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The authors have declared that no competing interests exist.

Conceived and designed the experiments: MMS JJC ENB. Performed the experiments: MMS JJC. Analyzed the data: MMS JJC. Contributed reagents/materials/analysis tools: MMS JJC ML KS. Wrote the paper: MMS ENB.

Medically-induced coma is a drug-induced state of profound brain inactivation and unconsciousness used to treat refractory intracranial hypertension and to manage treatment-resistant epilepsy. The state of coma is achieved by continually monitoring the patient's brain activity with an electroencephalogram (EEG) and manually titrating the anesthetic infusion rate to maintain a specified level of burst suppression, an EEG marker of profound brain inactivation in which bursts of electrical activity alternate with periods of quiescence or suppression. The medical coma is often required for several days. A more rational approach would be to implement a brain-machine interface (BMI) that monitors the EEG and adjusts the anesthetic infusion rate in real time to maintain the specified target level of burst suppression. We used a stochastic control framework to develop a BMI to control medically-induced coma in a rodent model. The BMI controlled an EEG-guided closed-loop infusion of the anesthetic propofol to maintain precisely specified dynamic target levels of burst suppression. We used as the control signal the burst suppression probability (BSP), the brain's instantaneous probability of being in the suppressed state. We characterized the EEG response to propofol using a two-dimensional linear compartment model and estimated the model parameters specific to each animal prior to initiating control. We derived a recursive Bayesian binary filter algorithm to compute the BSP from the EEG and controllers using a linear-quadratic-regulator and a model-predictive control strategy. Both controllers used the estimated BSP as feedback. The BMI accurately controlled burst suppression in individual rodents across dynamic target trajectories, and enabled prompt transitions between target levels while avoiding both undershoot and overshoot. The median performance error for the BMI was 3.6%, the median bias was -1.4% and the overall posterior probability of reliable control was 1 (95% Bayesian credibility interval of [0.87, 1.0]). A BMI can maintain reliable and accurate real-time control of medically-induced coma in a rodent model suggesting this strategy could be applied in patient care.

Brain-machine interfaces (BMI) for closed-loop control of anesthesia have the potential to enable fully automated and precise control of brain states in patients requiring anesthesia care. Medically-induced coma is one such drug-induced state in which the brain is profoundly inactivated and unconscious and the electroencephalogram (EEG) pattern consists of bursts of electrical activity alternating with periods of suppression, termed burst suppression. Medical coma is induced to treat refractory intracranial hypertension and uncontrollable seizures. The state of coma is often required for days, making accurate manual control infeasible. We develop a BMI that can automatically and precisely control the level of burst suppression in real time in individual rodents. The BMI consists of novel estimation and control algorithms that take as input the EEG activity, estimate the burst suppression level based on this activity, and use this estimate as feedback to control the drug infusion rate in real time. The BMI maintains precise control and promptly changes the level of burst suppression while avoiding overshoot or undershoot. Our work demonstrates the feasibility of automatic reliable and accurate control of medical coma that can provide considerable therapeutic benefits.

Medically-induced coma (also referred to as medical coma) is a drug-induced state of profound brain inactivation and unconsciousness used to treat refractory intracranial hypertension and status epilepticus, i.e., epilepsy that is refractory to standard medical therapies

No guidelines have been set to define what level of burst suppression should be achieved to maintain a medical coma

When used to control the delivery of anesthetic drugs, BMIs are often termed closed loop anesthetic delivery (CLAD) systems. During the last 60 years considerable work has been done on the development of CLAD systems for maintenance of general anesthesia and sedation (see

