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Several electrical neural oscillatory abnormalities have been associated with schizophrenia, although the underlying mechanisms of these oscillatory problems are unclear. Animal studies suggest that one of the key mechanisms of neural oscillations is through glutamatergic regulation; therefore, neural oscillations may provide a valuable animal–clinical interface on studying glutamatergic dysfunction in schizophrenia. To identify glutamatergic control of neural oscillation relevant to human subjects, we studied the effects of ketamine, an N-methyl--aspartate antagonist that can mimic some clinical aspects of schizophrenia, on auditory-evoked neural oscillations using a paired-click paradigm. This was a double-blind, placebo-controlled, crossover study of ketamine vs saline infusion on 10 healthy subjects. Clinically, infusion of ketamine in subanesthetic dose significantly increased thought disorder, withdrawal–retardation, and dissociative symptoms. Ketamine significantly augmented high-frequency oscillations (gamma band at 40–85Hz, p=0.006) and reduced low-frequency oscillations (delta band at 1–5Hz, p<0.001) compared with placebo. Importantly, the combined effect of increased gamma and reduced delta frequency oscillations was significantly associated with more withdrawal–retardation symptoms experienced during ketamine administration (p=0.02). Ketamine also reduced gating of the theta-alpha (5–12Hz) range oscillation, an effect that mimics previously described deficits in schizophrenia patients and their first-degree relatives. In conclusion, acute ketamine appeared to mimic some aspects of neural oscillatory deficits in schizophrenia, and showed an opposite effect on scalp-recorded gamma vs low-frequency oscillations. These electrical oscillatory indexes of subanesthetic ketamine can be potentially used to cross-examine glutamatergic pharmacological effects in translational animal and human studies.
Several electrical neural oscillatory abnormalities have been associated with schizophrenia. Many studies have focused on the gamma band, and in general identified gamma reduction in power or phase in schizophrenia (Kwon et al, 1999; Kissler et al, 2000; Lee et al, 2001; Gallinat et al, 2004; Symond et al, 2005; Cho et al, 2006). However, contrasting findings of increased gamma activities in schizophrenia also exist (Basar-Eroglu et al, 2007; Norra et al, 2004; Flynn et al, 2008). Abnormalities in lower frequency oscillations are even more prominent. Augmented low-frequency oscillations are observed in unmedicated, first-episode, and chronic schizophrenia patients (Clementz et al, 1994; Omori et al, 1995; Karson et al, 1988; Sponheim et al, 1994, 2003; Knott et al, 2001). A failure to suppress theta-alpha (~5 to 11Hz) activities during sensory gating significantly marks the genetic liability for schizophrenia (Hong et al, 2008b). However, negative and opposite findings also exist (Nagase et al, 1992; Tauscher et al, 1998; Keshavan et al, 1998). The underlying mechanisms of these abnormal clinical findings at gamma and low frequencies remain elusive.
On the other hand, mechanisms of neural oscillations have been extensively studied in animals. Neural oscillations may provide a needed bioassay platform for elucidating cellular and molecular mechanisms of human brain diseases, especially when we can draw parallels between oscillatory patterns of humans and animals. Scalp-recorded electrical oscillations are considered to be summations of local field potentials that are primarily originating from excitatory and inhibitory postsynaptic potentials, while the latter is closely related to glutamatergic and GABAergic mechanisms, respectively. It is therefore not surprising that current theories on neural oscillations focus on glutamatergic (Cunningham et al, 2006; Roopun et al, 2008) and GABAergic mechanisms (Whittington et al, 1995; Traub et al, 1999; Gonzalez-Burgos and Lewis, 2008).
This study focuses on the glutamatergic effects on oscillations in humans. Ketamine is a noncompetitive N-methyl--aspartate (NMDA) receptor antagonist. In subanesthetic dose, it mimics some features of schizophrenia and is often used as a pharmacological model for the NMDA hypofunction (Lahti and Tamminga, 1999; Heresco-Levy and Javitt, 1998; Meador-Woodruff and Healy, 2000; Coyle, 1996; Krystal et al, 1999). We examined ketamine-induced oscillatory responses during auditory paired-click sensory gating in normal controls using a discrete wavelet method and compared these ketamine-induced oscillatory responses to those seen in schizophrenia patients (Hong et al, 2008b). The wavelet method was believed to be sensitive for extracting single-trial-based oscillatory activities (Hong et al, 2008a).
