Impact of control on agitation–sedation dynamics

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Control Engineering Practice 13 (2005) 1139–1149 www.elsevier.com/locate/conengprac

Impact of control on agitation–sedation dynamics Andrew D. Rudgea,, J. Geoffrey Chasea, Geoffrey M. Shawb,c, Dominic Leed, Graeme C. Waked, Irene L. Hudsond, Lucy Johnstone a

Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand b Department of Intensive Care Medicine, Christchurch Hospital, New Zealand c Christchurch School of Medicine and Health Sciences, University of Otago, New Zealand d University of Canterbury, Department of Mathematics and Statistics, New Zealand e Department of Psychology, University of Canterbury, New Zealand Received 4 December 2003; accepted 4 October 2004 Available online 24 November 2004

Abstract Agitation in the critically ill damages patient health and increases length of stay and healthcare costs. The control model presented captures the essential dynamics of the agitation–sedation system, and is statistically validated using recorded infusion data for 37 patients. Derivative focused control is seen to provide an essentially bolus-driven management approach, which is shown to be an effective means of managing agitation, given consistent agitation measurement. Improved agitation management using feedback of patient agitation reduces the modelled mean and peak agitation levels 68.4% and 52.9% on average, respectively, illustrating the effectiveness of simple control in this non-linear system. r 2004 Elsevier Ltd. All rights reserved. Keywords: Biomedical control; Physiological models; PD controllers; Non-linear dynamics; Patient agitation; Sedation administration

1. Introduction Effective delivery of sedation in the intensive care unit (ICU) is fundamental to providing comfort and relief to the critically ill, yet common sedation practice often results in over-sedation. Insufficient sedation exacerbates anxiety and agitation, and increases the risk of self-extubation. Over-sedation is damaging to patient health and increases the length of stay and healthcare costs (Kress, Pohlman, O’Connor, & Hall, 2000). Several recent studies have highlighted the benefits of drug delivery protocols based upon sedation assessment scales (Brattebo et al., 2002; Smyrnios et al., 2002; Szokol & Vender, 2001; Barr & Donner, 1995). In particular, very simple protocols minimising oversedation have reduced the length of stay by up to Corresponding author. Tel.: +64 3 364 2987x7228; fax: +64 3 364 2078. E-mail address: [email protected] (A.D. Rudge).

0967-0661/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.conengprac.2004.10.010

35%, as well as reducing total drug requirements (Kress et al., 2000; Brattebo et al., 2002). Agitation–sedation cycling describes the oscillation between states of agitation and over-sedation observed in sedated, critically ill patients. The underlying nonlinear dynamics of the agitation–sedation cycle are not well understood, and many complex interactions contribute to observed patient behaviour. Traditional therapeutic treatment methods rely heavily upon the knowledge, experience and intuition of the medical staff, the ‘art of medicine’, introducing variability and inconsistency. Computerised sedative infusion protocols that enable consistency of care and minimise fluctuations in treatment can improve patient healthcare, simplify administration, and minimise drug consumption and staff duties, while reducing costs. In spite of these significant potential advantages, current computer-assisted infusion control systems in the ICU are still in their infancy (Shaw, Dove, Greenfield, Rudge, & Chase, 2003b; Smith & Reves, 1995).

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The primary limitations to the development of automated sedative infusion protocols include the lack of a consistently quantifiable objective agitation scale and a limited understanding of the underlying system dynamics. Protocols based upon subjective measures of agitation introduce variability between assessors and lack consistency over time. Recently developed quantitative agitation measures will enable better management of patient agitation (Lam, Starfinger, Chase, Shaw, & Agogue, 2003; Lam, 2003; Starfinger, Lam, Chase, Shaw, & Agogue, 2003; Starfinger, 2003; Shaw et al., 2003a; Chase, Starfinger, Lam, Agogue, & Shaw, 2004b). This research creates models that capture the essential dynamics required to enable agitation-based feedback control systems for automated sedation administration using these quantified agitation measurements. While a multitude of pharmacokinetic models have been developed, no models of their interaction with patient agitation dynamics exist. This paper presents a simple quantitative model to capture the essential agitation–sedation dynamics in the critical care patient. Model validation is achieved through statistical comparison of simulated infusion profiles with recorded infusion data for 37 ICU patients. Finally, the potential of this model to develop improved agitation management methods using patient agitation feedback control is demonstrated through simulations using derivative focused control.

