[Paper Review] Nonlinear functional mapping of the human brain

Nicholas Allgaier, Tobias Banaschewski+28 more|arXiv (Cornell University)|Sep 8, 2015

Functional Brain Connectivity Studies7 references3 citations

TL;DR

This paper introduces Nonlinear Functional Mapping (NFM), a machine learning method using symbolic regression and genetic programming to discover nonlinear interactions among brain regions of interest (ROIs) in resting-state fMRI data without assuming linearity. It reveals that drinkers show stronger, nonlinear coupling in emotion, reward, and interoceptive processing networks—particularly involving the left globus pallidus and fornix body—than non-drinkers, a pattern missed by standard correlation analysis.

ABSTRACT

The field of neuroimaging has truly become data rich, and novel analytical methods capable of gleaning meaningful information from large stores of imaging data are in high demand. Those methods that might also be applicable on the level of individual subjects, and thus potentially useful clinically, are of special interest. In the present study, we introduce just such a method, called nonlinear functional mapping (NFM), and demonstrate its application in the analysis of resting state fMRI from a 242-subject subset of the IMAGEN project, a European study of adolescents that includes longitudinal phenotypic, behavioral, genetic, and neuroimaging data. NFM employs a computational technique inspired by biological evolution to discover and mathematically characterize interactions among ROI (regions of interest), without making linear or univariate assumptions. We show that statistics of the resulting interaction relationships comport with recent independent work, constituting a preliminary cross-validation. Furthermore, nonlinear terms are ubiquitous in the models generated by NFM, suggesting that some of the interactions characterized here are not discoverable by standard linear methods of analysis. We discuss one such nonlinear interaction in the context of a direct comparison with a procedure involving pairwise correlation, designed to be an analogous linear version of functional mapping. We find another such interaction that suggests a novel distinction in brain function between drinking and non-drinking adolescents: a tighter coupling of ROI associated with emotion, reward, and interoceptive processes such as thirst, among drinkers. Finally, we outline many improvements and extensions of the methodology to reduce computational expense, complement other analytical tools like graph-theoretic analysis, and allow for voxel level NFM to eliminate the necessity of ROI selection.

Motivation & Objective

• Address the growing need for data-driven, nonlinear analytical methods in neuroimaging that can operate at the individual subject level.
• Overcome limitations of traditional linear models (e.g., GLM, correlation) that fail to detect complex, nonlinear interactions among brain regions.
• Identify and characterize nonlinear functional relationships among ROIs in resting-state fMRI data from a large adolescent cohort.
• Explore the clinical relevance of these nonlinear interactions, particularly in relation to behavioral phenotypes such as alcohol use.
• Develop a framework that can be extended to voxel-level analysis and integrated with other neuroimaging tools like graph theory.

Proposed method

• Employ symbolic regression via genetic programming (GP) to discover mathematical expressions modeling nonlinear interactions between time series of ROI signals.
• Use a proprietary GP tool (Eureqa) to evolve functional models that best predict one ROI’s signal from a combination of others, without assuming linearity.
• Generate interaction relationship (IR) maps for each subject by performing multiple random restarts of the GP algorithm across all ROIs.
• Apply statistical analysis to IR maps across the cohort to identify consistent, significant nonlinear interaction patterns.
• Compare results with a linear analog—pairwise correlation analysis—to highlight nonlinear effects missed by conventional methods.
• Explore hybrid approaches (e.g., FFX + GP) to reduce computational cost and enable future voxel-level analysis.

Experimental results

Research questions

• RQ1 Can nonlinear functional mapping (NFM) detect complex, non-linear interactions among brain regions in resting-state fMRI that are undetectable with linear methods?
• RQ2 Do nonlinear interactions in brain networks differ meaningfully between adolescents who drink alcohol and those who do not?
• RQ3 Can NFM identify biologically and clinically relevant functional relationships in brain circuits related to emotion, reward, and interoception?
• RQ4 How do the interaction patterns revealed by NFM compare to those found using standard linear correlation analysis?
• RQ5 To what extent can NFM be scaled to larger ROI sets or voxel-level data, and what computational optimizations are needed?

Key findings

• Nonlinear functional mapping (NFM) successfully identifies complex, nonlinear interactions among brain regions in resting-state fMRI data, with nonlinear terms being ubiquitous in the derived models.
• A significant nonlinear interaction between the left globus pallidus (ROI 6) and fornix body (ROI 18) is stronger among drinkers than non-drinkers, a difference undetected by pairwise correlation.
• Among non-drinkers, the functional connectivity within a network involving ROI 3, 18, 5, and 6 breaks down, with ROI 3 and 18 decoupled from the bilateral globus pallidus (ICN 3), suggesting a structural reorganization.
• The interaction strength between ROI 3, 18, 5, and 6 is twice as strong in non-drinkers compared to drinkers, indicating a more integrated network in non-drinkers.
• The NFM approach detects a functional distinction in emotion, reward, and interoceptive processing circuits between drinkers and non-drinkers, highlighting a novel, nonlinear neural signature of alcohol use.
• The method’s results show strong consistency with independent neurobiological findings, such as the role of the fornix in interoceptive processing, providing preliminary cross-validation.