Connectivity exploration with structural equation modeling: an fMRI study of bimanual motor coordination

Abstract

The present fMRI study explores the connectivity among motor areas in a bimanual coordination task using the analysis framework of structural equation modeling (SEM). During bimanual finger tapping at different frequency ratios, temporal correlations of activations between left/right primary motor cortices (MI), left/right PMdc (caudal dorsal premotor area) and supplementary motor cortex (SMA) were detected and used as inputs to the SEM analysis. SEM was extended from its traditional role as a confirmatory analysis to be used as an exploratory technique to determine the most statistically significant connectivity model given a set of cortical areas based on anatomic constraints. The resultant network exhibits coupling from left MI to right MI, links from both PMs to the two MIs, a negative interaction from left PM to right PM, and functional influence from SMA to right MI and right PM, revealing contributions of these areas to bimanual coordination.

Introduction

The coupling or interference between dual motor tasks by two hands is familiar in our daily experience and has been investigated in many psychophysical and MEG experiments (Chan and Chan, 1995, Franz et al., 1991, Jirsa et al., 1998, Mayville et al., 2001, Tuller and Kelso, 1989, Yamanishi et al., 1980). For example, in an experimental study on spatial coupling of dual motor tasks (Chan and Chan, 1995), participants were asked to perform continuous simultaneous drawing of circles and straight lines using both hands simultaneously. There was a strong tendency for the line to become more circle-like and the circle to become more line-like, as measured by orientation ratio (i.e., height/width) of the circle or line. Such phenomena were termed a spatial magnet effect, and such interference was referred to as “coupling” between the left and right motor systems (Franz et al., 1991, Kelso et al., 1988).

In addition to the interaction described above, the frequency ratios (between two hands) for which polyrhythmic bimanual movement is stable were found to follow a Farey series. Specifically, with a/b and c/d as two base levels of stable frequency ratios, the ratio (a + b) / (c + d) produces the frequency ratio for the next level of (decreased) stability (Treffer and Turvey, 1993). In the experiments of bimanual circle/line drawing task described above, it was shown that the spatial coupling (or interference, i.e., the deviation of orientation ratio of the drawn circles from that of the perfect circle) was the strongest at the ratio of 1/1 (Level 0), the second strongest at 1/2 (Level 1), and the third strongest at 2/3 (Level 2) (Chan and Chan, 1995).

In the context of similar bimanual coordination tasks, such as anti-phase vs. in-phase hand movement or poly-rhythmic finger tapping, recent functional imaging studies (Debaere et al., 2003, Debaere et al., 2004, De Weerd et al., 2003, Immisch et al., 2001, Jancke et al., 2000, Koeneke et al., 2004, Sadato et al., 1997, Toyokura et al., 1999) indicated strong involvement of SMA in motor coordination between two hands. The role of premotor area in the bimanual motor coordination was also studied in depth by fMRI (Debaere et al., 2003, Debaere et al., 2004, De Weerd et al., 2003, Immisch et al., 2001, Koeneke et al., 2004, Sadato et al., 1997). In recent fMRI and electrophysiological studies (Debaere et al., 2003, Debaere et al., 2004, De Weerd et al., 2003, Donchin et al., 1998, Koeneke et al., 2004, Toyokura et al., 1999), an interaction between contralateral primary motor cortices was found during bimanual coordination tasks. Subcortical structures such as basal ganglia and cerebellum were also found activated during bimanual tasks (Tracy et al., 2001, Debaere et al., 2003, Debaere et al., 2004).

Two biological models of motor coordination attempted to explain these coupling phenomena (Cardoso de Oliveira, 2002, Debaere et al., 2003, Debaere et al., 2004): generalized motor programs (GMP) and intermanual crosstalk model. The GMP was inspired by the strong tendency for spatiotemporal similarity of bimanual movements and proposed that there could be a common motor plan for both hands (Schmidt, 1975). In contrast to GMP, the theory of intermanual crosstalk generally suggested that the interactions between the movements of the two arms resulted from partial intermingling (crosstalk) between two independent manual motor plans (Marteniuk and MacKenzie, 1980). Alternatively, GMP could be applied in a hand-specific manner in which the two independent motor plans of the crosstalk model can be viewed as the lowest level of the GMP.