(2)

This model is intended to be the simplest necessary to capture the essential dynamics of the agitation–sedation system. Therefore, K 124 are assumed constant over time, although they can be treated as slow moving functions of time to model more complicated, very longterm phenomena such as tachyphylaxis or fatty tissue distribution (Hughes, Glass, & Jacobs, 1992). Eq. (1) represents the kinetics of drug infusion and distribution, while Eq. (2) represents the transport of sedative from the infusion site to the effect site, which for sedative and analgesic drugs is the central nervous system. An acceptable approximation for this effect site concentration is considered by some authors to be the drug concentration in the cerebrospinal fluid (Meineke et al., 2002; Cousins & Mather, 1984). The non-linear Eq. (3) was developed based upon physiological observations of critical care patient behaviour. Specifically, it states that the rate of change of agitation depends upon the magnitude of the stimulus relative to the cumulative effect of the sedative agent. Stimulus in this context refers to the combined effect of inherent pain, distress, or loss of inhibition caused by the diseased/injured state of the patient, and the therapeutic and diagnostic procedures performed by medical staff. Under constant stimulus levels, observed agitation typically falls or remains unchanged upon increased infusion of sedative agents. Similarly, patients become more agitated by increased stimulus, due to procedures or condition, if infusion rates are not increased. Patient agitation is primarily reduced by the cumulative effect of current and prior sedation administration, as modelled by the convolution term in Eq. (3). Eqs. (1)–(3) represent a model of the interaction between sedative agents and patient agitation–sedation dynamics to evaluate the effectiveness of sedative infusion protocols and automated infusion systems. More complex pharmacokinetics and pharmacodynamics can be added to identify and develop the level of complexity required to capture the essential system dynamics.

(3)

3. Model verification

2. Model The mathematical model builds upon a well-known two-compartment pharmacokinetic model (Wood & Wood, 1990), adding patient agitation as a third state variable: dC c U ¼ K 1 C c þ ; Vd dt dC p ¼ K 2 C p þ K 3 C c ; dt Z t dA ¼ w1 S  w2 C p ðtÞeK 4 ðttÞ dt; dt 0

(1)

where C c is the drug concentration in the central compartment in mg/L, C p is the drug concentration in the peripheral compartment in mg/L, U is the intravenous infusion rate in mg/min, V d is the volume of distribution in L, A is an agitation index, S is the stimulus invoking agitation, K 124 are parameters related to drug elimination and transport with units min1 ; and w1 and w2 are relative weighting coefficients of the stimulus and drug effect, respectively. Time is represented by t, and t is the variable of integration in the convolution integral of Eq. (3).

Sedative drug infusion data was recorded using an electronic drug infusion device (Greenfield, Dove, & Shaw, 2001; Shaw et al., 2003b; Rudge, Chase, Shaw, & Wake, 2003; Shaw et al., 2003a) for all ICU patients admitted to the Christchurch Hospital ICU during a nine month period and requiring more than 24 h of sedation. The device infuses a fixed sedative-analgesic solution, based on critical care nursing assessment of patient agitation using a modified version of the Riker Sedation Agitation Scale (Riker, Picard, & Fraser, 1999; Shaw et al., 2003b; Lam et al., 2003). These infusions are

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put through a fixed smoothing filter designed to titrate sedation to the minimum required, and reduce vulnerability to agitation assessment variability. Infusion data containing less than 48 h of continuous data, or data from patients whose sedation requirements were extreme, such as those with severe head injuries, were excluded. Verification of the model in Eqs. (1)–(3) is achieved through simulation of the nurse feedback protocol for 37 patients, and comparison of simulated results with the recorded nurse-controlled infusion profiles. The nursing assessment and feedback are modelled by a simple controller to match current practice. Numerical and graphical approaches are used to provide statistical measures of tracking to assess the model’s ability to capture the fundamental dynamics of the agitation– sedation system.

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Fig. 1. Diagram of the feedback loop employing nursing staff feedback of subjectively assessed patient agitation through the infusion controller.

