#### What We Already Know about This Topic

#### What This Article Tells Us That Is New

^{1–3}When treating status epilepticus, a hypnotic, such as propofol or a barbiturate, is used to directly inhibit seizure activity.

^{2},

^{3}After a brain injury these drugs are administered to provide brain protection by reducing cerebral blood flow and metabolism.

^{1}In both cases the anesthetic is titrated to achieve a specific clinical target that indicates a state of large-scale brain inactivation. A standard approach is to monitor the patient’s brain activity continuously with an electroencephalogram and use a specified level of burst suppression as the target. Burst suppression is an electroencephalogram pattern indicating a state of highly reduced electrical and metabolic activity during which periods of electrical bursts alternate with isoelectric periods termed suppressions.

^{4–6}

^{7–26}Although no CLAD system has been designed to manage medical coma in humans, Vijn and Sneyd

^{27}implemented a CLAD system to test new anesthetics in rodents using as the control signal the burst-suppression ratio; the fraction of time per 15 s that the electroencephalogram is suppressed. For several anesthetics they established nonmodel-based control of burst-suppression ratio levels measured in terms of group averages rather than individual control trajectories. Cotten

*et al.*

^{28}studied methoxycarbonyl etomidate with this paradigm in rodents and also reported only group average control results.

#### Materials and Methods

##### Animal Care and Use

^{27},

^{28}

##### Instrumentation and Preparation

^{29},

^{30}Briefly, general anesthesia was induced and maintained with isoflurane. A microdrill (Patterson Dental Supply Inc., Wilmington, MA) was used to make four holes at the following stereotactic coordinates: A0L0, A6L3, A6L-3, and A10L2 relative to the lambda.

^{29},

^{30}An electrode with mounting screw and socket (Plastics One, Roanoke, VA) was screwed into each hole, and the sockets were inserted in a pedestal (Plastics One). The screws, sockets, and pedestal were all permanently fixed with dental acrylic cement, and the animal underwent a minimum recovery period of 7 days. The potential difference between electrodes A0L0 and A6L-3 (left somatosensory cortex) was recorded. The signal was referenced to A10L2 and recorded using a QP511 Quad AC Amplifier System (Grass Instruments, West Warwick, RI) and a USB-6009 14-bit data-acquisition board (National Instruments, Austin, TX). The sampling rate was 512 Hz. A line filter with cutoff frequencies of 0.3 and 50 Hz was used.

##### CLAD System Design for Burst-suppression Control

^{31}A BSP value of 0 corresponds to an active electroencephalogram with no suppression, whereas a value of 1 corresponds to a completely isoelectric or suppressed electroencephalogram. We assume that a target level of burst suppression, BSP

_{target}, has been set as a number between 0 and 1 (step 0). We further assume that propofol is being administered by an infusion pump and that this infusion is producing a state of burst suppression, which we wish to control at BSP

_{target}(steps 1 and 2). The time course of the BSP computed from the electroencephalogram is the quantity that our CLAD system tracks. To do so, we segment the electroencephalogram into a binary time series (step 3) with a 20 ms resolution in which a burst is a 0 and a suppression is a 1 (Eqs. 19–21). The binary time series is input to the BSP filter algorithm (Eqs. 7–13), which computes a real-time BSP estimate (step 4).

_{target}(step 5). The difference between the estimated BSP and BSP

_{target}is the error signal. The error signal, transformed to concentration (Eqs. 14 and 15), is passed to a PI controller (step 6). The objective of the controller is to keep the error as close to 0 as possible, which means that the CLAD is maintaining the target BSP level. Therefore, the PI controller issues commands to the infusion pump to change the infusion rate based on the magnitude and sign of the error signal (step 7). The entire cycle from steps 1–7 takes 1 s, the update interval of our CLAD system.

##### CLAD System Identification

##### Experimental Protocol

_{target}of 0.2 for 5–15 min before starting the control experiment (fig. 1B). This allowed us to ensure correct communication between the software and the infusion pump. The initialization also ensured that each control experiment started with each animal in the same, low-level state of burst suppression. After the initialization, we set BSP

_{target}to the target BSP trajectory selected for that animal and let the CLAD system continue BSP control.

##### Analysis of CLAD System Performance

_{target}as the mean BSP traversed during the transition.

