Objectives The aims of this study were to: 1) assess the feasibility of left ventricular (LV) vortex flow analysis using contrast echocardiography (CE); and 2) characterize and quantify LV vortex flow in normal subjects and patients with LV systolic dysfunction. Background Vortices that form during LV filling have specific geometry and anatomical locations that are critical determinants of directed blood flow during ejection. Therefore, it is clinically relevant to assess the vortex flow patterns to better understand the LV function. Methods Twenty-five patients (10 normal and 15 patients with abnormal LV systolic function) underwent CE with intravenous contrast agent, Definity (Bristol-Myers Squibb Medical Imaging, Inc., North Billerica, Massachusetts). The velocity vector and vorticity were estimated by particle image velocimetry. Average vortex parameters including vortex depth, transverse position, length, width, and sphericity index were measured. Vortex pulsatility parameters including relative strength, vortex relative strength, and vortex pulsation correlation were also estimated. Results Vortex depth and vortex length were significantly lower in the abnormal LV function group (0.443 ± 0.04 vs. 0.482 ± 0.06, p Conclusions It was feasible to quantify LV vorticity arrangement by CE using particle image velocimetry in normal subjects and those with LV systolic dysfunction, and the vorticity imaging by CE may serve as a novel approach to depict vortex, the principal quantity to assess the flow structure.

Characterization and Quantification of Vortex Flow in the Human Left Ventricle by Contrast Echocardiography Using Vector Particle Image Velocimetry

I review the concept of optimal vortex formation and examine its relevance to propulsion in biological and bio-inspired systems, ranging from the human heart to underwater vehicles. By using examples from the existing literature and new analyses, I show that optimal vortex formation can potentially serve as a unifying principle to understand the diversity of solutions used to achieve propulsion in nature. Additionally, optimal vortex formation can provide a framework in which to design engineered propulsions systems that are constrained by pressures unrelated to biology. Finally, I analyze the relationship between optimal vortex formation and previously observed constraints on Strouhal frequency during animal locomotion in air and water. It is proposed that the Strouhal frequency constraint is but one consequence of the process of optimal vortex formation and that others remain to be discovered.

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Optimal Vortex Formation as a Unifying Principle in Biological Propulsion

Computational models of the electrical and mechanical function of the heart are reviewed. These models attempt to explain the integrated function of the heart in terms of ventricular anatomy, the structure and material properties of myocardial tissue, the membrane ion channels, and calcium handling and myofilament mechanics of cardiac myocytes. The models have established the computational framework for linking the structure and function of cardiac cells and tissue to the integrated behavior of the intact heart, but many more aspects of physiological function, including metabolic and signal transduction pathways, need to be included before significant progress can be made in understanding many disease processes.

Modeling total heart function.

Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function

Blood motion in the heart features vortices that accompany the redirection of jet flows towards the outlet tracks. Vortices have a crucial role in fluid dynamics. The stability of cardiac vorticity is vital to the dynamic balance between rotating blood and myocardial tissue and to the development of cardiac dysfunction. Moreover, vortex dynamics immediately reflect physiological changes to the surrounding system, and can provide early indications of long-term outcome. However, the pathophysiological relevance of cardiac fluid dynamics is still unknown. We postulate that maladaptive intracardiac vortex dynamics might modulate the progressive remodelling of the left ventricle towards heart failure. The evaluation of blood flow presents a new paradigm in cardiac function analysis, with the potential for sensitive risk identification of cardiac abnormalities. Description of cardiac flow patterns after surgery or device therapy provides an intrinsic qualitative evaluation of therapeutic procedures, and could enable early risk stratification of patients vulnerable to adverse cardiac remodelling.

The vortex--an early predictor of cardiovascular outcome?

A numerical study of the three-dimensional fluid dynamics inside a model left ventricle during diastole is presented. The ventricle is modelled as a portion of a prolate spheroid with a moving wall, whose dynamics is externally forced to agree with a simplified waveform of the entering flow. The flow equations are written in the meridian body-fitted system of coordinates, and expanded in the azimuthal direction using the Fourier representation. The harmonics of the dependent variables are normalized in such a way that they automatically satisfy the high-order regularity conditions of the solution at the singular axis of the system of coordinates. The resulting equations are solved numerically using a mixed spectral–finite differences technique. The flow dynamics is analysed by varying the governing parameters, in order to understand the main fluid phenomena in an expanding ventricle, and to obtain some insight into the physiological pattern commonly detected. The flow is characterized by a well-defined structure of vorticity that is found to be the same for all values of the parameters, until, at low values of the Strouhal number, the flow develops weak turbulence.

Three-dimensional filling flow into a model left ventricle

Fluid dynamics of the left ventricular filling in dilated cardiomyopathy.

Model and influence of mitral valve opening during the left ventricular filling.

Analysis of the properties of the left ventricle flow during filling (diastole) is known to allow early detection of potential malfunctions during the fundamental heart pumping phase (systole). Diagnoses are now usually based on Doppler measurement of the flow velocity for which interpretative schemes and quantitative references are sought. The flow inside an ideal model of the left ventricle is here studied numerically by a finite difference method in prolate spheroid moving coordinates. The axisymmetric assumption is employed in this first study. The vortex dynamics is characterised by the formation of a wake vortex attached at the valvular edge which is shed at the end of the ventricle expansion. Major features are its translation by self-induced velocity and vortex-induced separations from the ventricle internal wall. Results are represented as, and compared with, clinical data showing a good general agreement and allowing an improved physical interpretation of the latter.  2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Bernardo Baccani

Papers

Three-dimensional filling flow into a model left ventricle

Fluid dynamics of the left ventricular filling in dilated cardiomyopathy.

Model and influence of mitral valve opening during the left ventricular filling.

Vortex dynamics in a model left ventricle during filling