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Publisher: Automatic Control and Systems Engineering, University of Sheffield
Languages: English
Types: Book
Subjects:
It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional magnetic resonance imaging (fMRI), where the blood oxygen level dependent (BOLD) signals are recorded, the understanding and accurate modelling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modelling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model (ARX) structure. It is observed that neither the ordinary least squares (LS) method nor the classical total least squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data, in that the resultant ARX models may be unstable and thus cannot generate stable model predicted outputs. A regularized total least squares (RTLS) method is employed and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV.
L. A. Aguirre, S. A. Billings. Dynamical effects of overparametrization in nonlinear models. Physica D, 80, pp.26-40, 1995.
K. J. Astrom. Introduction to Stochastic Control Theory. Academic Press, New York, 1970.
P. Baraldi, A. A. Manginelli, M. Maieron, D. Liberati, C. A. Porroa. An ARX model-based approach to trial by trial identification of fMRI-BOLD responses. Neuroimage, 37, pp.189-201, 2007.
S. A. Billings, C. F. Fung. Recurrent radial basis function networks for adaptive noise cancellation. Neural Networks, 8, pp.273-290, 1995.
S. A. Billings, I. J. Leontaritis. Identification of nonlinear systems using parametric estimation techniques. Proc. IEE Conf. Control and its Applications, Warwick, pp. 183-187, 1981.
S. A. Billings, W. S. F. Voon. Structure detection and model validity tests in the identification of nonlinear system. Proc. Institution of Electronic Engineers, Pt D, 130, pp.193-199, 1983.
S. A. Billings, W. S. F. Voon. Correlation based model validity tests for non-linear models. Int. J. Control, 44, pp.235-244, 1986.
S. A. Billings, W. S. F. Voon. Piecewise linear identification of non-linear systems. Int. J. Control, 46, pp.215-235, 1987.
S. A. Billings, H. L. Wei, M. A. Balikhin. Generalized multiscale radial basis function networks. Neural Networks, 20, pp.1081-1094, 2007.
S. A. Billings, Q. M. Zhu. Model validation tests for multivariable nonlinear models including neural networks. Int. J. Control, 62, 749-766, 1995.
R. B. Buxton, E. C. Wong, L. R. Frank. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn Reson Med, 39, pp.855-864, 1998.
S. W. Chen. A two-stage description of cardiac arrhythmias using a total least squares-based prony modeling algorithm. IEEE Trans. Biomedical Engineering, 47, pp.1317-1327, 2000.
I. Daubechies. Ten Lectures on Wavelets. Philaelphia, PA: SIAM, 1992.
K. J. Friston. Bayesian estimation of dynamical systems: an application to fMRI. NeuroImage, 16, pp.513- 530, 2002.
K. J. Friston, A. Mechelli, R. Turner, C. J. Price. Nonlinear responses in fMRI: the balloon model, volterra kernels and other hemodynamics. Neuroimage, 12, pp.466-477, 2000.
K. J. Friston, A. P. Holmes, J. B. Poline, P. J. Grasby, S. C. Williams, R. S. Frackowiak, R. Turner. Analysis of fMRI time-series revisited. NeuroImage, 2, pp.45-53, 1995.
G. H. Golub. Some modified matrix eigenvalue problems. SIAM Rev. 15, 318-344, 1973.
G. H. Golub, P. C. Hansen, D. P. O'Leary. Tikhonov regularization and total least squares. SIAM J. Matrix Analysis and Applications, 21, pp.185-194, 1999.
G. H. Golub, C. F. Van Loan. An analysis of the total least squares problem. SIAM J. Numer. Anal. 17, 883-893, 1980.
R. L. Grubb, M. E. Raichle, J. O. Eichling, M. M. Ter-Pergossian. The effects of changes in PACO2 on cerebral blood volume, blood flow and vascular mean transit time. Stroke, 5, pp.630-639, 1974.
M. Jones, J. Berwick, D. Johnston, J. Mayhew. Concurrent optical imaging spectroscopy and laserDoppler flowmetry: the relationship between blood flow, oxygenation, and volume in rodent barrel cortex. Neuroimage, 13, pp.1002-1015, 2001.
M. Jones, J. Berwick, J. Mayhew. Changes in blood flow, oxygenation, and volume following extended stimulation of rodent barrel cortex. Neuroimage, 15, pp.474-487, 2002.
