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Terrence , 1073/pnas.1810572116/-/DCSupplemental nS.Tu,salcagsi al uioypoesn measures processing auditory early in changes in small Thus, deficits disability SZ. functional in to real-world processing and contribute symptoms, sensory clinical substantially cognition, auditory and early propagate and these measures model, proposed in cascade (1) impairments processing al. where information psychosocial et hierarchical Thomas and a across Recently, validated cognitive impairments 10). higher-order with (9, (ADR) functioning correlate of that response domains compo- SZ deviance multiple ADR in reorient- significant auditory reductions found the have the nent studies called Many as has wave (8). response to complex studied, negative MMN–P3a–RON referred less a This Although EAIP (7). been by (RON) P3a. of followed negativity called reflective ing is ms also P3a 250–300 component the at positive MMN peaks sounds. a standard that by presented interspersed followed frequently randomly of is sounds sequence a deviant in infrequent to response hsatcecnan uprigifrainoln at online information supporting contains article This 2 of conflicts potential 1 or interests the under financial Published biomedical no report interests. Boehringer- authors Takeda. Astellas, and other NeuroSig, to NASA, consultant The Merck, a Lundbeck, as Heptares, of served Neuroscience, Dart has University Ingelheim, G.A.L. R.N., statement: interest and of Conflict Research; Medical for paper. the Institute Helsinki. wrote G.A.L. Queensland and T.J.S., M.B., analysis; D.L.B., for N.R.S., Reviewers: data X.L., provided K.M., T.C.I. M.L.T., data; R.K., analyzed C.L., A.L.S., designed G.A.L. research; C.L., G.A.L. and performed and X.L., G.A.L. and and K.M., T.J.S., T.J.S., M.L.T., D.L.B., R.K., D.L.B., N.R.S., A.L.S., T.C.I., N.R.S., R.K., T.C.I., A.L.S., R.K., C.L., research; A.L.S., C.L., contributions: Author opeels fteCG netgtr a efudin found be can Investigators COGS the of list complete A [email protected], [email protected], Email: [email protected]. y addressed. or be may correspondence whom To rmcnetoa ehd omnyue ntesuyof study the in apparent used disorders. not neuropsychiatric commonly is methods ana- that conventional be information from impor- can dynamical extract large-scale to signals method tant unconventional brain rather a that using lyzed indicate Results network auditory–neurophysiological responses. to well-known schizophre- correspond preceding and states pro- subjects changes states dynamical healthy These information dynamical of patients. auditory cohorts nia unique large altered in detect and cessing that indeed normal show important can We underlying identify signals. method to brain this theory underlying features systems inte- nonlinear dynamical the method produce on a to describes intercon- based paper needed This to cognition. many is of is experience which of grated neuroscience regions, orchestration brain of seamless nected challenges the fundamental understand the of One Significance y y g ntttf Institut NSlicense.y PNAS b rTertsh hsk ehiceUniversit Technische Physik, Theoretische ur d,e ¨ nttt o erlCmuain nvriyof University Computation, Neural for Institute ae Man Karen , a,b,i,1 n rgr .Light A. 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NEUROSCIENCE I N contribute to deficits in higher-order functions and macroscopic X Y m x˙ = a x n,i , [1] manifestations of SZ. i τn The vast majority of ERP studies in neuropsychiatry have used i=1 n=1 linear analysis of EEG signals. These linear methods include where τn , mn,i ∈ N0 with x = x(t), xτn = x(t − τn ), relating the ERP peaks and latencies (11, 12), frequency (13) or time fre- signal derivative x˙ (t) to delayed versions of the signal. Most quency analyses (14, 15), and cross-frequency coupling (16, 17). of the terms in this template are set to zero depending on the Such conventional linear methods, while highly informative, data type. The following DDA model has been shown to capture focus on a priori determined time-locked events or frequency important dynamical information from EEG signals (26, 33–35): ranges (i.e., delta, theta, gamma bands) and therefore, fail to 2 capture important underlying nonlinear system dynamics. Thus, x˙ = a1x1 + a2x2 + a3x1 . [2] characterizing general dynamical components of broadband data without such restrictions may reveal information about altered This model was chosen through a structure selection proce- systems-level states associated with SZ. dure, repeated random subsampling cross-validation (36) (SI To characterize the large-scale, neural system-level dynamics Appendix), using separate EEG and intracranial EEG datasets present in brain electrical activity in patients with SZ, com- (26, 33–35). The coefficients a1,2,3 were used as features to putational models based on nonlinear dynamics and systems distinguish dynamical differences in time series data. Together theory recently emerged as a promising tool in neuroscience with these coefficients, the least squares error ρ was also con- (18, 19). In contrast to our prevailing focus on microscale neu- sidered. Therefore, the full DDA feature set was composed of ronal activity, methods that characterize large-scale, system-level {a1, a2, a3, ρ}. These previous studies have shown that the four dynamics may help us understand emergent phenomena of DDA parameters of Eq. 2 reflect both linear and nonlinear fea- behavior and cognition (18, 20). This perspective also underlies tures underlying nonlinear signals (25). Since previous results past work linking nonlinear analysis of the EEG to the “dis- converged on a3 as most informative (25), this parameter was connection hypothesis” of SZ (21, 22). Breakspear and Terry carried forward for detailed characterization in this dataset. (23) used a technique for estimating the nonlinear dynamical