Vortex formation time-to-left ventricular early rapid filling relation: model-based prediction with echocardiographic validation

Abstract

During early rapid filling, blood aspirated by the left ventricle (LV) generates an asymmetric toroidal vortex whose development has been quantified using vortex formation time (VFT), a dimensionless index defined by the length-to-diameter ratio of the aspirated (equivalent cylindrical) fluid column. Since LV wall motion generates the atrioventricular pressure gradient resulting in the early transmitral flow (Doppler E-wave) and associated vortex formation, we hypothesized that the causal relation between VFT and diastolic function (DF), parametrized by stiffness, relaxation, and load, can be elucidated via kinematic modeling. Gharib et al. (Gharib M, Rambod E, Kheradvar A, Sahn DJ, Dabiri JO. Proc Natl Acad Sci USA 103: 6305-6308, 2006) approximated E-wave shape as a triangle and calculated VFT(Gharib) as triangle (E-wave) area (cm) divided by peak (Doppler M-mode derived) mitral orifice diameter (cm). We used a validated kinematic model of filling for the E-wave as a function of time, parametrized by stiffness, viscoelasticity, and load. To calculate VFT(kinematic), we computed the curvilinear E-wave area (using the kinematic model) and divided it by peak effective orifice diameter. The derived VFT-to-LV early rapid filling relation predicts VFT to be a function of peak E-wave-to-peak mitral annular tissue velocity (Doppler E'-wave) ratio as (E/E')(3/2). Validation utilized 262 cardiac cycles of simultaneous echocardiographic high-fidelity hemodynamic data from 12 subjects. VFT(Gharib) and VFT(kinematic) were calculated for each subject and were well-correlated (R(2) = 0.66). In accordance with prediction, VFT(kinematic) to (E/E')(3/2) relationship was validated (R(2) = 0.63). We conclude that VFT(kinematic) is a DF index computable in terms of global kinematic filling parameters of stiffness, viscoelasticity, and load. Validation of the fluid mechanics-to-chamber kinematics relation unites previously unassociated DF assessment methods and elucidates the mechanistic basis of the strong correlation between VFT and (E/E')(3/2).

Vortex Ring Formation in the Left Ventricle of the Heart: Analysis by 4D Flow MRI and Lagrangian Coherent Structures

“…Using the vortex boundary delineation provided by LCS in combination with particle tracing 6 , other quantitative measures such as fluid entrainment 24 may be computed. Recent studies have also suggested that vortex formation is linked to the load, stiffness and relaxation of the LV during rapid filling in humans 9 , and to LV pressure drop and the movement of the mitral annulus in heart-like phantoms 15,16 .…”

Unravelling cardiovascular disease using four dimensional flow cardiovascular magnetic resonance

“…4D Flow CMR has enabled the characterization of the instantaneous time-evolution of 3D vortex ring flow within the LV over the complete diastole [44]. Formation of vortex ring flow has been suggested to help efficient MV closure and diastolic filling, minimize kinetic energy loss and prevent thrombus formation [1, 54, 64, 65]. Vortex flow patterns can change due to age, gender, blood pressure, ventricular geometry and mitral/atrioventricular valve abnormalities [45, 66].…”

Vortex flow during early and late left ventricular filling in normal subjects: quantitative characterization using retrospectively-gated 4D flow cardiovascular magnetic resonance and three-dimensional vortex core analysis

“…In a two dimensional (2D) four-chamber view a 3D vortex ring appears as a counter-rotating vortex pair, one distal to the anterior MV leaflet and another distal to the posterior leaflet. Such vortex formation may help in efficient MV closure [5], efficient diastolic filling, minimizing kinetic energy loss [4,6] and preventing thrombus formation [7]. An altered (early filling) vortex formation have been shown to develop in patients with diastolic dysfunction and dilated ischemic cardiomyopathy, suggesting a relation between abnormal vortex formation and LV dysfunction [7,8].…”