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.

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 [6], [15], [16]. During implantation, general anesthesia was induced with isoflurane. At the above four stereotactic coordinates, four holes were made using a microdrill (Patterson Dental Supply Inc., Wilmington, MA). An electrode with mounting screw and socket (Plastics One, Roanoke, VA) was screwed into each of these four holes. The sockets were in turn inserted in a pedestal. Dental acrylic cement was used to permanently fix the screws, sockets and pedestal. Recording began after at least 7 days of recovery following implantation.

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. Figure 1b shows the burst-suppression raw EEG, filtered EEG and threshold, and the resulting binary signal. The segmentation algorithm was run in real time. Several preliminary boluses of propofol were administered to each rat and the obtained BSP traces were used for system identification in each animal (see System Identification section below). The experiment was then conducted by giving the rat a manual propofol bolus to induce a burst suppression state, and the real-time BMI control experiment started once the BSP dropped to a level of 0.1–0.3. In the real-time BMI experiments, the goal was to acquire, maintain, and transition between three target BSP levels (low, medium, high). The order of the target levels was randomized. Each real-time BMI control experiment was conducted for an average of 62 min. Three rats were available for the experiments, weighing 366, 391, and 422 gr respectively. Each rat was used for two real-time experiments, resulting in six real-time experiments.

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 . Hence the corresponding state model in the estimator imposes a smoothness constraint on using a first-order linear Gaussian process [17]. Specifically, we use a special case of (10) as . Second, the corresponding BSP estimate is fitted using a non-linear least-squares procedure to minimize the sum-squared-error between the model predicted BSP and the estimated BSP. The system parameters are thus the solution to(29)where is the model predicted BSP given the values for the system parameters (see Results and Figure 2).

To characterize the performance of the BMI at steady state, we compute the error between the target BSP at each time, , and the controlled BSP, , as(30)

We use the error to calculate multiple standard metrics [18] of performance. These metrics are the median absolute deviation (MAD)(31)the median prediction error (MDPE)(32)and the median absolute performance error (MDAPE)(33)The MDPE is a measure of bias at steady state and the MDAPE is a measure of normalized error. We compute these metrics for low, medium, and high target BSP levels and across all levels for each experiment. The median is computed across data points at steady state. Finally we compute the median of all these measures across all experiments to quantify the overall performance of the BMI.

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(34)and calculate the median of this rate across all upward transitions and also across all downward transitions.

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 (Table 1), we also performed specific statistical assessments based on the error distribution at each level to examine the reliability of the BMI overall [19]. In particular, we considered the BMI to be reliable at each level if its absolute error measure, , was lower than a specified value with high probability. Experimentally we found that the absolute error at any time step in our BMI system was almost always below . Therefore we considered the BMI to be reliable at a given level if its absolute error at that level was less than 0.15 with probability ≥0.95 and highly reliable if the absolute error at each level was less than 0.10 with probability ≥0.95. This is equivalent to the 95th percentile of the absolute error distribution at a given level being less than 0.15 and 0.10, respectively. Hence we can compute from the absolute error distribution at each level the 95th percentile and consequently identify the BMI performance at each level as reliable or not.

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 , where min data point per minute and minutes data points per minute. Because these maximum correlations are effectively 0, assuming independence between levels is highly reasonable (we acknowledge that lack of correlation is not equivalent to independence). Hence the data between levels within animals are approximately independent so that the 20 levels serve as the unit of analysis in the overall assessments of reliability.

Denoting the probability that the BMI system is reliable at any level by , the total number of reliably controlled levels, , is binomially distributed with success probability out of independent levels. The number of successes is in turn equal to the number of levels for which the BMI is identified as reliable as described above. Given the binomial likelihood and taking the prior distribution for to be the uniform distribution on the interval (0, 1), it follows that the posterior distribution for is the beta distribution with parameters and [15], [20]. We thus estimate as the mode of this beta distribution and consider the BMI system reliable overall if the leftmost point of the 95% credibility interval for is greater than 0.

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 Materials and Methods). Figure 2 shows two sample BSP traces in response to boluses of propofol administered in preliminary experiments prior to BMI control, and the fitted system response of the second-order system in (2). The estimated parameters for Figures 2a and 2b are and , respectively. Once the system model was fitted, the real-time BMI control experiments were conducted. We use the fitted system model in Figure 2b for our simulation-based verification below.

