Auditory event-related potentials, bispectral index, and entropy for the discrimination of different levels of sedation in intensive care unit patients

BACKGROUND: Sedation protocols, including the use of sedation scales and regular sedation stops, help to reduce the length of mechanical ventilation and intensive care unit stay. Because clinical assessment of depth of sedation is labor-intensive, performed only intermittently, and interferes with sedation and sleep, processed electrophysiological signals from the brain have gained interest as surrogates. We hypothesized that auditory event-related potentials (ERPs), Bispectral Index (BIS), and Entropy can discriminate among clinically relevant sedation levels. METHODS: We studied 10 patients after elective thoracic or abdominal surgery with general anesthesia. Electroencephalogram, BIS, state entropy (SE), response entropy (RE), and ERPs were recorded immediately after surgery in the intensive care unit at Richmond Agitation-Sedation Scale (RASS) scores of -5 (very deep sedation), -4 (deep sedation), -3 to -1 (moderate sedation), and 0 (awake) during decreasing target-controlled sedation with propofol and remifentanil. Reference measurements for baseline levels were performed before or several days after the operation. RESULTS: At baseline, RASS -5, RASS -4, RASS -3 to -1, and RASS 0, BIS was 94 [4] (median, IQR), 47 [15], 68 [9], 75 [10], and 88 [6]; SE was 87 [3], 46 [10], 60 [22], 74 [21], and 87 [5]; and RE was 97 [4], 48 [9], 71 [25], 81 [18], and 96 [3], respectively (all P < 0.05, Friedman Test). Both BIS and Entropy had high variabilities. When ERP N100 amplitudes were considered alone, ERPs did not differ significantly among sedation levels. Nevertheless, discriminant ERP analysis including two parameters of principal component analysis revealed a prediction probability PK value of 0.89 for differentiating deep sedation, moderate sedation, and awake state. The corresponding PK for RE, SE, and BIS was 0.88, 0.89, and 0.85, respectively. CONCLUSIONS: Neither ERPs nor BIS or Entropy can replace clinical sedation assessment with standard scoring systems. Discrimination among very deep, deep to moderate, and no sedation after general anesthesia can be provided by ERPs and processed electroencephalograms, with similar P(K)s. The high inter- and intraindividual variability of Entropy and BIS precludes defining a target range of values to predict the sedation level in critically ill patients using these parameters. The variability of ERPs is unknown.

Rasmussen's spectral sequences and the \germslN-concordance invariants

Combining known spectral sequences with a new spectral sequence relating reduced and unreduced slN-homology yields a relations hip between the Homflypt-homology of a knot and its slN-concordance invariants. As an application, some of the slN-concordance invariants are shown to be linearly independent.

Comparison of Bispectral Index (BIS) and Patient State Index (PSI) as objective measures of sedation and analgesia in critically ill/injured patients

Critically ill and injured patients require pain relief and sedation to reduce the body's stress response and to facilitate painful diagnostic and therapeutic procedures. Presently, the level of sedation and analgesia is guided by the use of clinical scores which can be unreliable. There is therefore, a need for an objective measure of sedation and analgesia. The Bispectral Index (BIS) and Patient State Index (PSI) were recently introduced into clinical practice as objective measures of the depth of analgesia and sedation. ^ Aim. To compare the different measures of sedation and analgesia (BIS and PSI) to the standard and commonly used modified Ramsay Score (MRS) and determine if the monitors can be used interchangeably. ^ Methods. MRS, BIS and PSI values were obtained in 50 postoperative cardiac surgery patients requiring analgesia and sedation from June to December 2004. The MRS, BIS and PSI values were assessed hourly for up to 6-h by a single observer. ^ The relationship between BIS and PSI values were explored using scatter plots and correlation between MRS, BIS and PSI was determined using Spearman's correlation coefficient. Intra-class correlation (ICC) was used to determine the inter-rater reliability of MRS, BIS and PSI. Kappa statistics was used to further evaluate the agreement between BIS and PSI at light, moderate and deep levels of sedation. ^ Results. There was a positive correlation between BIS and PSI values (Rho = 0.731, p<0.001). Intra-class correlation between BIS and PSI was 0.58, MRS and BIS 0.43 and MRS and PSI 0.27. Using Kappa statistics, agreement between MRS and BIS was 0.35 (95% CI: 0.27–0.43) and for MRS and PSI was 0.21 (95% CI: 0.15–0.28). The kappa statistic for BIS and PSI was 0.45 (95% CI: 0.37–0.52). Receiver operating characteristics (ROC) curves constructed to detect undersedation indicated an area under the curve (AUC) of 0.91 (95% CI = 0.87 to 0.94) for the BIS and 0.84 (95% CI = 0.79 to 0.88) for the PSI. For detection of oversedation, AUC for the BIS was 0.89 (95% CI = 0.84 to 0.92) and 0.80 (95% CI = 0.75 to 0.85) for the PSI. ^ Conclusions. There is a statistically significant positive correlation between the BIS and PSI but poor correlation and poor test agreement between the MRS and BIS as well as MRS and PSI. Both the BIS and PSI demonstrated a high level of prediction for undersedation and oversedation; however, the BIS and PSI can not be considered interchangeable monitors of sedation. ^

Differential invariants of second-order ordinary differential equations

The notion of a differential invariant for systems of second-order differential equations on a manifold M with respect to the group of vertical automorphisms of the projection is de?ned and the Chern connection attached to a SODE allows one to determine a basis for second-order differential invariants of a SODE.

Rational invariants on the space of all structures of algebras on a two-dimensional vector space

Rational invariants on the space of all structures of algebras on a two-dimensional vector space

Image analysis by moment invariants using a set of step-like basis functions

Moment invariants have been thoroughly studied and repeatedly proposed as one of the most powerful tools for 2D shape identification. In this paper a set of such descriptors is proposed, being the basis functions discontinuous in a finite number of points. The goal of using discontinuous functions is to avoid the Gibbs phenomenon, and therefore to yield a better approximation capability for discontinuous signals, as images. Moreover, the proposed set of moments allows the definition of rotation invariants, being this the other main design concern. Translation and scale invariance are achieved by means of standard image normalization. Tests are conducted to evaluate the behavior of these descriptors in noisy environments, where images are corrupted with Gaussian noise up to different SNR values. Results are compared to those obtained using Zernike moments, showing that the proposed descriptor has the same performance in image retrieval tasks in noisy environments, but demanding much less computational power for every stage in the query chain.

Leçons sur les invariants intégraux ...

"Reproduction d'un cours professé pendant le semestre d'été 1920-1921 à la Faculté des sciences de Paris.--Introd.

Sur les progrès de la théorie des invariants projectifs.

Available on demand as hard copy or computer file from Cornell University Library.

Sur les invariants différentiels.

Available on demand as hard copy or computer file from Cornell University Library.

Invariants of the finite continuous groups of the plane.

Thesis (doctoral)--

Eigenvalues of Casimir invariants for Uq[osp(m|n)]

For each quantum superalgebra U-q[osp(m parallel to n)] with m > 2, an infinite family of Casimir invariants is constructed. This is achieved by using an explicit form for the Lax operator. The eigenvalue of each Casimir invariant on an arbitrary irreducible highest weight module is also calculated. (c) 2005 American Institute of Physics.