Quantum analysis of P3a and P3b from auditory single trial ERPs differentiates borderline personality disorder from schizophrenia

Traditional approaches to EEG modelling use the methods of classical physics to reconstruct scalp potentials in terms of explicit physical models of cortical neuron ensembles. The principal difficulty is that the multiplicity of cellular processes with an intricate array of deterministic and random factors prevents creation of consistent biophysical parameter sets. An original, empirically-testable solution has been recently achieved in our previous studies by a radical departure from the deterministic equations of classical physics to the probabilistic reasoning of quantum mechanics. This crucial step relocates elementary bioelectric sources of EEG signals from the cellular to the molecular level where positively and negatively ions are considered as elementary sources of electricity. The rationale is that despite dramatic differences in cellular machineries, statistical factors governed by the rules of central limit theorem produce EEG waveforms as a statistical aggregate of the synchronized activity of multiple closely-located microscale sources. Using the formalism of nonhomogeneous birth-and-death processes (BDP) the quantum models of microscale events are deduced and linked to the dynamics of macroscale EEG waveforms. This study expands these methods with new features for comprehensive analysis of event related potentials directly from single trials, i.e. the EEG segments which are closely related in timing to cognitive events. We derive a universal model of the components of single trial ERPs both in frequency and time domains. This, for the first time, enables us to quantify all significant cognitive components in single trial ERPs, providing an alternative to the traditional method of averaging. Given P300 as an important objective marker of psychiatric disorders, a methodology which reliably discloses the component compositions of this potential, may have specific diagnostic importance. In this study, reliable identification of the P3a and P3b components from an auditory oddball paradigm provided a means of differentiating borderline personality disorder from schizophrenia.