This study aimed to investigate whether neurological patients presenting with a bias in line bisection show specific problems in bisecting a line into two equal parts or their line bisection bias rather reflects a special case of a deficit in proportional reasoning more generally. In the latter case, the bias should also be observed for segmentations into thirds or quarters. To address this question, six neglect patients with a line bisection bias were administered additional tasks involving horizontal lines (e.g., segmentation into thirds and quarters, number line estimation, etc.). Their performance was compared to five neglect patients without a line bisection bias, 10 patients with right hemispheric lesions without neglect, and 32 healthy controls. Most interestingly, results indicated that neglect patients with a line bisection bias also overestimated segments on the left of the line (e.g., one third, one quarter) when dissecting lines into parts smaller than halves. In contrast, such segmentation biases were more nuanced when the required line segmentation was framed as a number line estimation task with either fractions or whole numbers. Taken together, this suggests a generalization of line bisection bias towards a segmentation or proportional processing bias, which is congruent with attentional weighting accounts of line bisection/neglect. As such, patients with a line bisection bias do not seem to have specific problems bisecting a line, but seem to suffer from a more general deficit processing proportions.

In acute stroke patients, arithmetic fact retrieval deficits have been observed due to disrupted white matter connections within a left-hemispheric network centered around the angular gyrus and middle temporal gyrus (Smaczny et al., 2023). However, it remains unclear which specific structural disconnections also hinder successful remediation in the chronic stage of stroke. In this study, 92 patients were examined to determine which impairments continue to affect multiplication performance even in the chronic phase after a first-time unilateral left-hemispheric stroke. Our results revealed a strong association between impaired multiplication performance and the disconnection of left long-term memory (para)hippocampal areas from left frontal and right parietal regions. Thus, unlike previous findings in the acute stroke phase, our results in the chronic phase emphasize the importance of (para)hippocampal regions for successful multiplication performance. We suggest that the affected areas and connections in chronic patients with persistent multiplication problems not only indicate areas that are crucial for the relearning of arithmetic facts, but also those crucial for the learning of arithmetic facts in general. More generally, we suggest that the acquisition of arithmetic facts depends on structural integrity of a network centered around the left (para)hippocampus, while the retrieval of consolidated arithmetic facts from memory relies on the integrity of a left-hemispheric network involving angular gyrus and middle temporal gyrus.