3.1. Existing sedative infusion method A variety of sedative infusion methods exist and studies have shown that the implementation of a protocol to maintain consistency of care has resulted in improved care and reduced length of stay (Brattebo et al., 2002; Kress et al., 2000). In spite of these results, many intensive care units apply no specific, quantified protocol to sedative infusion, relying upon the judgement and experience of the intensive care unit staff (Cohen, 2002). The currently implemented infusion protocol in the ICU at Christchurch Hospital utilises a fixed concentration morphine (1 mg/mL) and midazolam (0.5 mg/mL) solution to induce sedation and provide analgesia. Bedside nursing staff act as a form of patient agitation sensor and feedback controller. In addition, an Infinite Impulse Response (IIR) filter (Rorabaugh, 1998) is employed to ensure sedation is minimised in the absence of agitation, and eliminate variability due to errors and inconsistencies in assessment of agitation and/or sedation response. The IIR filter is defined as yn ¼

n1 1 X ½y þ xi ; 6 i¼n4 i

(4)

where yi and xi are the infusion rates given through continuous and bolus infusion, respectively, in the ith hour. Eq. (4) is intended to gradually reduce the infusion rate to minimise over-sedation. A significant amount of extra boluses are required to raise the continuous infusion rate. This protocol is implemented through an electronic infusion system developed locally (Greenfield et al., 2001). Safety limits, determined by patient age and condition, are also placed on the range of allowable drug delivery rates, and the infusion rate is updated hourly. Importantly, this protocol is a closed loop feedback controller, where nursing staff close the loop by

providing agitation sensing and feedback via the electronic infusion controller, as illustrated in Fig. 1. Staff assess agitation using a modified version of the Riker Sedation Agitation Scale (Riker et al., 1999), and respond to agitation with additional bolus sedation. Boluses provided in response to agitation lead to modifications of the continuous infusion rate via Eq. (4). The continuous infusion rate is therefore representative of efforts to control agitation, and is not influenced by any specific efforts to induce sedation, which is typically a minimal amount of the total sedation administered (Fraser & Riker, 2001). Recorded sedation administration patterns using this semi-automated protocol are presented in Fig. 2. Solid dark areas represent bolus drug delivery x, and lighter filled areas represent the resulting continuous infusion rate y. Note that the continuous infusion rate increases after large volumes of bolus delivery, and declines rapidly in the absence of boluses to minimise oversedation due to unnecessary sedation administration. The presence of sudden spikes and over-shoots are therefore likely a result of the variability and subjectivity of nursing staff assessment of agitation. 3.2. Simulation of agitation–sedation dynamics Bedside intensive care staff rely on monitored autonomous parameters (e.g. blood pressure, heart rate, etc.) and physical indicators (e.g. sweat, rapid motion, etc.) to subjectively gauge agitation levels (Riker et al., 1999; Kress et al., 2000; Cohen, 2002). Many primary indications of agitation are qualitative in nature and therefore difficult to assess consistently over time and between assessors (Chase et al., 2004b; Lam, 2003; Starfinger, 2003). As early as 1959 Helson showed perception to be relative to the mean or ‘‘adaptation

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Infusion Rate (mL/h)

Infusion Rate (mL/h)

Infusion Rate (mL/h)

Infusion Rate (mL/h)

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4 2 0

0

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100

150 200 Time (hours)

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15 10 5 0

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0

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120

140

Time (hours) 8 6 4 2 0

0

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Fig. 2. Recorded sedative administration patterns for four patients under nurse feedback control. Solid dark areas represent bolus drug delivery x, and lighter filled areas represent the resulting continuous infusion rate y.

level’’ in the whole environment (Helson, 1959). The perception of many properties of objects such as weight, colour and odour, accordingly, become subjective (Helson, 1959; Wallach, 1963; Pol, Hijman, Baare, & van Ree, 1998). For example, the evaluation of pain level varies as a function of past pain levels experienced (Dar, Ariely, & Frenk, 1995). This subjective adaptation level will lead to small changes in odour, colour, weight or pain having little impact on subjective experiences. Minor changes in agitation over long periods of time are therefore often overlooked, while more rapid changes, or derivatives, are more readily assessed. Specifically, the primary changes noticed are relative changes rather than absolute magnitudes. This form of observational sensing and feedback can be modelled as a derivative focused controller. Small changes over long periods (low derivative) have little effect on the output, while large changes over shorter periods of time (large derivative) significantly affect the commanded sedation administration. Similarly, an absolute change in vital indications only invokes action once it reaches a threshold level. Hence, the simulation of bedside intensive care staff in the control loop of Fig. 1 can be modelled as a Proportional-Derivative (PD) controller with agitation as the feedback quantity. The output U, can then be combined with the IIR filter in Eq. (4). The infusion rate U, in the form of a PD controller using agitation A, as the feedback quantity can be defined as _ U ¼ K p A þ K d A;

