A state space based approach in non-linear hemodynamic response modeling with fMRI data

In this paper we use the modified and integrated version of the balloon model in the analysis of fMRI data. We propose a new state space model realization for this balloon model and represent it with the standard A,B,C and D matrices widely used in system theory. A second order Padé approximation with equal numerator and denominator degree is used for the time delay approximation in the modeling of the cerebral blood flow. The results obtained through numerical solutions showed that the new state space model realization is in close agreement to the actual modified and integrated version of the balloon model. This new system theoretic formulation is likely to open doors to a novel way of analyzing fMRI data with real time robust estimators. With further development and validation, the new model has the potential to devise a generalized measure to make a significant contribution to improve the diagnosis and treatment of clinical scenarios where the brain functioning get altered. Concepts from system theory can readily be used in the analysis of fMRI data and the subsequent synthesis of filters and estimators.