Fast GPU Algorithm for Analyzing Effective Connectivity in Functional Brain Imaging

Abstract Functional imaging, such as functional Magnetic Resonance Imaging (fMRI), allows the in-vivo study of the human neuronal circuitry. By applying specific environmental stimuli to human subjects, functional imaging detects signals that could indicate direct or indirect neuronal connectivity when they exhibit certain levels of association between brain regions. However, the directed connections cannot be identified using simple statistical approaches, such as pair-wise correlations. Structural Equation Modeling (SEM) is more appropriate for analyzing the causal relationship, called the effective connectivity. SEM is aimed to fit a path model subject to the anatomical constraints using the data collected from imaging study. Such data-driven path analysis involves the minimization of a maximum likelihood (ML) discrepancy function with respect to some constrained path coefficients. The minimization process is iterative. In each of iterations, a constrained coefficient will be switched to unconstrained and added to the pool of the unconstrained for the minimization. The iterations continue until the model attains an acceptable level of parsimonious fit index. The computing time is a big issue because it increases geometrically with the number of unconstrained path coefficients, in other words, the number of iterations. Using Quad-Core Central Processing Unit (CPU), it takes a month for the iterations from 0 to 30 path coefficients. High speed computing hardware and software can be applied to the optimization process so as to cope with the above-mentioned issue. Graphical Processing Unit (GPU) is a kind of high speed hardware solution that performs ultra-fast algorithmic computation on huge data matrices. This study demonstrates the utilization of GPU with the parallel Genetic Algorithm (GA) replacing the Powell minimization in the standard analysis software package. It is shown in an example of 30 path coefficients that the time taken for the path analysis can be reduced from 30 days to 3.6 hours. The breakthrough of this study in high speed computing greatly relaxes the limitation on the number of paths to be investigated in functional imaging and maintains the performance of optimization.