Despite this great body of work, the underlying neural network responsible for bimanual coordination is far from well understood; questions remaining to be answered include where the GMP is generated and whether there exists crosstalk between bilateral primary motor cortices, premotor areas and SMA (Cardoso de Oliveira, 2002, Kelso et al., 1988). Neural interactions, or interchanges of neuronal (electrical or chemical) signals between different brain sites, may be one of the keys to understanding these motor coordination phenomena (Sadato et al., 1997), given that most existing literature (De Weerd et al., 2003, Immisch et al., 2001, Jancke et al., 2000, Koeneke et al., 2004, Toyokura et al., 1999) indicates that bimanual motor coordination requires a group of cortical regions but does not provide detailed information on interactions and couplings between these regions.

Many challenges exist in the analysis of fMRI data to ascertain connectivity relationships across motor cortices during bimanual coordination tasks. First, the widely used correlation analysis across multiple spatial regions cannot reveal causal directions. This is because a correlation coefficient only indicates the degree with which two time courses co-vary with each other, but is not able to provide directional information on the interaction between these two regions. A second challenge is that the observed temporal latency of the BOLD response between different brain areas cannot be used to ascertain the temporal order of neural activities. This occurs because the local hemodynamic response, which depends on the local physiology, could be region specific, blur or delay the temporal evolution of BOLD signals, and make it unable to reflect the timing of neuronal events at different brain sites. Consequently, observed temporal differences in event-related paradigms are not reliable for retrieving information about the direction of the interaction. The third challenge is that many traditional analysis methods fail to provide a complete account of interactions if more than two brain regions are involved. When studying more than two regions, each one can interact with several other regions. One region can affect another directly or indirectly, i.e., passing through a third party in the model, and can be affected by several regions. As a result, correlation of two areas could include both direct and indirect effects, and a correlation analysis cannot tease these apart. For this kind of “many-body problem” in neural interactions, structural equation modeling provides a unique analysis framework.

Structural equation modeling (SEM) is a statistical technique that is able to examine causal relationships between multiple variables. SEM approaches the data differently from the usual statistical methods such as multiple regression or ANOVA. The parameters in the SEM model are connection strengths or path coefficients between different variables, which reflect the effective connectivity in our neural network model. Parameters are estimated by minimizing the difference between the observed covariances and those implied by a structural or path model. SEM was initially developed and applied in biology, psychology, economics, and other social sciences (Wright, 1920). In 1994, hypothesizing a connectivity model based on prior knowledge of anatomy and connectivity, McIntosh and Gonzalez-Lima (1994) applied SEM to PET data, demonstrating the dissociation between ventral and dorsal visual pathways in object and spatial vision. SEM was also used to characterize connectivity changes within the motor system of Parkinsonian patients (Grafton et al., 1994). Büchel and Friston (1997) used SEM analysis in an fMRI study to investigate the nonlinear interactions among V1, V5, posterior parietal cortex, and prefrontal cortex. More recently, Maguire et al. (2001) compared the structural equation models between human brains with and without bilateral hippocampal damages during a memory retrieval task.

To date, SEM has been used as a confirmatory analysis technique. Most existing studies only compare a couple of possible connectivity models derived from prior knowledge. But in the case when most connections are not known or the complexity of the anatomic network leads to a large number of possibilities, the traditional network analysis method cannot be applied. In this paper, we adapt SEM for exploratory analysis of fMRI data and demonstrate that such an analysis is capable of identifying the best model from an ensemble of all possible models using comprehensive sorting of multiple fit indices. This is demonstrated in the functional neural network for bimanual motor coordination, using a finger-tapping task involving two hands at two frequency ratios.