(5)

where K p and K d are the proportional and derivative gains, respectively. The feedback controlled infusion U, in Eq. (5) represents the nursing response to agitation, and is updated once each hour, as per clinical practice in the Christchurch ICU, creating a piecewise constant infusion. The infusion rate U, is then put through the filter in Eq. (4) via xi ; implementing the sedative approach and filtered protocol used in Christchurch Hospital ICU to minimise over-sedation. Setting control gains such that K d bK p implements derivative focused control, which focuses on controlling the shape of the agitation response rather than its magnitude, and in this case is intended to capture the fundamental nursing response to patient agitation in Fig. 2. The simulated nursing sedative administration input U, is substituted into Eq. (1) to model the feedback loop created by their response to subjectively assessed patient agitation for validation. Combining Eqs. (1)–(3) with the simulated nurse control loop creates a model for simulating the patient dynamics and nursing staff response, respectively. Sedative drug infusion data, recorded through the electronic infusion system, provides a basis for comparison and model verification. Using stimulus profiles congruent with the recorded infusion patterns, each patient is simulated using identical model parameters and control protocol, using V d ¼ 100 L; K 1 ¼ 0:008 min1 ; K 2 ¼ 0:0046 min1 ; K 3 ¼ 0:09 min1 ; K 4 ¼ 0:0013 min1 ; w1 ¼ 200; and w2 ¼ 1: These parameters were estimated using the infusion rate data, and can be shown to lie within physiological ranges (Bolon et al.,

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2003; Meineke et al., 2002). Fig. 3 illustrates how the three state variables (C c ; C p and A) change over time in response to the infusion U, and the presence of the stimulus. Similarities between the simulated and recorded infusion profiles are clear. Fig. 4 presents the recorded and simulated infusion patterns for an additional four random patients. In these figures the solid dark lines represent the model responses to the simulated nurse infusion using filtered PD control, while the lighter filled areas represent the actual recorded infusion profile. The agitation index is scaled to the range of 0–100, where 100 represents extreme agitation.

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3.3. Statistical model verification Overlaying the simulated nurse and recorded infusion profiles allows clear comparison between simulated infusion and recorded infusion data. Upon inspection, the control input patterns for four patients, presented in Fig. 4, clearly show the ability of the simulated nurse and proposed model to capture the essential dynamics in the recorded data from the nursing inputs and the IIR filter. To objectively assess how well Eqs. (1)–(3) model the agitation–sedation system, two methods of comparing the recorded and simulated infusion profiles are utilised:

Stimulus

0.3 0.2 0.1 0

Cc (mg/L)

0.1

0.05

0

Cp (mg/L)

0.1

0.05

0

Agitation, A

100

50

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0

10

5

0 0

20

40

60 80 Time (hours)

100

120

Fig. 3. Example of modelled responses of simulated and recorded infusion patterns, illustrating how the three state variables (C c ; C p and A) change over time in response to the infusion U, and the presence of stimulus.

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Infusion Rate (mL/h)

8 6 4 2

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Fig. 4. Comparison between simulated and recorded infusion patterns for four patients using identical gains K p and K d : Solid dark lines represent the model responses to the simulated nurse infusion using filtered PD control, while the lighter filled areas represent the actual recorded infusion profile.

a Numerical Approach and a Graphical Approach. Both methods, based on accepted statistical analyses, were developed to provide a more objective, quantified understanding of the model’s ability to capture essential dynamics present in the recorded infusion data. Detailed development of the statistical techniques employed can be found in work by Lee et al. (2003) and Chase et al. (2004a). 3.3.1. Numerical approach to model verification It is clear from Figs. 3 and 4 that the simulated infusion profile tracks the average recorded infusion

profile, rather than the instantaneous variations in infusion rate. The severe local variations in the recorded infusion rate are likely a result of the variability and subjectivity inherent in a ‘human-based’ feedback protocol, and are not observed in simulations where the simulated nurse is 100% consistent. Therefore, to objectively compare the recorded and simulated infusion profiles, the recorded profile is first smoothed using local linear kernel regression (Wand & Jones, 1995; Hastie & Loader, 1993). The smoothed recorded infusion lays the foundation for a Tracking Index (TI), which is a quantitative

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parameter indicating how well the simulated infusion profile represents the average recorded infusion profile over the entire time series Pn

 TI ¼

1



jm^  U i j i¼1 Pn i i¼1 m^i

100;

