Distinct Contributions of the Cerebellum and Basal Ganglia to Arithmetic Procedures

Abstract

Humans exhibit complex mathematical skills attributed to the exceptional enlargement of neocortical regions throughout evolution. In the current work, we initiated a novel exploration of the ancient subcortical neural network essential for mathematical cognition. Using a neuropsychological approach, we report that degeneration of two subcortical structures, the cerebellum and basal ganglia, impairs performance in symbolic arithmetic. We identify distinct computational impairments in male and female participants with cerebellar degeneration (CD) or Parkinson's disease (PD). The CD group exhibited a disproportionate cost when the arithmetic sum increased, suggesting that the cerebellum is critical for iterative procedures required for calculations. The PD group showed a disproportionate cost for equations with increasing addends, suggesting that the basal ganglia are critical for chaining multiple operations. In Experiment 2, the two patient groups exhibited intact practice gains for repeated equations at odds with an alternative hypothesis that these impairments were related to memory retrieval. Notably, we discuss how the counting and chaining operations relate to cerebellar and basal ganglia function in other task domains (e.g., motor processes). Overall, we provide a novel perspective on how the cerebellum and basal ganglia contribute to symbolic arithmetic. Our studies demonstrate the constraints on the computational role of two subcortical regions in higher cognition.

Keywords: Parkinson's disease; arithmetic; ataxia; subcortex.

Figure 1.

A, RT as a function of sum for two-addend problems (left) and three-addend problems (right). Error bars = 95% confidence interval. B, The left panel shows the effect of complexity, defined as the difference in mean RT for the three- and two-addend problems. The right panel shows the effect of sum, defined as the slope of the function relating RT to the sum. Note that the data were log-transformed to fit the assumptions of the LME model. Thus, the values in this figure represent the difference between the conditions in log(RT). Dots indicate the performance of each individual participant. Error bars = SEM; *p < 0.001.

Figure 2.

A, RT as a function of learning cycle for the Repetition and No Repetition conditions. Error bars = 95% confidence interval. B, Rate of improvement across cycles for each group for the No Repetition (left) and Repetition (right) conditions. Dots indicate performance of each individual participant. Error bars = SEM; *p < 0.001.