The presented BMI applies an EEG-guided, closed-loop infusion of propofol to control the level of burst suppression in medically-induced coma in a rodent model using a stochastic control framework. In this framework, we use the concept of the burst suppression probability (BSP) to define the brain's instantaneous probability of being in the suppressed state and quantify the burst suppression level. We use a two-dimensional linear compartment model to characterize the effect of propofol on the EEG. For each animal, we estimate the parameters of the compartment model by nonlinear least-squares in an experiment prior to initiating control. The BMI consists of two main components: an estimator and a controller. We derive a two-dimensional state-space algorithm to estimate the BSP in real time from the EEG thresholded and segmented into a binary time-series. Taking the BSP estimate as the control signal, we derive controllers using both a linear-quadratic-regulator (LQR) and a model predictive control strategy. We first verify the performance of the developed stochastic control framework in a simulation study based on the model parameters estimated from the actual experimental data. We then illustrate the application of our BMI system by demonstrating its ability to maintain precise control of time-varying target levels of burst suppression and to promptly transition between changing target levels without overshoot or undershoot in individual rodents.

Animal studies were approved by the Subcommittee on Research Animal Care, Massachusetts General Hospital, Boston, Massachusetts, which serves as our Institutional Animal Care and Use Committee. Animals were kept on a standard day-night cycle (lights on at 7:00 AM, and off at 7:00 PM), and all experiments were performed during the day.

We use a stochastic optimal control paradigm to design a real-time BMI to control medical coma using burst suppression (

(a) The BMI records the EEG, segments the EEG into a binary time-series by filtering and thresholding, estimates the BSP or equivalently the effect-site concentration level based on the binary-time series, and then uses this estimate as feedback to control the drug infusion rate. (b) A sample burst suppression EEG trace. Top panel shows the EEG signal, middle panel shows the corresponding filtered EEG magnitude signal (orange) and the threshold (blue) used to detect the burst suppression events, and bottom panel shows the corresponding binary time-series with black indicating the suppression and white indicating the burst events. (c) The two-compartmental model used by the BMI to characterize the effect of propofol on the EEG.

(a) and (b) show two sample fitted system responses. The measured BSP trace in response to a preliminary bolus of propofol is shown in grey and the response of the second-order system model in (2) fitted using nonlinear least-squares is shown in red.

Our goal is to control the anesthetic state of the brain in burst suppression, which depends on the effect-site (i.e., brain) drug concentration. The burst suppression state or the effect-site concentration, however, are not directly observable. What we observe is the EEG signal, a stochastic process that depends on the burst suppression state. To design the closed-loop BMI, we present a certainty-equivalent optimal feedback control approach

As our measure of the burst suppression state, we use the burst suppression probability (BSP) by filtering and thresholding the EEG signal in small intervals to identify the activity in each interval as a burst or a suppression event (see Experimental Procedure;

To develop the estimator and the controller, we construct a state model for the drug concentration state that describes its dynamics in response to propofol infusion. Pharmacokinetic models characterize the dynamics of a drug's absorption, distribution, and elimination in the body (e.g.

Given the two compartments in the model, the concentration state is two-dimensional and is denoted by

We first derive a recursive Bayesian estimator of the burst suppression level from the EEG thresholded and segmented into a binary time-series. We then derive an optimal feedback-controller that uses this estimate as a feedback signal to decide on the drug infusion rate in real time.

We now develop a recursive Bayesian estimator for the drug concentrations and consequently for the BSP based on the binary observations of the thresholded EEG signal. Since the drug concentration state,

A recursive Bayesian estimator consists of two probabilistic models: the prior model on the time sequence of the concentration states, and the observation model relating the EEG signal to these states

The observation in the estimator is the binary time-series of the burst suppression events obtained by thresholding the EEG (see Experimental Procedure;

Using the prior and observation models in (6) and (7), we now derive the recursive Bayesian estimator. The estimator's goal is to causally and recursively find the minimum mean-square error (MMSE) estimate of the state

We denote the mean of the posterior, i.e.,

As the second approximation, we make a Gaussian approximation to the posterior density. Doing so, from (9) the prediction density will be approximately Gaussian since