interdependence of several EEG channels across and within Results both hemispheres and found significant differences in the topog- ADR Complex. Consistent with established methods (10), individ- raphy of dynamical interdependence across the scalp between ual subject deviant minus standard waveform averages derived SZ patients and matched healthy comparison subjects (24). from the preprocessed ERP signals showed significantly reduced Here, we apply a distinct but related technique to probe the MMN and P3a positivity components for the SZ patients nonlinear dynamics of a single EEG channel, which allows us (Fig. 1A, Upper). The group-averaged signals (Fig. 1A, Lower) to investigate the nonlinear properties of a broader range of also revealed significantly diminished ADR complex composed data. Delay differential analysis (DDA) is designed to capture of MMN, P3a positivity, and RON for the SZ group. large-scale dynamics present in nonlinear time series signals Performing the DDA on the difference waveforms and com- (25–28). DDA operates in the time domain and maps unpro- puting individual subject a3 averages showed significantly lower cessed data onto a functional embedding basis. Embeddings a3 values across the SZ patients in the 180- to 240-ms time win- are used in nonlinear dynamics to reveal invariant dynami- dow (Fig. 1B, Upper) (mean t value = 10.8, mean Cohen’s d = cal properties underlying a more extensive, largely unknown 0.55). The group-averaged a3 signals revealed three distinct dynamical system (i.e., the brain) when only a single time series areas corresponding to the ADR components (numbered areas (e.g., EEG data) is available. Previous studies have shown that in Fig. 1B, Lower). Interestingly, the timing of the three DDA DDA can be used to extract disease-specific dynamical fea- peaks occurred before their corresponding ADR components tures: Parkinson’s movement data (29, 30), ECG recordings (27, identified in the group-averaged ERP signals. For instance, the 31), sleep EEG (26), classification of Parkinson’s disease EEG peak group difference in area 1 in Fig. 1B occurred 70 ms before data (32, 33), and data for epileptic seizure the peak group difference in the ERP MMN window in Fig. 1A. characterization (34). This suggests that DDA reflects dynamical state changes (as esti- In this study, DDA was applied to the unprocessed EEG mated by the amplitude changes in a3) occurring immediately recordings from SZ patients and nonpsychiatric comparison sub- before each of the ERP ADR components. Thus, DDA not only jects (NCSs) who participated in the Consortium on the Genetics captures the group differences but also, identifies the underly- of Schizophrenia (COGS-2), a multicenter case-control study of ing dynamical state changes that contribute to the linear ERP SZ and related endophenotypes (10). In contrast to our prior changes of the ADR complex components. focus on linear ERP features (MMN and P3a amplitudes) (1, 10), this study aimed to determine (i) whether nonlinear dynam- Responses to Constituent Deviant and Standard Tones. To deter- ics can be detected in raw EEG recordings and if so, (ii) if mine whether findings in the deviant minus standard difference they can be used to differentiate SZ patients from NCSs; by waves were driven by effects to constituent tones, responses mapping the trial information onto the DDA feature space, to deviant and standard tones were also examined separately. we also aimed to determine (iii) whether the MMN, P3a, and Consistent with the results presented above, similar waveform RON responses reflect nonlinear processes even after control- morphology and magnitude of SZ impairment were observed ling for SZ–NCS amplitude differences, which would provide an in both ERP and DDA results. Also consistent with the previ- important perspective on EAIP deficits in SZ. Such information ous section, peaks observed with DDA, including those related may be important for guiding future studies of the genomic and to SZ deficits, occurred earlier than those observed in the ERP neural substrates of SZ and may provide targets for treatment analysis. developments. Responses to deviant tones. Averaging the ERP signals corre- sponding to only deviant tones revealed three ERP components DDA (Fig. 2A) that were reduced for the SZ group, consistent with We developed and applied a signal processing technique, DDA, other studies (10). DDA identified dynamical changes unique based on embedding theory in nonlinear dynamics. DDA com- to each group occurring before each of the ERP components bines two types of embeddings via a delay differential equa- (Fig. 2B). In addition, the dynamical states of the NCS group tion: delay embedding and derivative embedding. The general were significantly different from those of the SZ patients during nonlinear DDA model can be formulated as the 50- to 100-ms time window (black arrow in Fig. 2B) (mean t

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NEUROSCIENCE Responses to standard tones. Unlike the robust group differ- the nonlinear features captured via DDA provide a more prox- ences observed in the ERP responses to the deviant tones, the imal and direct readout of the neurophysiological substrate of group differences in the standard tone ERP responses were ERP measures and the earliest detectable changes in the brain much more modest as shown in Fig. 3A. DDA identified a simi- representing deviance detection. lar group difference occurring between 90 and 130 ms (Fig. 3B). DDA utilizes embeddings to reveal the underlying dynami- Consistent with ERP analysis of the standard tones, no signifi- cal patterns of brain activity in the feature space. These pat- cant dynamical changes were detected in the 50- to 100-ms time terns, which are otherwise not observable in the EEG using window. conventional linear ERP methods, are sensitive to even small perturbations in brain