Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

First Advisor

Chris M. Danforth

Second Advisor

Peter S. Dodds


The field of neuroimaging has truly become data rich, and as such, 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 this dissertation we introduce just such a method, called nonlinear functional mapping (NFM), and demonstrate its application in the analysis of resting state fMRI (functional Magnetic Resonance Imaging) from a 242-subject subset of the IMAGEN project, a European study of risk-taking behavior in adolescents that includes longitudinal phenotypic, behavioral, genetic, and neuroimaging data.

Functional mapping 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. 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. One such nonlinear interaction is discussed in the context of a direct comparison with a procedure involving pairwise correlation, designed to be an analogous linear version of functional mapping. Another such interaction suggests a novel distinction in brain function between drinking and non-drinking adolescents: a tighter coupling of ROI associated with emotion, reward, and interceptive 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 possibly allow for voxel level functional mapping to eliminate the necessity of ROI selection.



Number of Pages

75 p.