Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2015:2015:389875.
doi: 10.1155/2015/389875. Epub 2015 Jan 26.

Nonlinear Bayesian estimation of BOLD signal under non-Gaussian noise

Ali Fahim Khan  1 , Muhammad Shahzad Younis  2 , Khalid Bashir Bajwa  3
Affiliations

Nonlinear Bayesian estimation of BOLD signal under non-Gaussian noise

Ali Fahim Khan et al. Comput Math Methods Med. 2015.

Abstract

Modeling the blood oxygenation level dependent (BOLD) signal has been a subject of study for over a decade in the neuroimaging community. Inspired from fluid dynamics, the hemodynamic model provides a plausible yet convincing interpretation of the BOLD signal by amalgamating effects of dynamic physiological changes in blood oxygenation, cerebral blood flow and volume. The nonautonomous, nonlinear set of differential equations of the hemodynamic model constitutes the process model while the weighted nonlinear sum of the physiological variables forms the measurement model. Plagued by various noise sources, the time series fMRI measurement data is mostly assumed to be affected by additive Gaussian noise. Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment. In this paper, we present a data assimilation scheme that assumes additive non-Gaussian noise, namely, the e-mixture noise, affecting the measurements. The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment. Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF.

PubMed Disclaimer

Figures

Figure 1
Figure 1
The hemodynamic approach illustration.
Figure 2
Figure 2
Framework of the MAGSF.
Figure 3
Figure 3
fMRI synthetic data generation scheme.
Figure 4
Figure 4
fMRI synthetic data synthesis against a periodic stimulus. s, f, v, and q denote flow inducing signal, cerebral blood flow, cerebral blood volume, and deoxyhemoglobin level, respectively.
Figure 5
Figure 5
The greatest activated voxels considered for data assimilation.
Figure 6
Figure 6
State and parameter estimate results of MAGSF and EKF against synthetic data in impulsive noise. Note that the BOLD signal is not directly estimated from the algorithm. Rather, it is constructed from the estimated states and parameters.
Figure 7
Figure 7
Root-mean-squared-error (RMSE) evolution with time of the joint estimates produced by the two filters applied to synthetic data.
Figure 8
Figure 8
State and parameter estimate results of MAGSF and EKF using real data.
See this image and copyright information in PMC

Similar articles

See all similar articles

Cited by

References

    1. Friston K. J., Holmes A. P., Worsley K. J., Poline J.-P., Frith C. D., Frackowiak R. S. J. Statistical parametric maps in functional imaging: a general linear approach. Human Brain Mapping. 1994;2(4):189–210. doi: 10.1002/hbm.460020402. - DOI
    1. Aguirre G. K., Zarahn E., D'Esposito M. The variability of human, BOLD hemodynamic responses. NeuroImage. 1998;8(4):360–369. doi: 10.1006/nimg.1998.0369. - DOI - PubMed
    1. Duann J.-R., Jung T.-P., Kuo W.-J., et al. Single-trial variability in event-related BOLD signals. NeuroImage. 2002;15(4):823–835. doi: 10.1006/nimg.2001.1049. - DOI - PubMed
    1. Gandolla M., Ferrante S., Molteni F., et al. Re-thinking the role of motor cortex: context-sensitive motor outputs? NeuroImage. 2014;91:366–374. doi: 10.1016/j.neuroimage.2014.01.011. - DOI - PMC - PubMed
    1. Buxton R. B., Wong E. C., Frank L. R. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magnetic Resonance in Medicine. 1998;39(6):855–864. doi: 10.1002/mrm.1910390602. - DOI - PubMed

LinkOut - more resources