Fractional-Order Time Series Models for Extracting the Haemodynamic Response From Functional Magnetic Resonance Imaging Data

The postprocessing of functional magnetic resonance imaging (fMRI) data to study the brain functions deals mainly with two objectives: signal detection and extraction of the haemodynamic response. Signal detection consists of exploring and detecting those areas of the brain that are triggered due to an external stimulus. Extraction of the haemodynamic response deals with describing and measuring the physiological process of activated regions in the brain due to stimulus. The haemodynamic response represents the change in oxygen levels since the brain functions require more glucose and oxygen upon stimulus that implies a change in blood flow. In the literature, different approaches to estimate and model the haemodynamic response have been proposed. These approaches can be discriminated in model structures that either provide a proper representation of the obtained measurements but provide no or a limited amount of physiological information, or provide physiological insight but lacks a proper fit to the data. In this paper, a novel model structure is studied for describing the haemodynamics in fMRI measurements: fractional models. We show that these models are flexible enough to describe the gathered data with the additional merit of providing physiological information.