Nonlinear dynamics underlying sensory processing dysfunction in schizophrenia

Abstract

Natural systems, including the brain, often seem chaotic, since they are typically driven by complex nonlinear dynamical processes. Disruption in the fluid coordination of multiple brain regions contributes to impairments in information processing and the constellation of symptoms observed in neuropsychiatric disorders. Schizophrenia (SZ), one of the most debilitating mental illnesses, is thought to arise, in part, from such a network dysfunction, leading to impaired auditory information processing as well as cognitive and psychosocial deficits. Current approaches to neurophysiologic biomarker analyses predominantly rely on linear methods and may, therefore, fail to capture the wealth of information contained in whole EEG signals, including nonlinear dynamics. In this study, delay differential analysis (DDA), a nonlinear method based on embedding theory from theoretical physics, was applied to EEG recordings from 877 SZ patients and 753 nonpsychiatric comparison subjects (NCSs) who underwent mismatch negativity (MMN) testing via their participation in the Consortium on the Genetics of Schizophrenia (COGS-2) study. DDA revealed significant nonlinear dynamical architecture related to auditory information processing in both groups. Importantly, significant DDA changes preceded those observed with traditional linear methods. Marked abnormalities in both linear and nonlinear features were detected in SZ patients. These results illustrate the benefits of nonlinear analysis of brain signals and underscore the need for future studies to investigate the relationship between DDA features and pathophysiology of information processing.

Keywords: EEG; delay differential analysis; mismatch negativity; nonlinear dynamics; schizophrenia.

Fig. 1.

DDA identified dynamical state changes preceding each of the ADR complex components. (A) NCSs demonstrated robust MMN, P3a, and RON components as shown in the heat map of the individual subject difference (deviant tone ERP − standard tone ERP) average signals (Upper). All three components of the ADR (MMN, P3a, and RON) can be appreciated in the group-level average signals (Lower). (B) DDA $a_3$ coefficient values averaged within each subject revealed significantly decreased $a_3$ in the SZ patients (Upper). As with the ERP results, the DDA group averages displayed three components with homologous waveform morphology and severity of deficits in SZ, but the DDA components (numbered 1–3 in Lower) preceded their corresponding ERP peaks identified in A by 71, 54, and 82 ms, respectively. The shaded regions in the group average signals represent group differences that are statistically significant after adjusting for multiple comparisons (false discovery rate). Cohen’s d, t values, and degrees of freedom are shown in SI Appendix, Fig. S9.

Fig. 2.

ADR components were evident from both ERP analysis and DDA of waveforms elicited by deviant auditory tones. (A) Individual subject average signals from deviant tones revealed pronounced MMN and P3a components in the NCSs (Upper). The grand average signals from the two groups showed significantly different ADR component signals (Lower). (B) DDA $a_3$ amplitude changes were observed before each of the ADR components (numbered 1–3 in Lower). Furthermore, statistically significant differences in $a_3$ amplitude between groups were detected during the earliest time window (50–100 which ms) in an auditory tone could be processed as deviant (black arrow; mean t value = −2.6, mean Cohen’s d = −0.13).

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 $a_3$ changes were reduced for the SZ group during this time window.

Fig. 4.

Subjects in both SZ and NCS groups were presented with auditory stimuli consisting of 50-ms standard tones with randomly interspersed 100-ms deviant tones. Data were analyzed according to a traditional ERP paradigm (Left) and using DDA to assess nonlinear dynamics (Right). In the standard ERP approach, EEG time series from standard (dashed lines) and deviant trials (solid lines) were averaged after preprocessing, and the difference waveform was computed from these averages. With DDA, a three-term delay differential equation was applied to the data, and the nonlinear coefficient $a_3$ was computed for both standard and deviant trials. Both ERP difference waveforms and the DDA $a_3$ coefficient time courses are aligned to tone onset, which is marked with vertical dashed lines at 0 ms.

Fig. 5.

Estimation of the features $a_{\mathrm{1,2,3}}$ for a data window of length $L$ for Eq. 2.