Group search algorithm recovers effective connectivity maps for individuals in homogeneous and heterogeneous samples

Abstract

At its best, connectivity mapping can offer researchers great insight into how spatially disparate regions of the human brain coordinate activity during brain processing. A recent investigation conducted by Smith and colleagues (2011) on methods for estimating connectivity maps suggested that those which attempt to ascertain the direction of influence among ROIs rarely provide reliable results. Another problem gaining increasing attention is heterogeneity in connectivity maps. Most group-level methods require that the data come from homogeneous samples, and misleading findings may arise from current methods if the connectivity maps for individuals vary across the sample (which is likely the case). The utility of maps resulting from effective connectivity on the individual or group levels is thus diminished because they do not accurately inform researchers. The present paper introduces a novel estimation technique for fMRI researchers, Group Iterative Multiple Model Estimation (GIMME), which demonstrates that using information across individuals assists in the recovery of the existence of connections among ROIs used by Smith and colleagues (2011) and the direction of the influence. Using heterogeneous in-house data, we demonstrate that GIMME offers a unique improvement over current approaches by arriving at reliable group and individual structures even when the data are highly heterogeneous across individuals comprising the group. An added benefit of GIMME is that it obtains reliable connectivity map estimates equally well using the data from resting state, block, or event-related designs. GIMME provides researchers with a powerful, flexible tool for identifying directed connectivity maps at the group and individual levels.

Introduction

Brain connectivity maps represent the state-of-the-art methods for understanding brain processing. Despite great advances in the field, the utility and robustness of these methods often fall short (Smith et al., 2011). One routinely overlooked cause of inaccuracies in connectivity maps, also called “networks”, is the aggregation of the data across individuals prior to estimation (Kherif et al., 2003, Ramsey et al., 2010). Statistical and empirical work has demonstrated that in cases where processes are heterogeneous across individuals, aggregation of the data to arrive at a “group” solution may fail to describe any individual in the sample (Miller and Van Horn, 2007, Molenaar and Campbell, 2009). While researchers acknowledge that the group model may not describe any one individual, they rarely assess the degree to which the resulting model describes the individuals comprising the group. Hence it typically remains unknown if the published findings derived from data aggregated in this manner relate to how individuals' brains actually function. This is particularly evident in the case of effective, or directed (Friston, 2007), connectivity mapping approaches.

There are three primary ways that group models may fail to describe individuals in the context of effective connectivity modeling. First, the beta weights (parameters associated with the couplings of two regions) may vary across participants. Evidence exists for beta weights systematically varying across subjects (e.g., Kim et al., 2007), and examination of how variation in beta weight estimates relates to clinical diagnoses or performance is a focal point for many researchers. Only if the influence that other ROIs might have on the target ROI is explicitly accounted for may unbiased estimates be obtained for the beta weight of interest. Hence, acquiring reliable connectivity map structures is a first requirement for analysis on the beta weights.

Second, the network of couplings among ROIs may differ. Emerging evidence suggests that much heterogeneity in brain processes exists across individuals both in terms of the presence of relations among regions (Fair et al., 2010, Hillary et al., 2011) and which regions become active (Kherif et al., 2003, Kherif et al., 2009, Miller and Van Horn, 2007, Miller et al., 2002, Seghier et al., 2008). When traditional group-level analysis is conducted on processes which differ, spurious findings emerge (e.g., Miller and Van Horn, 2007, Miller et al., 2002). To date, the predominate methods for analyzing brain data assume homogeneity across individuals despite these findings that individuals may differ greatly (although one study found evidence for similarities in connectivity maps, see James et al., 2009). Taken together, it appears that there may be some paths that are common to the majority of individuals comprising the group while some paths may be unique to certain individuals or to a subgroup of individuals. This may be because of different relations among the regions selected for connectivity analysis, or perhaps because for some individuals a region is not part of the connectivity map. If the presence of paths differs among individuals, then the aggregated results may not represent any of the individuals comprising the group (Molenaar and Campbell, 2009). Currently, no method utilizes shared information during model selection to find paths common to the group while allowing for paths unique to individuals.

