## Abstract

Analysis of velocity acceleration proximal to a regurgitant valve has been proposed as a method to quantify the regurgitant flow rate (Q_{o}). Previous work has assumed inviscid flow through an infinitesimal orifice, predicting hemispheric isovelocity shells, with calculated flow rate given by Q_{c}=2_{π}r_{N}^{2}V_{N}, where V_{N} is user-selected velocity of interest and r_{N} is the distance from that velocity to the orifice. To validate this approach more rigorously and investigate the impact of finite orifice size on the assumption of hemispheric symmetry, numerical and in vitro modeling was used. Finite-difference modeling demonstrated hemispheric shape for contours more than two orifice diameters from the orifice. More proximal than this (where the measured velocity V_{N} exceeded 3% of the orifice velocity V_{O}), flow was progressively underestimated, with a proportional error Δ_{Q}/Q_{O} nearly identical to the ratio of contour velocity to orifice velocity, V_{N}/V_{O}. For the in vitro investigations, flow rates from 4.3 to 150 cm^{3}/sec through 0.3 and 1.0 cm^{2} circular orifices were imaged with color Doppler with aliasing velocities from 19 to 36 cm/sec. Overall, the calculated flow (assuming hemispheric symmetry) correlated well with the true flow, Q_{c}=0.88Q_{O}-7.82 (r=0.945, SD=12.2 cm^{3}/sec, p<0.0001, n=48), but progressively underestimated flow when the V_{N} approached the orifice velocity V_{O}. Applying a correction factor predicted by the numerical modeling, ΔQ was improved from -13.81±13.01 cm^{3}/sec (mean±SD) to+1.54±5.67 cm^{3}/sec. These data indicate that flow can be accurately calculated using the hemispheric assumption as Q_{c}=2_{πrN}^{2}V_{N} when V_{N}<<V_{O}. For larger V_{N}, flow is systematically underestimated, but a more accurate estimate may be obtained by multiplying Q_{c} by V_{O}(V_{O}-V_{N}). These observations lend additional support for the clinical use of the proximal acceleration concept and suggest a simple correction factor to make a more accurate estimation of valvular regurgitation.

Original language | English (US) |
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Pages (from-to) | 923-930 |

Number of pages | 8 |

Journal | Circulation research |

Volume | 70 |

Issue number | 5 |

State | Published - May 1992 |

## Keywords

- Doppler echocardiography
- Finite-difference modeling
- Flow rate calculation
- Fluid dynamics
- In vitro modeling
- Proximal flow convergence

## ASJC Scopus subject areas

- Cardiology and Cardiovascular Medicine
- Physiology