Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 961967, 7 pages
Research Article

Reliable and Efficient Approach of BOLD Signal with Dual Kalman Filtering

State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China

Received 25 May 2012; Accepted 11 July 2012

Academic Editor: Huafeng Liu

Copyright © 2012 Cong Liu and Zhenghui Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.