# Meta-analysis of the functional neuroimaging literature with probabilistic logic programming

The use-case examples of NeuroLang shed light on the utility of probabilistic logic semantics in representing neuroscience hypotheses that cannot be readily expressed with standard meta-analysis tools. In the first example, we use between-network segregation queries to infer the unique functional roles of three canonical functional networks: the dorsal attention network (DAN), default mode network (DMN), and frontoparietal cognitive control network (FPCN). In the second example, we explore potential associations between topics and activity within the visual word-form area (VWFA), when it either coactivates with regions of the dorsal attention network or those of the language network. In the third and fourth examples, we study the functional heterogeneity of the FPCN, uncovering differential activation profiles for a number of mental functions and varying connectivity patterns with other brain networks.

### Representing neuroscientific knowledge under uncertainty

Before exploring use-case examples of NeuroLang, we describe how heterogeneous neuroimaging data are represented by using fact and rule tables. A table is a set of tuples or rows, each representing a data instance and having a set of k elements representing columns. Probabilities can be ascribed to the rows of a table to quantify the level of uncertainty in the data presented by each, in which case the table is said to be probabilistic.

Studies in a CBMA database report a set of peak activations that we store in a table named PeakReported. This table contains one row (xyzs) for each peak that a study s has reported at location (xyz) in the Montreal Neurological Institute (MNI) standard space. Moreover, the uncertainty around the spatial location of peaks can be encoded in a rule table by assuming each peak’s 10 mm neighboring voxels to be equivalently reported, similar to the multilevel kernel density analysis (MKDA)16. This rule table is called VoxelReported, and it includes a row (xyzs) for each voxel at location (xyz) within a radius ($$r<10$$ mm) of a peak reported by study s. The choice of using a 10 mm radius is consistent with the smoothing radii commonly used in the functional neuroimaging literature17. More details on how other spatial smoothing priors can be encoded in NeuroLang, such as the probabilistic prior used by the activation likelihood estimation (ALE)18 algorithm, are provided in the Supplementary Materials.

Further, each study within a meta-analytic corpus is associated with cognitive processes or concepts addressed by its experiments. Fully automated meta-analytic tools like Neurosynth calculate statistical term-frequency features on study texts or abstracts, and threshold them to establish these links in a data-driven manner3. We store these associations within a TermAssociation table, containing one row (ts) for each term t associated with study s. Moreover, we incorporate data-driven topic models, learned and openly shared by Neurosynth19, within a TopicAssociation probabilistic table, containing one row $$(t, s,\mathbf{P} )$$ for each uncertain association between a topic t and a study s. In probabilistic logic, we write $$\texttt {TopicAssociation}(t, s) {:}{:} \mathbf{P}$$ to state ‘study s has a probability P of being associated with topic t20. This data representation process is illustrated in Fig. 1.

Similarly to Neurosynth, we assume each study within the meta-analytic database to be an independent equiprobable sample of neuroscientific knowledge3,18. This assumption is encoded by a SelectedStudy probabilistic table, depicted in the bottom left part of Fig. 1, which gives studies an equal weight 1/N in any meta-analysis, where N is the total number of studies within the meta-analytic database. This makes it possible to estimate statistics on CBMA databases in the absence of statistical power indicators (e.g., sample size).

It is common for meta-analyses to integrate anatomical or functional brain parcellations11 to enhance interpretability and reduce computational burdens. In the examples, we use the DiFuMo-256 atlas21, which is part of a multiscale “soft” parcellation estimated from thousands of subjects across 27 studies that include both task and resting-state fMRI experiments. This data-driven functional atlas is argued to achieve comparable statistical performance as voxel-level analyses while simultaneously reducing computational cost and enhancing interpretability. We represent the 256 functional regions from DiFuMo in a RegionVoxel table, containing a row (rxyz) for each brain voxel at MNI location (xyz) belonging to a DiFuMo-256 region r. An excerpt of the RegionVoxel table is depicted on the right part of Fig. 1. We also incorporate a table NetworkRegion that contains a row (nr) for each region r that significantly overlaps with some network n from the 7 or 17-network parcellations22. The network membership of regions is provided as part of the DiFuMo meta-data file. The experiments that follow will use this unified framework of knowledge representation to express probabilistic logic programs that drive meta-analytical findings.

