Validation of a Semi-Classical Signal Analysis Method for Stroke Volume Variation Assessment: A Comparison with the PiCCO Technique

Abstract

This study proposes a Semi-Classical Signal Analysis (SCSA) method for stroke volume (SV) variations assessment from arterial blood pressure measurements. One of the SCSA parameters, the first systolic invariant (INVS₁), has been shown to be linearly related to SV. To technically validate this approach, the comparison between INVS₁ and SV measured with the currently used PiCCO technique was performed during a 15-min recording in 20 mechanically ventilated patients in intensive care. A strong correlation was estimated by linear regression and cross-correlation analysis (mean coefficient = 0.90 ± 0.01 SEM at the two tests).

A novel algorithm for image representation using discrete spectrum of the Schrödinger operator

“…Moreover, κ i,n,h resp. ρ j,m,h are the negative eigenvalues of the one dimensional semi-classical Schrödinger operator given by (17), (resp. (18)…”

“…The element [i, j] is then considered twice, which justifies the 1 2 in the potentials of the one dimensional operators (17) and (18).…”

“…Thanks to their interesting properties [10,14,20], the SCSA method has proved its performance in several applications. For instance, interesting results have been obtained in the analysis of arterial blood pressure signals [14,16,17] and the analysis of the performance of turbo-machinery [9]. Moreover, it has been shown in [18], that the SCSA method can cope with noisy signals, making this method a potential tool for denoising, for concrete example, the filtering property of the SCSA method is currently under study through in-vivo experiments with Magnetic Resonance Spectroscopy data [15].…”

Spectral data de‐noising using semi‐classical signal analysis: application to localized MRS

“…It is found that, when h tends to zero, the reconstructed spectrum s h converges towards the true spectrum s. This is in compliance with the semi-classical properties of the Schrödinger operator where the number N h of negative eigenvalues and consequently the number of eigenfunctions increases when h decreases. [17][18][19][20][21] Since the main goal of the technique is to separate the useful information from noise, it is preferable to represent the input signal with the minimum number possible of eigenfunctions (SL functions). This is achieved by choosing a large value of the parameter h to minimize N h , and iteratively lowering it to increase N h to include more eigenfunctions until the noiseless spectrum s h is accurately reconstructed.…”

“…This is in agreement with the properties of the eigenfunctions ψ(f), where it has been shown that the nth squared eigenfunction ψ 2 nh f ð Þ has n wells, implying that the first squared eigenfunction ψ 2 1h f ð Þ is represented by a single well function localized at its maximum, the second squared eigenfunction ψ 2 2h f ð Þ has two wells, and so on. [17][18][19][20][21] By analogy, one can see that the squared eigenfunctions with low nh values represent, in a broad manner, the profiles of the peaks of the spectrum, whereas the functions with high nh values characterize more the fine details of these profiles. Therefore, by incorporating squared eigenfunctions with higher nh values, the peaks are accurately represented into the reconstructed spectrum s h .…”