Efficient hemodynamic states stimulation using fNIRS data with the extended Kalman filter and bifurcation analysis of balloon model

Abstract

This paper introduces a stochastic hemodynamic system to describe the brain neural activity based on the balloon model. A continuous-discrete extended Kalman filter is used to estimate the nonlinear model states. The stability, controllability and observability of the proposed model are described based on the simulation and measurement data analysis. The observability and controllability characteristics are in- troduced as significant factors to validate the preference of different hemodynamic factors to be considered for diagnosis and monitoring in clinical applications. This model also can be efficiently applied in any monitoring and control platform include brain and for study of hemodynamics in brain imaging modalities such as pulse oximetry and functional near infrared spectroscopy. The work is on progress to extend the proposed model to cover more hemodynamic and neural brain signals for real-time in-vivo application.

Share and Cite:

Kamrani, E. , Foroushani, A. , Vaziripour, M. and Sawan, M. (2012) Efficient hemodynamic states stimulation using fNIRS data with the extended Kalman filter and bifurcation analysis of balloon model. Journal of Biomedical Science and Engineering, 5, 609-628. doi: 10.4236/jbise.2012.511076.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Johnston, L.A., Duff, E., Mareels, I. and Egan, G.F. (2008) Nonlinear estimation of the BOLD signal. NeuroImage, 40, 504-514. doi:10.1016/j.neuroimage.2007.11.024
[2] Friston, K.J., Mechelli, A., Turner, R. and Price, C.J. (2000) Nonlinear responses in fMRI: The balloon model, Volterra kernels, and other hemodynamics. NeuroImage, 12, 466-477. doi:10.1006/nimg.2000.0630
[3] Banaji, M., Mallet, A., Elwell, C.E., Nicholls, P. and Cooper, C.E. (2008) A model of brain circulation and metabolism: NIRS signal changes during physiological challenges. PLoS Computational Biology, 4, e1000212. doi:10.1371/journal.pcbi.1000212
[4] Aquino, K.M., Schira, M.M., Robinson, P.A., Drysdale, P.M. and Breakspear, M. (2012) Hemodynamic traveling waves in human visual cortex. PLoS Computational Biology, 8, e1002435. doi:10.1371/journal.pcbi.1002435
[5] Steinbrink, J., Villringer, A., Kempf, F., Haux, D., Boden, S. and Obrig, H. (2006) Illuminating the BOLD signal: Combined fMRI-fNIRS studies. Magnetic Resonance Imaging, 24, 495-505. doi:10.1016/j.mri.2005.12.034
[6] Schira, M.M., Tyler, C.W., Breakspear, M. and Spehar, B. (2009) The foveal confluence in human visual cortex. The Journal of Neuroscience, 29, 9050-9058. doi:10.1523/JNEUROSCI.1760-09
[7] Kamitani, Y. and Tong, F. (2005) Decoding the visual and subjective contents of the human brain. Nature Neuroscience, 8, 679-685. doi:10.1038/nn1444
[8] Strangman, G., Culver, J.P., Thompson, J.H. and Boas, D.A. (2002) A quantitative comparison of simultaneous BOLD fMRI and NIRS recordings during functional brain activation. NeuroImage, 17, 719-731. doi:10.1006/nimg.2002.1227
[9] Zheng, Y., Martindale, J., Johnston, D., Jones, M., Berwick, J. and Mayhew, J., (2002) A model of the hemodynamic response and oxygen delivery to brain. NeuroImage, 16, 617-637. doi:10.1006/nimg.2002.1078
[10] Logothetis, N.K., Pauls, J., Augath, M., Trinath, T., Oeltermann, A. (2001) Neurophysiological investigation of the basis of the fMRI signal. Nature, 412, 150-157. doi:10.1038/35084005
[11] Duncan, A., Meek, J.H., Clemence, M., Elwell, C.E., Tyszczuk, L., Cope, M., et al. (1995) Optical pathlength measurements on adult head, calf and forearm and the head of the newborn infant using phase resolved optical spectroscopy. Physics in Medicine and Biology, 40, 295-304. doi:10.1088/0031-9155/40/2/007
[12] Kohl, M., Nolte, C., Heekeren, H.R., Horst, S., Scholz, U., Obrig, H., et al. (1998) Determination of the wavelength dependence of the differential pathlength factor from near-infrared pulse signals, Physics in Medicine and Biology, 43, 1771-1782. doi:10.1088/0031-9155/43/6/028
[13] Daunizeau, J., Kiebel, S.J. and Friston, K.J. (2009) Dynamic causal modelling of distributed electromagnetic responses. NeuroImage, 47, 590-601. doi:10.1016/j.neuroimage.2009.04.062
[14] Breakspear, M., Jirsa, V. and Deco, G. (2010) Computa-tional models of the brain: From structure to function. NeuroImage, 52, 727-730. doi:10.1016/j.neuroimage.2010.05.061
[15] Buxton, R.B., Wong, E.C. and Frank, L.R. (1998) Dynamics of blood flow and oxygenation changes during brain activation: The balloon model. Magnetic Resonance in Medicine, 39, 855-864. doi:10.1002/mrm.1910390602
