Path Complexity in Virtual Water Maze Navigation: Differential Associations with Age, Sex, and Regional Brain Volume

Abstract

Studies of human navigation in virtual maze environments have consistently linked advanced age with greater distance traveled between the start and the goal and longer duration of the search. Observations of search path geometry suggest that routes taken by older adults may be unnecessarily complex and that excessive path complexity may be an indicator of cognitive difficulties experienced by older navigators. In a sample of healthy adults, we quantify search path complexity in a virtual Morris water maze with a novel method based on fractal dimensionality. In a two-level hierarchical linear model, we estimated improvement in navigation performance across trials by a decline in route length, shortening of search time, and reduction in fractal dimensionality of the path. While replicating commonly reported age and sex differences in time and distance indices, a reduction in fractal dimension of the path accounted for improvement across trials, independent of age or sex. The volumes of brain regions associated with the establishment of cognitive maps (parahippocampal gyrus and hippocampus) were related to path dimensionality, but not to the total distance and time. Thus, fractal dimensionality of a navigational path may present a useful complementary method of quantifying performance in navigation.

Keywords: age; brain; fractal dimensionality; hippocampus; spatial navigation.

© The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Figures

Figure 1.

Three example paths are shown with calculated FD, path length (virtual units), and travel time (s). Example paths (A and B) show that low fractal dimensionality (approaching 1) can occur in long paths, whereas (C) demonstrates an increasingly random search pattern (FD approaching 2).

Figure 2.

Age distribution of the sample.

Figure 3.

The figures depict age differences in average time (A; r = 0.23, P = 0.01), distance (B; r = 0.51, P < 0.001), and FD (C; r = 0.52, P < 0.001) across the 6 learning trials. Error bars represent standard error of the mean.

Figure 4.

The figure shows the average change in time (A; P = 0.02), distance (B; P = 0.01), and FD (C; P = 0.09) across the 6 learning trials. Error bars represent standard error of the mean.

Figure 5.

The scatter plot and regression of the relationship between fractal dimensionality on trial 1 and hippocampal volume. Gray circles mark data points that were winsorized.