### Between-network segregation: reverse inference of brain network function

In this example, we perform a segregation-based meta-analysis to infer the likelihood of a topic to be present in a study given activation in a brain network, with an additional constraint that there exists no activation in other networks. The goal of this example is to show that a segregation query can identify which network’s activation pattern is preferentially more predictive of the presence of topic terms related to certain mental functions.

We use the Neurosynth CBMA database3, consisting of 14,371 studies, and its associated v5-topics-100 topic model19. The networks included in this example are the DMN, FPCN and DAN defined using the coarse 7-Network atlas22. These networks exhibit coupling dynamics in support of an array of internally and externally-directed mental functions23. However, each one of them is believed to subserve a unique set of cognitive processes7,23,24. The FPCN contributes to a wide variety of tasks by engaging top-down control processes, the DAN is concerned with orienting attention towards salient cues, and the DMN is involved in abstract self-referential, social and affective functions. Using a segregation query, we can quantitatively identify the specific functional roles of these networks from the literature.

First, we have to represent useful heterogeneous data in NeuroLang. For instance, we assume a DiFuMo-256 component r to be reported by a study s whenever a peak activation is reported by the study within that region. In NeuroLang, this is expressed by the following logic rule

which translates, in plain English, to ‘region r is reported by study s if s reports a peak at location (xyz) that falls within region r’. All letters in this code represent variables. Furthermore, we model the reporting of networks by studies in a probabilistic table. The probabilities are based on the total volume of the reported regions that belong to a network. This table accounts for the uncertainty in the location of reported peak activation coordinates as well as the number of potentially reported regions. More precisely, we consider that each study has a probability of reporting a network, proportional to the number of reported regions belonging to the network.

This is implemented by the following rules in NeuroLang

In plain English, a network n is considered to be reported by study s with probability v/V, where v is the total volume of regions within network n that are reported active by study s, and V is the total volume of all regions in the network. This program makes use of NeuroLang’s ability to express probabilistic rules -i.e. NetworkReported-, aggregations via the built-in count and sum functions, and probabilistic inference capabilities.

Next, we define a rule that infers the probability that studies are associated with a topic given activation in only one of the three networks. That is, we query the probability that a topic t reported by study s is associated with activation in some network n reported by s and there exists no other network reported by study s. In NeuroLang, this corresponds to the following rule that infers the probability of preferential association between a topic and a network across the whole dataset:

where the // operator is read as given, representing probabilistic conditioning. This rule contains a negated existential expression, $$\sim$$exists($$\cdots$$), that prevents two or more networks from being reported by a study at the same time. NeuroLang only allows stratified negation25. For a detailed description of Neurolang’s semantics, please refer to Zanitti et al.26.

We report the resulting functional profiles in Fig. 2. We observe that topics related to sensory processing of direct environmental demands such as eye movements, visual attention, and spatial orientation are more likely to appear in studies reporting activations in the DAN only. Also, we observe that topics related to cognitive control such as task switching, task demands, response inhibition, and performance monitoring are more likely to be mentioned in studies reporting activations in the FPCN. Finally, topics related to higher-order abstract cognitive and memory-related processes are mostly associated with studies reporting DMN activations only. Each probability value represents a ratio of the number of studies in which a topic is reported alongside an activation in only one network to the total number of studies that report activation only in that network.

### Meta-analysing the role of the visual word-form area in attention circuitry

The visual word-form area (VWFA) has attracted controversy over the years with recent findings suggesting it takes part in the attention circuitry not only in the language network27. Can this relationship be inferred solely from a meta-analysis of past studies that have reported activations in the left ventral occipitotemporal cortex without necessarily identifying it as the VWFA?

To answer this question, we write queries that infer the most probable topic associations among studies that report activations close to the VWFA region, while simultaneously reporting activations within regions of the attention network, but not reporting activations within regions of the language network.

