Multivariate Linear Time-Series Modeling and Prediction of Cerebral Physiologic Signals: Review of Statistical Models and Implications for Human Signal Analytics

Nuray Vakitbilir ^1* Amanjyot Singh Sainbhi ¹ Abrar Islam ¹ Alwyn Gomez ² Kevin Yuwa Stein ¹ Logan Froese ³ Tobias Bergmann ¹ Davis Mcclarty ⁴ Rahul Raj ⁵ Frederick Adam Zeiler ⁶

• ¹ Faculty of Graduate Studies, University of Manitoba, Winnipeg, Canada
• ² Department of Surgery, Max Rady College of Medicine, University of Manitoba, Winnipeg, Manitoba, Canada
• ³ Department of Clinical Neuroscience, Karolinska Institutet (KI), Stockholm, Stockholm, Sweden
• ⁴ Rady Faculty of Health Sciences, University of Manitoba, Winnipeg, Manitoba, Canada
• ⁵ Department of Neurosurgery, Helsinki University Central Hospital, Helsinki, Uusimaa, Finland
• ⁶ Department of Surgery, Max Rady College of Medicine ,University of Manitoba, Winnipeg, Manitoba, Canada

Cerebral physiological signals embody complex neural, vascular, and metabolic processes that provide valuable insight into the brain's dynamic nature. Profound comprehension and analysis of these signals are essential for unraveling cerebral intricacies, enabling precise identification of patterns and anomalies. Therefore, the advancement of computational models in cerebral physiology is pivotal for exploring the links between measurable signals and underlying physiological states. This review provides a detailed explanation of computational models, including their mathematical formulations, and discusses their relevance to the analysis of cerebral physiology dynamics. It emphasizes the importance of linear multivariate statistical models, particularly autoregressive (AR) models and the Kalman filter, in time series modeling and prediction of cerebral processes. The review focuses on the analysis and operational principles of multivariate statistical models such as AR models and the Kalman filter. These models are examined for their ability to capture intricate relationships among cerebral parameters, offering a holistic representation of brain function. The use of multivariate statistical models enables the capturing of complex relationships among cerebral physiological signals. These models provide valuable insights into the dynamic nature of the brain by representing intricate neural, vascular, and metabolic processes. The review highlights the clinical implications of using computational models to understand cerebral physiology, while also acknowledging the inherent limitations, including the need for stationary data, challenges with high dimensionality, computational complexity, and limited forecasting horizons.