A fully automated smoothing procedure for uniformly-sampled datasets is described. The algorithm, based on a penalized least squares method, allows fast smoothing of data in one and higher dimensions by means of the discrete cosine transform. Automatic choice of the amount of smoothing is carried out by minimizing the generalized cross-validation score. An iteratively weighted robust version of the algorithm is proposed to deal with occurrences of missing and outlying values. Simplified Matlab codes with typical examples in one to three dimensions are provided. A complete user-friendly Matlab program is also supplied. The proposed algorithm - very fast, automatic, robust and requiring low storage -provides an efficient smoother for numerous applications in the area of data analysis.

Reduced SAC is a frequent occurrence in elderly patients with AS, where it independently contributes to increased afterload and decreased LV function. Systemic arterial compliance should be taken into consideration when evaluating these patients with regard to diagnosis and treatment.

Doppler echocardiography remains the most extended clinical modality for the evaluation of left ventricular (LV) function. Current Doppler ultrasound methods, however, are limited to the representation of a single flow velocity component. We thus developed a novel technique to construct 2D time-resolved (2D+t) LV velocity fields from conventional transthoracic clinical acquisitions. Combining color-Doppler velocities with LV wall positions, the cross-beam blood velocities were calculated using the continuity equation under a planar flow assumption. To validate the algorithm, 2D Doppler flow mapping and laser particle image velocimetry (PIV) measurements were carried out in an atrio-ventricular duplicator. Phase-contrast magnetic resonance (MR) acquisitions were used to measure in vivo the error due to the 2D flow assumption and to potential scan-plane misalignment. Finally, the applicability of the Doppler technique was tested in the clinical setting. In vitro experiments demonstrated that the new method yields an accurate quantitative description of the main vortex that forms during the cardiac cycle (mean error for vortex radius, position and circulation). MR image analysis evidenced that the error due to the planar flow assumption is close to 15% and does not preclude the characterization of major vortex properties neither in the normal nor in the dilated LV. These results are yet to be confirmed by a head-to-head clinical validation study. Clinical Doppler studies showed that the method is readily applicable and that a single large anterograde vortex develops in the healthy ventricle while supplementary retrograde swirling structures may appear in the diseased heart. The proposed echocardiographic method based on the continuity equation is fast, clinically-compliant and does not require complex training. This technique will potentially enable investigators to study of additional quantitative aspects of intraventricular flow dynamics in the clinical setting by high-throughput processing conventional color-Doppler images.

Background-We sought to investigate the use of a new parameter, the projected effective orifice area (EOA proj ) at normal transvalvular flow rate (250 mL/s), to better differentiate between truly severe (TS) and pseudo-severe (PS) aortic stenosis (AS) during dobutamine stress echocardiography (DSE). Changes in various parameters of stenosis severity have been used to differentiate between TS and PS AS during DSE. However, the magnitude of these changes lacks standardization because they are dependent on the variable magnitude of the transvalvular flow change occurring during DSE. Methods and Results-The use of EOA proj to differentiate TS from PS AS was investigated in an in vitro model and in 23 patients with low-flow AS (indexed EOA Ͻ0.6 cm 2 /m 2 , left ventricular ejection fraction Յ40%) undergoing DSE and subsequent aortic valve replacement. For an individual valve, EOA was plotted against transvalvular flow (Q) at each dobutamine stage, and valve compliance (VC) was derived as the slope of the regression line fitted to the EOA versus Q plot; EOA proj was calculated as EOA proj ϭEOA rest ϩVCϫ(250ϪQ rest ), where EOA rest and Q rest are the EOA and Q at rest. Classification between TS and PS was based on either response to flow increase (in vitro) or visual inspection at surgery (in vivo). EOA proj was the most accurate parameter in differentiating between TS and PS both in vitro and in vivo. In vivo, 15 of 23 patients (65%) had TS and 8 of 23 (35%) had PS. The percentage of correct classification was 83% for EOA proj and 91% for indexed EOA proj compared with percentages of 61% to 74% for the other echocardiographic parameters usually used for this purpose. Conclusions-EOA