To define regions corresponding to the VWFA, the dorsal attention and language networks, we use locations defined by Chen et al.27 and store them in a RegionSeedVoxel table. This table contains a row (xyzr) for each region r’s seed location (xyz). A database table NetworkRegion contains rows (nr) for each region r belonging to network n. A brain region is considered to be reported by a study if it reports a peak activation within $$10\,\text {mm}$$ of the region seed location. The choice of a $$10\,\text {mm}$$ radius was used to facilitate comparisons with the range of smoothing kernels that are typically used within meta-analyses. This is expressed in NeuroLang as:

where EUCLIDEAN is a built-in function that calculates the Euclidean distance between two locations in MNI space, and thus its value is assigned to a variable; The decision to use a function application and equality to express the EUCLIDEAN builtin function is purely a syntactic choice in order to make built-in-generated values readable. Furthermore, in this example, a network is considered to be reported by a study if it reports one of the network’s regions. In NeuroLang, this rule is:

Finally, to test our hypothesis, we use the following probability encoding rule

which calculates the probability of finding an association with topic t among studies that report the activation of both the VWFA and network n, but do not report the activation of any other network $$n_2$$, where $$n_2 \ne n$$. Because only two networks, language and attention, are present in the Network table, this rule simultaneously calculates the probabilities for each pair of networks, including one while segregating the other.

Results are shown in Table 1. Topic 32 was found to be significantly associated with studies that report activations within the VWFA and the attention network but that do not report activations within the ‘language’ network. This topic loads on terms related to object recognition—a task for which attention circuitry is essential28. This result suggests that the VWFA may play a role in attention, as studies that report its activations are significantly associated with object recognition, and supports the running hypothesis that the VWFA plays a role in processing multiple categories of visual stimuli27. We also observe a significant association with topic 21, which loads on terms related to the task of reading words—the putative role of the VWFA.

The opposite segregation query selects studies reporting the VWFA and the ‘language’ network but not reporting the attention network ($$N = 318$$). This analysis did not yield any significant topic association after correction for multiple comparisons. However, a similar topic association analysis, but without segregating studies that report activation in the attention network, does yield a significant association with topic 21, linked to the ‘reading words’ ($$\chi ^2(1, N =852) = 56.86, p_\text {FDR} = 0.000081$$). This result might have more than one explanation, but a plausible explanation could be the relative decrease in statistical power (i.e. smaller number of studies) in the segregation query compared to the non-segregation query.

### Inferring differential activation patterns within the FPCN using topic segregation queries

In this example, we perform forward inference using topic-based segregation queries to derive activation patterns within the frontoparietal cognitive control network (FPCN). As a major part of the multiple demand system29, the FPCN is associated with a large set of tasks, themselves belonging to disparate and overlapping cognitive processes such as working memory, memory retrieval, task switching, and semantic processing, to name a few. Moreover, there is evidence for a heterogeneous internal organization in the FPCN, whereby a different combination of regions may be involved in a different domain of control processing30. Thus, the goal of this example is to infer activation patterns within the FPCN predicted by the presence of topic terms related to one process and the simultaneous absence of topic terms related to other processes. In this sense, segregation queries can enhance the relative specificity of meta-analytic forward inferences by minimizing the amount of overlap amongst related topics.

From the set of 200 Neurosynth topics (version-5), we select five exemplar topics representing a subset of the cognitive processes often attributed to the FPCN, along with the loading values of studies on each topic. These topics are working memory, decision making, task set switching, semantic control, and memory retrieval23,29,31,32. Then, we express the following NeuroLang program which performs topic segregation queries, yielding an activation map for each topic separately. This program is written as follows:

We report the resulting topic-based activations within the FPCN in Fig. 3. The results of this segregation query show that the FPCN exhibits a varied activation profile across topics, corroborating previous findings of flexible adaptation of activity within this network as task demands change. Specifically, working memory and task set switching tends to activate, to some extent, spatially interleaved, frontal, and parietal regions of the FPCN network. Semantic processing, on the other hand, dominantly activates a left-lateralized ventral frontal regions. Finally, decision making and memory retrieval are associated with activation in the cingulo-medial portion of the FPCN, the pre-supplementary motor/dorsal anterior cingulate cortex (decision making), and a precuneus/posterior cingulate cortex network (memory retrieval).