(6)

where m^i is the smoothed recorded infusion rate, and U i is the simulated control infusion rate, at point i in the time series. A TI ¼ 100 represents perfect tracking when the simulated control infusion profile is identical to the smoothed recorded infusion profile. To determine the reliability of the Tracking Index for a given patient’s infusion profile, the moving blocks bootstrap is utilised (Efron & Tibshirani, 1993). By sampling blocks with replacement from the entire timeprofile, n ¼ 2000 bootstrap realisations are generated for each recorded patient infusion profile (Chase et al., 2004a). A TI; as defined in Eq. (6), can then be evaluated for each bootstrap realisation, providing a collection of 2000 different values of the TI 122000 ; for each recorded patient infusion profile. The median Tracking Index and its standard error SE, can then be reported for each patient (Hettmansperger & McKean, 1998). A high SE indicates poor tracking index reliability, and no conclusion regarding the performance of the simulation can be made. Poor reliability may be caused by insufficient data, the specific kernel selected, the smoothing technique utilised, or the model simulation. The Relative Total Dose, defined as the total drug dose delivered by the simulation as a percentage of the total recorded drug dose, is also calculated for each patient, providing the modelled total drug usage compared to the recorded drug dose for further verification. The low median SE in Table 1 indicates high reliability of the median TI: There are 6 patients for whom, despite high TI values, no conclusion can be drawn from the TI due to large SE. The high values of the median TI for the reliable infusion profiles indicate the validity of the developed model. A median patient specific TI across all patients of 87.0 with a 95% interpolated confidence interval (ICI) (Sheather, 1987) of (85.9, 88.1), while dependent upon the definition of Table 1 TI statistical summary for 37 patients

Max. 75th%. Med. 95% ICI 25th%. Min. SE

Median TI

SE

Relative total dose (%)

94.6 89.2 87.0 (85.9, 88.1) 84.5 75.9 0.7

0.105 0.068 0.033 — 0.023 0.011 0.004

95.0 90.4 89.1 — 87.5 77.0 0.6

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the TI; gives significant merit to the developed model and its physiological validity. Further, a median Relative Total Dose of 89.1% indicates that the simulated and recorded total drug dose are similar, with the simulator consistently administering slightly less than 100% of the recorded actual sedative dose. The slightly lower values are associated with the sudden-response nature of the recorded infusion profiles, in contrast to the consistent, smooth characteristic of the simulated infusion profile. These features are primarily a result of the consistency of the computer-implemented simulation in contrast to the variability of different nurses’ assessment of agitation and their resulting effect on sedation administration. 3.3.2. Graphical approach to model verification While the numerical approach assesses overall performance over an entire record, a graphical method of identifying instances in time where the model and nursecontroller are less than adequate would identify regions of differing performance within a record. The development of a probability band for the recorded infusion profile (Lee et al., 2003) enables a visual assessment of the performance of the simulation. The band is constructed using Chebychev’s inequality (Chase et al., 2004a), and represents the target region of the simulated infusion controller. A simulated infusion profile that lies entirely within the probability band represents excellent performance, while regular departures from the band illustrate where the model does not effectively capture behaviour. A probability band is constructed for each of the 37 patient profiles, and the time and duration of any deviations from the probability band are recorded. A 90% probability band is used because it represents a region of high probability without creating a band so wide that it loses meaning. Fig. 5 presents examples of the probability band, with the simulated infusion overlaid, for four randomly selected patients. In Fig. 5 the grey area represents the 90% probability band, the thin line represents the recorded infusion profile, and the solid dark line represents the simulated infusion profile. Fig. 5 shows that the simulated infusion profile lies predominantly within the grey 90% probability band, and tracks the mean recorded infusion rate closely for these four randomly selected patients. Similar graphs are observed for all 37 patients, as demonstrated by the high median time within the band of 85.9% across all patients seen in Table 2. With the exception of eight patients, all simulated infusion profiles lie within the probability band at least 70% of the time. These results indicate that the simulations are a good representation of the essential dynamics captured in the recorded infusion profile. Importantly, the primary reason for reduced total time within the probability band is often a single, but

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Time (Hours) 15 10 5 0

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25 30 Time (Hours)

35

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80

100

6 4 2 0

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120

140

160

180

Fig. 5. Probability bands with simulated infusion profile for four patients (patient numbers 8, 18, 34 and 35 from top to bottom). The grey area represents the 90% probability band, the thin line represents the recorded infusion profile, and the solid dark line represents the simulated infusion profile. Table 2 Simulated infusion profile compatibility with probability band for 37 patients

Max. Med. Min.

