Computational evaluation of intraventricular pressure gradients based on a fluid-structure approach

Estimation of maximum intraventricular pressure: a three-dimensional fluid-structure interaction model

Background

The aim of this study was to propose a method to estimate the maximum pressure in the left ventricle (MPLV) for a healthy subject, based on cardiac outputs measured by echo-Doppler (non-invasive) and catheterization (invasive) techniques at rest and during exercise.

Methods

Blood flow through aortic valve was measured by Doppler flow echocardiography. Aortic valve geometry was calculated by echocardiographic imaging. A Fluid–structure Interaction (FSI) simulation was performed, using an Arbitrary Lagrangian–Eulerian (ALE) mesh. Boundary conditions were defined as pressure loads on ventricular and aortic sides during ejection phase. The FSI simulation was used to determine a numerical relationship between the cardiac output to aortic diastolic and left ventricular pressures. This relationship enabled the prediction of pressure loads from cardiac outputs measured by invasive and non-invasive clinical methods.

Results

Ventricular systolic pressure peak was calculated from cardiac output of Doppler, Fick oximetric and Thermodilution methods leading to a 22%, 18% and 24% increment throughout exercise, respectively. The mean gradients obtained from curves of ventricular systolic pressure based on Doppler, Fick oximetric and Thermodilution methods were 0.48, 0.41 and 0.56 mmHg/heart rate, respectively. Predicted Fick-MPLV differed by 4.7%, Thermodilution-MPLV by 30% and Doppler-MPLV by 12%, when compared to clinical reports.

Conclusions

Preliminary results from one subject show results that are in the range of literature values. The method needs to be validated by further testing, including independent measurements of intraventricular pressure. Since flow depends on the pressure loads, measuring more accurate intraventricular pressures helps to understand the cardiac flow dynamics for better clinical diagnosis. Furthermore, the method is non-invasive, safe, cheap and more practical. As clinical Fick-measured values have been known to be more accurate, our Fick-based prediction could be the most applicable.

Outflow Conditions for Image-Based Hemodynamic Models of the Carotid Bifurcation: Implications for Indicators of Abnormal Flow

Computational fluid dynamics (CFD) models have become very effective tools for predicting the flow field within the carotid bifurcation, and for understanding the relationship between local hemodynamics, and the initiation and progression of vascular wall pathologies. As prescribing proper boundary conditions can affect the solutions of the equations governing blood flow, in this study, we investigated the influence to assumptions regarding the outflow boundary conditions in an image-based CFD model of human carotid bifurcation. Four simulations were conducted with identical geometry, inlet flow rate, and fluid parameters. In the first case, a physiological time-varying flow rate partition at branches along the cardiac cycle was obtained by coupling the 3D model of the carotid bifurcation at outlets with a lumped-parameter model of the downstream vascular network. Results from the coupled model were compared with those obtained by imposing three fixed flow rate divisions (50/50, 60/40, and 70/30) between the two branches of the isolated 3D model of the carotid bifurcation. Three hemodynamic wall parameters were considered as indicators of vascular wall dysfunction. Our findings underscore that the overall effect of the assumptions done in order to simulate blood flow within the carotid bifurcation is mainly in the hot-spot modulation of the hemodynamic descriptors of atherosusceptible areas, rather than in their distribution. In particular, the more physiological, time-varying flow rate division deriving from the coupled simulation has the effect of damping wall shear stress (WSS) oscillations (differences among the coupled and the three fixed flow partition models are up to 37.3% for the oscillating shear index). In conclusion, we recommend to adopt more realistic constraints, for example, by coupling models at different scales, as in this study, when the objective is the outcome prediction of alternate therapeutic interventions for individual patients, or to test hypotheses related to the role of local fluid dynamics and other biomechanical factors in vascular diseases.

Fluid-Structure Interactions of the Mitral Valve and Left Heart: Comprehensive Strategies, Past, Present and Future

The remodeling that occurs after a posterolateral myocardial infarction can alter mitral valve function by creating conformational abnormalities in the mitral annulus and in the posteromedial papillary muscle, leading to mitral regurgitation (MR). It is generally assumed that this remodeling is caused by a volume load and is mediated by an increase in diastolic wall stress. Thus, mitral regurgitation can be both the cause and effect of an abnormal cardiac stress environment. Computational modeling of ischemic MR and its surgical correction is attractive because it enables an examination of whether a given intervention addresses the correction of regurgitation (fluid-flow) at the cost of abnormal tissue stress. This is significant because the negative effects of an increased wall stress due to the intervention will only be evident over time. However, a meaningful fluid-structure interaction model of the left heart is not trivial; it requires a careful characterization of the in-vivo cardiac geometry, tissue parameterization though inverse analysis, a robust coupled solver that handles collapsing Lagrangian interfaces, automatic grid-generation algorithms that are capable of accurately discretizing the cardiac geometry, innovations in image analysis, competent and efficient constitutive models and an understanding of the spatial organization of tissue microstructure. In this manuscript, we profile our work toward a comprehensive fluid-structure interaction model of the left heart by reviewing our early work, presenting our current work and laying out our future work in four broad categories: data collection, geometry, fluid-structure interaction and validation.

