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Wavelets, fractals and fMRI of brain adaptivity
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Developing new wavelet-based methods of data analysis for functional magnetic imaging (fMRI) and applying these methods to investigate normal age-related changes in neurotransmitter mechanisms for brain systems function.
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Our focus on wavelet-based methodological development is motivated by the potential for wavelets to provide a multiresolutional analysis of non-stationary signals and images. Preliminary work by our group has highlighted the statistical convenience of the whitening or decorrelating property of the wavelet transform applied to signals with fractal or 1/f-type error structure. For example, we have proposed a "wavestrapping" (bootstrapping in the wavelet domain) technique for resampling 1-dimensional fMRI time series [1] and we have shown that it is possible efficiently to estimate the signal and noise parameters of the general linear model in the wavelet domain - a technique we called wavelet-generalised least squares [2]. In the course of the project, we intend to develop these ideas further in several ways including: i) an extension of multiresolutional analysis to 2- and 3-dimensional spatial maps; ii) an evaluation of connectivity analysis in the wavelet domain; iii) application and evaluation of a wavelet-based algorithm for multiresolutional image registration in the context of second-level (group and factorial) analysis of fMRI data; and iv) application of wavelet-based estimators for fractal dimension or 1/f spectral exponent of fMRI time series.
We have chosen to conduct a pharmacological fMRI study as the main neuroscience component of the project for two main reasons: i) such studies provide a suitably complex and challenging context in which to evaluate the merits of new methods in direct comparison to existing alternatives; and ii) we have a long term interest in the potential value of pharmacological fMRI as a tool for assaying changes in transmitter-dependent brain function in the course of normal development. In particular we are interested in the hypothesis that some aspects of adaptivity and connectivity of large scale brain systems may be mediated by specific transmitter systems. Some prior work in support of this hypothesis includes our fMRI study of normal elderly volunteers, scanned following treatment with a variety of generic compounds, which indicated that adaptivity to task difficulty (load) in a fronto-striatal system might be specifically susceptible to dopaminergic and cholinergic (but not GABAergic) drugs and that functional and effective connectivity of the striatum was specifically modulated by dopaminergic drugs [3,4].
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1) Bullmore ET et al (2001) Colored noise and computational inference in neurophsyiological (fMRI) time series analysis: resampling methods in time and wavelet domains. Human Brain Mapping 12, 61-78.
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2) Fadili J & Bullmore ET (2002) Wavelet-generalized least squares: a new BLU estimator of linear regression models with 1/f errors. NeuroImage 15, 217-232.
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3) Bullmore ET et al (2003) Practice and difficulty evoked anatomically and pharmacologically dissociable brain activation dynamics. Cerebral Cortex 13, 144-154.
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4) Honey GD et al (2003) Dopaminergic drug effects on physiological connectivity in a human cortico-striato-thalamic system. Brain, in press.
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