Hence (14)–(17) give the estimator recursions. The estimator finds the MMSE estimate of the state or equivalently the posterior mean at time

The recursive Bayesian estimator derived above provides us with a real-time estimate of the concentration states at each time step. We now design a real-time optimal feedback-controller that takes as feedback this state estimate and decides on the sequence of drug infusion rates

In the general LQR formulation above, however, the goal is to derive the states close to

Note that the LQR formulation does not impose any constraints, such as positivity of the control variables. In practice we can impose these constraints by bounding the LQR control solution in (25) appropriately (for example if the solution is negative, use zero instead). Another way to solve optimal control problems with constraints is to use a model predictive control approach as we develop next.

One approach to solve the optimal control problem while explicitly imposing constraints on the state and control variables is to use a model predictive controller that approximately solves the constrained optimal control problem at each time step

In our BMI, we implement both the bounded LQR controller and the model predictive controller in which such constraints (such as positivity of drug infusion rates) are explicitly imposed in the formulation. We show that in our problem, in which there are only constraints on the drug infusion rate or equivalently the control variable, the two approaches yield approximately the same infusion rates. However, as we expand on in the

Surface EEG recordings were collected using extradural electroencephalogram electrodes that were surgically implanted at the following 4 stereotactic coordinates relative to lambda: A (Anterior) 0 mm L (Lateral) 0 mm, A6L3, A6L-3, and A10L2

During the experiment, the potential difference between electrodes A0L0 and A6L3 was recorded and 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 binary signal was acquired at a sampling rate of 500 Hz and fed into our BMI. Our algorithm was implemented in a simulink-matlab framework on a HP Probook 5430 s laptop. This setup controlled a Physio 22 syringe pump (Harvard Apparatus, Holliston, MA) to deliver the propofol infusion rate. A 24 gauge intravenous catheter was placed in a lateral tail vein during brief general anesthesia with isoflurane (2% to 3%) in oxygen, and then the animal was allowed to fully recover from the isoflurane general anesthetic in room air before the start of the experiment. The temperature of the animal was monitored and maintained in the normothermic range for the duration of the experiment.

For all experiments, the magnitude of the raw EEG signal was low-pass filtered below 5 Hz and then thresholded to convert it into a binary signal. At the start of an experiment, the threshold level was empirically chosen based on visual inspection of the BSP and the corresponding binary data and based on the values of the filtered EEG over the bursts and suppressions.

Our system identification procedure is conducted prior to real-time BMI control for each animal in a preliminary experiment and consists of two steps. First, a BSP signal is estimated from the binary thresholded EEG trace using a special case of our recursive Bayesian estimator in which we take the state to be the scalar variable

To characterize the performance of the BMI at steady state, we compute the error between the target BSP at each time,

We use the error to calculate multiple standard metrics

To characterize the performance of the BMI in transitioning between target BSP levels, we calculate the rise time for an upward transition and the fall time for a downward transition. These are defined as the time it takes, once the target is changed, for the BSP to reach within 0.05 BSP units of the new target BSP. We then find the rate of BSP change defined as

In addition to calculating the steady-state error metrics above for the low, medium, and high levels in each experiment, across all levels for each experiment, and across all experiments (

