  Task difficulty is widely cited in current theory regarding cognitive control
and fronto-parietal function. Ongoing debate surrounds the extent to which
global difficulty across multiple cognitive demands is the main driver of
lateral frontal activity. Here, we examine a commonly cited behavioral marker
of difficulty in these accounts: time-on-task (ToT), as assessed by response
time. Specifically, we investigate the task-dependent scaling of frontal BOLD
responses with ToT during hierarchical cognitive control. We observe a
paradoxical relationship, whereby rostral regions show greater scaling with ToT
on a first-order task, despite showing greater recruitment on a second-order
task; caudal regions show the converse relationships. Together, these results
demonstrate that ToT does not reflect a single dimension of difficulty that
uniformly drives lateral frontal activity. Rather, this discrepancy in the mean
and scaling of BOLD requires that multiple, distinct processes are instantiated
across these fronto-parietal regions in the service of cognitive control
function.