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 Figure 2b. Note that all the fitted system models in our experiments were controllable.

To specify the cost function (see (27) and Supporting Text (S.18)), we take . We choose this since the main goal is to have the effect-site concentration close to the target value and since the effect-site concentration is the observable through the EEG. The choice of in turn depends on how fast we desire the controller response to be. Smaller values of result in faster controller response since the cost on the amount of drug infusion is reduced. Here we pick for our desired response.

We take the discretization step to be sec. This means that the closed-loop system updates its estimate of the BSP and its drug infusion rate every second. To simulate a trial of the closed-loop controlled system response, at each time we use and to find using (2) with initial condition , . To get the binary output of the thresholded EEG within this time step, we generate a realization of the binomial distribution in (7) with mean and using a sampling rate of 10 Hz (i.e., taking ). Given this binomial realization, we use the recursive Bayesian estimator to estimate the concentration state , and then use this estimate as feedback in the controller to decide on the infusion rate .

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 . For example, to impose positivity and for negative control solutions we use zero instead. We can similarly do this for constraints on the maximum drug infusion rate.

Figure 3 shows sample closed-loop controlled BSP traces for each of the 6 possible permutations of the desired target trajectories. Here the only imposed constraint is positivity of the drug infusion rates. In each subfigure, the top panel shows the BSP traces and the bottom panel shows the drug infusion rate. The stochastic control framework can achieve successful control of burst-suppression. The framework is particularly successful in changing the BSP level without overshoot or undershoot.

We also tested the model predictive controller with various time horizons, . In the model predictive controller, we impose the constraints on the control inputs (i.e., drug infusion rates) explicitly in the formulation and thus find the constrained (approximately) optimal solution. Since our goal is to compare the bounded LQR and MPC control strategies in this set of simulations, we assume that both controllers know the BSP perfectly at each time (i.e., we use the true as feedback in the controller). We compare the MPC drug infusion rate with the bounded LQR infusion rate in Figure 4, where the constraint is positivity on the drug infusion rate. As we increase the optimization horizon, the two solutions converge. This shows that, in this problem, solving the unconstrained LQR and then bounding it is approximately optimal. The controlled BSP in Figure 3 is noisier than in Figure 4 because in the former the BSP is estimated from a stochastic binary time-series emulating the segmented EEG (Figure 1b) and in the latter BSP is assumed to be perfectly known to the controllers. We can also show that, similarly, when an upper-bound on the drug infusion rate is desired, the two solutions again converge (Figure 5). It is important to note, however, that in our problem no constraints are placed on the state. Our recursive Bayesian estimator combined with the implemented real-time MPC can extend our framework to solving more complex problems with constraints also on the state variables, such as blood pressure (see Discussion).

Even though simulation-based validations are helpful in assessing the behavior of the BMI, the true test of the BMI is in in vivo experiments as we present below.

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. Figure 6 shows the BSP and the drug infusion rate in 6 closed-loop BMI sessions that were run in real time in rodents (see also Supporting Figure S1 that shows the evolution of in these experiments). Figure 6a–e were run with the bounded LQR controller and Figure 6f was run with the MPC. All experiments except for the one in Figure 6e consisted of 3 target levels, identified as low, medium, and high levels for the purpose of metric calculation. The experiment in Figure 6e consisted of 5 target BSP levels and hence we identify the lowest two levels as the low level and the highest two levels as the high level to calculate the metrics.

As is evident in Figure 6, the BMI could successfully and promptly transition between levels and accurately maintain the BSP at a desired target level. At steady state, the BMI-controlled BSP closely followed the target BSP level. The real-time variations in the drug infusion rate at higher levels of BSP, e.g., at 0.9, were larger than at the lower levels since larger amounts of propofol are needed to keep the EEG in suppression 90% of the time while allowing for the bursts 10% of the time (this can also be seen from (1) by observing that is monotonically increasing with ). The MDAPE (measure of normalized error) across all experiments for the low, medium, and high target BSP levels was only 7.32%, 3.02%, and 2.78%, respectively. When considering all levels, the MDAPE was only 3.61% (Table 1). Moreover, the deviation between the target BSP level and the BMI-controlled BSP, measured through MAD, was 0.03 BSP units or less for any level. Across all levels the MAD was only 0.02 BSP units (Table 1), a negligible error in practice. Finally, the MDPE was small across all levels. Together, these results demonstrate that the BMI achieved precise control of multiple target burst suppression levels at steady state within the same experimental session.

