#### What We Already Know about This Topic

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

*via*“flip-flop” mechanisms, or by shifting phases. Theories of general anesthesia related to neural information synthesis would predict a graded, continuous transition from general anesthesia to consciousness during emergence.

^{1}Theories of general anesthesia that relate to sleep-wake neurobiology might predict a binary “flip-flop” from unconsciousness to consciousness.

^{2}Still other frameworks suggest that emergence relates to a number of discrete phase transitions.

^{3–5}It is also possible that anesthetic state transitions have both continuous and discrete components that can be dissociated. Furthermore, recent data suggest that anesthetic induction and emergence are not simply “mirror images” of one another, but are characterized by a distinct neurobiology.

^{2,6}The nature of anesthetic induction and emergence will be important to clarify for a more precise understanding of general anesthetic mechanisms as well as for the development of more sophisticated intraoperative neurophysiologic monitors.

^{7–17}Graph theory is one method by which to represent networks in the brain, where neural regions can be considered the

*nodes*of the graph and the relationship between them the

*edges*. Brain networks have a conserved organization across species and spatial scales that enable optimal information processing among distributed neural network elements.

^{18}This “small world” network organization is similar to that of an airport system, in which certain hubs act as densely connected nodes that can enhance the efficiency of travel. That two nodes are connected by an edge reflects the structure or

*topology*of a network; however, edges may vary as reflected by their

*connection strength*. Thus, global network efficiency in the brain can be deconstructed into the elements of topologic structure and connection strength (discussed further in the Materials and Methods section). By delineating the effects of general anesthesia on these two elements independently, we can more precisely characterize the network properties of anesthetic state transitions.

^{19,20}Finally, given the proposed importance of the frontal-parietal network in the mechanism of general anesthesia,

^{21–23}we assessed whether the components of network topology and connection strength were differentially altered in these brain regions.

#### Materials and Methods

##### Drug Administration and Electroencephalography

^{12}but underwent a completely different analysis for the current study; novel data from another 10 subjects were included for the current investigation. Each volunteer fasted for 8 h before study drug administration. We excluded volunteers who had known allergy to propofol, medical conditions, abnormal laboratory findings with clinical significance, or a body weight that was not within 30% of ideal range. The average age was 23 ± 2 yr (range, 20–28 yr).

*via*facemask to maintain an end-tidal carbon dioxide concentration of 35–45 mmHg. Manual ventilation was discontinued when the spontaneous respiratory rate exceeded 12 breaths/min and end-tidal carbon dioxide was less than 45 mmHg. Time to return of consciousness (ROC) after the intravenous bolus of 2.0 mg/kg of propofol was determined by the recovery of response to verbal command; this assessment started 10 min after LOC. Upon completion of the measurement of electroencephalographic activity, subjects were transferred to the postanesthesia care unit, breathing room air. During the recovery period, subjects were monitored with electrocardiography, pulse oximetry, and noninvasive blood pressure measurement for 1 h. If vital signs were stable and full recovery from sedation was confirmed, the subject was discharged from the hospital.

##### Reconstruction of “Genuine Networks” from Electroencephalographic Data

^{24}In a finite-size dataset, lower-frequency power spectra of the electroencephalogram produce larger spurious cross-correlations. Müller

*et al.*suggested a method to estimate genuine, spurious, and total cross-correlation strengths of multichannel electroencephalograms based on surrogate (

*i.e.*, randomized) electroencephalographic data.

^{20}For a given electroencephalographic dataset, spurious correlation strength

*c*

_{s}is estimated by the cross-correlation values of randomized data. The surrogate dataset has the same power spectra and the same data length as the original electroencephalographic data, but no genuine cross-correlation because of phase randomization.

^{25}Thus, if the surrogate data have a cross-correlation value, it must have resulted from the finite-size effect by a combination of the finite data length used and the power spectra of the given electroencephalogram. Genuine correlation strength of the original electroencephalographic data

*c*

*g*is defined as the deviation from this randomized dataset. Both correlation strengths

*c*

*g*and

*c*

*s*are normalized values within 0 and 1.

##### Global Efficiency of Genuine Networks

^{18,26}The hubs of the airport system also result in a small world network. This optimal network structure is slightly changed in various cognitive tasks, but significant disruptions have been reported in disease states such as epilepsy, schizophrenia, and dementia.

^{27–30}To quantify the overall state of a brain network with one index, we used a measure of global efficiency

*E*

*g*. Global efficiency is a representative index for network properties and quantifies the information transmission capacity of a network.

