Computation for the Implicit Components of ERP in Attention Dezhong Yao* + Summary: EEG reveals brain functions with high temporal resolution. Yet, multiple implicit variables may be involved in limited ERP measures. Spe- cial computation techniques are needed to recover these parameters. In the study of attention, we can obtain the ERP in attended (V) and unattended (U) conditions. Usually, the effect of attention is computed as the difference (D) between V and U with the assumption that D and U are independent. Yet, they should be related. Treating V as a function of U, a linear model V = W + GU is assumed, where W and G are implicit in the ERP measures. G is the gain control on the unattended function. Provided G and W are constant over a local brain region, we can use the Total Least Square (TLS) algo- rithm to compute their values. In the experiment, participants attended to one side of a fixed point, and stimulus of circular checkerboard was flashed either to the attended or the unattended side. The values of W and G as functions of V and U were computed showing that multiple implicit variables are involved in attention. The gain amplification (G) is found to be greater than 1 before 200 msec and much less than 1 afterwards. The values of G and W may shed light on the nature of attention. Key words: Computation; Attention; ERP. Introduction Because of its finite computational resources, the hu- man brain must process information selectively so as to process some stimuli more thoroughly than others. Se- lective attention has been studied with psychological methods for many years, but recent cognitive neurosci- ence studies using brain-imaging techniques have dem- onstrated that sensory processing can be strongly modulated by attention. They have shown that some of these modulations can be anticipatory, while other com- ponents reflect a changed neural response to an incom- ing stimulus (Driver and Frackowiak 2001). To analyze the neural mechanisms of selective atten- tion, we need not only to identify the participating brain regions but also the temporal information flow among the regions involved. Although imaging methods of ce- rebral blood flow have proved highly effective for defin- ing the anatomical areas that are activated during cognitive operations, these methods are severely limited in their ability to reveal the patterns of temporal activa- tion. Fine-grained information about the temporal microstructure of neural activation patterns can be ob- tained through noninvasive recordings of event-related potentials (ERPs) with a resolution of the order of milli- seconds. However, the estimation of ERP generator loca- tions is an ill-posed problem which can not be solved uniquely (Yao 2002). An ideal way is to combine ERP and blood-flow neuroimaging techniques in the same experi- mental framework (Hillyard and Anllo-Vento 1998). In literatures, there are many methods to reveal the implicit variables in brain spontaneous electric activities (EEG), such as the non-linear parameters characterized by the correlation dimension and complexity etc. How- ever, for ERPs, the main parameters involved in the cur- rent data interpretation are the amplitudes and delays of some characteristic components (Hillyard and Anllo- Vento 1998; Naatanen 1990; Ao, Fan, He and Chen 2001). Yet, multiple implicit variables may be involved in lim- ited ERP measures. Special computation techniques are needed to recover these parameters. In this work, a linear computation model is suggested for the ERP data analy- sis collected in a paired experiment of attention. * School of Life Science and Technology, University of Electronic Science and Technology of China, PR China. + Beijing Cognitive Lab, Biophysics research institute, Chinese Academy of Sciences, Beijing, PR China. Accepted for publication: July 24, 2003. Supported by NSFC #90208003 and,#30200059; Key research pro- ject of science and technology of MOE, China; Sichuan youth Re- searcher Foundation, Doctor Training Fund of MOE, China; TRAPOYT and EYPT. The data were collected from ten subjects by a Neuroscan system at the Beijing Cognitive Lab, Institute of Biophysics, Academy of China, thanks to Prof Chen L, Fan SL and Mr Ao for providing the data, and Thanks Prof TC Chan at Chinese University of Hong Kong for comments on the draft. Correspondence and reprint requests should be addressed to Dezhong Yao, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu 610054, PR China. E-mail: dyao@uestc.edu.cn Copyright © 2003 Human Sciences Press, Inc. Brain Topography, Volume 16, Number 1, Fall 2003 (© 2003) 65