### Inferring varying meta-analytic connectivity profiles of FPCN subnetworks

Recent findings suggest that the frontoparietal cognitive control network (FPCN) can be decomposed into sub-systems associated with disparate and overlapping mental processes. Dixon et al.7 studied two broad subsystems of the FPCN that also appear as separate networks in the influential 17-network model from Yeo et al.22. Using the same nomenclature, we label these two subsystems FPCN-A and FPCN-B. Dixon et al. observed preferential connectivity between FPCN-A and the default mode network (DMN), and between FPCN-B and the dorsal attention network (DAN). We reproduce these results by conducting a similar, but more compact, meta-analysis with NeuroLang.

For this analysis, we use the NeuroQuery33 database instead of Neurosynth. We express conditional probabilistic queries that include studies reporting activations in each of the two FPCN sub-networks. By contrasting their posterior probability maps, we identify a distinct meta-analytic connectivity pattern associated with each sub-network. Using the same probabilistic definition of network reported by studies as in the first example, we express a rule that calculates the coactivation pattern of each FPCN sub-network. In NeuroLang, we use the following rule to calculate the conditional probability of a region being reported given that a network is also reported

whose resulting ans table contains rows (rnp), where p is the probability of region r being reported active given that network n, where n is either FPCN-A or FPCN-B.

A likelihood-ratio test and an FDR correction ($$\alpha = 0.05$$) for multiple comparisons are used to identify statistically significant coactivating regions. To provide evidence that the results are not driven by one choice of studies, we estimate the conditional probabilities in 1000 random sub-samples of the NeuroQuery database (each sub-sample is 50% of the entire database). Note that statistical significance is determined in each of the 1000 sub-samples separately using the likelihood-ratio test.

In Fig. 4, we show scatter plots of the probabilities that each DiFuMo-256 brain region is active given activation of the FPCN-A or FPCN-B sub-networks are defined by Yeo 17-network parcellation. In the top right panel of Fig. 4, we show the results of regions that exhibit a statistically significant coactivation with at least one FPCN sub-network, based on a likelihood-ratio test. Statistical significance is assessed through sub-sampling of the NeuroQuery database In the left panel, regions are color-coded by their network membership according to the coarser Yeo 7-network parcellation to facilitate interpretation.

In general, regions belonging to the somatomotor, visual, and salience networks do not preferentially coactivate with either the FPCN-A or FPCN-B. In contrast, regions of the coarse FPCN show a dichotomy in their coactivations with either FPCN-A or FPCN-B. That is, meta-analysis supports the hypothesis that FPCN can be functionally divided into two sub-systems7. Importantly, we find a clearer dichotomy in the coactivation profiles of the DMN and the DAN with the FPCN sub-networks. On the one hand, 31 out of 32 DMN regions coactivate more with FPCN-A, while only one DMN region (a sub-region in the middle frontal gyrus) seem to exhibit a preferential coactivation with FPCN-B. In Fig. 5, we illustrate a meta-analytic coactivation contrast map between FPCN-A and FPCN-B, showing that the former coactivates to a greater extent with the core regions of the DMN, than does the latter. On the other hand, without indicating any preference, we observe that 21 out of 30 DAN regions exhibit statistically significant coactivations with FPCN-A, while 19 DAN regions show significant coactivations with FPCN-B. However, only 11 regions have a higher probability of activating, given an FPCN-B activation than FPCN-A, while the others have comparable probabilities of coactivating with either sub-networks. This is in line with the findings from Dixon et al.7, showing less distinction in the DAN with respect to coactivation with the FPCN sub-networks. Nonetheless, FPCN-B coactivates to a greater extent with the core regions of the DAN, the superior parietal lobule and frontal eye fields, than FPCN-A, as seen from the coactivation contrast map in Fig. 5.

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