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TECHNICAL PAPERS: Fluids/Heat/Transport

The Effect of Vortex Formation on Left Ventricular Filling and Mitral Valve Efficiency

[+] Author and Article Information
Olga Pierrakos

Department of Mechanical Engineering, School of Biomedical Engineering and Sciences, Virginia Tech, 100 Randolph Hall, Blacksburg, VA 24061opierrak@vt.edu

Pavlos P. Vlachos

Department of Mechanical Engineering, School of Biomedical Engineering and Sciences, Virginia Tech, 114 Randolph Hall Blacksburg, VA 24061pvlachos@vt.edu

J Biomech Eng 128(4), 527-539 (Feb 03, 2006) (13 pages) doi:10.1115/1.2205863 History: Received March 29, 2005; Revised February 03, 2006

A new mechanism for quantifying the filling energetics in the left ventricle (LV) and past mechanical heart valves (MHV) is identified and presented. This mechanism is attributed to vortex formation dynamics past MHV leaflets. Recent studies support the conjecture that the natural healthy left ventricle (LV) performs in an optimum, energy-preserving manner by redirecting the flow with high efficiency. Yet to date, no quantitative proof has been presented. The present work provides quantitative results and validation of a theory based on the dynamics of vortex ring formation, which is governed by a critical formation number (FN) that corresponds to the dimensionless time at which the vortex ring has reached its maximum circulation content, in support of this hypothesis. Herein, several parameters (vortex ring circulation, vortex ring energy, critical FN, hydrodynamic efficiencies, vortex ring propagation speed) have been quantified and presented as a means of bridging the physics of vortex formation in the LV. In fact, the diastolic hydrodynamic efficiencies were found to be 60, 41, and 29%, respectively, for the porcine, anti-anatomical, and anatomical valve configurations. This assessment provides quantitative proof of vortex formation, which is dependent of valve design and orientation, being an important flow characteristic and associated to LV energetics. Time resolved digital particle image velocimetry with kilohertz sampling rate was used to study the ejection of fluid into the LV and resolve the spatiotemporal evolution of the flow. The clinical significance of this study is quantifying vortex formation and the critical FN that can potentially serve as a parameter to quantify the LV filling process and the performance of heart valves.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 3

Two orientations of the SJM Bileaflet mechanical heart valve in the mitral valve position: (left) anatomical, (right) anti-anatomical

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Figure 4

Typical results of the vortex identification scheme. (a) Vorticity distribution at a specific instant and the corresponding (b)λ2 contour distribution showing the exact location of a vortex.

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Figure 5

Schematic of the two control volumes used in the analysis of deriving the efficiencies for the MV and the vortex ring

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Figure 6

Instantaneous velocity fields downstream of the mitral valve at time equal to 0.1secs, (a) anatomical, (b) anti-anatomical, and (c) porcine configurations. These velocity fields are shown to illustrate vortex formation for each of the three valve configurations

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Figure 7

Instantaneous velocity program upstream of the mitral valve for the three valve configurations

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Figure 8

Maximal instantaneous velocity downstream of the mitral valve for the three valve configurations

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Figure 9

Experimental and theoretical circulation for the three valve configurations

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Figure 10

Experimentally measured (DPIV), Hill’s spherical vortex energy approximation (HSVEA)-based, and theoretical (lowest solid line) energies for the three valve configurations

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Figure 13

Contours of λ2 during formation times (a)T=0.50, (b)T=1.0, and (c)T=1.8 for the porcine configuration

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Figure 14

Vortex ring propagation speed as a function of the formation number

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Figure 15

Hydrodynamic efficiencies (ηMV,ηVR,ηDiastole) for the three valve configurations

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Figure 2

Pressure and flow rate waveforms upstream of the mitral valve. These were acquired using an in-house mock circulatory loop (41).

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Figure 11

Contours of λ2 during formation times (a)T=0.25, (b)T=0.35(FNC), and (c)T=0.60 for the anatomical orientation

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Figure 12

Contours of λ2 during formation times (a)T=0.25, (b)T=0.60(FNC), and (c)T=0.80 for the anti-anatomical orientation

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Figure 1

Schematic of vortex ring formation in the left ventricle

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