^{18}By definition, if the correlation across nodes increases, the global efficiency also increases. However, global efficiency depends on both the topologic structure and correlation or connection strength of the nodes. For example, if the topologic structure is not amenable to efficient information transfer (as in a regular lattice structure), the increase in global efficiency would be small even though the correlation across nodes was large. Therefore, the decomposition of the effects of the two network elements (topologic structure and connection strength) on the global efficiency provides more detailed information about the network. In terms of neurophysiology, rapid changes in connection strength may be mediated by variations of synchronization.

^{31}

*E*

*g*quantifies the efficiency of information transmission of a network based on the average weight of edges that must be traversed to go from one node to another. By definition, the global efficiency

*E*

*g*is the inverse of the average shortest path length (1/

*d*

*ij*) over all pairs of nodes in a network

*G*. It is defined as follows,

*d*

*ij*is the shortest path length between node

*i*and

*j*. The

*d*

*ij*is defined with inverse genuine correlation strength

*c*

*g*(

*i, j*). If

*c*

*g*(

*i, j*) = 1 for a perfectly coherent case, then

*d*

*ij*= 1. On the other hand, if

*c*

*g*(

*i, j*) = 0 for a completely uncorrelated case, then

*d*

*ij*is infinite. Therefore, the path length

*d*

*ij*has a value between 1 and infinity. Here, the path length is defined by the correlation between two neural events as a measure of functional similarity. It is important to stress that the “length” of the path has a

*functional*definition rather than a spatial one. More strongly connected nodes are functionally “closer” to one another and therefore transfer information more efficiently. Consider the analogy of a cell phone and assume you had to transmit information to both a friend next door and a friend across town. If you were unable to call your friend next door because of lost connection strength, but were nonetheless able to call your friend across town, then you would have a functionally shorter path length to your cross-town friend in comparison with your spatially close neighbor.

##### Dissociating the Effects of Network Structure and Connection Strength on Global Efficiency

*e*

_{str}was defined as the ratio between the global efficiencies of a genuine network and an unweighted network (which has no contribution from strength because it is unweighted).

*d*

_{ij}

^{b}is the shortest path length between node

*i*and

*j*in the unweighted network.

*e*

_{top}was defined as the ratio between the global efficiencies of the unweighted network and a totally connected network, in which all shortest path lengths are 1.

*E*

*t*is always 1 so it was used only for conceptual symmetry in both definitions. Both indices,

*e*

_{str}and

*e*

_{top}, have a value between 0 and 1.

##### Moving Window Method

*e*

_{str},

*e*

_{top}, and

*E*

_{g}were calculated (see Supplemental Digital Content 1, which describes more detailed methods, http://links.lww.com/ALN/A679).

##### Pharmacokinetic Simulation

^{32}stochastic and deterministic simulations for plasma and effect-site concentrations of propofol were performed using NONMEM 712 (ICON Development Solutions, Dublin, Ireland). The blood-brain equilibration rate constant (

*k*

*e0*) of propofol in these models was obtained using the Bispectral Index as a surrogate measure of propofol effect on the central nervous system. Individual pharmacokinetic parameters included in simulations of propofol effect-site concentrations were calculated using the patient's age and point estimates of fixed effect parameters. Point estimates of fixed and random effect parameters were used in stochastic simulations. Variances of random effect (interindividual and residual) parameters were fixed at 0 in a deterministic simulation, which produces the same plasma and effect-site concentrations of propofol as predicted by a target-controlled infusion system. Two thousand stochastic simulations were conducted.

##### Statistical Analysis

*B*aseline state was separated into B1 (from 0 to 2.5 min) and B2 (from 2.5 min to 5 min), the

*A*nesthetized state was separated into A1 (0 to 2 min after LOC) and A2 (−2.5 to 0 min before ROC), and the

*R*ecovery state was separated into R1 (0 to 2.5 min after ROC) and R2 (2.5 to 5 min after ROC). Because the duration of the anesthetized state is different for each subject, we separated the substates based on the LOC and ROC times to facilitate statistical comparison. The correlation strengths,

*e*

_{str},

*e*

_{top}, and

*E*

*g*, were compared across the six substates; the significance was assessed by a repeated measures one-way ANOVA and a

*post hoc*analysis using the Tukey multicomparison test. For the comparison of

*e*

_{str}and

*e*

_{top}between the frontal and parietal regions across six substates, the repeated measure two-way ANOVA and the

*post hoc*analysis using the Bonferroni multicomparison test were applied. A

*P*value of <0.05 was considered significant. The mean ± SD and the results of the

*post hoc*test are presented in Supplemental Digital Contents 2–6 (http://links.lww.com/ALN/A680, http://links.lww.com/ALN/A681, http://links.lww.com/ALN/A682, http://links.lww.com/ALN/A683, http://links.lww.com/ALN/A684). The D'Agostino-Pearson omnibus normality test was conducted before performing the ANOVA test. A formal statistical consultation was obtained at the Center for Statistical Consultation and Research at the University of Michigan (Ann Arbor, MI), and the GraphPad Prism Version 5.01 (GraphPad Software Inc., San Diego, CA) was used.

