Phase space electroencephalography (EEG): A new mode of intraoperative EEG analysis

Abstract

Intraoperative monitoring of electroencephalography (EEG) data can help assess brain integrity and/or depth of anesthesia. We demonstrate a computer generated technique which provides a visually robust display of EEG data plotted as 'phase space trajectories' and a mathematically derived parameter ('dimensionality') which may correlate with depth of anesthesia. Application of nonlinear mathematical analysis, used to describe complex dynamical systems, can characterize 'phase space' EEG patterns by identifying attractors (geometrical patterns in phase space corresponding to specific ordered EEG data subjects) and by quantifying the degree of order and chaos (calculation of dimensionality). Dimensionality calculations describe the degree of complexity in a signal and may generate a clinically useful univariate EEG descriptor of anesthetic depth. In this paper we describe and demonstrate phase space trajectories generated for sine waves, mixtures of sine waves, and white noise (random chaotic events). We also present EEG phase space trajectories and dimensionality calculations from a patient undergoing surgery and general anesthesia in 3 recognizable states: awake, anesthetized, and burst suppression. Phase space trajectories of the three states are visually distinguishable, and dimensionality calculations indicate that EEG progresses from 'chaos' (awake) to progressively more 'ordered' attractors (anesthetized and burst suppression).

Complexity measures of the electroencephalograph capture loss and recovery of consciousness in patients anesthetized with propofol

“…Our results agree with previous reports of the utility of complexity analyses to discriminate between the subtle EEG changes that occur in operating room patients during induction (Eagleman, Vaughn, et al, 2018;Watt & Hameroff, 1988) and emergence Walling & Hicks, 2006) from anesthesia. We demonstrate here that these approaches provide equivalent discrimination between periods preceding and following LOR, and improved discrimination between periods preceding and following ROR.…”

“…The brain itself performs computations in both linear and nonlinear fashions, and both cognitive and arousal states have been characterized using analyses based on nonlinear dynamics (Ma, Shi, Peng, & Yang, 2018;Stam, 2005;Walling & Hicks, 2006;Watt & Hameroff, 1988;. An example of such a method is the use of timedelayed embeddings derived from EEG signals.…”

“…An example of such a method is the use of timedelayed embeddings derived from EEG signals. Anesthesiologists have noted that such embeddings could distinguish anesthetic depth (Watt & Hameroff, 1988; as well as recovery of consciousness in surgical patients (Walling & Hicks, 2006). Sometimes, time-delayed embedding signals are observed to explore only a limited region of all possible states in a multidimensional space in which they are embedded; instead, they settle onto attractors in state space, and can thus be seen as probes of the underlying dynamics.…”

“…To make sense of this shape change, we compared this analysis to other complexity measures such as the correlation dimension and multiscale entropy, and found a significant correlation with multiscale entropy (Eagleman, Vaughn, et al, 2018). Characterization of attractors using correlation dimension (CD) has been proposed to provide a measure of complexity or information content of EEG signals (Walling & Hicks, 2006;Watt & Hameroff, 1988). Currently, it is unknown whether either correlation dimension or our geometric phase-space analysis is sensitive to recovery of consciousness for propofol anesthesia.…”

The Study of EEG Dynamics During Anesthesia with Cross-Recurrence Rate

“…This is evident from (i) the large variations in classification accuracy or prediction probabilities used to assess the performance of different algorithms (see, e.g., table 5 in [5]), and (ii) the disagreement between different commercially available depth of anesthesia monitors in assessing patient state of hypnosis [6][7][8]. In addition to commercially available monitors, other algorithms utilized so far for monitoring awareness include spectrum-based methods [9][10][11][12], entropy-based methods [13][14][15], and methods from non-linear dynamics and complexity [13,14,16]. Recently, the use of recurrence methods has been introduced to study how the EEG activity is affected by the administration of anesthetic agents during general anesthesia and results indicate that such methods are highly promising for monitoring anesthetic depth.…”