Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article


Doctor of Philosophy




Neufeld, Richard W. J.

2nd Supervisor

Tremblay, Paul F.



We study known and potential numerical earmarks of schizophrenia through mathematical methods. One known numerical characteristic of schizophrenia is that of prolonged encoding latencies in response to cognitive stimuli. Motivated by the need to explain interaction patterns in 2 x 2 factorial data where one factor is encoding load and the other is diagnostic status, we define a class of general serial mixture models based on the number of encoding subprocesses executed and the speed at which they are executed. Mathematical derivations performed on these models yield closed form expressions for the mean encoding latency and average intertrial variance, which in turn yield expressions for the mean interaction contrast and variance interaction contrast. Different interaction signatures correspond to different members of the model class. A wealth of examples are provided linking various potential physical and neurophysiological encoding mechanisms to members of the model class. We also derive results for a specific subset of the general model class where only the number of subprocesses is allowed to vary over factorial cells. Our development includes a numerical test (verified by theory and simulation methods) to determine if the number of encoding subprocesses varies over trials. Theoretical results are then developed for the case where the speed of encoding subprocesses is allowed to vary. Secondly, by means of an exhaustive literature search and application of contingency tables, we investigate whether a collection of numerical indices, called nonlinear indices or complexity indices, can be utilized to support or refute a conjecture in the literature which states that complexity in EEG recordings tends to be higher in schizophrenia patients than controls with this tendency being dampened (and even inverted) by medication, increasing age, and decreasing symptomatology. Our analysis indicates only weak effects due to age and medication, and suggests that symptomatology may play a greater role. Moreover, we observe a strong ``study effect'' which suggests that laboratory procedures may also play a role. Our systematic review of nonlinear indices does, however, indicate that heart rate variability is reduced in schizophrenia and bipolar disorder.

Summary for Lay Audience

Schizophrenia is a mental disorder which is usually described in behavioural terms. A person with schizophrenia will often exhibit symptoms of delusions (strongly-held false beliefs) or hallucinations (the experience of sensations or perceptions without supporting stimulus events accessible to others). Other symptoms may include incoherent speech and disorganized thought. This thesis, however, focuses on characteristics of schizophrenia that can be quantified numerically. One such characteristic is that of prolonged encoding times. Encoding is the process by which a person mentally transforms an observed event or object into a format which facilitates the task at hand, e.g., transforms a word into a picture for comparison with another picture. Experimental evidence has shown that schizophrenia patients require longer encoding times than normal controls or even other psychiatric controls. This thesis develops a family of mathematical models which can be used to describe and investigate the possible physical and psychological mechanisms that underlie the encoding process. These models are constrained to fit known experimental data in which encoding load and diagnostic status are manipulated. Secondly, the thesis investigates whether a collection of numerical indices, called nonlinear indices or complexity indices, can be used to differentiate schizophrenia (and bipolar disorder) patients from normal controls in EEG and ECG studies. In particular, we examine the question of whether there is a tendency toward greater complexity in the EEG of schizophrenia patients, with this tendency dampened or even reversed with medication, increasing age, and reduced symptomatology. This analysis was spurred by a large literature with contradictory findings. We found only weak effects due to age and medication, and noted that symptomatology as well as laboratory procedures may play a greater role in outcomes. On the other hand, nonlinear indices seem to consistently indicate lower complexity in the heart rate of both schizophrenia and bipolar patients.