Interpreting and Utilising Intersubject Variability in Brain Function

Abstract

We consider between-subject variance in brain function as data rather than noise. We describe variability as a natural output of a noisy plastic system (the brain) where each subject embodies a particular parameterisation of that system. In this context, variability becomes an opportunity to: (i) better characterise typical versus atypical brain functions; (ii) reveal the different cognitive strategies and processing networks that can sustain similar tasks; and (iii) predict recovery capacity after brain damage by taking into account both damaged and spared processing pathways. This has many ramifications for understanding individual learning preferences and explaining the wide differences in human abilities and disabilities. Understanding variability boosts the translational potential of neuroimaging findings, in particular in clinical and educational neuroscience.

Keywords: brain structure; cognitive strategies; covariance; functional variability; individualised predictions; neuroimaging.

Figure I

The 6D Output of a Typical Multisubject Experiment.

Figure I

Averaging Images with Variable Features.

Figure II

Cumulative Sums of Integers via Three Possible Strategies.

Figure 1

Key Figure: Individual-Specific Brain Parameterization and Variability in Brain Function The brain is a dynamical system that is plastic and noisy. The changes in brain status over time are a function of its current state, the current environment or inputs, and the particular parameterisation (i.e., illustrated by the vector of parameters ‘θ’). The perpetual action of many variables generates noise that fluctuates in time . For example, noise can lead to transitions between coexisting deterministic stable states or attractors , and, perhaps more interestingly, noise can induce new stable states that have no deterministic counterparts . Each observed individual functional map is in essence the system output under a particular parameterisation for that individual. This parameterisation impacts upon cognitive states (cognitive strategies, learning styles, and expectations) and mood states (familiarity, cooperation, motivation, and stress). Because not all parameters are independent, we can reasonably assume that the number of true free parameters (i.e., degrees of freedom) is smaller. Decoding variability between subjects allows the range of some parameters ‘θ’ to be estimated. The exact modelling (e.g. generative/forward models) of this multi-input/multi-output system at the neuronal and physiological level is proving to be increasingly plausible , .

Figure 2

Segregation of Networks with Across-Subject Covariance Analyses. The figure illustrates the use of covariance analysis to segregate different networks associated with different strategies. Basically, if different personal biases for particular cognitive strategies exist, they can be distinguished from random errors by looking at similarity across brain regions in the between-subject variance. Top: different neuronal systems that can sustain the same task are dissociated using (clustering) algorithms that cluster together voxels if their associated deviations covary across subjects. Δ is the set of individual deviations from the population average. S_i is an activation summary of subject i, like an effect size, after collapsing the data across time or scans, and Δ_i codes potential biases including the personal bias of subject i to a particular cognitive strategy. Each Δ_i is a whole-brain map (for subject i), and ε codes inconsistent (measurement) noise. For example, Δ (in its simplest form) can represent a set of residuals from a group (mean) analysis, or a set of eigenimages after running a principal components analysis. Bottom: some of the networks that were segregated for a semantic matching task using an unsupervised fuzzy clustering algorithm (illustrated as red-to-yellow clusters projected on anatomical axial slices). In this example, subjects were asked to indicate with a button press if visually presented words were semantically related or not. Voxels were clustered together if their associated deviations covaried across subjects. This clustering revealed many networks, including motor, visual, semantic, default mode and oculomotor networks. More details about this example can be found elsewhere .