The dimensionalities of lesion-deficit mapping

Lesion-deficit mapping remains the most powerful method for localising function in the human brain. As the highest court of appeal where competing theories of cerebral function conflict, it ought to be held to the most stringent inferential standards. Though at first sight elegantly transferable, the mass-univariate statistical framework popularized by functional imaging is demonstrably ill-suited to the task, both theoretically and empirically. The critical difficulty lies with the handling of the data's intrinsically high dimensionality. Conceptual opacity and computational complexity lead lesion-deficit mappers to neglect two distinct sets of anatomical interactions: those between areas unified by function, and those between areas unified by the natural pattern of pathological damage. Though both are soluble through high-dimensional multivariate analysis, the consequences of ignoring them are radically different. The former will bleach and coarsen a picture of the functional anatomy that is nonetheless broadly faithful to reality; the latter may alter it beyond all recognition. That the field continues to cling to mass-univariate methods suggests the latter problem is misidentified with the former, and that their distinction is in need of elaboration. We further argue that the vicious effects of lesion-driven interactions are not limited to anatomical localisation but will inevitably degrade purely predictive models of function such as those conceived for clinical prognostic use. Finally, we suggest there is a great deal to be learnt about lesion-mapping by simulation-based modelling of lesion data, for the fundamental problems lie upstream of the experimental data themselves.