Experiment # | 1 | 2 | 3 | 4 | 5 | 6 | Median |

Low Level | |||||||

Median Abs. Dev. | 0.027 | 0.043 | 0.017 | 0.032 | 0.034 | 0.031 | |

Median Abs. Perf. Error | 5.43 | 10.72 | 4.90 | 11.44 | 8.47 | 6.18 | |

Median Pred. Error | −0.80 | 10.72 | 1.79 | −11.44 | −8.47 | −3.04 | |

Mid Level | |||||||

Median Abs. Dev. | 0.018 | 0.016 | 0.019 | 0.017 | 0.052 | 0.019 | |

Median Abs. Perf. Error | 2.62 | 2.32 | 3.80 | 3.35 | 7.37 | 2.68 | |

Median Pred. Error | 1.75 | 1.00 | −0.40 | −1.45 | −7.37 | −0.06 | |

High Level | |||||||

Median Abs. Dev. | 0.012 | 0.016 | 0.031 | 0.038 | 0.043 | 0.017 | |

Median Abs. Perf. Error | 1.35 | 1.75 | 3.69 | 4.35 | 4.81 | 1.87 | |

Median Pred. Error | −0.81 | −1.73 | −3.69 | −4.35 | −4.81 | −1.84 | |

All Levels | |||||||

Median Abs. Dev. | 0.019 | 0.022 | 0.021 | 0.032 | 0.041 | 0.022 | |

Median Abs. Perf. Error | 2.82 | 3.01 | 4.14 | 4.98 | 5.61 | 3.07 | |

Median Pred. Error | −0.13 | 0.99 | −1.24 | −4.87 | −5.60 | −1.63 |

After evaluating the reliability of the BMI at each level separately, we use a Bayesian analysis to identify the reliability of the BMI across all levels. To do so, we combine the results of the reliability assessments across all levels to compute an overall assessment of reliability for the experiment. In our experiments, we tested the BMI over 20 levels with the time duration at each level between target transitions being 18.6 minutes on average. For the purpose of steady-state error calculation, we remove 5 minutes of data after an upward transition and 7 minutes of data after a downward transition to ensure that the system is at steady-state and to ensure approximate independence between levels. The independence assumption between levels is justified because if we assume even a high first-order serial correlation of 0.98 between adjacent data points separated by one second and we allow between 5 to 7 minutes for the transition between levels before making the steady-state error calculations, then the maximum correlation between the closest two points in immediately adjacent levels is between

Denoting the probability that the BMI system is reliable at any level by

To test our closed-loop BMI system for control of medical coma, we perform both simulation-based verification as well as real-time

For each experiment, we first performed the system identification step for each animal using the scalar filtering and the nonlinear least-squares model fitting (see

We first perform a set of simulations to verify the performance of the closed-loop BMI system. In our simulations, we assume that the anesthesia drug delivery period is a total of 45 minutes and that the goal is to keep the BSP at three desired target levels, 0.4, 0.7, 0.9, each for 15 minutes. We simulate all 6 possible order permutations of these levels. To run the simulations, we use the estimated system model in

To specify the cost function (see (27) and Supporting Text (S.18)), we take

We take the discretization step to be

We impose the constraints on the control (i.e., drug infusion rate) by first finding the unconstrained control solution from (25) and then using the closest value to it in the constrained feasible set

In each subfigure, the top panel shows the BSP traces and the bottom panel shows the drug infusion rate. In the top panels, sample trials of the closed-loop controlled BSP traces are shown in black and the corresponding estimated BSP traces are shown in grey. The time-varying target BSP level is shown in green. The bottom panel shows the corresponding controller infusion rates. Each subfigure (a–f) corresponds to one possible permutation of the 3 BSP target levels.

We also tested the model predictive controller with various time horizons,

In each subfigure, the top panel shows the closed-loop controlled BSP traces using the bounded LQR control strategy and using the MPC strategy with various time horizons,

In each subfigure, the top panel shows the closed-loop controlled BSP traces using the bounded LQR control strategy and using the MPC strategy with various time horizons,

Even though simulation-based validations are helpful in assessing the behavior of the BMI, the true test of the BMI is in

We implemented our BMI in experiments with rodents and tested it for controlling the level of burst suppression in real time. The BMI used the recursive Bayesian estimator combined with either the bounded LQR controller or the MPC. The BMI in both cases could successfully and accurately control the BSP level in rodents in real time.

The control sessions lasted an average of 62 minutes and consisted of at least 3 target BSP levels, thus requiring at least 3 transitions.