A multi-scale computational method applied to the quantitative evaluation of the left ventricular function

A multi-scale computational method, which combines a lumped parameter model of the cardiovascular system (CVS) with a three-dimensional (3D) left ventricle (LV) hemodynamic solver, is developed for quantitatively evaluating the LV function. The parameter model allows reasonable predictions of the cardiac variables in a closed-loop manner under both normal and various pathological conditions. On the basis of the parameter-model-predicted results, 3D hemodynamic computations further provide quantitative insights into the detailed intraventricular flow patterns. Based on a series of computations, it is demonstrated that the pathological change in the shape and size of the LV has a significant effect on the LV pumping performance.

Simultaneous measurement of blood and myocardial velocity in the rat heart by phase contrast MRI using sparseq-space sampling

PURPOSE

To measure cardiac blood flow patterns and ventricular wall velocities through the cardiac cycle in anesthetized Wistar Kyoto (WKY) rats.

MATERIALS AND METHODS

A gradient-echo cine pulse sequence incorporating pulsed field gradients (PFGs) provided phase contrast (PC) motion encoding. We achieved a range of velocity sensitivity that was sufficient to measure simultaneously the large flow velocities within the cardiac chambers and aortic outflow tract (up to 70 cm s(-1) during systole), and the comparatively small velocities of the cardiac wall (0-3 cm s(-1)). A scheme of sparsely sampling q-space combined with a probability-based method of velocity calculation permitted such measurements along three orthogonal axes, and yielded velocity vector maps in all four chambers of the heart and the aorta, in both longitudinal and transverse sections, for up to 12 time-points in the cardiac cycle.

RESULTS

Left ventricular systole was associated with a symmetrical laminar flow pattern along the cardiac axis, with no appearance of turbulence. In contrast, blood showed a swirling motion within the right ventricle (RV) in the region of the pulmonary outflow tract. During left ventricular diastole a plume of blood entered the left ventricle (LV) from the left atrium. The ventricular flow patterns could also be correlated with measurements of left ventricular wall motion. The greatest velocities of the ventricular walls occurred in the transverse cardiac plane and were maximal during diastolic refilling. The cardiac wall motion in the longitudinal axis demonstrated a caudal-apical movement that may also contribute to diastolic refilling.

CONCLUSION

The successful measurements of blood and myocardial velocity during normal myocardial function may be extended to quantify pathological cardiac changes in animal models of human cardiac disease.

Finite element modelling and simulations in cardiovascular mechanics and cardiology: A bibliography 1993–2004

The paper gives a bibliographical review of the finite element modelling and simulations in cardiovascular mechanics and cardiology from the theoretical as well as practical points of views. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1993 and 2004. At the end of this paper, more than 890 references are given dealing with subjects as: Cardiovascular soft tissue modelling; material properties; mechanisms of cardiovascular components; blood flow; artificial components; cardiac diseases examination; surgery; and other topics.

An Annular Prosthesis for the Treatment of Functional Mitral Regurgitation: Finite Element Model Analysis of a Dog Bone–Shaped Ring Prosthesis

BACKGROUND

Undersized annuloplasty is commonly used in the treatment of functional mitral regurgitation. However, in the case of severely dilated ventricles, annuloplasty may be inadequate to counteract leaflet tethering. My colleagues and I hypothesized that modifying the shape of the annular prosthesis to account for the specific anatomy of functional mitral regurgitation could challenge extreme leaflet tethering.

METHODS

Using finite element model simulations, we tested valve competence after the implantation of conventional D-shaped versus dog bone-shaped annuloplasty rings, the latter of which was designed to selectively reduce the septolateral dimension of the annulus. Three models were compared: model A, simulating the native mitral valve; model B, simulating the same valve after annuloplasty with a conventional D-shaped annuloplasty; and model C, simulating a dog-bone annuloplasty ring implantation. Each model was then challenged by progressively pulling the tip of the papillary muscles away from the annulus plane to simulate ventricular remodeling and leaflet tethering. Valve competence was compared in each model for each degree of leaflet tethering.

RESULTS

After maximal leaflet tethering simulation (4-mm apical displacement of the papillary tips), the regurgitant area increase was 70.4 mm2 for model A and 52.9 mm2 for model B. In model C, the regurgitant area was only negligibly affected by papillary displacement, increasing to 3.9 mm2.