Most previous studies of ketamine effects on sensory gating have found no significant effect of ketamine based on averaged evoked potentials (AEPs) in humans (van Berckel et al, 1998; Oranje et al, 2002) or animals (de Bruin et al, 1999). However, ketamine has shown to impair gating of responses to repeated clicks presented at 100ms intervals (Boeijinga et al, 2007) and reduce AEP response to the first click in rodents (Amann et al, 2009). The endogenous NMDA antagonist kynurenic acid also disrupts AEP N40 sensory gating (Shepard et al, 2003).
AEP-based sensory gating findings in schizophrenia are somewhat mixed, with most studies showing a deficit (Siegel et al, 1984; Clementz et al, 1998; Myles-Worsley, 2002; Sanchez-Morla et al, 2008), while some are negative (Kathmann and Engel, 1990; Arnfred et al, 2003; de Wilde et al, 2007). Gating of evoked oscillations in theta-alpha range could have more robust group differences (Hong et al, 2008b; Brockhaus-Dumke et al, 2008). Therefore, our study focused on the effect of ketamine on single-trial-based oscillatory responses. We aimed to determine whether the effect of ketamine on neural oscillations in healthy humans resembles oscillations observed in NMDA animal models and oscillatory problems associated with schizophrenia patients, potentially providing a glutamatergic account on the part of the oscillatory problems found in schizophrenia patients that may index glutamatergic abnormalities.
A total of 10 healthy subjects (aged 34.5±11.7 years, 4 females) participated in a double-blind, placebo-controlled, crossover study of bonus intravenous 0.3mg/kg ketamine or saline placebo while double-click testing was administered. Subjects were 21–55 years of age, with no history of psychiatric illnesses. All subjects gave written informed consent in accordance with the University of Maryland Institutional Review Board guidelines. Subjects received pretreatment double-click event-related potential (ERP) testing, and then received ketamine (or placebo) in a 1-min infusion, followed immediately by 20min of post-treatment ERP testing. This was repeated after 1 week with the placebo (or ketamine) administration. The drug order was considered not randomized in this study because of a miscommunication with nursing staff for the order of intravenous administration in a few cases, where the randomization table was not followed (six received placebo first and four ketamine first); although all clinical ratings by a psychiatrist were given double-blinded to the drug conditions. All data were processed under the blinded condition. Clinical interviews included the 20-item Brief Psychiatric Rating Scale (BPRS) (Hedlund and Vieweg, 1980) and the Clinician-Administered Dissociative States Scale (CADSS) (Bremner et al, 1998) immediately after each ERP testing. Following previous ketamine studies (Malhotra et al, 1996), we calculated the BPRS total score and four empirically derived factors: thought disorder, withdrawal–retardation, hostility, and depressive–anxious symptom factors. The CADSS has 27 items, each scored from 0 to 4, including 19 subject-rated items (‘subjective symptoms') and 8 observer-rated items (‘objective symptoms') (Bremner et al, 1998).
EEGs were recorded in a sound-attenuated chamber, using a cap containing six midline tin electrodes (Electro-Cap International, Eaton, OH) referenced to linked earlobes. Subjects were asked to relax with eyes open and listen to 150 pairs of click stimuli (1ms duration, 75dB amplitude, 500ms interclick interval, and 10s intertrial interval) delivered through a pair of loudspeakers positioned 50cm away from their ears. Electrooculograms were recorded around the left eye. EEGs were sampled at 1kHz using a NeuroScan Synamp amplifier (Neurosoft, El Paso, TX; 200Hz low pass, 1.0Hz high pass) to yield 500ms epochs, including a 100-ms prestimulus window. Movement artifacts were removed from single trials with a rejection criterion of ±75μV followed by visual inspection. Electrode impedance was maintained below 5kΩ. The central channel (CZ) was used for the P50 (Nagamoto et al, 1989; Freedman et al, 1997; Clementz et al, 1998). Data from all six channels were used for oscillatory measures.
The single-trial records were baseline-corrected, 3–100Hz (24 octave slopes) bandpass filtered, and averaged to obtain P50 waves. P50 response to the first stimulus (S1) was defined as the largest positive-going wave occurring 35–75ms after the stimulus, measured from the trough of the preceding wave to the P50 peak. The S2 P50 was set to ±10ms of the latency to S1 P50 (Nagamoto et al, 1989). P50 gating was the S2/S1 P50 ratio. P50 was scored blind to drug information.
