Bilinear dynamical systems

Area of Science:

• Neuroscience
• Computational Biology
• Signal Processing

Background:

• Functional magnetic resonance imaging (fMRI) measures haemodynamic responses, which are indirect indicators of neuronal activity.
• Deconvolving fMRI time-series is crucial for accurately estimating underlying neuronal signals.
• Existing methods may lack the sophistication to fully capture the complex dynamics between neuronal activity and haemodynamic responses.

Purpose of the Study:

• To propose and evaluate bilinear dynamical systems (BDS) for model-based deconvolution of fMRI time-series.
• To enable informed deconvolution of haemodynamic time-series to disclose underlying neuronal activity.
• To provide a method for estimating neuronal responses essential for brain functional integration and connectivity models.

Main Methods:

• Development of a stochastic bilinear neurodynamical model in discrete time.
• Incorporation of linear convolution kernels to model haemodynamics.
• Derivation of an expectation-maximization (EM) algorithm for parameter estimation.
• Application of the EM algorithm with deconvolution in the E-step and parameter updates in the M-step.

Main Results:

• Preliminary results demonstrate the utility of BDS for fMRI time-series deconvolution.
• The study investigates the implications of the stochastic nature of the neurodynamic model.
• Performance comparison of the proposed BDS method against Wiener deconvolution is presented.

Conclusions:

• Bilinear dynamical systems offer a promising framework for model-based fMRI deconvolution.
• This approach enhances the ability to infer neuronal activity from haemodynamic signals.
• The findings contribute to more accurate modeling of brain functional integration and connectivity.