CONCLUSIONS

An annular prosthesis with selective reduction in the septolateral dimension is more effective than a conventional prosthesis for treating leaflet tethering in functional mitral regurgitation. Use of disease-specific annular prostheses is needed to improve the results of valve reconstruction.

Computational modeling of vascular anastomoses

Recent development of computational technology allows a level of knowledge of biomechanical factors in the healthy or pathological cardiovascular system that was unthinkable a few years ago. In particular, computational fluid dynamics (CFD) and computational structural (CS) analyses have been used to evaluate specific quantities, such as fluid and wall stresses and strains, which are very difficult to measure in vivo. Indeed, CFD and CS offer much more variability and resolution than in vitro and in vivo methods, yet computations must be validated by careful comparison with experimental and clinical data. The enormous parallel development of clinical imaging such as magnetic resonance or computed tomography opens a new way toward a detailed patient-specific description of the actual hemodynamics and structural behavior of living tissues. Coupling of CFD/CS and clinical images is becoming a standard evaluation that is expected to become part of the clinical practice in the diagnosis and in the surgical planning in advanced medical centers. This review focuses on computational studies of fluid and structural dynamics of a number of vascular anastomoses: the coronary bypass graft anastomoses, the arterial peripheral anastomoses, the arterio-venous graft anastomoses and the vascular anastomoses performed in the correction of congenital heart diseases.

Haemodynamics and mechanics following partial left ventriculectomy: a computer modeling analysis

Mechanics following partial left ventriculectomy is still poorly understood. A computational cylindrical model of the left ventricle was developed, based on the myocardial fibre behaviour for the evaluation of the mechanical and haemodynamical effects of the operation. A healthy left ventricle with physiological geometry and function and a dilated hypokinetic heart were investigated. Haemodynamic and mechanical data were obtained at baseline and compared with those obtained at different degrees of volume reduction. Data included: ejection fraction (EF); stroke volume (SV); end-systolic and end-diastolic pressure-volume relationships (ESPVR and EDPVR), and efficiency. EF increases following volume reduction in both simulation but, concurrently, SV shows modest improvement (dilated ventricle) or reduction (healthy ventricle) at progressive degrees of resection. The ESPVR and EDPVR slope increases and shifts leftward with the resection extent, but the increase of the ESPVR slope is more pronounced in dilated ventricle. Efficiency is improved in the dilated heart after resections, while does not improve when the healthy-heart volume is reduced. The simulation of partial left ventriculectomy suggests an improvement of systolic performance, counterbalanced by increased diastolic stiffness following inverse remodelling. Efficiency of simulated dilated ventricles is enhanced by volume reduction, suggesting a favourable effect of reduction of the metabolic demand of the failing heart.

A computational study of the hemodynamics after "edge-to-edge" mitral valve repair

Edge-to-edge mitral valve repair consists in suturing the free edge of the leaflets to re-establish coaptation in prolapsing valves. The leaflets are frequently sutured at the middle and a double orifice valve is created. In order to study the hemodynamic implications, a parametric model of the left heart has been developed. Different valve areas and shapes have been investigated. Results show that the simplified Bernoulli formula provides a good estimation of the pressure drop and that the pressure drop may be predicted on the basis of the pre-operative geometric and hemodynamics data by means of customized models.

Computer simulation of intraventricular flow and pressure gradients during diastole

A two-dimensional axisymmetric computer model is developed for the simulation of the filling flow in the left ventricle (LV). The computed results show that vortices are formed during the acceleration phases of the filling waves. During the deceleration phases these are amplified and convected into the ventricle. The ratio of the maximal blood velocity at the mitral valve (peak E velocity) to the flow wave propagation velocity (WPV) of the filling wave is larger than 1. This hemodynamic behavior is also observed in experiments in vitro (Steen and Steen, 1994, Cardiovasc. Res., 28, pp. 1821-1827) and in measurements in vivo with color M-mode Doppler echocardiography (Stugaard et al., 1994, J. Am. Coll. Cardiol., 24, 663-670). Computed intraventricular pressure profiles are similar to observed profiles in a dog heart (Courtois et al., 1988, Circulation, 78, pp. 661-671). The long-term goal of the computer model is to study the predictive value of noninvasive parameters (e.g., velocities measured with Doppler echocardiography) on invasive parameters (e.g., pressures, stiffness of cardiac wall, time constant of relaxation). Here, we show that higher LV stiffness results in a smaller WPV for a given peak E velocity. This result may indicate an inverse relationship between WPV and LV stiffness, suggesting that WPV may be an important noninvasive index to assess LV diastolic stiffness, LV diastolic pressure and thus atrial pressure (preload).

