Incorporating Error-Rate-Controlled Prior in Modelling Brain Functional Connectivity

Abstract

Inferring effective connectivity using fMRI is of in- creasing importance for understanding brain function. Dynamic Bayesian network (DBN) modeling has been suggested as a promising and suitable method for this purpose. However, in practice, the success of DBN modeling is largely limited for rea- sons of intensive computational complexity in large networks and of accurately controlling the error rate of the model structural features. Very recently, we have developed a framework that is able to control the false discovery rate (FDR) of the discovered network edges. In this paper, we propose incorporating an FDR- controlled network-structure prior into DBN modeling for brain functional connectivity. Simulation results show that the proposed method can significantly accelerate the DBN learning process while simultaneously controlling the FDR. Its application to a real fMRI study revealed that certain functional connectivities in Parkinson's disease patients' brain are by L-dopa medication, and also that extra connections between brain regions may represent compensatory mechanisms. I. INTRODUCTION Functional Magnetic Resonance Imaging (fMRI) allows non-invasive assessment of brain activity and has the potential for enhancing insight into brain functioning. Effective brain connectivity, defined as the neural influence that one brain region exerts over another, is of critical importance for the understanding of brain function, and its impairment may be associated with neuro-degenerative diseases such as Parkin- son Disease (PD). Several mathematical models have been proposed to discover brain connectivity using fMRI, such as structural equation modeling (SEM) and multivariate au- toregressive models (MAR). Among them, dynamic Bayesian networks (DBNs) have recently attracted increasing attention (1) due to their solid basis in statistics. DBN models repre- sent fMRI region-of-interest (ROI) time courses as variable nodes connected by directed arcs denoting their probabilistic dependence. Despite the advantages of DBN modeling, there are nev- ertheless some concerns that may restrict its current suit- ability for fMRI analysis. First, the computational costs of the time-consuming structure-searching of large DBNs can be prohibitive, making exploratory analysis less practical. Secondly, current structure-learning algorithms for DBNs do not explicitly control the error rate of the discovered net- works, since score-based search methods generally assess the suitability of a given structure by the overall goodness-of-fit. However, for studying brain connectivity, a desirable network- learning model should not only fit data well, but also be able to control the error rate of connectivity features in the learned networks (e.g. edges), as this is often the important feature for meaningful neuroscience interpretation. As for many real world applications involving multiple hypothesis testing, controlling the False Discovery Rate (FDR) (2) of the learned edges is a more suitable error rate criterion than the traditional type-I and type-II error rates. We have therefore proposed a general theoretical framework to control the FDR of the recovered connections (3), in which discrete models were studied for demonstration. We demonstrated that the proposed FDR-controlled PC algorithm is computationally efficient and can control the FDR closely around the user- specified level. Very recently we have extended the framework in (3) to learning the structure of DBNs from continuous fMRI data. Therefore, in this paper, to facilitate both the structure- searching and control the FDR of the learned connectivity edges in DBN modeling, we propose incorporating an FDR- controlled network-structure prior into DBN modeling for inferring brain functional connectivity. The basic idea is to derive a prior probability distribution over network structures based on the output of the FDR-controlled PC algorithms and further to learn the DBN model with the derived prior distribution. We will demonstrate the performance of the proposed approach by simulations. Finally a real fMRI study on Parkinson's disease will be discussed.