For oscillatory measures, artifact-free single trials filtered at 0.5–100Hz were used. A discrete wavelet transform (DWT) approach was used. Wavelet transform of single-trial recording has the advantage of not being biased by trial-to-trial temporal variability because it extracts both stationary and nonstationary energy. There is no reason to believe that most biological or pharmacological actions use only a stationary (time-locked) mechanism. Therefore, single-trial-based analysis, by means of extracting both stationary and nonstationary energy, may be advantageous. The theory and methodology of using DWT to decompose evoked potential data have been examined (Hong et al, 2008a). We used an eight-level discrete biorthogonal wavelet (bio5.5, Wavelet Toolbox; MathWorks Natick, MA) to separate evoked responses into eight details (D1–D8), which represent eight frequency bands. By simulation, we estimated the frequency band of each detail: D1–D3 corresponded to very fast gamma frequency activities >85Hz; D4: 40–85Hz; D5: 20–40Hz; D6: 12–20Hz; D7: 5–12Hz; and D8: 1–5Hz (more details of the methodology are described in Hong et al, 2008a).
In previous studies using 125ms epochs, we found that gating and schizophrenia patient–control differences on theta-alpha band responses are largely limited to the 25–275ms post-stimulus interval (Hong et al, 2008a,2008b). Therefore, we elected to use a 300-ms post-stimulus epoch for oscillatory response extraction in this study. The longer epoch of 300ms (as compared with the previous 125ms epoch) also allowed better resolution for extracting lower frequency oscillations, especially at D8 (~1 to 5Hz). Energy within each epoch of each frequency band (detail) was measured by power spectrum density (PSD) using the nonparametric Welch method (Welch, 1967; Kay, 1988). Sensory gating of each time-frequency component was calculated as the S2 PSD/S1 PSD ratio, and averaged across all trials for each participant.
A four-way repeated-measures ANOVA was used to compare drug (placebo vs ketamine), time (pre- and postdrug), site (FZ, FCZ, CZ, CPZ, PZ, OZ), and frequency (D1–D8) effects on oscillatory-dependent measures. Significant findings were followed by corresponding post-hoc tests. Greenhouse–Geisser corrections were applied to adjust for non-sphericity. The primary interests were effects of ketamine; therefore, post-hoc tests were carried out when there were significant interactions involving a time × drug interaction. Significant time × drug findings on frequency and/or site were followed by post-hoc paired t-tests to determine whether differences between ketamine and placebo were significant at the indicated frequency and/or site. Potential effect of drug administration order was explored by examining the effect of order on time, site, and frequency. To account for potential differences at baseline (pre- and postdrug order effect), post-hoc testing also compared baseline-adjusted measures ((post-ketamine minus pre-ketamine) vs (post-placebo minus pre-placebo)). Nominal significance (p<0.05) and Bonferroni corrected significance after correcting for eight detail levels (p<0.05/8=0.00625) were reported. This procedure was carried out for oscillatory response to the initial auditory sensory stimulus (S1 only) and sensory gating (S2/S1 ratio) separately. Oscillatory response to S2 was not separately evaluated but rather evaluated in the context of the gating ratio. AEP P50 and clinical measures were compared using two-way repeated-measures ANOVA to examine significant drug × time effects, followed by corresponding post-hoc paired t-tests. All tests were two-tailed. Relationships between clinical and electrophysiological measures significantly affected by ketamine were examined using either bivariate Pearson's correlations or regression analyses if more than one predictor was involved.
Compared with baseline and placebo, ketamine significantly increased BPRS total scores and thought disorder and withdrawal symptom factors (significant drug × time interaction), with the largest effect size on the withdrawal symptoms (Table 1). For CADSS, ketamine significantly increased the total score and the subjective symptom subscore, but not the objective symptom subscore, compared with baseline and placebo.
There was no significant drug × time interaction on P50 amplitudes (Figure 1). Ketamine did not significantly affect P50 gating (Figure 1, right panel; drug × time interaction (F(1, 9)=1.97, p=0.19)). Exploratory comparison showed that post-drug ketamine reduced gating compared with post-drug placebo, although this was not statistically significant (t=2.15, p=0.06).
