**1. Introduction**

Pain management is increasingly recognised as a formal medical subspecialty worldwide [1]. Optimal sedation and analgesic strategies, combined with delirium management, are a challenge when caring for critically ill patients. Sedation in ICU aims to provide patient pain reflief, comfort and safety. For sedation monitoring, the most extensively used tools are RASS (Richmond Agitation and Sedation Scale) [2] and SAS (Sedation Agitation Scale) [3]. Despite extensive improvements in analgesia medication there are still barriers to nurses' assessment, management, documentation, and reassessment of pain [4–6].

Pain is the most common reason that patients come to the emergency department. Emergency nurses have an indispensable role in the management of this pain [7, 8]. Sedation in the intensive care unit (ICU) is challenging, as both over- and undersedation are detrimental. Current methods of assessment, such as the Richmond Agitation Sedation Scale (RASS), are measured intermittently and invariable depend on patients' behavioural response to stimulation, as such may interrupt sleep and rest. A non-stimulating method for continuous sedation monitoring may be beneficial and allow more frequent assessment., noting that appropriate sedation cycling has to accommodate patients' oscillations between states of agitation and over-sedation, which are detrimental to patient health and increases hospital length of stay [9–14].

As such there also have been recent studies exploring the impact of augmenting sedation assessment with physiologic monitors [15] and studying the correlation between observational scales of sedation and bispectral index scores [16]. Recently the feasibility of continuous sedation monitoring of ICU patients using the NeuroSENSE was studied and suggested that such a non-stimulating method for continuous sedation monitoring may benefit patient care and allow increased A-S assessment [17]. The authors advocated use of incorporating some degree of automation into sedative drug administration, e.g. closed-loop control based on feedback from a processed EEG monitor, and various studies have suggested the limitations of RASS as a stand-alone measure of sedation levels, and pointed to benefit of adjunct continuous e.g., brain monitoring [17].

Earlier, Rudge, Chase, Shaw, Lee [12] discussed target controlled infusion (TCI) systems to deliver drugs to maintain target plasma concentrations, using a pharmacokinetic model, shown to be feasible when anaesthesia is given over short periods of reduced consciousness and well-known pharmacology is invoked. Infusion systems that regulate the infusion rate to maintain target agitation levels, to regulate the primary metric for longterm sedation, are one approach to improving care in the ICU. The data analysed in this chapter pertains to the scenario and data type studied earlier by [9–14].

Assessing the severity of agitation is a challenging clinical problem as variability related to drug metabolism for each individual is often subjective. A multitude of previous studies suggest that the assessment accuracy of the sedation quality conducted by nurses tend to suffer from subjectivity and lead to sub-optimal sedation [14, 15, 18]. For example, [19] strongly recommend lighter than deeper levels of sedations. Moreover, [20, 21] argue that sedation should be reviewed and adjusted regularly. Whilst agitation management methods frequently rely on subjective agitation assessment [2, 3] the carers then select an appropriate infusion rate based upon their evaluation of these scales, experience, and intuition [21]. This approach usually leads to largely continuous infusions which lack a bolus-focused approach, commonly resulting in over or under-sedation. The work of [11–13] aimed to enhance feedback protocols for medical decision support systems and eventually automated sedation administration. A minimal differential equation model to predict or simulate each patient's agitation-sedation status over time was presented in [12] for 37 ICU patients

*Modelling Agitation-Sedation (A-S) in ICU: An Empirical Transition and Time to Event… DOI: http://dx.doi.org/10.5772/intechopen.105480*


**Table 1.**

*Time to the patient-specific 1st violation V1, second violation V2 and third violation V3, total number of violations, total ICU time and WPB% values.*

and was shown to capture patient A-S dynamics. The use of quantitative modelling to enhance understanding of the agitation-sedation (A-S) system and provision of an A-S simulation platform are one of the key tools in this area of patient critical care. A more refined A-S model, which utilised regression with an Epanechnikov kernel was formulated by [12]. A Bayesian approach using densities and wavelet shrinkage methods was later suggested by [9] to assess a previously derived deterministic, parametric A-S model [10–14], thus successfully challenging the practice of sedating ICU patients using continuous infusions. Wavelets approaches [9, 10] were shown to provide reliable diagnostics and visualisation tools to assess A-S models, giving alternative metrics of A-S control to assess validity of the earlier A-S deterministic models (**Table 1** in [10]).

This suite of wavelet metrics based on the discrete wavelet transform (DWT) were able to establish the value of earlier deterministic agitation-sedation (A-S) models against empirical (recorded) dynamic A-S infusion profiles, providing robust performance metrics of A-S control and excellent tools, as based on the classification of patients into poor and good trackers based on Wavelet Probability Bands (WPBs). Importantly, the WPBs were shown as a useful patient-specific method by which to identify and detect regions in the patient's A-S profile i.e., times whilst in ICU, where the simulated infusion rate performs poorly, thus providing visual and quantified ways to help improve and distil the deterministic A-S model and in practice be a guage to alert carers.

In this chapter Empirical Transition Matrix (ETM) approach of multi-state counting process (survival analytic) models of Allignol and coauthors [22, 23], aligned with the counting process/event history work in [24–26], which use the times patients transition to varying states of violations (a violation being an A-S measure outside the 90% WPB bands), confirm the utility of defining trackers and non-trackers according to these control limits and wavelet diagnostic rules of Kang et al., [9, 10]. In this chapter ETM and multi-state modelling are found to be valuable for developing advanced optimal infusion controllers and also to assist coding of nurses A-S scores, which potentially offer significant clinical potential of improved agitation management and reduced length of stay, as an augmented approach to also using RASS and SAS. Establishing patient-specific thresholds of poor A-S management and control has significant implications for the effective administration of sedatives, as improved management of A-S states will allow clinicians to improve the efficacy of care and reduce healthcare costs [27–29].
