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The relationship between systolic vector flow mapping parameters and left ventricular cardiac function in healthy dogs

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Vector flow mapping (VFM) is a novel echocardiographic technology that shows blood flow vectors and vortexes, enabled the hydrokinetic evaluation of hemodynamics within the left ventricle. VFM provides several unique parameters: circulation, vorticity, vortex area, and energy loss. The present study aims to reveal a relationship between VFM parameters and cardiac function. Five healthy Beagle dogs were anesthetized and administered with dobutamine (0, 2, 4, 8, 12 µg/kg/min). Pressure–volume diagrams were acquired to assess cardiac function using pressure–volume conductance catheter. Systolic maximum circulation, vorticity, vortex area, and energy loss were measured using VFM. The systolic maximum circulation, systolic vorticity, systolic vortex area, and systolic energy loss were increased by dobutamine administration. There was a strongly significant correlation between the systolic maximum circulation and ejection fraction (r = 0.76), maximal positive left ventricular (LV) pressure derivatives (dP/dt max) (r = 0.80), and end-systolic LV elastance (r = 0.73). Systolic vorticity and systolic vortex area were strongly correlated with ejection fraction (r = 0.76, 0.68) and dP/dt max (r = 0.76, 0.69), and end-systolic LV elastance (r = 0.62, 0.74), respectively. Systolic energy loss was strongly correlated with dP/dt max (r = 0.78), systolic maximum circulation (r = 0.81), and systolic vorticity (r = 0.82). The present study revealed that systolic VFM parameters are associated with the LV contractility. Furthermore, systolic energy loss was susceptible to the systolic vortex parameters such as systolic vorticity and systolic maximum circulation. Systolic VFM parameters are new hydrokinetic indices reflecting LV contractility.

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Correspondence to Seijirow Goya.

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The authors declare that there is no conflict of interest.


This research received no specific Grant from any funding agency in the public, commercial, or not-for-profit sectors.

Ethical approval

During the study, the dogs were managed and cared for in accordance with the standards established by the Tokyo University of Agriculture and Technology (TUAT) and described in its ‘‘Guide for the Care and Use of Laboratory Animals”. This study was approved by the Experimental Animal Committee of TUAT (Acceptance No. 26-95).

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Online Resource 1. Intra-ventricular hemodynamics during one cardiac cycle in isoflurane-anesthetized dogs was recorded by VFM. Red circles show the occurred vortex. Circulation and vortex area are automatically calculated and displayed on the upper left of the screen (MP4 1817 kb)



$$ ``{\text{Vorticity}}{\mkern 1mu} (\omega ) = \left( {\begin{array}{*{20}c} {\frac{\partial w}{\partial y} - \frac{\partial v}{\partial z}} \\ {\frac{\partial u}{\partial z} - \frac{\partial w}{\partial x}} \\ {\frac{\partial v}{\partial x} - \frac{\partial u}{\partial y}} \\ \end{array} } \right)" $$

u, v, w is the velocity components in x, y, z axes directions, respectively.

In 2D flow with w = 0,

$$ \begin{aligned} {\text{Vorticity}}{\mkern 1mu} (\omega ) & = \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y} \\ `` {\text{Circulation}} & = \iint_{s} {\omega_{n} {\text{d}}S}" \\ \end{aligned} $$

S is the arbitrary curved surface surrounded by a closed curve; \( \omega_{n} \) is the normal component of vorticity \( \omega \).

$$`` {\text{Energy loss }} = \int {\mu \frac{1}{2}\sum\limits_{i,j } {\left( {\frac{{\partial u_{i} }}{{\partial x_{j} }} + \frac{{\partial u_{j} }}{{\partial x_{i} }}} \right)^{2} } {\text{d}}v} = \mu \int {\left( {2\frac{\partial u}{\partial x}^{2} + \left( {\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}} \right)^{2} + 2\frac{\partial v}{\partial y}^{2} } \right){\text{d}}v} " $$

μ is the coefficient of blood viscosity; u, v is the velocity components in x, y axes directions, respectively.

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Goya, S., Wada, T., Shimada, K. et al. The relationship between systolic vector flow mapping parameters and left ventricular cardiac function in healthy dogs. Heart Vessels 33, 549–560 (2018).

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