There were significant three-way time × drug × frequency (F(2.4, 19.3)=4.35, p=0.02), drug × frequency (F(1.5, 11.9)=5.70, p=0.02), and weak evidence of site × frequency (F(2.1, 17.1)=3.17, p=0.06) and site (F(5, 40)=2.12, p=0.08) effects. Post-hoc tests showed significant drug (post-placebo vs post-ketamine) × frequency interactions at the CZ (F(7, 18.1)=4.87, p=0.04)) and weak evidence of drug × frequency effects at the FCZ (p=0.08) and FZ (p=0.06), but not at the posterior sites (all p>0.21 in the CPZ, PZ, and OZ sites). Subsequent post-hoc tests focused on the CZ, although most findings from the FZ were similar (data not shown). Ketamine had an opposite effect on gamma and low-frequency bands at the CZ: ketamine increased gamma PSD (D4 or 40–85Hz: t=3.6, p=0.006) and reduced low-frequency PSD (D7 or theta-alpha at 5–12Hz: t=−2.4, p=0.04; D8 or delta at 1–5Hz: t=−6.8, p<0.001) compared with placebo during post-drug testing (Figure 2, top). The results were similar in post-drug minus pre-drug differences (ie, adjusted for baseline) analyses: ketamine increased gamma (D4: t=3.5, p=0.006) and reduced low-frequency power compared with placebo (D7: t=−2.7, p=0.02; D8: t=−3.7, p=0.005) (Figure 2, bottom). The effects on D4 (gamma) and D8 (delta), but not on D7 (theta-alpha), were significant after Bonferroni corrections. The D4 and D8 responses of each subject were plotted in Figure 3. There were no significant time × drug interactions on frequency or site when oscillatory responses to S2 were examined (data not shown). Finally, there were no significant effects of drug order on frequency or site.
To summarize, ketamine significantly increased gamma and reduced low-frequency oscillations in response to auditory sensory stimuli, an effect most prominently shown at the CZ site.
There were significant three-way time × drug × frequency (F(3.2, 29.2)=2.29, p=0.038), two-way drug × frequency (F(3.4, 30.8)=4.60, p=0.007), time × frequency (F(2.4, 22.0)=2.97, p=0.03), and site × frequency (F(4.0, 35.6)=3.36, p=0.02) interactions. The three-way time × drug × frequency interaction was significant only at the CZ (F(3.5, 31.9)=2.84, p=0.046) and with weak evidence for interaction at the neighboring CPZ (p=0.09) and FCZ (p=0.07). We again used only the CZ for post-hoc analyses. Ketamine increased the S2/S1 ratio (reduced gating) at D7 (t=4.97, p=0.001) and D8 (t=2.65, p=0.03) compared with placebo during post-drug testing (Figure 4 top). The results were similar after adjusting for baseline: ketamine increased the ratio at D7 (t=3.84, p=0.004) and D8 (t=2.68, p=0.02) compared with placebo (Figure 4 bottom). The effect on D7 gating was significant after the Bonferroni correction.
To limit multiple comparisons, only measures significantly affected by ketamine were examined in their relationships with clinical ratings. Only clinical and electrophysiological data recorded during the ketamine infusion session were used because participants essentially have no clinical symptoms during the other three sessions (ie, little or no clinical variance, see Table 1).
To examine potential contributions of S1 oscillatory responses at D4 (gamma at CZ) and D8 (delta at CZ) and their interaction to clinical ratings, a regression model was used, in which the dependent measure was a clinical rating and the predictors were D4, D8, and their interaction term. For BPRS total and factor scores, the only significant model was with the withdrawal symptom factor (model R2 change=79.3%, F(3,9)=7.7, p=0.018). The D4 × D8 interaction term was significant (standardized beta=−5.7, t=−3.1, p=0.02). Partial correlation suggested that the severity of withdrawal symptoms experienced by the subjects were positively correlated with D4 and negatively correlated with D8 (Figure 5). This finding is interesting because withdrawal symptoms also showed the most robust ketamine effect (Table 1) and a D4 × D8 interaction explained a large proportion of the withdrawal–retardation experience. We failed to find significant regression models that may explain the CADSS total or subscale scores.
