A model investigation of the velocity and pressure spectra in vascular murmurs

Development of a CFD urethral model to study flow-generated vortices under different conditions of prostatic obstruction

A novel, non-invasive method to diagnose bladder outlet obstruction involves the recording of noise with a contact microphone pressed against the perineum (between anus and scrotum). This noise results from flow-generated vortices caused by prostatic obstruction. We developed a computational fluid dynamic (CFD) urethral model including urethral geometry to study the relation between generated noise and the degree of obstruction. This model comprised a bladder, bladder neck, prostate and urethra. Calculations were carried out at four bladder pressures, five degrees of obstruction and three obstruction shapes. For each of the sixty simulations, the velocity and pressure distributions along the urethra were calculated including wall shear stresses to localize flow transition from disturbed to normal. Negative pressures at the obstruction outlet induced recirculation of flow. The location of transition was independent of the applied bladder pressure, but it depended primarily on the degree and secondarily on the shape of the obstruction. Based on the presented results, we hypothesize that the location of the maximum amplitude of perineal noise mainly depends on the degree and shape of the prostatic obstruction. Our future aim is to test our hypothesis in male patients and to extend the presented model to 3D with a viscoelastic urethral wall to calculate the fluid-wall interaction.

Fluid mechanics of regurgitant jets and calculation of the effective regurgitant orifice in free or complex configurations

The velocity fields of turbulent jets can be described using a single formula which includes two empirical constants: k(core) determining the length of the central core and k(turb) the jet widening. Flow models simulating jet adhesion, confinement and noncircular orifices were studied using laser Doppler anemometer and the modifications of the constants were derived from series of velocity profiles. In circular free jets, k(core) was found equal to 4.1 with a variability of 1.4%. In complex configurations, its variability was equal to 15.2%. For k(turb), the value for free circular jets was of 45.2 with a variability of 6.0% and this variability in complex configurations was significantly higher (30. 1%, p=0.025). The correlation between the actual orifice size and the jet extension was poor (r=0.52). However, the almost constant value of k(core) allowed to define a new algorithm calculating the regurgitant orifice diameter with the use of outlines of the jet image (r=0.89). In conclusion, the fluid mechanics of regurgitant jets is modified in complex configurations but, due to the relative independency of the central core, velocity fields could be used to evaluate the dimensions of the effective regurgitant orifice.

In vitro flow mapping of regurgitant jets. Systematic description of free jet with laser Doppler velocimetry

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: V(x,y,t peak) = V(O,O,t peak).4.(d/x).10(-45(y/x)2) (r = .92).

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.

Bio-acoustic signals from stenotic tube flow: state of the art and perspectives for future methodological development

To study the degree of stenosis from the acoustic signal generated by the turbulent flow in a stenotic vessel, so-called phonoangiography was first suggested over 20 years ago. A reason for the limited use of the technique today may be that, in the early work, the theory of how to relate the spectrum of the acoustic signal to the degree of the stenosis was not clear. However, during the last decade, the theoretical basis for this and other biological tube flow applications has been clarified. Now there is also easy access to computers for frequency analysis. A further explanation for the limited diagnostic use of bio-acoustic techniques for tube flow is the strong competition from ultrasound Doppler techniques. In the future, however, applications may be expected in biological tube flow where the non-invasive, simple and inexpensive bio-acoustic techniques will have a definite role as a diagnostic method.

In vitro analysis of a model of intracardiac jet: analysis of the central core of axisymmetric jets

In order to provide physical information supporting the clinical use of flow mapping, an in vitro model was designed to measure the velocity fields in a pulsatile hydraulic turbulent jet. We used a peak velocity ranging from 2.5 to 5.5 m.s-1, an orifice diameter ranging from 5.8 to 11.3 mm and confined the jet in a receiving tube whose diameter ranged from 16 to 30 mm, thus simulating a large variety of valvular leaks. In steady flow conditions, our results agreed with previously reported descriptions. Under pulsatile conditions, the same structure was found at peak velocity and during the beginning of the deceleration. Below a threshold velocity, the length of the central core was independent of the peak velocity and proportional to about six times the orifice diameter. Above the threshold velocity, this relationship was no longer true, the threshold value being related to the ratio of the orifice diameter to the diameter of the receiving tube.

Continuous spectral analysis of heart murmurs for evaluating stenotic cardiac lesions

Severity of stenotic heart lesions affects timing, quality and pitch of associated heart murmurs. This quantitative study investigated the relation between instantaneous sound frequencies contained in heart murmurs and magnitudes of Doppler jet velocities measured distal to associated obstructions. Heart murmurs were recorded from 18 patients, ages 1 day to 23 years, with 21 separate murmurs resulting from abnormal valves (18 studies) or left-to-right shunts (3 studies). Recorded murmurs were digitized and divided into 12.3-ms time segments for computer frequency analysis using the maximum entropy method. Murmur spectra were plotted in gray scale against time. All murmurs contained dominant frequencies that varied with time. Dominant murmur frequencies and associated Doppler jet velocities at equivalent points in time were measured at 50-ms intervals. For 88 points analyzed, instantaneous dominant frequencies ranged from 130 to 410 Hz (mean +/- standard deviation 282 +/- 70 Hz) and instantaneous jet velocities ranged from 110 to 460 cm/s (290 +/- 80 cm/s). For the 21 murmurs studied, peak murmur frequencies ranged from 200 to 410 Hz (308 +/- 70 Hz) and peak jet velocities ranged from 165 to 460 cm/s (320 +/- 78 cm/s). Instantaneous dominant frequency correlated to instantaneous jet velocity (r = 0.85) and peak dominant frequency correlated to peak jet velocity (r = 0.89). This in vivo study demonstrates that dominant frequencies contained in heart murmurs are related to instantaneous jet velocities distal to associated obstructions.

Analysis of break frequencies downstream of a constriction in a cylindrical tube

Experiments were performed to correlate steady-flow power spectra downstream of a stenosis in a cylindrical tube with the flow geometry and velocity. The experiments were motivated by the need to improve quantitative phonoangiography. An objective break frequency (fb) was computed from spectra of velocity fluctuations, as measured with a hot film anemometer. Least squares fits with two independent variables were used to find an empirical relationship between a Strouhal number (S2), the contraction ratio (ds/D) and the Reynolds number (Re). The variables D and ds, are, respectively, the unobstructed tubing diameter and the inner diameter of the stenosis. The relationship found was S2 = Re 0.72(ds/D)0.26 The contraction ratio ds/D, can be found from the empirical relation in terms of known parameters. For the hot wire data the average error between the computed value of ds/D and the known value was 2.3%.