The middle house or the middle floor: bisecting horizontal and vertical mental number lines in neglect

Abstract

This study explores the processing of mental number lines and physical lines in five patients with left unilateral neglect. Three tasks were used: mental number bisection ('report the middle number between two numbers'), physical line bisection ('mark the middle of a line'), and a landmark task ('is the mark on the line to the left/right or higher/lower than the middle of the line?'). We manipulated the number line orientation purely by task instruction: neglect patients were told that the number-pairs represented either houses on a street (horizontal condition) or floors in a building (vertical condition). We also manipulated physical line orientation for comparison. All five neglect patients showed a rightward bias for horizontally oriented physical and number lines (e.g. saying 'five' is the middle house number between 'two' and 'six'). Only three of these patients also showed an upward bias for vertically oriented number lines. The remaining two patients did not show any bias in processing vertical lines. Our results suggest that: (1) horizontal and vertical neglect can associate or dissociate among different patients; (2) bisecting number lines operates on internal horizontal and vertical representations possibly analogous to horizontal and vertical physical lines; (3) at least partially independent mechanisms may be involved in processing horizontal and vertical number lines.

Fig. A.1

Typical trial sequence for one block in Experiment 2, illustrating the function of the adaptive algorithm (patient 4 in horizontal condition) for each of the quadrants of stimulus presentation. The landmark switches between leftwards and rightwards offsets (negative and positive values on the y-axis, respectively) each time the subject's ‘left’ vs. ‘right’ responses change, making progressively smaller increments with each successive switch, until finally converging on the subjective midpoint at which either of the ‘left’ or ‘right’ responses were equally likely. In this example the convergence points are shifted towards the right of the horizontal line.

Fig. A.2

An example stimulus used in the landmark task. The dot indicates where participants should fixate their gaze. The four numbers indicate the possible positions in one of four quadrants of the screen (upper left, upper right, lower left and lower right), fixed at 1.15° eccentricity from central fixation. The veridical midpoint of each long line was always centred on one of these four positions (measured not in scale).

Fig. A.3

Psychometric functions and least-square fits for the two patients tested with Experiment 3. See Appendix B for detailed explanation.

Fig. 1

The patients’ brain scan.

Fig. 2

Mental number bisection task (Task 1). Patients’ and control subjects’ deviations from the veridical midpoint in horizontal (A) and vertical (B) number lines in units.

Fig. 3

Physical line bisection task (Task 2). Patients’ and control subjects’ deviations from the veridical midpoint in horizontal (A) and vertical (B) physical lines in cm.

Fig. 4

Estimated PSE values and their 95% confidence limits for patients 1 and 4 and control subjects. Separate data-points are shown for horizontal and vertical line conditions, pooled across quadrants and blocks.