#### Results

##### Spurious and Genuine Network Connections

*P*< 0.0001), increasing after loss of consciousness and returning to the baseline level after the recovery state. By contrast, the genuine correlation strength showed the opposite change over the course of the experiment (F(5,95) = 20.1,

*P*< 0.0001). The genuine correlation strength decreased after LOC and recovered quickly to the baseline level. The total correlation strength also significantly changed across states (F(5,95) = 6.16,

*P*< 0.0001), increasing after LOC and returning to the original level by A2. Therefore, total correlation strength followed the spurious correlation strength pattern rather than the genuine correlation strength pattern in the anesthetized state (see Supplemental Digital Content 2, which is a table showing mean ± SD, http://links.lww.com/ALN/A680).

##### Dissociable Effects of Network Structure and Connection Strength

*E*

*g*is displayed together with the effects of network structure

*e*

_{top}and connection strength

*e*

_{str}, demonstrating distinct patterns of

*e*

_{str}and

*e*

_{top}at LOC and ROC. After LOC,

*e*

_{top}decreased steeply, whereas

*e*

_{str}decreased slowly; at ROC,

*e*

_{str}increased precipitously after

*e*

_{top}had already been restored. Data from this subject demonstrate that the temporal evolution patterns of

*e*

_{top}and

*e*

_{str}can be dissociable from one another and behave independently at LOC and ROC.

*e*

_{top}and

*e*

_{str}for the 20 subjects are shown in figure 4. Based on the typical pattern of

*e*

_{str}, the subjects were classified according to two types of anesthetic responses. A subject was classified as “type 1” if there was a large increase of

*e*

_{str}at the ROC moment that exceeded the maximum

*e*

_{str}of the baseline state. If there was no increase of

*e*

_{str}, the subject was classified as “type 2.” Eight of 20 subjects were classified as type 1 and the remaining 12 subjects were classified as type 2. Figure 3 is a salient example from the type 1 group. Figure 4A and 4B demonstrate the individual traces of

*e*

_{top}(upper tracing in each panel) and

*e*

_{str}(lower tracing in each panel) for type 1 and type 2 subjects; figure 4C and 4D demonstrate the average patterns of

*e*

_{top},

*e*

_{str}, and

*E*

*g*for type 1 and type 2 groups.

*e*

_{top}(topology) in the baseline state are close to 1, indicating that the brain network in this state has optimal information transmission capacity. The

*e*

_{top}of the type 1 group was significantly changed across the six substates (F(5,35) = 10.5,

*P*< 0.0001). After induction with propofol, the

*e*

_{top}immediately decayed from 1 and gradually returned to the baseline level a few minutes

*before*ROC. The

*e*

_{str}of the type 1 group also significantly changed across the six substates (F(5,35) = 6.94,

*P*< 0.0001). After induction, it gradually decreased and recovered in the A2 state before ROC. After ROC, it was fully recovered to baseline level. The recovery process of

*e*

_{top}and

*e*

_{str}for the type 1 group began from the A2 state in the unconscious state.

*e*

_{top}and

*e*

_{str}significantly changed across the six substates (F(5,55) = 17.07,

*P*< 0.0001; F(5, 66) = 21.84,

*P*< 0.0001, respectively). The

*e*

_{top}decreased after LOC and recovered before ROC. The

*e*

_{str}also decreased after induction but was not fully recovered at the A2 period as was

*e*

_{top}, which already had a value comparable to those of the recovery states. The level of the baseline state recovered by the end of the experiment. This implies that the

*e*

_{str}was not fully recovered immediately after emergence but slowly returned to the original level. As a consequence, the behaviors of

*e*

_{str}in the A2 period (the period before emergence) and the R1 period (the period after emergence) were different between the type 1 and 2 groups.

*e*

_{top}showed a similar anesthetic response pattern for most subjects, whereas

*e*

_{str}had two distinctive anesthetic response patterns. At induction and emergence, the

*e*

_{str}of the type 1 group showed a pattern of slow decay and sudden return; by contrast, the

*e*

_{str}of the type 2 group showed a pattern of sudden decay and slow return. Patterns of connection strength did not mirror changes in electroencephalographic power or high-frequency activity, suggesting that the observed changes were not due to electromyographic or other artifact (data not shown). (See Supplemental Digital Content 3–4 for tables including mean ± SD and statistical results, http://links.lww.com/ALN/A681, http://links.lww.com/ALN/A682.)