To examine the effect of D7 gating on clinical symptoms, Pearson's correlations were carried out between the D7 S2/S1 ratio and clinical ratings. No significant correlations were found for BPRS or CADSS.
We found that subanesthetic dose of ketamine has opposite effects on human gamma and low-frequency oscillations: ketamine augmented gamma (40–85Hz) and reduced delta (1–5Hz) and, to some extent, theta-alpha (5–12Hz) frequency oscillations compared with placebo. This finding replicated similar protocols in mouse (Ehrlichman et al, 2009; Lazarewicz et al, 2009) and rats (Hunt et al, 2009), in which ketamine increased gamma and reduced low-frequency oscillations, although the clinical correlates of these oscillatory effects were not clear from earlier animal studies. Subanesthetic ketamine is known to reliably increase thought disorder and withdrawal–retardation symptoms as measured by corresponding BPRS factors in healthy controls (Krystal et al, 1994; Malhotra et al, 1996; Newcomer et al, 1999; Lahti et al, 2001) and worsen these symptoms in schizophrenia patients (Lahti et al, 1995, 2001; Malhotra et al, 1997), whereas its effects on BPRS hostility and mood symptoms were usually statistically insignificant (Malhotra et al, 1997; Lahti et al, 2001). This clinical profile was replicated in this sample (Table 1). Importantly, the withdrawal symptoms were significantly predicted by the gamma and low-frequency interaction: the withdrawal experience was positively correlated with D4 or gamma and negatively correlated with D8 or delta power during ketamine administration.
The following discussion focuses on whether the ketamine effect on oscillatory pattern mimics those observed in NMDA animal studies and abnormal oscillations in schizophrenia patients.
Increased gamma power by ketamine is a consistent finding in human (Plourde et al, 1997) and in vivo (anesthetized or awake) animal studies (Hunt et al, 2006; Pinault, 2008; Ehrlichman et al, 2009). In vitro studies initially described reduced gamma by ketamine (Cunningham et al, 2006; Zhang et al, 2008), although subsequent studies have refined this description by suggesting a regionally specific ketamine effect such that ketamine increases gamma at the primary auditory cortex but reduces or has no effect in other brain regions (Roopun et al, 2008). Therefore, the observed gamma augmentation at D4 (40–85Hz) is consistent with prior observations. NMDA receptor antagonists increase the spontaneous firing rate of neurons in the medial PFC and nucleus accumbens (NAc) (Jackson et al, 2004; Hunt et al, 2008). Whether the effect on increased gamma observed in the human scalp is related to the corresponding rodent anatomical locations require further studies. We did not find significant ketamine effects on the low range of gamma (20–40Hz). One study reported that general anesthetic dose (2mg/kg) ketamine did not change 30–40Hz power in response to auditory click in humans (Schwender et al, 1993).
Whether the increased gamma by ketamine is mimicking schizophrenia is less clear. As discussed in the Introduction, although most studies have shown a gamma band reduction in schizophrenia, increased gamma band in schizophrenia has also been shown. Previous data also showed that gamma band is positively correlated to the severity of psychosis (Spencer et al, 2004). Our finding suggests that ketamine-induced gamma augmentation, or rather a ‘theta-to-gamma shift' (Ehrlichman et al, 2009), is positively correlated to the severity of withdrawal symptoms. However, it should be cautioned that the psychotomimetic withdrawal–retardation symptoms reported under acute ketamine may not be equivalent to negative symptoms in schizophrenia, because these symptoms occur while the person may be simply more occupied by internal subjective experience rather than a true avolitional pathology.
Although ketamine induces NMDA receptor hypofunction, acute ketamine leads to increased glutamate in the extracellular space in animals (Moghaddam et al, 1997) and increased glutamate in humans as measured by magnetic resonance spectroscopy (Rowland et al, 2005). Glutamate level is reduced in chronic schizophrenia (Theberge et al, 2003; Ohrmann et al, 2005, 2007) but increased in early psychosis (Theberge et al, 2002; Bartha et al, 1997). In parallel, gamma is often reported to be reduced in chronic schizophrenia, although increased gamma is found in early psychosis (Flynn et al, 2008). NMDA receptor blockade may cause hyperexcitation of glutamatergic neurons by disinhibition of GABAergic interneurons (Homayoun and Moghaddam, 2007). Perhaps, a mild shift in the excitation/inhibition balance toward excitation could result in gamma augmentation observed under subanesthetic ketamine. Taken together, we speculate that the augmented gamma indexes an increased glutamate secondary to NMDA antagonism. Further animal and clinical studies are required to investigate this possibility.