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 (Materials and Methods). The data at different levels within animal are approximately independent so that the 20 levels serve as the unit of analysis in the overall assessment of reliability. The 95th percentile of the absolute error distribution at each of the 20 levels was less than 0.15 giving a mode of the posterior density for (probability that the BMI is reliable at any level) of and a 95% credibility (Bayesian confidence) interval for of (0.87 to 1.00) (Figure 7). The lower bound of the 95% credibility interval of 0.87 is well above 0, the point of no control. These findings establish that the system is reliable. In addition, for 17 out of 20 of the levels the 95th percentile of the absolute error distribution was less than 0.1, giving a mode of the posterior density for of and a 95% credibility interval for of (0.67 to 1.00) (Figure 7). This finding suggests that furthermore the BMI system meets our definition of being highly reliable overall. We therefore conclude that the BMI system is highly reliable for real-time control of medical coma using burst suppression across dynamic targets.

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.

Our work contributes to the extensive BMI research in anesthesiology aimed at controlling brain states under general anesthesia. This field began in the 1950s [21]–[23] and developed further in the 1980s [24]. BMI systems for control of sedation are now commercially available [25] and have been recently approved for use in the United States. The most commonly used control signal is the Bispectral Index (BIS) [26]–[40]. Other control signals include an auditory evoked potential index [41], the spectrogram median frequency [24], [42], [43], a wavelet-based index [44] and an entropy measure [45]. Both standard and non-standard control paradigms [24], [27], [35], [41], [45] have been used in these systems with the principal objective being control of unconsciousness [24], [26]–[32], . A recent report controlled both antinociception and unconsciousness [45]. Although several criteria have been established for successful control, a criterion used in BIS studies has been maintaining BIS not at a specific value but in the broad range between 40 to 60 [26]–[39]. Vijn and Sneyd [6] and Cotten et al. [7] controlled constant target levels of burst suppression in rodent models and reported average control results over rodents. Schwilden demonstrated control of median frequency in individual human subjects [24]. None of these studies considered control of dynamic time-varying trajectories.

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 (Eqs. (2) and (6)). This model-based two-dimensional state estimator is one major reason that the current BMI largely avoided overshoot and undershoot. By incorporating the two-dimensional stochastic dynamic model and computing both and at each update (Eqs. (14)–(17)), the estimator predicted the effect of the real-time drug infusion rate on the BSP. In upward transitions, this avoided underestimating the BSP in response to drug infusion that would result in overestimating the required amount of drug and hence in an overshoot. This similarly prevented undershoot in downward transitions. Our framework is thus analogous to maintaining control in a navigation system by estimating both position and velocity.

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 [46]–[50]. MPC has been widely used in process control and chemical industries [51]–[53] and has been previously applied to closed-loop administration of analgesics [54], for sedation control using the BIS as the control signal [55] and in a simulation study for control of BIS during surgery [40]. The LQR and MPC controllers are both formulated in an optimal feedback control framework [8]. They specify the control objective as a cost function to be minimized by selecting the optimal infusion rates. We can therefore adjust the behavior of these controllers, for example the speed of transitions, by adjusting the penalty on various terms in the cost function. While our LQR implementation imposes constraints on the drug infusion rates by bounding the control solution, our MPC implementation allows us to impose explicitly any required constraints on both the states and the drug infusion rates, such as non-negative or bounded infusion rates, by solving a constrained optimization problem at each time step in real time. For example, if the BMI system always needed to keep the drug infusion rate below a specified maximum level, the MPC controller could impose this explicitly in the solution. Since the only constraints in our problem were on the control variable (i.e., the infusion rate), the LQR and MPC strategies performed similarly (Figure 5). However, the recursive Bayesian estimator combined with the real-time MPC strategy can be used to solve problems that require constraints on the state variables as well. This situation could arise in problems requiring joint control of multiple state variables, such as controlling simultaneously the anesthetic level and other physiological variables such as blood pressure and heart rate.