##### Pharmacologic and Behavioral Data for Type 1 and Type 2 Response Groups

Table 1 Image Tools |
Fig. 5 Image Tools |
Table 2 Image Tools |

*vs.*type 2) = 1.32

*versus*3.78 min and 1.31

*versus*3.74 min, respectively. Unusually delayed ROC was observed in one volunteer in the type 2 group (table 2). However, the tendency remained unchanged even if this volunteer was excluded from the analysis: SD of time to ROC and duration of unconsciousness (type 1

*vs.*type 2) = 1.32

*versus*1.75 min and 1.31

*versus*1.70 min, respectively. The percentage of volunteers who demonstrated consistently quiet behavior during the period of unconsciousness was twice as high in the type 1 group compared with the type 2 group (table 2).

##### Differential Effects in the Frontal and Parietal Lobes

*e*

_{top}and

*e*

_{str}over 20 subjects for the frontal and parietal networks. For both parameters (

*e*

_{top}and

*e*

_{str}), the repeated measures two-way ANOVA test (two factors: the state and the local network) yielded a significant main effect of state (F(5,190) = 18.20,

*P*< 0.0001 for

*e*

_{top}; F(5,190) = 17.56,

*P*< 0.0001 for

*e*

_{str}), a nonsignificant effect of brain region (F(1,190) = 4.066,

*P*= 0.0509 for

*e*

_{top}; F(1,190) = 3.61,

*P*= 0.065 for

*e*

_{str}), and a significant interaction between state and brain region (F(1,190) = 18.12,

*P*< 0.0001 for

*e*

_{top}; F(1,190) = 2.477,

*P*= 0.0335 for

*e*

_{str}). The

*post hoc*analysis using the Bonferroni multicomparison test revealed significant differences between the frontal and parietal networks at the A1 state for both parameters (

*e*

_{top}and

*e*

_{str}) (t(19) = 8.486,

*P*< 0.001 for

*e*

_{top}; t(19) = 3.281,

*P*< 0.01).

*e*

_{top}of the frontal network was not significantly changed over the course of the experiment, maintaining the optimal information transmission capacity (F(5,95) = 0.439,

*P*= 0.82). By contrast, the

*e*

_{top}of the parietal network significantly lost its optimal information transmission capacity during the period after induction (A1). The decrease of

*e*

_{str}took place in both local networks (F(5,95) = 24.93,

*P*< 0.0001 for the frontal network; F(5, 95) = 43.23,

*P*< 0.0001 for the parietal network), but the parietal network was more significantly disrupted than the frontal network in terms of information transmission. (See Supplemental Digital Content 5–6 for tables including mean ± SD and statistical results, http://links.lww.com/ALN/A683, http://links.lww.com/ALN/A684).

#### Discussion

##### Genuine *Versus* Spurious Networks

^{33}With a finite dataset the linear cross-correlation measure can have a correlation value, even though the observed data are random. In particular, such spurious correlation becomes more exaggerated when the frequency spectra contained are lower.

^{20}In our data, the spurious correlation strength significantly increased after LOC and moved in the direction opposite that of the change of genuine correlation strength. This finding suggests that during reconstruction of brain networks with electroencephalograms of the anesthetized patient, the genuine correlation strength must be calculated rather than conventional cross-correlation, which is conceptually the same as the total correlation strength and which is prone to artifact from spurious correlations.

##### Distinct Network Properties and Emergence Patterns

^{34}—as well as clinical experience of heterogeneous recovery from anesthesia—it is not surprising that there may be distinct pathways to emergence. However, significantly more study is required before making a direct link between the underlying neurobiology of sleep-wake states and our findings at the network level.

##### Evidence for an Important Role of Parietal Processing

^{35}We and others have found that there is a selective inhibition of feedback activity from frontal to parietal regions in association with anesthetic-induced unconsciousness.

^{9,12}It is unclear, however, whether the frontal lobe plays a critical role in anesthetic hypnosis induced by different agents.

^{36}Hudetz

^{23}has suggested that an agent-invariant “final common pathway” to unconsciousness may be the disruption of information integration in a network of the posterior parietal cortex. It is possible that the critical change in cortical information transfer within local circuits of the posterior parietal cortex leads to a generalized failure of information synthesis. Our data support Hudetz's hypothesis. Further supporting data for a critical role of the parietal region are derived from a computational modeling study. Computational “lesioning” based on anatomic connectivity data from the macaque monkey demonstrated that lesions of parietal regions had the greatest potential to disrupt the integrative aspects of neocortical function.

^{37}Our data regarding the differential effects of frontal and parietal networks have clinical relevance, because most cerebral function monitors developed for the detection of anesthetic state transitions are based on electrophysiologic recording from the frontal region.