^{32}

##### Statistical Analysis

^{33}A preliminary study of our system indicated that the absolute errors were less than 0.2. Therefore, for a given target level, we defined reliability of the CLAD system as the absolute error being less than 0.15 with high probability. We set that probability at 0.95. This criterion can be easily evaluated as it is equivalent to the 95th percentile of the absolute error distribution being 0.15 or less. We computed the absolute error distribution at a given level as the absolute values of e-tracking (Eq. a) at that level. We used 900 data points (60 points per min × 15 min per level) to compute the absolute error distribution at a level. There were six animals and three levels per animal or 18 levels in total. We assessed reliability on each of the 18 levels separately and overall by considering all levels across animals.

*P*value less than 0.05. If zero was below (above) the 2.5th (97.5th) percentile the systems had a positive (negative) bias. If zero was inside the 50% CI,

*i.e.*, between the 25th and 75th percentiles, we considered the system to be highly accurate. We assessed accuracy on each of the 18 levels separately and overall by considering all levels across animals.

^{29},

^{34}We performed the overall reliability analysis across the 18 levels assuming levels within animals were independent. Independence is a reasonable assumption because if we assume a high first-order serial correlation of 0.98 between adjacent data points separated by 1 s and if we allow between-level transitions of 5–10 min then, the maximum correlation between the closest two points in immediately adjacent levels is between ((0.98)

^{600}= 5.4 × 10

^{−6}; (0.98)

^{300}= 2.3 × 10

^{−3}), where 300 (600) = 5 (10) min × 60 data points per min.

^{35}That is, control activity separated by 5 min or more is unrelated.

*p*denote the probability that the CLAD system is reliable at a level. The analysis of reliability across levels yields a binomial probability model with

*n*= 18 assessments of which on

*k*levels the system was reliable and on

*n*−

*k*levels the system was not reliable. Being reliable at a given level is defined as the system satisfying the reliability criterion that the 95th percentile of the absolute error distribution was 0.15 or less. If we assume a uniform probability distribution on the interval (0, 1) for the previous distribution of

*p*then it is well known that the posterior distribution of

*p*is a β distribution.

^{29},

^{34}We estimate the probability that the CLAD system is reliable across all levels as the mode of the posterior distribution. We consider the experiment to have established reliability of our CLAD system across levels if 0 is less than the left endpoint of the 95% Bayesian credibility (confidence) interval for

*p*.

*P*.

#### Results

##### Real-time Electroencephalogram Segmentation and BSP Estimation

*α*(Eqs. 20 and 21), to distinguish the amplitude envelope of bursts from the background suppression level. Similarly, we show that the amplitude threshold

*v*

_{threshold}partitioned bursts from suppressions assigning a 0 (1) when the filtered electroencephalogram was less than (exceeded)

*v*

_{threshold}. The forgetting factors were 0.995 for animals 1 and 2, 0.595 for animals 3 and 4, and 0.695 for animals 5 and 6 whereas, the thresholds were 3 × 10

^{−5}μV for animals 1 and 2, 1.5 × 10

^{−6}μV for animal 3, and 4.3 × 10

^{−6}μV for animals 4, 5, and 6. A larger forgetting factor (more forgetting) corresponds to more filtering, meaning that the animal had a noisier electroencephalogram (

*e.g*., fig. 2B), whereas a smaller forgetting factor (less forgetting) is more suitable for easily discernible bursts, meaning the animal had sharper electroencephalogram signals (fig. 2A).

Fig. 3 Image Tools |
Fig. 4 Image Tools |
Fig. 5 Image Tools |

Table 1 Image Tools |

##### Rodent Pharmacokinetics Models Are Identified Online

^{36}commonly used to represent propofol.

##### Real-time Closed-loop Tracking of BSP Target Levels Is Achieved in Individual Rodents

*i.e.*, a probability of 0.9 of being suppressed, is easier to estimate from the electroencephalogram recordings than the BSP states of 0.4 and 0.65. The variance of a binomial random variable (Eq. 4) is lowest for

*p*

_{t}closer to either 0 and 1, and highest for

*p*

_{t}close to 0.5. The larger errors during the transitions likely reflect anticipated limitations in the controller performance (see Discussion).

#### Discussion

##### CLAD System Development

^{10}and later reappeared in the 1980s.

^{24}There have been several clinical studies of CLAD systems, and versions are now commercially available.

^{37}The most frequently used control signal has been the Bispectral Index (BIS).

^{7–9},

^{11},13,14,17,18,21–23,38–40 Other control signals have included a wavelet-based index,

^{12}entropy measures,

^{16}an auditory evoked potential index,

^{15}and the spectrogram median frequency.