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 [11], simulated human [11], and actual rodent experiments [19]. The experimental studies differed from the ones presented here in that the transitions between target levels were carried out in 5 to 10 minutes ramps. Also, the BSP estimation algorithm in those studies was one rather than two dimensional. Given the stochastic two-dimensional dynamic model and the EEG signal, here we used a stochastic control paradigm consisting of a two-dimensional estimator and an optimal feedback controller in place of the one dimensional estimator and the deterministic PI controller. The model-based two-dimensional state estimator in our framework is one major reason that the current BMI can both make prompt and reliable transitions between levels (median rise time of 49 seconds and fall time of 4.45 minutes) and avoids BSP overshoots and undershoots in any transitions. The stochastic control framework also offers tremendous flexibility. In particular, the MPC allows us to extend the BMI to control with constraints on the control variable and a vital variable such as blood pressure. The stochastic optimal formulation also provides a framework for adjusting the behavior of the BMI by simply modifying the cost function. Finally, while the mathematical derivation for the stochastic framework may be more complex, the final infusion rate solution is straight forward. The LQR solution is given simply by a linear function of the state estimate at each time. The MPC controller optimization problem is convex and can be solved using existing convex optimization software. Indeed we ran the MPC in real-time in our rodent experiments on a standard laptop (Figure 6f).

We chose levels of burst suppression as a control target because it is a physiologically defined brain state [4], [5] with a well-defined EEG signature that can be readily characterized in real time for the purpose of control. The linear two-dimensional state model (Eq. (2)) is the simplest pharmacokinetics representation for relating the concentrations of anesthetic in the blood and in the brain to BSP (Eq. (1)) computed from burst suppression in the EEG. This simplified two-compartment model was sufficient in our experiments to achieve reliable and accurate control of burst suppression.

Our Bayesian state estimator (Eqs. (14)–(17)) computes the central compartment and the effect-site concentrations in real time from the EEG converted into binary observations. Here, both the prior state model (Eq. (6)) and the binomial observation model (Eq. (7)) are non-linear functions of the state. We thus use two approximations at each time step to derive the estimator recursions, a linear approximation to the prior model at that step and a Gaussian approximation to the posterior model. Gaussian Laplace-type approximations have been successfully used in many applications for example in our previous work estimating states with linear prior models from point process observations of neural spiking activity [12], [13], [47]–[50], [56]–[59]. Our system identification procedure used the one-dimensional version of the binary filter, coupled with a non-linear least squares procedure to estimate model parameters (Eq. (2)) for each animal and thereby, implement individually tailored control strategies. Future work can extend this system identification procedure to an efficient expectation-maximization (EM) algorithm by replacing the one-dimensional binary filter algorithm with the current Bayesian state estimator [13], [60], or can design an adaptive estimator that not only computes the BSP but also updates the system parameters during the several hours of real-time control.

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 (Figure 6). Similarly, visual inspection of the EEG does not provide an accurate estimate of the state of burst suppression. The current work establishes the feasibility of implementing automated, accurate and reliable control of medical coma in a rodent model suggesting that a BMI could be developed to study whether such accurate control improves patient outcomes. For example, reliable and accurate control of medical coma could offer the possibility of ensuring adequate brain protection for intracranial hypertension and adequate therapy for status epilepticus while using the least amount of anesthetic and minimizing overshoots when transitioning to a desired level of burst suppression. Reliable and accurate control would also make it easier to induce periodic arousals to conduct neurological assessments and prevent anesthetic overdose syndrome [61]. To establish these potential therapeutic benefits of reliable and accurate control of medical coma, outcome studies in rodent models of intracranial pressure and status epilepticus will be required before proceeding to human investigations.

We have also shown that other states of general anesthesia have well defined EEG signatures [62], [63]. Therefore, the ability of our BMI to track accurately changing target levels of burst suppression further suggests that it could be adapted to control states of general anesthesia and sedation for patients requiring surgical or non-surgical procedures. Our stochastic estimation paradigm and model predictive controller could also be used to control jointly the state of general anesthesia and physiological variables such as blood pressure. These investigations will be the topics of future reports.