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.

Adaptive estimation of the mean frequency of a Doppler signal from short data windows.

The color Doppler estimator (CE1), which is calculated from the phase of the first correlation lag of the Doppler signal, is compared to the general mean frequency estimator (CEn), which is based on a weighted summation of all the available correlation lags, for long and short Doppler data sets (typically 48 and 8 Doppler samples). A new estimator of the Doppler signal mean frequency is derived from the results of this study. It optimizes the compromise between the range of analyzable frequencies and the estimation variance for the characteristics of the Doppler signal. Demonstration is provided that the behavior of this estimator shifts from that of CE1 to that of CEn, according to the setting of a single parameter. An adaptive version of this estimator is implemented and applied to Doppler recordings. Applications can be contemplated for color Doppler imaging.

Improved estimation of low velocities in color Doppler imaging by adapting the mean frequency estimator to the clutter rejection filter.

An adaptive mean frequency estimator is proposed for color flow imaging. It is based on a series expansion of the first derivative of the autocorrelation function of the Doppler signal at origin. Its bias can be reduced by shifting the integration bounds in the series expansion and its variance adjusted by adapting the coefficients of the serial development. This estimator can be fitted to the specific characteristics of the clutter rejection filter using the signal-to-noise ratio (SNR) of the Doppler signal as an adaptive parameter. Its performance is compared to that of the usual correlation angle estimator, and its thresholded version, as well as that of the general mean frequency estimator, using a model of Doppler signal. The detection of low frequencies was significantly improved. The mean square error (MSE) was reduced an average 15 fold over a 25-dB range on the SNR, compared to the correlation angle estimator (CAE) or the general mean frequency estimator. A two-fold reduction in the MSE was obtained compared to the thresholded correlation angle estimator.

Smoothed power spectrum estimate applied for analysis of the Doppler signal from blood flow.

A simple method for the improvement of the definition of the instantaneous spectrum estimate of Doppler signal is proposed. A short review of the stochastical properties of FFT spectrum estimates is presented. This review allowed us to develop a concept of the 'estimation noise' as an interpretation of the stochastic uncertainty of the estimation. This, in turn, permitted us to propose a method of adaptive filtering of spectral estimation to minimise the effects of the 'estimation noise'. Proposed filtering in the frequency domain corresponds to a procedure known as smoothing of the estimate. Two different smoothing procedures are presented: classical, linear smoothing and nonlinear, homomorphic smoothing. The performances of the smoothed spectrum estimate are theoretically and experimentally studied, showing that their effectiveness depends mostly on the shape of the Doppler spectrum. Although smoothing always reduces the spectral resolution, the important limitation of the variance of estimation can be achieved without meaningful deterioration of the resolution in our application. Thus, the proposed procedures may sensibly improve the accuracy of the relationship between the shape of the spectrum and the flow parameters. As a result, more exact determination of flow characteristics such as stability or maximum velocity, even in cases of low signal-to-noise power ratio, should be possible.

Influence of pulsatility on the development of intracardiac jets: an in vitro laser Doppler study.

So far, it has been hypothesized that numerical data obtained in steady flow conditions apply to pulsatile flows. In order to study the modifications of the velocity fields due to pulsatility, jets were produced by 8 orifices (with a diameter "D" of 4.4 to 11.3 mm) included in a chamber of 50 mm. The velocity was measured using laser Doppler anemometry with a pulsatile flow ("pf") and compared to the values obtained in steady ("sf"): at maximum velocity, the longitudinal velocity profile is qualitatively similar to this observed in steady flow: it is made of a plateau followed by an hyperbolic velocity decay in the turbulent area. The length of the core ("Lpf") is strongly related to "D" (Lpf = 3.72 D + 5.49, r = .99) and the velocity decay depends on the ratio between the distance "x" from the orifice and "D" (V/Vo = 2.83D/x + 3.46, r = .85, where V is the velocity at "x" and Vo the initial velocity). During the acceleration and the deceleration, the laminar core is disturbed by turbulences. The comparison of "pf" data with "sf" data demonstrated similar diameters at the origin of the jets (Dpf = 0.96 Dsf + .12, r = .99), but significant (p less than .0001) differences both for "L" and "V/Vo": Lpf = .91Lsf + 6.58, r = .97, V/Vopf = .63 V/Vosf + .34, r = .76. Thus, pulsatility modifies velocity fields and the results obtained in steady flow conditions do not apply to pulsatile jets.

A new adaptive mean frequency estimator: application to constant variance color flow mapping.

A class of adapted mean frequency estimators is proposed for color flow mapping. These estimators can be fitted to the specific characteristics of a given Doppler signal to optimize the compromise between the range of analysable frequencies and the variance of mean frequency estimation. A sub-optimal estimator is derived for real-time applications, and an adaptive criterion based on the Doppler signal variance is developed for color flow mapping applications. Its performance is compared to that of the usual correlation phase estimator on simulated Doppler signals and on synthetic Doppler images. An improvement in image quality is achieved, mainly for low signal-to-noise ratio Doppler signals.

Automatic detection of left ventricular borders on electron beam CT sequential cardiac images using an adaptive algorithm.

Detection of myocardial borders on sequences of electron beam CT images is carried out using an adaptive segmentation algorithm developed to enhance dynamic analysis of cardiac function. Adaptivity is based on description of the myocardial borders from the mean and standard deviation of the grey level and gradient distributions on each image of the sequence. Comparison of segmentations from five experimentators with automatically determined borders on a set of 416 endocardial and epicardial contours indicated differences between automatic and manual tracing very close to differences due to inter-observer reproducibility.