^{24–26}These systems have been constructed with standard and nonstandard control paradigms

^{15},

^{16},

^{23},

^{24},

^{40}and used principally to control unconsciousness.

^{7},

^{9},

^{12},

^{14},

^{16},

^{18},

^{23},

^{24},

^{38},

^{39}A recent report investigated control of both antinociception and unconsciousness.

^{16}The criteria for successful control differed across these studies. Schwilden

*et al.*

^{24}demonstrated control of median frequency in individual human subjects. In contrast, several of the studies that used BIS as the control signal defined successful control as a BIS value between 40 and 60, and reported BIS time courses averaged across subjects.

^{7–9},

^{11},13,14,17,18,21–23,38–40 Control using BIS as a control signal is achieved with a 20- to 30-s delay required to compute the BIS updates.

^{41}In contrast, our system updates the control input every second with no delay. Those CLAD systems that have been developed to study burst suppression have also only shown results for time courses averaged across subjects.

^{27},

^{28}None of these studies considered control of dynamic trajectories nor conducted a formal statistical assessment of reliability and accuracy.

##### A CLAD System for Burst-suppression Control

^{42}the state of the brain in burst suppression is well-defined neurophysiologically.

^{4},

^{5}Furthermore, burst suppression has a well-defined electroencephalogram signature that can be quantified in real time, and therefore, controlled. Our two-dimensional pharmacokinetics model (Eqs. 1–2) provides a simple and sufficient representation for capturing the essential properties of burst suppression. This model was the starting point for designing our CLAD system. We formulated this model based on observations made while monitoring the electroencephalogram of patients under general anesthesia in the operating room. We noticed that once the state of burst suppression is achieved increasing or decreasing the rate of a propofol infusion directly increases or decreases the rate of suppression events. However, because intravenous injection of propofol does not deliver the drug directly to the brain, a burst-suppression model must have a minimum of two compartments. Therefore, for control of burst suppression, our simpler second-order model can replace more detailed four-compartment models

^{36}because the objective is to control a single brain state and not the wide range of brain states that could be represented by the higher-order model.

^{43}uses the one-to-one relationship between the BSP (Eq. 3) and the effect-site anesthetic level (Eq. 12) to estimate in real time the effect-site anesthetic level. We have previously shown that the BSP filter algorithm gives more credible burst-suppression estimates than the burst-suppression ratio.

^{31}The burst-suppression ratio can require up to 5 min to estimate the brain’s burst-suppression state,

^{44}a feature that would substantially limit its use in real-time control.

^{45}

^{33}Current performance measures for CLAD systems have been adapted from those used to assess performance of target-controlled infusion systems.

^{32}Recently, CLAD systems have been evaluated by comparing their performance to performance using manual control.

^{19}Our Bayesian paradigm should facilitate design and testing of future CLAD systems by making it possible to assess performance in terms of specified properties on a system’s error distribution.

##### Improving CLAD System Design

^{5}As an alternative to our deterministic PI controller, we could model system noise explicitly and apply a stochastic control strategy.

^{46}A model predictive control strategy could be adopted to formally impose constraints such as nonnegative infusion rates.

^{47}The BSP filter algorithm (Eqs. 7–10) could be improved by using instead of the first-order random walk model (Eq. 6), a stochastic version of our two-dimensional state model (Eq. 1) to estimate simultaneously the BSP and its rate of change. This is equivalent to estimating both the peripheral and effect-site anesthetic levels from the binary time series. Modifying the BSP filter in this way could improve tracking performance during transitions by allowing more rapid increases in transitions from lower to higher target levels (fig. 5A) and preventing undershoot in transitions from higher to lower levels (fig. 5D). By doing so, we would be adopting the common practice of using the same model for state estimation and control. Tight control during transitions was not a primary design consideration in the current work because large and frequent level changes are not usually required to manage medically induced coma.

##### CLAD Systems for Control of Medically Induced Coma and States of General Anesthesia

^{48}and using intensive care unit staff more efficiently.

^{49}This is a tractable yet, nontrivial estimation problem.

#### Appendix

##### Closed-loop Anesthetic Delivery Theory

##### A State Model of Burst Suppression

*x(t) = (x*

_{1t}

*, x*

_{2t}) be the state of the system at time

*t*where

*x*

_{1t}is the amount of anesthetic in the peripheral compartment, and

*x*

_{2t}is the amount of the anesthetic in the brain or the effect-site compartment. We let

*I(t)*denote the infusion rate of the anesthetic at time

*t*. We assume that the anesthetic enters into the peripheral compartment; the anesthetic flows back and forth between the peripheral and the effect-site compartments; the anesthetic is eliminated from the body only through the peripheral compartment; and the amount of anesthetic in the effect-site compartment determines the electroencephalogram level of burst suppression.

