Kalman filter based estimation algorithm for the characterization of the spatiotemporal hemodynamic response in the brain Journal Article
| Authors: | Belkhatir, Z.; Mechhoud, S.; Laleg-Kirati, T. M. |
| Article Title: | Kalman filter based estimation algorithm for the characterization of the spatiotemporal hemodynamic response in the brain |
| Abstract: | The characterization of the spatiotemporal hemodynamic response (stHR) in the brain is important for understanding the interaction between neighboring brain voxels and regions. In this paper, we design an identification algorithm for the characterization of the cerebral stHR which is modeled by a system of coupled hyperbolic partial differential equation (PDE) and infinite-dimensional ordinary differential equation (ODE). The proposed algorithm provides estimates of the hemodynamic variables (cerebral blood flow and mass density contributed by blood) and physiological parameters using non-invasive Blood Oxygenation Level Dependent (BOLD) data measured with functional Magnetic Resonance Imaging (fMRI) modality. The proposed solution concept follows three main steps: (i) discretization of the stHR model using Galerkin-based finite element method; (ii) estimation of the output derivative using high-order sliding mode differentiator; and (iii) estimation of the state, input, and parameters from sampled-in-space measurements using the reduced-order approximation model and a constrained extended Kalman filter with unknown input algorithm. In addition, sufficient conditions that depend on the chosen discretization scheme, and which guarantee the structural identifiability of the input and parameters, and also the observability of the system are provided. The performance of the proposed algorithm is assessed using both synthetic and real data. The set of the used real data represents the 1-D BOLD signal collected from the visual cortex and acquired in 3 Tesla fMRI scanner. © 2019 Elsevier Ltd |
| Keywords: | magnetic resonance imaging; blood; functional magnetic resonance imaging; hemodynamics; hemodynamic response; parameter estimation; data reduction; functional neuroimaging; approximation algorithms; ordinary differential equations; physiological models; approximate structural identifiability; constrained extended kalman filter with unknown input; parameters and input estimation; spatiotemporal hemodynamic response; extended kalman filters; sliding mode control; input estimation; structural identifiability; unknown inputs |
| Journal Title: | Control Engineering Practice |
| Volume: | 89 |
| ISSN: | 0967-0661 |
| Publisher: | Pergamon Press |
| Date Published: | 2019-08-01 |
| Start Page: | 180 |
| End Page: | 189 |
| Language: | English |
| DOI: | 10.1016/j.conengprac.2019.05.017 |
| PROVIDER: | scopus |
| DOI/URL: | |
| Notes: | Article -- Export Date: 1 July 2019 -- Source: Scopus |
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