Limitations of ultrasound imaging and image restoration.

The definition of medical ultrasound images is strongly limited by the need for low examination frequencies which is imposed by the high attenuation of acoustic waves in tissues. The filtering effect of imaging systems is described and quantified for echography, transmission tomography and reflection tomography. Improvement of image definition is demonstrated to be the result of a numerical restoration of the received echoes implemented, in the present case, by a simplified Kalman filter. The improvement in definition obtained is emphasized on simulated data and tissue images. The comparison between the results obtained from the three techniques shows that: if only echography provides a real-time acquisition of signals, tomographic methods lead to faster processing associated with a better signal-to-noise ratio on the reconstructed images, and reflection tomography offers the best definition.

High-resolution, reflection mode tomographic imaging. Part I: Principles and methods.

A general method for improving image resolution is derived and applied to ultrasound signals; it combines the principles of both reflection mode tomography and deconvolution. The different possibilities of applying these principles allow two types of approaches to be defined, depending upon whether image reconstruction is achieved on radiofrequency or detected signals. A thorough description of three methods that are of particular interest due to their lower computation costs is presented, and their results quantified. They permit a gain in resolution of the order of ten with respect to two-dimensional deconvolution of images, as well as an improvement of the S/N ratio, which is related to the square root of the number of projections used in the reconstruction process, and a decrease of about four in computation time.

High-resolution, reflection mode tomographic imaging. Part II: Application to echography.

Principles of high-resolution, ultrasonic imaging using data acquisition by a compound scanning with a sector echograph are presented. The signal processing is based on both deconvolution and reflection mode tomography. Three of the methods that can be derived from these principles are selected due to their lower computation costs. Applications of these methods to synthetic data and test targets demonstrate that, with respect to 2D deconvolution, they offer: a gain in computation time of more than 8, an improvement in resolution of the order of 10 and an increase of S/N ratio of the order of 4. Finally, both the effects of limited acquisition angular window and of a variable propagation speed are illustrated.

In vitro validation of a new approach for quantitating regurgitations using proximal isovelocity surface area.

The present work has been designed to validate the calculation of the effective regurgitant orifice (ERO) area with the use of a new formula that takes into account the velocity profile (V(r) vs r) and that is insensitive to errors in the determination of the position of the orifice. Assuming a hemispheric model, ERO = 2 pi r(2). V(r)/V(o) (with V(o) = velocity at the orifice) and (V(o)/V(r))(0.5) = (2 pi/ERO)(0.5) r. Thus, the slope of the corresponding linear regression allows ERO to be calculated as: ERO = 2 pi/slope(2). This approach was tested in vitro in pulsatile conditions on circular, conical, and slit-like orifices. The calculated ERO was compared with the actual jet cross sectional area derived from the transverse velocity profile at the jet origin. For the purpose of comparison, the "classical" ERO was calculated for all the configurations, angulations, and threshold velocities. The relationship between (V(o)/V(r))(0.5) was linear (r > 0.98) over a wide range of velocities. The nonhemispheric components were found to modify the constant and not the slope. The mean variation of the calculated ERO was 6.5%. The correlation between the calculated and the actual ERO was very close (>0.97) with slope equal to 0.96. By comparison with the new method, the classical formula gave an underestimation of the ERO that dramatically increased when studying the flow closer to the orifice or in the case of error on the measurement of r. In conclusion, a method using velocity profiles instead of isolated values improves the accuracy of the proximal isovelocity surface area (PISA) method for measuring the ERO.

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.

Effect of myocardial infarction and ischemia on induction of cardiac reentries and ventricular fibrillation.

The present work is aimed at investigating the effects of myocardial infarction and ischemia on induction of ventricular fibrillation. Electrophysiologic effects of global and local ischemia (variation of the dispersion of refractory periods as well as conduction velocity) on initiation of reentry mechanisms was studied by means of computer simulations based on a cellular automata model of propagation of activation wave through a ventricular surface element. A local area of ischemia where effects of the dispersion of refractory periods are investigated is then simulated. This is made using a Gaussian distribution characterized by its mean and standard deviation. These simulations show that ischemia is capable of initiating reentry phenomena which propagate through the whole ventricle; they are responsible for ventricular fibrillation which causes sudden cardiac death, even when ischemia only involves limited parts of the myocardium. Statistical study of the probability of reentries as a function of both of the size of ischemic zones and the rate of dispersion of refractory periods shows that the latter parameter is of primary importance in triggering cardiac reentries.

Spatial regularization of flow patterns in magnetic resonance velocity mapping.

A technique dedicated to spatial regularization of magnetic resonance (MR) velocity data has been implemented to improve flow image quality. It is assumed that neighboring flow-velocity pixels are partially correlated, although large-velocity discontinuities remain possible. Increasing MR signal magnitude due to the in-flow effect also is used to enhance further reliability of the estimated velocity. By using an eight-step Fourier-encoding approach, 162 "reference" velocity images acquired in the ascending aorta from six healthy volunteers were compared with "raw" and "regularized" images that were computed from only two gradient steps. The mean square error decreased from 0.12 m(2) x s(-2) to 0.06 m(2) x s(-2) (P < 10-9) for velocity pixel values and from 1929 ml(2) x s(-2) to 1336 ml(2) x s(-2) (P < 0.01) for instantaneous flow rates. The regularization of two-step data sets provides the same velocity image quality as that found after using three-step data sets without regularization. The method can be applied to phase-velocity data sets of any MR technique to reduce velocity noise. J. Magn. Reson. Imaging 1999;10:851-860.