network dynamics—including those on Discussion a small regional scale. The extracted features also provide In this study, DDA, a technique based on dynamical systems a natural measure of the magnitude of dynamical changes, theory, was used to determine whether nonlinear features sig- which may correspond to the severity of dysfunction in neu- nificantly contribute to leading neurophysiologic biomarker can- ropsychiatric illness. In addition to revealing important infor- didates of EAIP. The concept that nonlinear, chaos theory- mation about nonlinear dynamics hidden in the EEG sig- based perturbations occur early in information processing in nals, DDA offers a number of important technical advantages SZ patients has been hypothesized for some time (36). In this over commonly used ERP measures: it is computationally fast, context, these early dynamical state changes precede commonly provides fine temporal resolution (10-ms data windows), and studied ERP features in both groups. SZ-related impairments requires only minimal preprocessing (i.e., demeaning of the in DDA metrics may contribute to impairments in higher-order data) to avoid discarding meaningful contextual information. neurocognitive and psychosocial functioning. A challenge has Since time-consuming preprocessing steps (e.g., blink correc- been with the identification and quantification of these early non- tion and filtering) are not required for DDA, even very large linear abnormalities in the information processing cascade of datasets can be analyzed in minutes rather than days, weeks, or function (1). DDA may provide a solution to this longstanding even months. challenge. Although DDA has great promise, several caveats should be DDA was used on large cohorts of 877 SZ patients and 753 noted. As a measure, DDA findings do not neatly map onto the NCSs using a well-validated paradigm from the COGS-2 multi- vast existing literature, which has nearly exclusively relied on lin- center study. DDA revealed nonlinear dynamical state changes, ear methods; DDA findings, therefore, may be challenging to which preceded well-established ADR components of the ERP. interpret. Likewise, the DDA methods have not undergone the Importantly, the dynamical information extracted from EEG same degree of validation for use in clinical studies (e.g., reli- may also provide additional information about the underlying ability, suitability for use as a repeated measure, sensitivity to nature of the MMN, P3a, and RON components of the ADR. therapeutic interventions). As with the original papers describ- Interestingly, nonlinear features are evident nearly instanta- ing the underlying data used in this report, another caveat is neously in response to standard and deviant auditory stimulus that medications in the SZ patients were not experimentally onset as well as in the deviant minus standard comparison that controlled. It is possible that some of the observed deficits in is commonly used for measuring the ADR components. DDA the DDA features of the SZ patients could be attributable to detected nonlinear activity > 50 ms before conventional ERP differences in their medication status. Likewise, other clinical peaks. Since this early DDA effect does not seem to be an arti- factors could also influence DDA findings. It is noteworthy that fact of the analysis method, questions remain as to the functional the large COGS-2 dataset allows for additional tests to verify significance of these early nonlinear effects. It is possible that that the observed SZ-related effects are not driven by group

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Fig. 3. DDA of standard tones detected significant dynamical state alterations preceding the P150 window. (A) ERP signals corresponding to the standard tones revealed a reduced P150 component in the SZ grand average signal (Lower). (B) Dynamic changes preceding the P150 ERP changes were observed in the 90- to 130-ms window (Lower; mean t value = 3.3, mean Cohen’s d = 0.17). The a3 changes were reduced for the SZ group during this time window.

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NEUROSCIENCE the raw data are processed for each data window separately. To improve NCS groups as observed in both traditional trial mean difference waveforms the performance and to reduce the number of trials needed, cross-trial DDA and the DDA a3 coefficient. The false discovery rate was adjusted using the was used (SI Appendix, Fig. S3). Using the ergodic hypothesis (37), data win- Benjamini–Hochberg procedure. The optimal delays for the COGS-2 dataset dows of multiple trials were combined, and features were computed across were τ = (3, 8) time points, corresponding to (3, 8) ms. trials. The DDA coefficients were estimated simultaneously from 150 trial windows (SI Appendix, Figs. S1–S11). Supervised structure selection was used ACKNOWLEDGMENTS. This work was supported in part by NIH Grants R01- to identify the delays that led to optimal group classification (A0) (32). Note MH065571, R01-MH042228, R01-MH07977, K23-MH102420, R01-MH065554, R01-MH65707, R01-MH65578, R01-MH65558, R01-MH059803, and R01- that these delays have no frequency correspondence due to the nonlinear MH094320. This work was also supported by the Sidney R. Baer, Jr. Foun- nature of the DDA model (25). Results from a3, the most salient feature, are 0 dation; the Department of Veterans Affairs; the Medical Research Service of presented. As a measure of classification performance, the area A under the Veterans Affairs San Diego Health Care System; the Department of Vet- the receiver operating characteristic was used (38). An unpaired Student’s t erans Affairs Desert Pacific Mental Illness Research, Education, and Clinical test was used to assess the significance of differences between the SZ and Center; and the Brain and Behavior Research Foundation.

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