In Vitro Flow Mapping of Regurgitant Jets

Background Color Doppler and magnetic resonance imaging give pictures of abnormal jets within which the respective contribution of fluid mechanics and image artifacts are difficult to establish because of current technical limitations of these modalities. We conducted the present study to provide numerical descriptions of the velocity fields within regurgitant free jets. Methods and Results Laser Doppler measurements were collected in rigid models with pulsatile flow conditions, giving several series of two-dimensional flow images. The data were studied with the use of two-dimensional or M-mode flow images as well as regular plots. Numerical descriptions validated in steady flow conditions were tested at the various times of the cycle. In these free jets, the momentum was conserved throughout the cycle. The transverse velocity profiles were approximately similar. A central laminar core was found at peak ejection and during the deceleration. Its length ( l =4.08 d −0.036 mm, r =.99) and its diameter ( d ) were proportional to the orifice diameter. At peak ejection, the velocity decay was hyperbolic, and the transverse velocity profiles were clearly gaussian. The different relations that were tested could be combined in a single formula describing the velocity field: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(\mathit{V}(\mathit{x},\mathit{y},\mathit{t}_{\mathit{peak}}){=}\mathit{V}(0,0,\mathit{t}_{\mathit{peak}}){\cdot}4{\cdot}(\mathit{d}/\mathit{x}){\cdot}10^{{-}45(\mathit{y}/\mathit{x})^{2}}\ (\mathit{r}{=}.92).\) \end{document} Conclusions These in vitro measurements demonstrated the presence of a central laminar core and similar transverse velocity profiles in free turbulent jets. This allowed us to validate a series of numerical relations that can be combined to describe the velocity fields at peak ejection. On the other hand, further studies are needed to describe the various singularities often encountered in pathology.