Z. Q. Lang, S. A. Billings. Output frequency characteristics of nonlinear systems. Int. J. Control, 64, pp.1049-1067, 1996.
J. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright. Convergence properties of the Nelder-Mead simplex method in low dimensions. SIAM J. Optim., 9, pp. 112-147, 1998.
I. J. Leontaritis, S. A. Billings. Input-output parametric models for non-linear systems-part I: Deterministic non-linear systems. Int. J. Control, 41, pp.303-328, 1985a.
I. J. Leontaritis, S. A. Billings. Input-output parametric models for non-linear systems-part II: Stochastic non-linear systems. Int. J. Control, 41, pp.329-344, 1985b.
I. J. Leontaritis and S. A. Billings. Model selection and validation methods for non-linear systems. Int. J. Control, 45, pp. 311-341, 1987a.
I. J. Leontaritis and S. A. Billings. Experimental-design and identifiability for non-linear systems. Int. J. Systems Science, 18, pp. 189-202, 1987b.
R. M. Lewis, V. Torczon, M. W. Trosset. Direct search methods: then and now. J. Computational and Pllied Mathematics, 124, pp.191-207, 2000.
L. Ljung. System Identification: Theory for the User. Englewood Cliffs : Prentice-Hall, 1987.
J. B. Mandeville, J.J. Marota, C. Ayata, G. Zaharchuk, M.A. Moskowitz, B.R. Rosen, R. M. Weisskoff. Evidence of a cerebrovascular postarteriole Windkessel with delayed compliance. J. Cereb. Blood Flow Metab, 19, pp.679-689, 1999.
J. Martindale, J. Mayhew, J.Berwick, M. Jones, C. Martin, D. Johnston, P. Redgrave and Y. Zheng. The hemodynamic impulse response to a single neural event. J Cereb Blood Flow Metab, 23, pp.546-555, 2003.
V. Mesarovic, N. Galatsanos, A. Katsaggelos. Regularizad constrained total least squares image restoration, IEEE Trans. Image Process, 4, pp.1096-1108, 1995.
G. D. Mitsis, M. J. Poulin, P. A. Robbins, V. Z. Marmarelis. Nonlinear modeling of the dynamic effects of arterial pressure and co2 variations on cerebral blood flow in healthy humans. IEEE Trans. Biomed. Eng., 51, pp.1932-1943, 2004.
J. A. Nelder, P. Mead. A simplex method for function minimization. Computer Journal, 7, pp.308-313, 1965.
R. B. Panerai, D. M. Simpson, S. T. Deverson, P. Mahony, P. Hayes, D. H. Evans. Multivariate dynamic analysis of cerebral blood flow regulation in humans. IEEE Trans. Biomed. Eng., 47, pp.419-423, 2000.
R. K. Pearson, Discrete-Time Dynamic Models, New York: Oxford University Press, 1999.
J. C. Peyton-Jones, S. A. Billings. Interpretation of non-linear frequency response functions. Int. J. Control, 52, pp.319-346, 1990.
J. Riera, J. Bosch, O. Yamashita, R. Kawashima, N. Sadato, T. Okada, T. Ozakic. fMRI activation maps based on the NN-ARx model. Neuroimage, 23, pp.680-697, 2004.
G. F. Shou, L. Xia, M. F. Jiang, Q. Wei, F. Liu, S. Crozier. Truncated total least squares: A new regulation method for the solution of ECG inverse problems. IEEE Trans. Biomedical Engineering, 55, pp.1327-1335, 2008.
D. M. Sima, S. Van Huffel, G. H. Golub. Regularized total least Squares based on quadratic eigenvalue problem solvers. BIT Numer. Math. 44, pp.793-812, 2004.
T. Söderström, P. Stoica. System Identification. New York : Prentice Hall, 1989
A. N. Tikhonov, V. Arsenin. Solution of Ill-Posed Problems. New York: Wiley & Sons, 1977.
S. Van Huffel (Ed.). Recent advances in total least squares techniques and errors-in-variables modeling. SIAM Proceedings Series, SIAM, Philadelphia, 1997.
S. Van Huffel, P. Lemmerling (Eds.). Total Least Squares and Errors-in-variables Modeling: Analysis, Algorithms and Applications. Kluwer Academic Publishers, Dordrecht, 2002.
S. Van Huffel, J. Vandewalle. The Total Least Squares Problem: Computational Aspects and Analysis. SIAM, Philadelphia, 1991.