Ventricular motion during the ejection phase: a computational analysis

In the present paper, the study of the ventricular motion during systole was addressed by means of a computational model of ventricular ejection. In particular, the implications of ventricular motion on blood acceleration and velocity measurements at the valvular plane (VP) were evaluated. An algorithm was developed to assess the force exchange between the ventricle and the surrounding tissue, i.e., the inflow and outflow vessels of the heart. The algorithm, based on the momentum equation for a transitory flowing system, was used in a fluid-structure model of the ventricle that includes the contractile behavior of the fibers and the viscous and inertial forces of the intraventricular fluid. The model calculates the ventricular center of mass motion, the VP motion, and intraventricular pressure gradients. Results indicate that the motion of the ventricle affects the noninvasive estimation of the transvalvular pressure gradient using Doppler ultrasound. The VP motion can lead to an underestimation equal to 12.4 +/- 6.6%.

The hemodynamic effects of double-orifice valve repair for mitral regurgitation: a 3D computational model

OBJECTIVES

A 3D computational model has been implemented for the evaluation of the hemodynamics of the double orifice repair. Critical issues for surgical decision making and echo-Doppler evaluation of the results of the procedure are investigated.

METHODS

A parametric 3D computational model of the double-orifice mitral valve based on the finite elements model has been constructed from clinical data. Nine different geometries were investigated, corresponding to three total inflow areas (1.5, 2.25 and 3 cm2) and to three orifice configurations (two equal orifices, two orifices of different areas, i.e. one twice as much the other one, and a single orifice). The simulations were performed in transit; the fluid was initially quiescent and was accelerated to the maximum flow rate with a cubic function. For each case, some characteristic values of velocity and pressure were determined: velocities were calculated downstream of each orifice, at the centre of it (Vcen1, Vcen2). The maximum velocity was also determined for each orifice (Vmax1, Vmax2). Maximum pressure drops (deltap(max)) across the valve were compared with the estimations (deltap(Bernoulli)) based on the Bernoulli formula (4 V2).

RESULTS

In each simulation, no notable difference was observed between Vcen1 and Vcen2, and between Vmax1 and Vmax2, regardless of the valve configuration. Maximum velocity and deltap(max) were related to the total orifice area and were not influenced by the orifice configuration. Deltap(Bernoulli) calculated with Vmax was well correlated with the deltap(max) obtained throughout the simulations (y = 0.9126x + 0.3464, r = 0.996); on the contrary the pressure drops estimated using Vcen underestimated (y = 0.6757x + 0.3073, r = 0.999) the actual pressure drops.

CONCLUSIONS

The hemodynamic behaviour of a double orifice mitral valve does not differ from that of a physiological valve of same total area: pressure drops and flow velocity across the valve are not influenced by the configuration of the valve. Echo Doppler estimation of the maximum velocities is a reliable method for the calculation of pressure gradients across the repaired valve.

Intraventricular pressure drop and aortic blood acceleration as indices of cardiac inotropy: a comparison with the first derivative of aortic pressure based on computer fluid dynamics

This paper presents a computational approach to ventricular fluid mechanics to evaluate three inotropic indices of early ejection: the intraventricular pressure drop (deltap). the first derivative of aortic flow rate (df/dt) and the first derivative of aortic pressure dp/dt. dp/dt is one of the most frequently used indices for assessing myocardial inotropy. Deltap and df/dt are characteristic of inertia driven flows and reflect the impulsive nature of the flow inside the ventricle during the ejection phase. The study is based on an axisymmetric fluid dynamics model of the left ventricle, developed according to the finite element approach. The fluid cavity is bounded by a shell containing two sets of counter-rotating contractile fibres. Two simulation sets were performed: the former to investigate the sensitivity of deltap and df/dt peaks (deltap(max) and df/dt(max)) with respect to changes in the inotropic state of the fibre. The latter allows the evaluation of the dependency of deltap(max) and df/dt(max) on afterload by means of two supravalvular stenoses of 50% and 70%. The model simulates the inertial features of ventricle behaviour. The calculated values of the indices investigated are in close agreement with those reported in the literature. The sensitivities of deltap(max) df/dt(max) and dp/dt(max) are calculated for the two simulation sets. Data are normalised with respect to the maximum values reached in the simulation set. The comparison indicates that deltap(max) has a greater sensitivity (3.4 vs. 3.1 ) and a more linear pattern than dp/dt(max) for changes in the inotropic state of the fibre. df/dt(max), shows a sensitivity close to dp/dt(max). Results confirm that the afterload does not affect dp/dt(max), in accordance with experimental observations, while deltap(max) and, to a major degree, df/dt(max) decrease when the afterload is increased.