Time within band (%)

Max. departure time (%)

100.0 85.9 58.4

20.2 5.6 0.0

lengthy, departure from the probability band, rather than a consistently poor performance throughout the length of the simulation. This feature is observed in the lower two plots of Fig. 5 for patients 34 ( 25–40 h) and 35 ( 135–155 h), and indicated by the fact that most patients for whom the simulated infusion profile lies in the band less than 80% of the time also show a large maximum departure time from the band of 10% or more. This result implies that, while performing well most of the time, the simulated infusion rate deviates from the recorded infusion rate over some particular period, and takes some time before tending towards the recorded infusion rate again. Note that the generally high values of TI imply that these deviations are not very large in magnitude. In particular, the TI values for the eight patients who are within the band for less than 70% of the time range from 75.7 to 87.3. The periods where the simulated infusion rate departs from the 90% probability band indicate the areas where

the model may not capture certain dynamics. These periods may represent periods of particular distress or physiological change due to patient condition. In particular, a common reason for the departure of the simulation profile from the probability band is apparent time-lag, as observed in the lower two plots of Fig. 5. Often, small departures from the probability band follow rapid increases or decreases in the recorded patient infusion rate, scenarios in which the simulated infusion appears to lag behind. Hence, these differences may be a result of medical staff over- or underassessment of, or reaction to, patient agitation. It must be remembered that while stimulus profiles are specific to each patient, all simulations in this paper utilise identical parameters for all patients, including drug clearance and distribution. When parameters are adjusted to suit each particular patient, the ability of the simulation to remain within the probability band greatly improves. However, the results presented are a good indication that the proposed system model captures the essential underlying dynamics common to most patients, and is both physiologically valid and generalisable, given the use of identical model parameters for all 37 patients.

4. Improved agitation management Having established the minimal model presented as a platform for developing control parameters, the

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simulated nurse results can be used as a benchmark for assessing the effects of different infusion control systems. In particular, the effect of removing the smoothing filter and increasing the simulated nurse’s derivative focused control gains is investigated. Identical model parameters are still used for all patients in all cases. Peak and mean agitation levels, relative to those resulting from use of the simulated nurse, measure the improvement in agitation management achieved through direct feedback control. Without the filter, this approach tests the impact of a quantified agitation measurement system and simple controllers. Several biological control systems employ simple forms of feedback control (Carson & Cobelli, 2001). Studies have shown that artificial controllers in firstorder systems similar to the agitation–sedation system model defined in Eqs. (1)–(3) have benefited from derivative focused control (Lam, Lee, Hwang, Chase, & Wake, 2002; Doran, Chase, Shaw, Moorhead, & Hudson, 2004a; Doran, Moorhead, Hudson, Chase, & Shaw, 2004b). Hence, an infusion rate U, in the form of a PD controller using agitation A, as the feedback quantity can be defined as in Eq. (5). Specifically for a control systems context, the derivative control gain K d is 1000 times greater than the proportional control gain K p for all simulations presented in this paper, to focus on controlling the shape of the agitation response rather than its magnitude. Using this derivative focused approach sedative is typically not administered while agitation is falling to avoid over-sedation. As the control gains are increased, the observed infusion profiles become more exaggerated and the peak

Infusion, U (mL/h)

10

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infusion rate increases. While the peaks of the infusion rate profile are considerably higher, the infusion rate also drops dramatically in the absence of agitation, representing a bolus-focused approach to sedation administration, as seen in the results for one patient shown in Fig. 6. The solid lines in Fig. 6 are for doubled control gains compared to those used for the simulated nurse, the dotted lines are for tripled control gains, and the grey filled area is the benchmark for comparison. Reductions in agitation are observed in Fig. 6 as the unfiltered gains are uniformly increased. Table 3 shows that the reductions in agitation are also achieved without significant changes in the delivered dose. By increasing the gains by a factor of two the peak agitation level was reduced 37.8% on average, and mean patient agitation levels are reduced 44.2% on average. Further reductions of 52.9% (peak) and 68.4% (mean) are observed when the gains are uniformly increased by a factor of three. When the control gains are tripled the increased, sharper response to patient agitation leads to Table 3 Summary simulation results for 37 patients

Max. Ave. Min. STD.

