

We use the dimensional parameters previously derived (Bull. Math. Biophysics,28, 355–362, 1966), the ventricular pressure expressed as a Fourier series, and several additional assumptions to derive expressions for the mechanical parameters of the ventricle: flow, muscle segment length, surface area, transmural force, wall tension and work. The wall of the ventricle is assumed to consist of three layers of muscle. Each of the mechanical parameters is expressed in terms of Fourier series.     

Combined experimental and numerical analysis of the flow structure into the left ventricle

Fluid dynamics is used for diagnosis in cardiology only to a partial extent. Indeed several aspects of cardiac flows and their relation with pathophysiology are unknown. The flow that develops into the left ventricle is here studied by using a combination of numerical and experimental models. The former allows a detailed three-dimensional analysis, the latter can be used in conditions, like in presence of turbulence, that are out of reach of the current computational power. The three-dimensional flow dynamics is analyzed in terms of its vortical structure. The study, within its limitations, provides further physical understanding about the intraventricular flow structure. This could eventually support the development of cardiac diagnostic indicators based on fluid dynamics.     

Quantification of presystolic blood flow organization and energetics in the human left ventricle

Intracardiac blood flow patterns are potentially important to cardiac pumping efficiency. However, these complex flow patterns remain incompletely characterized both in health and disease. We hypothesized that normal left ventricular (LV) blood flow patterns would preferentially optimize a portion of the end-diastolic volume (LVEDV) for effective and rapid systolic ejection by virtue of location near and motion towards the LV outflow tract (LVOT). Three-dimensional cine velocity and morphological data were acquired in 12 healthy persons and 1 patient with dilated cardiomyopathy using MRI. A previously validated method was used for analysis in which the LVEDV was separated into four functional flow components based on the blood's locations at the beginning and end of the cardiac cycle. Each component's volume, kinetic energy (KE), site, direction, and linear momentum relative to the LVOT were calculated. Of the four components, the LV inflow that passes directly to outflow in a single cardiac cycle (Direct Flow) had the largest volume. At the time of isovolumic contraction, Direct Flow had the greatest amount of KE and the most favorable combination of distance, angle, and linear momentum relative to the LVOT. Atrial contraction boosted the late diastolic KE of the ejected components. We conclude that normal diastolic LV flow creates favorable conditions for ensuing ejection, defined by proximity and energetics, for the Direct Flow, and that atrial contraction augments the end-diastolic KE of the ejection volume. The correlation of Direct Flow characteristics with ejection efficiency might be a relevant investigative target in cardiac failure.     

Effects of stents under asymmetric inflow conditions

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 effect of boundary conditions on epicardial potential distributions

This study presents a comparison of semi-analytical and numerical solution techniques for solving the passive bidomain equation in simple tissue geometries containing a region of subendocardial ischaemia. When the semi-analytical solution is based on Fourier transforms, recovering the solution from the frequency domain via fast Fourier transforms imposes a periodic boundary condition on the solution of the partial differential equation. On the other hand, the numerical solution uses an insulation boundary condition. When these techniques are applied to calculate the epicardial surface potentials, both yield a three well potential distribution which is identical if fibre rotation within the tissue is ignored. However, when fibre rotation is included, the resulting three-well distribution rotates, but through different angles, depending on the solution method. A quantitative comparison between the semi-analytical and numerical solutiontechniques is presented in terms of the effect fibre rotation has on the rotation of the epicardial potential distribution. It turns out that the Fourier transform approach predicts a larger rotation of the epicardial potential distribution than the numerical solution. The conclusion from this study is that it is not always possible to use analytical or semi-analytical solutions to check the accuracy of numerical solution procedures. For the problem considered here, this checking is only possible when it is assumed that there is no fibre rotation through the tissue.     

The left ventricle proteome differentiates middle-aged and old left ventricles in mice

Middle-aged and old left ventricles (LVs) are structurally and functionally very similar. Compared to a young LV, both show increased wall thickness and increased cavity size, with preserved cardiac function. However, when a stressor such as myocardial infarction occurs, striking differences are revealed between young and old LVs and there is a marked reduction in survival rates for the old group. The objective of this study was to investigate the proteomic basis of age-related changes in the LV of male mice in order to identify proteins that are differentially expressed between middle-aged and old groups and to gain mechanistic insight into effects of aging on the unstressed heart. Young (3 months old; n = 6), middle-aged (MA; 15 months old; n = 6), and old (23 months old; n = 5) LVs were examined by echocardiography, homogenized, and separated into soluble and insoluble protein fractions using differential extraction. We found that the LV mass-to-tibia ratio increased from 6.4 +/- 0.2 mg/mm in young to 11.0 +/- 0.6 and 10.1 +/- 0.7 mg/mm in MA and old, respectively (both p < 0.05 vs young), which was caused by increases in both LV wall thickness and volume. Using two-dimensional gel electrophoresis, we detected age-related alterations in the levels of 73 proteins (all p < 0.05). Among these proteins were mortalin, peroxiredoxin 3, epoxide hydrolase, and the superoxide dismutases SOD-1 (Cu/ZnSOD) and SOD-2 (MnSOD), which have been previously associated with aging and/or cardiovascular disease. Together, these results reveal proteomic changes that occur in the LV with age. The proteins identified here may be useful markers of cardiac aging and may help in deducing mechanisms to explain the inability of the old heart to withstand challenge.     