Third, connectivity maps may evidence heterogeneity across individuals in terms of the direction of an effect. Much attention has been given to the inadequacy of most individual-level effective connectivity approaches for arriving at models that identify both the presence and direction of connections (Smith et al., 2011). In this examination of both effective and functional connectivity mapping approaches, methods for arriving at connectivity maps that are agnostic in terms of directionality when detecting the presence of a relation prevailed. Hence little is known about the true degree of heterogeneity that may exist across individuals in terms of the direction of effects between a given pair of ROIs since previous inferences (particularly those drawn from lagged methods) may have relied on spurious findings.

Examination of functional heterogeneity in brain processing across individuals first requires reliable recovery of true effects. This is true for the examination of varying strengths or different patterns of relations among regions. One potential solution would be to first arrive at individual-level maps and then identify subgroups (should they exist) using graphical clustering across individuals (Van den Heuvel et al., 2008). Given recent evidence that even the best methods fail to recover the structure of effective connectivity maps at the individual level when certain types of noise and conditions are present (Smith et al., 2011), this approach may lead to spurious findings since the subgroups will be based on unreliable maps. On the other end of the spectrum, Ramsey et al. (2011) have achieved great success when using a multi-sample approach for estimating effective connectivity maps. Building from the Greedy Equivalence Search (GES; Meek, 1997), an approach which identifies candidate paths to free up using a score function based on the maximum likelihood estimations, the approach capitalizes on commonalities among individuals to arrive at a group model (Ramsey et al., 2010). Extensions of this approach were recently applied to the Smith et al. (2011) data sets and have surfaced as the first set of methods for identifying true connections as well as the directionality with as few as 10 individuals in a group (Ramsey et al., 2011). James et al. (2009) developed a promising model selection approach that applies all viable models to data concatenated across individuals and selects the best one. Going one step further than many researchers, James et al. (2009) assessed the degree to which the group-derived model fit individuals. The group-derived model for an empirical data set fit 85% of the individuals excellently. Clearly powerful procedures which offer an improvement upon connectivity models to date, both require concatenation across individuals much like other current methods, suggesting that it may be best for situations in which homogeneity is suspected.

The presence of noise in fMRI data further confounds the issue of heterogeneity. An approximation of neural activity, fMRI data is subject to many sources of noise due to measurement error which may make individuals' processes look different when they are same. The Smith et al. (2011) simulations provided an excellent opportunity to investigate the impact of varied neural–hemodynamic relations on the ability to recover reliable connectivity maps. Their results have become the benchmark for success when evaluating the utility of novel analytic methods. In the scenario where one neuronal input influences activity across all ROIs, the best of 38 methods tested recovered only 50% of the true connections. In the face of shortened neural lags and shared inputs the best recovery rates neared 70%. In this way, individual nuances outside the control or the measurement of the researcher may produce maps which appear heterogeneous when in fact the neural structure is homogeneous across individuals.

These realities place researchers at a quandary. On the one hand, true heterogeneity in individual processes may make group-level findings erroneous because the resulting map may not apply to any one individual (Miller and Van Horn, 2007, Molenaar, 2004, Ramsey et al., 2010). On the other hand, the signal-to-noise ratio in fMRI data may be too low for reliable recovery at the individual level, making designs which capitalize on shared information across individuals appear to be a promising approach. Recently, a suggestion has been made for the development of a procedure that enables individual-level modeling while arriving at robust similarities across individuals (Smith, 2012). We present a timely, reliable, and novel approach, the Group Iterative Multiple Model Estimation (GIMME), which addresses the issue of heterogeneity (i.e., the need for individual-level maps) in effective connectivity mapping while capitalizing on shared information to arrive at group inferences. The model estimation procedure incorporates the following improvements. First and foremost, the selection procedure of candidate paths utilized by GIMME appropriately picks up signal from noise to arrive at a common structure among individuals (should one exist) that appropriately describes the majority of individuals. Second, GIMME continues to evaluate candidate paths at the individual level, freeing those paths for that individual which will improve the model fit. Taken together, this approach enables reliable group inferences with a model selection algorithm similar to those based on maximum likelihood improvements (James et al., 2009, Ramsey et al., 2011) that diverges from these approaches by enabling reliable estimation of paths unique to the individual and not forcing a group model. This paper presents the formal aspects of GIMME and demonstration of GIMME using the homogeneous Smith et al. (2011) data and heterogeneous in-house data.