Reliable and Efficient Approach of BOLD Signal with Dual Kalman Filtering

By introducing the conflicting effects of dynamic changes in blood flow, volume, and blood oxygenation, Balloon model provides a biomechanical compelling interpretation of the BOLD signal. In order to obtain optimal estimates for both the states and parameters involved in this model, a joint filtering (estimate) method has been widely used. However, it is flawed in several aspects (i) Correlation or interaction between the states and parameters is incorporated despite its nonexistence in biophysical reality. (ii) A joint representation for states and parameters necessarily means the large dimension of state space and will in turn lead to huge numerical cost in implementation. Given this knowledge, a dual filtering approach is proposed and demonstrated in this paper as a highly competent alternative, which can not only provide more reliable estimates, but also in a more efficient way. The two approaches in our discussion will be based on unscented Kalman filter, which has become the algorithm of choice in numerous nonlinear estimation and machine learning applications.

[1]  M. Moskowitz,et al.  Importance of Nitric Oxide Synthase Inhibition to the Attenuated Vascular Responses Induced by Topical L-Nitroarginine during Vibrissal Stimulation , 1994, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[2]  Zhenghui Hu,et al.  Exploiting Magnetic Resonance Angiography Imaging Improves Model Estimation of BOLD Signal , 2012, PloS one.

[3]  Zhenghui Hu,et al.  Sensitivity Analysis for Biomedical Models , 2010, IEEE Transactions on Medical Imaging.

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

[5]  G. Crelier,et al.  Investigation of BOLD signal dependence on cerebral blood flow and oxygen consumption: The deoxyhemoglobin dilution model , 1999, Magnetic resonance in medicine.

[6]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

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

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

[9]  Ying Zheng,et al.  A Model of the Hemodynamic Response and Oxygen Delivery to Brain , 2002, NeuroImage.

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

[11]  Huafeng Liu,et al.  Concurrent bias correction in hemodynamic data assimilation , 2012, Medical Image Anal..

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

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

[14]  Rudolph van der Merwe,et al.  The square-root unscented Kalman filter for state and parameter-estimation , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[15]  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.

[16]  Thomas T. Liu,et al.  Discrepancies between BOLD and flow dynamics in primary and supplementary motor areas: application of the balloon model to the interpretation of BOLD transients , 2004, NeuroImage.

[17]  Zhenghui Hu,et al.  Quantitative Evaluation of Activation State in Functional Brain Imaging , 2012, Brain Topography.

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

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

[20]  Karl J. Friston,et al.  Biophysical models of fMRI responses , 2004, Current Opinion in Neurobiology.

[21]  Karl J. Friston,et al.  Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models , 2009, Physica D. Nonlinear phenomena.

[22]  Zhenghui Hu,et al.  Nonlinear Analysis of BOLD Signal: Biophysical Modeling, Physiological States, and Functional Activation , 2007, MICCAI.

[23]  C. Price,et al.  Haemodynamic modelling , 2022 .

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

[25]  Gary F. Egan,et al.  Particle Filtering for Nonlinear BOLD Signal Analysis , 2006, MICCAI.