On the characterization of single-event related brain activity from functional Magnetic Resonance Imaging (fMRI) measurements

We propose an efficient numerical technique for calibrating the mathematical model that describes the single-event related brain response when fMRI measurements are given. This method employs a regularized Newton technique in conjunction with a Kalman filtering procedure. We have applied this method to estimate the biophysiological parameters of the Balloon model that describes the hemodynamic brain responses. Illustrative results obtained with both synthetic and real fMRI measurements are presented.

[1]  E. Haacke,et al.  Theory of NMR signal behavior in magnetically inhomogeneous tissues: The static dephasing regime , 1994, Magnetic resonance in medicine.

[2]  Karl J. Friston,et al.  Nonlinear Responses in fMRI: The Balloon Model, Volterra Kernels, and Other Hemodynamics , 2000, NeuroImage.

[3]  M. Raichle,et al.  The Effects of Changes in PaCO2 Cerebral Blood Volume, Blood Flow, and Vascular Mean Transit Time , 1974, Stroke.

[4]  Evan Haskell.  Mathematics and the Brain , 2007 .

[5]  C. Vogel.  Computational Methods for Inverse Problems , 1987 .

[6]  E. Woo,et al.  Nonlinear Inverse Problems in Imaging , 2012 .

[7]  Amos J. Storkey,et al.  Continuous Time Particle Filtering for fMRI , 2007, NIPS.

[8]  Karl J. Friston,et al.  Bayesian Estimation of Dynamical Systems: An Application to fMRI , 2002, NeuroImage.

[9]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[10]  Karl J. Friston.  Variational filtering , 2008, NeuroImage.

[11]  D. Langleben,et al.  Using Brain Imaging for Lie Detection: Where Science, Law, and Policy Collide , 2013 .

[12]  Michael Brady,et al.  Improved Optimization for the Robust and Accurate Linear Registration and Motion Correction of Brain Images , 2002, NeuroImage.

[13]  N. Gol’dman,et al.  Regularization of Ill-Posed Problems by Iteration Methods , 1999 .

[14]  S. B. Childs,et al.  INVERSE PROBLEMS IN PARTIAL DIFFERENTIAL EQUATIONS. , 1968 .

[15]  Karl J. Friston,et al.  Nonlinear event‐related responses in fMRI , 1998, Magnetic resonance in medicine.

[16]  B. Rosen,et al.  Evidence of a Cerebrovascular Postarteriole Windkessel with Delayed Compliance , 1999, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[17]  P. Yuri,et al.  Well-posed, Ill-posed, and Intermediate Problems with Applications , 2005 .

[18]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[19]  J. R. Baker,et al.  The intravascular contribution to fmri signal change: monte carlo modeling and diffusion‐weighted studies in vivo , 1995, Magnetic resonance in medicine.

[20]  R. Buxton,et al.  Modeling the hemodynamic response to brain activation , 2004, NeuroImage.

[21]  B. Rosen,et al.  Microscopic susceptibility variation and transverse relaxation: Theory and experiment , 1994, Magnetic resonance in medicine.

[22]  Karl J. Friston,et al.  DEM: A variational treatment of dynamic systems , 2008, NeuroImage.

[23]  Karl J. Friston,et al.  Analysis of functional MRI time‐series , 1994, Human Brain Mapping.

[24]  Iven M. Y. Mareels,et al.  Nonlinear estimation of the BOLD signal , 2008, NeuroImage.

[25]  Vince D. Calhoun,et al.  Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering , 2011, NeuroImage.

[26]  R. Buxton,et al.  A Model for the Coupling between Cerebral Blood Flow and Oxygen Metabolism during Neural Stimulation , 1997, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[27]  Suresh B. Srinivasamurthy.  Methods of Solving Ill-Posed Problems , 2012, 1205.5323.

[28]  R. Buxton,et al.  Dynamics of blood flow and oxygenation changes during brain activation: The balloon model , 1998, Magnetic resonance in medicine.

[29]  Albert Tarantola,et al.  Inverse problem theory - and methods for model parameter estimation , 2004 .

[30]  Olivier Faugeras,et al.  Using nonlinear models in fMRI data analysis: Model selection and activation detection , 2006, NeuroImage.

[31]  Heinz W. Engl,et al.  Inverse and Ill-Posed Problems , 1987 .

[32]  Naoki Miura,et al.  A state-space model of the hemodynamic approach: nonlinear filtering of BOLD signals , 2004, NeuroImage.

[33]  L. Shah,et al.  Functional magnetic resonance imaging. , 2010, Seminars in roentgenology.

[34]  J. Hadamard,et al.  Lectures on Cauchy's Problem in Linear Partial Differential Equations , 1924 .

[35]  Ravi S. Menon,et al.  Functional brain mapping by blood oxygenation level-dependent contrast magnetic resonance imaging. A comparison of signal characteristics with a biophysical model. , 1993, Biophysical journal.

[36]  Jean-Baptiste Poline,et al.  Unsupervised robust nonparametric estimation of the hemodynamic response function for any fMRI experiment , 2003, IEEE Transactions on Medical Imaging.

[37]  S. Ogawa,et al.  Oxygenation‐sensitive contrast in magnetic resonance image of rodent brain at high magnetic fields , 1990, Magnetic resonance in medicine.

[38]  S. Kabanikhin.  Inverse and Ill-posed Problems: Theory and Applications , 2011 .

[39]  Epifanio Bagarinao,et al.  Real-time Fmri Applied to Pain Management Nih Public Access Author Manuscript Real-time Functional Mri Motivation , 2022 .

[40]  P. Bandettini,et al.  Spatial Heterogeneity of the Nonlinear Dynamics in the FMRI BOLD Response , 2001, NeuroImage.

[41]  Huafeng Liu,et al.  Nonlinear Analysis of the BOLD Signal , 2009, EURASIP J. Adv. Signal Process..

[42]  J. Rajapakse,et al.  Human Brain Mapping 6:283–300(1998) � Modeling Hemodynamic Response for Analysis of Functional MRI Time-Series , 2022 .

[43]  M. Raichle,et al.  Focal physiological uncoupling of cerebral blood flow and oxidative metabolism during somatosensory stimulation in human subjects. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[44]  Karl J. Friston,et al.  Stochastic Designs in Event-Related fMRI , 1999, NeuroImage.

[45]  Mustafa Khammash,et al.  Parameter Estimation and Model Selection in Computational Biology , 2010, PLoS Comput. Biol..