##### Observation Model and the Definition of the Burst-suppression Probability

*n*

_{t}be the binary time series constructed from the filtering and thresholding, where

*n*

_{t}

*= 1*if there is a suppression at time

*t*, and

*n*

_{t}

*= 0*if there is a burst at time

*t*(Eqs. 19–21). We define the burst-suppression probability (BSP) as

*p*

_{t}defines the probability of a suppression event at time

*t*given

*x*

_{2t}it follows that

*n*

_{t}obeys the Bernoulli process

*p*

_{t}, a well-defined probability on the interval (0, 1). In this way,

*p*

_{t}provides an instantaneous output of the probability of the brain being suppressed.

##### State Estimation: The BSP Algorithm

*p*

_{t}or equivalently, the brain state

*x*

_{2t}, from the binary time series

*n*

_{t}. We develop a version of a binary filter algorithm

^{31},

^{43}to compute estimates of

*p*

_{t}and

*x*

_{2t}in real time. We assume a simplified, stochastic version of the state model in equation 1 by taking

*z*

_{t}obeys the Gaussian random walk model

*v*

_{t}are independent, zero mean Gaussian random variables with variance

*x*

_{2t}remains nonnegative. Given estimates of

*z*

_{0}and

*n*

_{t}to compute

*p*

_{t}and

*x*

_{2t}.

^{31},

^{43}It is

*t = 1, ..., T*and the notation

*z*

_{ts}denotes the estimate of

*z*

_{t}, given the data up through time

*s*. It follows from equations 3, 7, and 9 that at time

*t*the estimates of

*x*

_{2t}and

*p*

_{t}are, respectively,

##### System Identification for the BSP Algorithm and the State Model

*z*

_{0}and

*A, b*, the parameters of the state model, in a two-step procedure. First, we assume that a preliminary experiment is conducted in which a bolus dose of the anesthetic sufficient to induce burst suppression is administered to the subject and the electroencephalogram is converted into the binary time series by filtering and thresholding (see Electroencephalogram Segmentation Algorithm below). We estimate

*z*

_{0}and

^{31},

^{43}to the state space model defined by equations 4 and 6. The expectation maximization algorithm also provides

*z*

_{tT}the estimate of z

_{t}given all of the binary observations in the bolus experiment, and as a consequence, by equation 12,

*x*

_{2tT}the estimate of

*x*

_{2t}. In the second step, we use the estimated state,

*x*

_{2tT}as data to estimate

*A*and

*b*by nonlinear least squares.

##### Design of a Proportional-integral Controller

*p*

_{target}is the target level of burst suppression, then it follows from equation 3 that the corresponding target effect-site concentration of the anesthetic is

*t*is

^{45}

*u(t)*is the control signal at time

*t*,

*t*

_{0}is the start time of the control interval and

*a*

_{p},

*a*

_{i}are control parameters to be determined. If we take as our design criterion the implementation of a proportional-integral controller that achieves a fast rise time up to a specified level of burst suppression while minimizing the overshoot then it follows from standard control theory arguments that

^{45}we take

*a*

_{10}

*, a*

_{12}

*, a*

_{21}, and

*b*are defined in equation 2. Equations 17 and 18 show that once we have estimated the parameters of the pharmacokinetics model, the parameters for the controller are completely defined.

##### Electroencephalogram Segmentation Algorithm

*x*

_{2t}through the binary time series

*n*

_{t}. We convert the electroencephalogram signal

*y*

_{t}into

*n*

_{t}using the following algorithm. At each observation time we compute the following time-varying mean and variance, and evaluate the threshold criterion

*α*is a forgetting factor between 0 and 1 and

*v*

_{threshold}is a threshold voltage we set to define a burst. A value of α closer to 0 (1) corresponds to less (more) forgetting. The algorithm in equations 19–21 tracks

*s*

^{2}, the time-varying mean and variance, respectively. If the time-varying variance exceeds the threshold, then the electroencephalogram is in a burst and

*n*

_{t}

*= 0*, whereas if the time-varying variance does not exceed the threshold, then the electroencephalogram is in a suppression and

*n*

_{t}

*= 1*.