Relative total dose (%)

Relative performance (%)

Gains 2

Gains 2

Gains 3

Peak

Mean

Peak

Mean

72.5 62.2 54.2 4.8

63.5 55.8 42.5 3.9

62.8 47.1 33.7 6.8

42.9 31.6 8.4 9.2

116.4 89.5 64.1 10.4

Gains 3

129.1 72.6 6.3 25.8

Control gains x 2 Control gains x 3 Recorded infusion profile

8 6 4 2 0

Control gains x 2 Control gains x 3 Simulated Nurse

Agitation Index, A

50 40 30 20 10 0

0

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40

60

80

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120

140

Time (hours)

Fig. 6. Effect of increasing control gains K p and K d on control input U, and agitation A, for one patient. The solid lines represent doubled control gains compared to those used for the simulated nurse, the dotted lines are for tripled control gains, and the grey filled area is the benchmark for comparison.

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a small reduction in total dose, indicating the effectiveness of a bolus based approach, aligned with proven sedation administration protocols (Barr & Donner, 1995; Kress et al., 2000). Table 3 shows that peak and mean agitation levels can be reduced by up to 52.9% and 68.4%, respectively, averaged across all patients, using direct agitation feedback control. These reductions represent real benefits to the ICU patient. If the peak agitation level reaches a certain threshold, length of stay increases and self-extubation becomes a serious threat (Cohen, 2002). If the mean agitation level is too high, recovery rate slows and the length of stay rises (Cohen, 2002). These improvements in agitation management are achieved without increasing the average drug dose across all patients. Doubling and tripling the gains result in administering 89.5% and 72.6% of the recorded drug dose, respectively, compared to the 89.1% administered by the simulated nurse benchmark. Derivative focused control based upon agitation feedback delivers doses of sedative agents comparable to that administered by ICU nurses, but delivers the drug in shorter more severe bursts, as needed. The resulting drug infusion profile typically consists of higher than expected infusion rates, or boluses, during short periods of elevated agitation levels. The inherent sensitivity to increasing agitation of the derivative weighted feedback control means that agitation is rapidly regulated through increased drug delivery. It should be noted that for certain sedatives, extreme infusion rates can have negative side effects such as cardiopulmonary depression (Barr & Donner, 1995; Wagner & O’Hara, 1997). Therefore, safety limits on peak infusion rates and, more importantly total drug dose, are necessary to ensure safe practical implementation. However, in spite of specific physiological and practical limitations, there is substantial room for improved infusion protocols based upon derivative focused agitation feedback control, given a physiologically quantified measure of patient agitation such as those under development (Lam et al., 2003; Starfinger et al., 2003; Chase et al., 2004b).

Simulations show that a reduction in both the magnitude of agitation and the severity of agitation– sedation cycling are possible. Derivative focused control based on agitation feedback is shown to be an effective means of managing agitation when consistent agitation sensors, currently being developed, become available. Mean and peak agitation levels are reduced by 68.4% and 52.9%, respectively, on average, with some patients showing over 90% reduction in mean agitation level through increased control gains. Furthermore, while an increased maximum infusion rate is required, these benefits are achieved without significant increases in control effort, and hence the drug dose required. Improved agitation management is enabled using simple derivative focused feedback control of sedation administration, which provides an essentially bolusdriven management approach. The models and methods are shown to be applicable to a broad range of ICU patients through the use of generic parameters over all 37 patients studied. The extensive model verification ensures that the model is suitable for development of more advanced, optimal infusion controllers. Design and implementation of automated feedback infusion controllers based on this control model could offer simple and effective drug delivery, without significant increases in drug consumption and expense.

Acknowledgements The authors wish to acknowledge Kathryn Greenfield and Richard Dove from the Medical Engineering and Physics Department at Christchurch Hospital, and Assoc. Prof. David Wall from the Department of Mathematics and Statistics at the University of Canterbury for their input to this work. Funding for this research was provided by the New Zealand Foundation for Research, Science and Technology through a Bright Futures Top Achiever Doctoral Scholarship, and by the Todd Foundation through the Award for Excellence.

References 5. Conclusions The minimal model presented captures the essential dynamics of the agitation–sedation system. The proposed model of the agitation–sedation system and simulated nurse is shown to reliably and consistently simulate and track the drug infusion data from 37 ICU patients. It is therefore an appropriate foundation for comparison of improved sedation administration controllers and gains.

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