Caveats and Nuances of Model-Based and Model-Free Representational Connectivity Analysis

Abstract

Brain connectivity analyses have conventionally relied on statistical relationship between one-dimensional summaries of activation in different brain areas. However, summarizing activation patterns within each area to a single dimension ignores the potential statistical dependencies between their multi-dimensional activity patterns. Representational Connectivity Analyses (RCA) is a method that quantifies the relationship between multi-dimensional patterns of activity without reducing the dimensionality of the data. We consider two variants of RCA. In model-free RCA, the goal is to quantify the shared information for two brain regions. In model-based RCA, one tests whether two regions have shared information about a specific aspect of the stimuli/task, as defined by a model. However, this is a new approach and the potential caveats of model-free and model-based RCA are still understudied. We first explain how model-based RCA detects connectivity through the lens of models, and then present three scenarios where model-based and model-free RCA give discrepant results. These conflicting results complicate the interpretation of functional connectivity. We highlight the challenges in three scenarios: complex intermediate models, common patterns across regions, and transformation of representational structure across brain regions. The article is accompanied by scripts (https://osf.io/3nxfa/) that reproduce the results. In each case, we suggest potential ways to mitigate the difficulties caused by inconsistent results. The results of this study shed light on some understudied aspects of RCA, and allow researchers to use the method more effectively.

Keywords: functional connectivity; multi-dimensional connectivity; multivariate pattern analysis; representational connectivity analysis; representational similarity analysis.

FIGURE 1

Arrangement of the simulated conditions in the representational dissimilarity matrices (RDMs), model and neural RDMs and their pairwise correlations. (A) There are 16 conditions in the RDM consisting of four semantic categories of objects in four distinct positions. Example stimuli are from Kriegeskorte et al. (2008) available at http://www.cns.nyu.edu/kianilab/ Datasets.html. (B) Top matrices show the ground truth for the two ROIs that represent “positions” (left) and “semantic categories” (right). The neural RDMs shown in the bottom were generated by adding noise to the activity patterns used to generate the two top model RDMs. Therefore, the simulated neural RDMs are highly correlated to the ground truth (r = 0.96). The correlations between the (model and/or neural) RDMs of the two different ROIs are negative (r < –0.2) implying no connectivity between them.

FIGURE 2

An intermediate model RDM can lead to the wrong conclusion that two uncorrelated ROIs (RDMs) are connected. RDMs can be represented as a vector emanating from the origin in the N-dimensional space [N = number of elements in the RDM, i.e., n(n–1)/2 with n being the number of conditions]. (A) Shows a situation where a model RDM has equal angles to two orthogonal (unrelated) neural RDMs. Looking from the lens of this model can leave the impression that the two neural RDMs are similar as they project similarly on the model RDM. (B) Shows a situation where two neural RDMs are positively correlated, but might look unrelated (disconnected) when looking at them through the lens of the model RDM. This is because only one has a component along the model RDM’s vector and the other is orthogonal. (C) The model RDM used in Simulation 1, which has components of the representations in ROI 1 (position) and ROI 2 (semantic category). This model RDM has equal correlations (= 0.6) to the models used to generate neural RDMs of the two ROIs (shown in Figure 1, top); almost similar correlations to the neural RDMs (0.6). (D) The correlation between the neural RDM of the two ROIs (model-free RCA) and between the neural and model RDMs of each ROI (model-based RCA). Red asterisks show significant above-chance correlation values (connectivity) as evaluated by a one-sided Wilcoxon’s signed rank test against zero.

FIGURE 3

(A) Simulation settings, a common input is added to the responses in both ROIs, so that the patterns in the two ROIs covary at each time-point. (B) Example RDMs from the two ROIs before and after adding the common input. RDMs originally had a negative correlation (–0.22). The correlations went up from –0.22 to 0.84 due to the common input.

FIGURE 4

Addition of common pattern to pair of ROIs can make them look connected in model-free and 1-model RCA but not 2-model RCA if the ROIs are distinct enough. (A) Addition of common non-structured (noise) patterns to both ROIs leads to significant connectivity when evaluated using model-free and 1-model RCA, but not 2-model RCA because the two ROIs dominantly represent information that is negatively correlated (see Figure 1B). Red asterisks show significant above-chance correlation values (connectivity) as evaluated by one-sided Wilcoxon’s signed rank test against zero. (B) The more distinct the dominant information represented across the ROIs, the less the effect of added common noise on their connectivity. Dots show the amount of change in connectivity as a function of correlation between the information represented in the two model RDMs used in 2-model RCA. Each dot represents data from a single simulated subject. The line shows the best linear fit to the data. The correlation and the significance of correlations are also shown as calculated using Pearson’s linear correlation.

FIGURE 5

2-model RCA allows us to detect transformation of information if the temporal dynamics across ROIs are statistically related/congruent. (A) Time course of information encoding in the two ROIs at a delay of 20 samples [congruent (cng), solid gray line] and a delay of –20 from ROI 1 to ROI 2 [incongruent (inc), dashed gray line]. The delay was variable across simulated subjects. The time courses show the correlation between each ROI and its corresponding model (position model for ROI 1 and semantic-category model for ROI 2). (B) Transformation of information across ROIs causes all model-free and model-based RCAs to miss the connectivity except when the information appears congruently across ROIs (first in ROI 1 followed by ROI 2) and using 2-model RCA. Red asterisk shows significant above-chance correlation value (connectivity) as evaluated by one-sided Wilcoxon’s signed rank test against zero.

FIGURE 6

Different types of inference about functional connectivity: top left and top right show the response patterns for N experimental conditions in two ROIs. Larger activations in a voxel are shown by lighter colors. One classical approach would be to reduce the dimensionality of data in each ROI to 1, and summarize the rich patterns of activity by a single vector containing one number for each experimental condition (or time-point for the case of resting-state data). Significant correlation between these vectors implies co-activation, i.e., that activations in ROI1 and ROI2 co-vary. Multi-dimensional connectivity methods that we consider in this article characterize the response patterns for different conditions by a representational dissimilarity matrix (RDM). Direct comparison of the RDMs (model-free RCA) tests for shared information (i.e., whether the two sets of response patterns in the two ROIs have any shared information with regards to the experimental conditions). Incorporation of models, i.e., model-based RCA, when a common model is used for both ROIs (1-model RCA) tests for shared information about a specific aspect of task/stimuli. This hypothesis in RCA is specified in the ROI-common model. Finally, model-based RCA with ROI-specific models (2-model RCA) detects potential transformation of information.