[16] Hettiarachchi, I.T., Pathirana, P.N. and Brotchie, P. (2010) A state space based approach in non-linear hemodynamic response modeling with fMRI data. IEEE Annual International Conference on Engineering in Medicine and Biology (EMBC), Buenos Aires, 31 August 2010-4 September 2010, 2391-2394. doi:10.1109/IEMBS.2010.5627400
[17] Glover, G.H. (1999) Deconvolution of Impulse Response in Event Related BOLD fMRI. NeuroImage, 9, 416-429.
[18] Dale, M.A. and Buckner, R.L. (1997) Selective averaging of rapidly presented individual trials using fMRI. Human Brain Mapping, 5, 329-390. doi:10.1002/(SICI)1097-0193
[19] Obata, T., Liu, T.T., Miller, K.L., Luh, W.-M., Wong, E.C., Frank, L.R. and Buxton, R.B. (2004) Discrepancies between BOLD and flow dynamics in primary and supplementary motor areas: Application of the balloon model to the interpretation of BOLD transients. NeuroImage, 21, 144-153. doi:10.1016/j.neuroimage.2003.08.040
[20] Fritson, K.J., Josephs, O., Rees, G. and Turner, R. (1998) Nonlinear event-related responses in fMRI. Magnetic Resonance in Medicine, 39, 41-52. doi:10.1002/mrm.1910390109
[21] Fritson, K.J., Jezzard P. and Turner, R. (1994) Analysis of functional MRI time series. Human Brain Mapping, 1, 153-171.
[22] Kong, Y.Z., et al. (2004) A model of the dynamic relationship between blood flow and volume changes during brain activation. Journal of Cerebral Blood Flow & Metabolism, 24, 1382-1392. doi:10.1097/01.WCB.0000141500.74439.53
[23] Deneux, T. and Faugeras, O. (2006) Using nonlinear models in fMRI data analysis: Model selection and activation detection. NeuroImage, 32, 1669-1689. doi:10.1016/j.neuroimage.2006.03.006
[24] Buxton, R.B., Uluda?, K., Dubowitz, D.J. and Liu, T.T. (2004) Modeling the hemodynamic response to brain activation. NeuroImage, 23, 220-233. doi:10.1016/j.neuroimage.2004.07.013
[25] Johnston, L.A., Duff, E., Mareels, I. and Egan, G.F. (2008) Nonlinear estimation of the BOLD signal. NeuroImage, 40, 504-514. doi:10.1016/j.neuroimage.2007.11.024
[26] Hu, Z., Zhao, X., Liu, H. and Shi, P. (2009) Nonlinear analysis of the BOLD signal. EURASIP Journal on Advances in Signal Processing, 2009, 1-14. doi:10.1155/2009/215409
[27] Engel, S.A., Glover, G.H. and Wandell, G.H. (1997) Retinotopic organization in human visual cortex and the spatial precision of functional MRI. Cerebral Cortex, 7, 181-192. doi:10.1093/cercor/7.2.181
[28] Kriegeskorte, N., Cusack, R. and Bandettini, P. (2010) How does an fMRI voxel sample the neuronal activity pattern: Compact-kernel or complex spatiotemporal filter? NeuroImage, 49, 1965-1976. doi:10.1016/j.neuroimage.2009.09.059
[29] Magri, C., Schridde, U., Murayama, Y., Panzeri, S. and Logothetis, N.K. (2012) The amplitude and timing of the BOLD signal reflects the relationship between local field potential power at different frequencies. The Journal of Neuroscience, 32, 1395-1407. doi:10.1523/JNEUROSCI.3985-11.2012
[30] Bailey, C. J., Sanganahalli, B. G., Herman, P., Blumenfeld, H., Gjedde, A. and Hyder, F. (2012) Analysis of time and space invariance of BOLD responses in the rat visual system. Cerebral Cortex, In Press. doi:10.1093/cercor/bhs008
[31] Friston, K. J., Fletcher, P., Josephs, O., Holmes, A., Rugg, M.D. and Turner, R. (1998) Event-related fMRI: Characterizing differential responses. NeuroImage, 7, 30-40. doi:10.1006/nimg.1997.0306
[32] Javed, F., et al. (2012) Recent advances in the monitoring and control of haemodynamic variables during haemodialysis: A review. Physiological Measurement, 33, R1-R31. doi:10.1088/0967-3334/33/1/R1
[33] Javed, F., Savkin, A.V., Chan, G.S.H., Mackie, J.D. and Lovell, N.H. (2011) Identification and control for auto-mated regulation of hemodynamic variables during hemodialysis. IEEE Transactions on Biomedical Engineering, 58, 1686-1697. doi:10.1109/TBME.2011.2110650
[34] Buxton, R.B., Uluda?, K., Dubowitz, D.J. and Liu, T.T. (2004) Modeling the hemodynamic response to brain activation. NeuroImage, 23, S220-S233. doi:10.1016/j.neuroimage.2004.07.013
[35] Mandeville, J.B., Marota, J.J., Ayata, C., Zararchuk, G., Moskowitz, M.A., Rosen, B. and Weisskoff, R.M. (1999) Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. Journal of Cerebral Blood Flow & Metabolism, 19, 679-689. doi:10.1097/00004647-199906000-00012
[36] Hoge, R.D., Atkinson, J., Gill, B., Crelier, G.R., Marrett, S. and Pike, G.B. (1999) Linear coupling between cerebral blood flow and oxygen consumption in activated human cortex. Proceedings of the National Academy Sciences, 96, 9403-9408. doi:10.1073/pnas.96.16.9403
[37] Jacobsen, D.J. (2006) Hemodynamic modelling of BOLD fMRI: A machine learning approach. Ph.D. Thesis, Technical University of Denmark, Copenhagen. doi:10.1.1.85.3860

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.