Flow dynamics and energy efficiency of flow in the left ventricle during myocardial infarction

Cardiovascular disease is a leading cause of death worldwide, where myocardial infarction (MI) is a major category. After infarction, the heart has difficulty providing sufficient energy for circulation, and thus, understanding the heart’s energy efficiency is important. We induced MI in a porcine animal model via circumflex ligation and acquired multiple-slice cine magnetic resonance (MR) images in a longitudinal manner—before infarction, and 1 week (acute) and 4 weeks (chronic) after infarction. Computational fluid dynamic simulations were performed based on MR images to obtain detailed fluid dynamics and energy dynamics of the left ventricles. Results showed that energy efficiency flow through the heart decreased at the acute time point. Since the heart was observed to experience changes in heart rate, stroke volume and chamber size over the two post-infarction time points, simulations were performed to test the effect of each of the three parameters. Increasing heart rate and stroke volume were found to significantly decrease flow energy efficiency, but the effect of chamber size was inconsistent. Strong complex interplay was observed between the three parameters, necessitating the use of non-dimensional parameterization to characterize flow energy efficiency. The ratio of Reynolds to Strouhal number, which is a form of Womersley number, was found to be the most effective non-dimensional parameter to represent energy efficiency of flow in the heart. We believe that this non-dimensional number can be computed for clinical cases via ultrasound and hypothesize that it can serve as a biomarker for clinical evaluations.     

Inlet boundary conditions for blood flow simulations in truncated arterial networks

In the context of patient-specific cardiovascular applications, hemodynamics models (going from 3D to 0D) are often limited to a part of the arterial tree. This restriction implies the set up of artificial interfaces with the remaining parts of the cardiovascular system. In particular, the inlet boundary condition is crucial: it supplies the impulsion to the system and receives the reflected backward waves created by the distal network. Some aspects of this boundary condition need to be properly defined such as the treatment of backward waves (reflected or absorbed) and the value of the imposed hemodynamic wave (total or forward component). Most authors prescribe as inlet boundary condition (BC) the total measured variable (pressure, velocity or flow rate) in a reflective way. We show that with this type of inlet boundary condition, the model does not produce physiological waveforms. We suggest instead to prescribe only the forward component of the prescribed variable in an absorbing way. In this way, the computed reflected waves superpose with the prescribed forward waves to produce the total wave at the inlet. In this work, different inlet boundary conditions are implemented and compared for a 1D blood flow model. We test our boundary conditions on a truncated arterial model presented in the literature as well as on a patient-specific lower-limb model of a femoral bypass. We show that with this new boundary condition, a much better fitting is observed on the shape and intensity of the simulated pressure and velocity waves.     

Effect of prosthetic mitral valve geometry and orientation on flow dynamics in a model human left ventricle

Pulsatile flow dynamics through bileaflet (St Jude and Duromedics), tilting disc (Bjork-Shiley and Omniscience), caged ball (Starr-Edwards), pericardial (Edwards) and porcine (Carpentier-Edwards) mitral valves in a model human left ventricle (LV) were studied. The model human ventricle, obtained from an in situ diastolic casting, was incorporated into a mock circulatory system. Measurements were made at various heart rates and flow rates. These included the transvalvular pressure drop and regurgitation in percent and cm3 beat-1. The effect of valve geometry and the orientation of the valve with respect to the valve annulus was analyzed using a flow visualization technique. Qualitative flow visualization study indicates certain preferred orientations for the tilting disc and bileaflet valve prostheses in order to obtain a smooth washout of flow in the LV chamber.     

The left ventricle and hemodynamic patterns in essential hypertension

Hemodynamic patterns in hypertensive patients by radionuclide techniques and tomographic gamma camera were evaluated. In younger hypertensive patients, the hyperkinetic state reflected an increase in heart rate and, consequently, an increased cardiac index and left ventricular ejection fraction (LVEF). Older hypertensive patients, however, showed a different hemodynamic pattern, with reduced systolic and diastolic function at rest compared with normotensive elderly people, and marked depression of cardiac systolic and diastolic reserve during exercise. They also showed strikingly higher hyperresistance and reduced peripheral perfusion. These hemodynamic differences need to be taken into account when considering antihypertensive treatment. In a study in 106 elderly hypertensive patients, treatment with four different antihypertensive drugs produced a significant decrease in total peripheral resistance and blood pressure, together with a reduction in left ventricular (LV) afterload and an increase in cardiac output and LVEF (tending towards normal values). The LV peak filling rate was also increased and evaluation of systolic and diastolic cardiac reserve during exercise showed positive changes in cardiac performance. Left ventricular hyperthropy (LVH) is a powerful predictor of cardiac events. Long-term increases in BP predispose to LVH, impaired diastolic relaxation and, ultimately, ventricular dysfunction. A reduction in LVH produces a number of different beneficial effects. Coronary flow reserve was evaluated in hypertensive patients. Coronary flow reserve was highly impaired in comparison with normotensive controls, and increases in arteriolar wall thickness, collagen content and diastolic dysfunction were also noted. A marked improvement in coronary flow reserve in patients who received antihypertensive therapy was confirmed.