In each subfigure, the top panel shows the estimated closed-loop controlled BSP trace (black) and the time-varying target level (green), and the bottom panel shows the corresponding BMI drug infusion rate using the bounded LQR strategy (a–e) and the MPC strategy (f).

As is evident in

We also performed a Bayesian analysis to assess overall reliability of the BMI based on the steady state error distributions at each of the 20 levels used in the experiments (

Each subfigure (a–f) corresponds to one of the six real-time BMI experiments (

In addition to accurate and reliable control at steady state, the BMI was especially successful in promptly transitioning between target BSP levels. The BMI could increase the level of BSP rapidly, while avoiding overshoot. To increase the BSP, the BMI immediately increased the drug infusion rate once the target was increased, and then gradually reduced the infusion rate until the BSP approached the new target level. The rate at which the BMI increased the BSP level was 0.32 BSP units per minute. The median rise time in our experiments was under a minute (49 seconds).

The BMI was also able to decrease the BSP level without undershoot. To decrease the BSP, the BMI first stopped the drug infusion and then gradually restarted it once the BSP approached the lower target BSP level. The rate at which the BMI could decrease the BSP level was 0.11 BSP units per minute. In decreasing the level of BSP, the time response of the BMI is mainly governed by the clearance rate in the pharmacokinetic model of the rat. Hence although the controller stopped the drug infusion immediately once the target was dropped, it took a few minutes for the BSP to go down to the desired target level. The median fall time in our experiments was 4.45 minutes.

These results thus demonstrate the feasibility of automatic reliable and accurate control of medically-induced coma using a BMI.

To study the feasibility of automating control of medically-induced coma, we developed a BMI to control burst suppression in a rodent model. Our BMI system reliably and accurately controlled burst suppression in individual rodents across dynamic target trajectories. The BMI promptly changed the BSP in response to a change in target level without overshoot or undershoot and accurately maintained a desired target BSP level with a median performance error of 3.6% and a percent bias of -1.4%.

Our work contributes to the extensive BMI research in anesthesiology aimed at controlling brain states under general anesthesia. This field began in the 1950s

We developed a BMI for real-time control of burst suppression across time-varying target levels in individual rodents using a stochastic control framework. Our stochastic control framework consists of a two-dimensional state estimator and an optimal feedback controller. In our formulation, we assumed a stochastic form of the log transformed version of our system to incorporate both the two-dimensional system model and noise in our estimates and to ensure non-negative concentration estimates (

In addition to the two-dimensional estimation algorithm, the BMI consists of LQR and MPC controllers. Controllers using MPC and LQR strategies have been used successfully in many applications. We recently demonstrated the success of a LQR paradigm to control a motor neuroprosthetic device using point process observations of spiking activity and a linear Gaussian kinematic state model

Other approaches can also be used for anesthesia control. We recently reported successful control of burst suppression using a proportional-integral (PI) controller in simulated rodent

We chose levels of burst suppression as a control target because it is a physiologically defined brain state

Our Bayesian state estimator (

We demonstrated in a rodent model that the BMI achieved reliable and accurate control of burst suppression. It would also be valuable as a next step to test this BMI in a rodent model of refractory seizures or intractable intracranial hypertension prior to testing it in humans.

A BMI system to automatically control medically-induced coma could provide considerable cost-saving and therapeutic benefits. Although the state of medical coma is often required for several days, it is achieved by manually adjusting the anesthetic infusion rate to maintain a specified level of burst suppression assessed by continual visual inspection of the EEG. Automated control would allow much more efficient use of intensive care unit personnel as a single nurse per shift would not have to be solely dedicated to the task of manually managing the drug infusion of a single patient for several days. Hence even assuming the same patient outcomes between automated and manual control, there could be important savings in intensive care unit resources under the automated control regimen.

In addition to the inefficient use of the intensive care unit staff, manual manipulation of the infusion rate does not approximate the infusion rate changes of an automatic controller (

We have also shown that other states of general anesthesia have well defined EEG signatures

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