Judgments of spatial relationships are often made when the object or observer are moving. Behaviourally, there is evidence that these ‘dynamic’ judgments of spatial extent differ from static judgments. Here I used three separate techniques for exploring dynamic judgments: first, a line bisection paradigm was employed to study ocular and pointing judgments of spatial extent while manipulating line length, position, speed, acceleration, and direction of scanning (Experiments 1-4); second, functional MRI (fMRI) was used to examine whether distinct brain regions were involved in dynamic versus static judgments of spatial extent (Exp 5); and finally, a mathematical and computational model of dynamic judgments was developed to provide a framework for interpreting the experimental results. In the behavioural experiments, substantial differences were seen between static and dynamic bisection, suggesting the two invoke different neural processes for computing spatial extent. Surprisingly, ocular and pointing judgments produced distinct bisection patterns that were uncorrelated, with pointing somewhat more impervious to manipulations such as scan direction and position than ocular bisections. However, a new experimental task for probing dynamic judgments (the ‘no line’ Experiment 4) found that scan direction can influence both hand behaviour. Functional MRI demonstrated that dynamic relative to static judgments produced activations in the cuneus and precuneus bilaterally, left cerebellum, and medial frontal gyrus, with reduced activation relative to static judgments observed in the supramarginal gyrus bilaterally. Dynamic bisections relative to a control condition produced activations in the right precuneus and left cerebellum, as well as in left superior parietal lobule, left middle temporal gyrus, and right precentral gyrus. It may be the case that velocity processing and temporal estimates are integrated primarily in the cuneus and precuneus bilaterally to produce estimates of spatial extent under dynamic scanning conditions. These results highlight the fact that dynamic judgments of spatial extent engage brain regions distinct from those employed to make static judgments, supporting the behavioural results that these are separate and distinct. Finally, a mathematical model was proposed for dynamic judgments of spatial extent, based on the idea that, rather than using an ‘all-or-none’ approach, spatial working memory actually takes about 100 ms to reach full representational strength for any given point in space. The model successfully explains many of the effects seen in the behavioural experiments including the effects of scan direction, velocity, line length, and position. In conjunction with the neuroimaging data, it also suggests why neglect patients may fail to show rightward bisection biases when making dynamic judgments of spatial extent. Overall, this work provides novel insights into how the brain executes dynamic judgments of spatial extent.

Judgments of spatial relationships are often made when the object or observer are moving. Behaviourally, there is evidence that these ‘dynamic’ judgments of spatial extent differ from static judgments. Here I used three separate techniques for exploring dynamic judgments: first, a line bisection paradigm was employed to study ocular and pointing judgments of spatial extent while manipulating line length, position, speed, acceleration, and direction of scanning (Experiments 1-4); second, functional MRI (fMRI) was used to examine whether distinct brain regions were involved in dynamic versus static judgments of spatial extent (Exp 5); and finally, a mathematical and computational model of dynamic judgments was developed to provide a framework for interpreting the experimental results. In the behavioural experiments, substantial differences were seen between static and dynamic bisection, suggesting the two invoke different neural processes for computing spatial extent. Surprisingly, ocular and pointing judgments produced distinct bisection patterns that were uncorrelated, with pointing somewhat more impervious to manipulations such as scan direction and position than ocular bisections. However, a new experimental task for probing dynamic judgments (the ‘no line’ Experiment 4) found that scan direction can influence both hand behaviour. Functional MRI demonstrated that dynamic relative to static judgments produced activations in the cuneus and precuneus bilaterally, left cerebellum, and medial frontal gyrus, with reduced activation relative to static judgments observed in the supramarginal gyrus bilaterally. Dynamic bisections relative to a control condition produced activations in the right precuneus and left cerebellum, as well as in left superior parietal lobule, left middle temporal gyrus, and right precentral gyrus. It may be the case that velocity processing and temporal estimates are integrated primarily in the cuneus and precuneus bilaterally to produce estimates of spatial extent under dynamic scanning conditions. These results highlight the fact that dynamic judgments of spatial extent engage brain regions distinct from those employed to make static judgments, supporting the behavioural results that these are separate and distinct. Finally, a mathematical model was proposed for dynamic judgments of spatial extent, based on the idea that, rather than using an ‘all-or-none’ approach, spatial working memory actually takes about 100 ms to reach full representational strength for any given point in space. The model successfully explains many of the effects seen in the behavioural experiments including the effects of scan direction, velocity, line length, and position. In conjunction with the neuroimaging data, it also suggests why neglect patients may fail to show rightward bisection biases when making dynamic judgments of spatial extent. Overall, this work provides novel insights into how the brain executes dynamic judgments of spatial extent.