The finding of ketamine-induced theta-alpha and delta reduction is also consistent with the animal literature: NMDA and glutamate infusions augment hippocampal delta, theta, and alpha oscillations (Bonansco and Buno, 2003; Bland et al, 2007; Carre and Harley, 2000), whereas NMDA antagonists attenuate the augmentation effect (Bland et al, 2007). Delta-range oscillations are shown to correlate with the NAc neuron membrane potential changes (O'Donnell and Grace, 1995). NMDA antagonist reduces NAc delta power (Hunt et al, 2009) and induces glutamate release in NAc (Razoux et al, 2007). It has been suggested that this ketamine effect in NAc may mediate a psychotic-like effect of ketamine through the potentiation of synaptic efficacy in the prefrontal cortex–accumbens pathway (Razoux et al, 2007). It would be interesting to investigate whether this mechanism could explain a correlation between reduced delta and more ketamine-induced withdrawal symptoms. Importantly, the seemingly analogous pattern of ketamine effects on gamma and low frequencies between rodents and humans is encouraging because it provides an opportunity to study the NMDA mechanisms in schizophrenia in translational preclinical–clinical studies using oscillations as intermediate bioassays.
Subanesthetic ketamine appears to mimic some but not all aspects of sensory gating deficits in schizophrenia. Ketamine significantly reduced single-trial-based theta-alpha gating. This replicated the same finding in schizophrenia patients under essentially the same data processing methods (Hong et al, 2008b), which showed that patients and their non-ill first-degree relatives have significantly reduced theta-alpha gating while the reduction of P50 gating was not significant. The question of whether sensory gating is under the control of NMDA receptors has been evaluated. The lack of ketamine effect on AEP-based P50 is a replication of previous reports, all of which showed that ketamine itself did not significantly affect P50 gating in humans (van Berckel et al, 1998; Oranje et al, 2002). Animal studies suggest that ketamine has either no effect (de Bruin et al, 1999) or even increase in P20/N40 (the rodent AEP component believed to be equivalent to human P50) (Connolly et al, 2004). The negative findings can be due to a lack of significant NMDA receptor involvement in sensory gating, insufficient dose of ketamine, or methodology issues. We observed much similarity between ketamine and schizophrenia on gating of theta-alpha oscillation, indicating that the negative AEP-based findings may in part be due to insensitive methodology.
This observation would suggest that sensory gating problems observed in schizophrenia might in part be associated with a NMDA receptor deficit or antagonism. However, we also observed one distinct difference: the reduced theta-alpha gating in schizophrenia patients was observed on the background of elevated theta-alpha oscillations compared with healthy controls (Hong et al, 2008b; Figure 2). Here, we observed an opposite effect such that ketamine reduced low-frequency oscillations. The reason for this contradiction is not known and may seem at odd with the finding of similar theta-alpha gating deficit between schizophrenia and ketamine challenge. However, acute ketamine does not necessarily mimic all aspects of schizophrenia. Acute ketamine in similar dose and study design has also generated an opposite effect on prepulse inhibition compared with that in schizophrenia, by increasing rather than decreasing prepulse inhibition (Abel et al, 2003).
To summarize, glutamatergic receptors are integral components of current theories on rhythmatogenesis (Cunningham et al, 2006; Gonzalez-Burgos and Lewis, 2008; Roopun et al, 2008) and may also be associated with abnormal electrical brain oscillations in schizophrenia. We observed that acute ketamine affects both gamma and low-frequency bands in humans, which mimic some aspects of the oscillatory pattern observed in schizophrenia. Our finding also suggests that the ketamine-induced gamma/delta reversal seen in animal studies (Ehrlichman et al, 2009) maybe indexing some aspects of schizophrenia-like symptoms. Given the small sample size, our study might have missed some other important electrophysiology–clinical correlates. Overall, this study illustrates the potentials of using frequency-based neural oscillations to complement and, in some cases, to replace AEP for animal-clinical translational studies.
The study was supported by the National Institute on Health grants MH70644, 79172, 49826, 77852, and 68580.
The authors declare no conflict of interest.