Figure 1.
Results for more difficult mental arithmetic (e.g., 54+38 = ?).
Panel A reflects cortical regions showing increase of fMRI signal due to increasing values of the conjunction of unit sum as well as decade sum (uncorrected p-value of<.005, cluster size k = 10 voxels). Activated areas for magnitude-related processing include IPS, pIPS, BA 44, BA 45, BA 47, SMA, FEF, and the visual number form (VNF), most of them bilaterally. Panel B depicts identified pathways in a 3D volume rendering with PIBI values>0.0148. It can be observed that for more difficult mental arithmetic a system of both dorsal (SLF) and ventral (EC/emC) connections is recruited (depicted in red). Panel C gives a detailed view on the course of the fiber tracts in axial orientation (depicted in red), demonstrating a dorsal vs. ventral fiber pathway profile, encompassing the SLF system and the EC/EmC system. Abbreviations: BA = Brodmann area; EC = external capsule; EmC = extreme capsule; FEF = frontal eye fields; IPS = intraparietal sulcus; pIPS = posterior intraparietal sulcus; SLF = superior longitudinal fascicle; SMA = supplementary motor area.
Table 1.
Cortical regions activated significantly more due to either the conjunction of increasing or decreasing unit sum and decade sum.
Figure 2.
Results for relatively easier mental arithmetic (e.g., 14+3 = ?).
Panel A reflects cortical regions showing increase of fMRI signal due to decreasing values of the conjunction of unit sum as well as decade sum (uncorrected p-value of<.005, cluster size k = 10 voxels). Activated areas for fact-retrieval related processing include left AG, STG, MTG, insula, retro-splenial cortex (RC), and medial FG. Panel B shows identified pathways for easier mental arithmetic in a 3D volume rendering (PIBI values>0.0148) indicating prominently ventral (MdLF) connections (depicted in green). Furthermore, a dorsal connection via the cingulate bundle was tracked linking retro-splenial cortex with the medial frontal gyrus. Panel C again gives a detailed view on the course of the fiber tracts in axial orientation illustrating the prominently ventral fiber pathway profile. The ventral connection encompassed the MdLF and the more superior and medial part of the EC/EmC system (depicted in green). Abbreviations: AG = angular gyrus; cb = callosal bundle; medial FG = medial frontal gyrus; MdLF = middle longitudinal fascicle; MTG = middle temporal gyrus; RC = retrosplenial cortex; SMG = supramarginal gyrus; STG = superior temporal gyrus.
Table 2.
Seed regions and connections included. Seed regions were centered at the MNI coordinates given in parentheses.
Figure 3.
Overlay of fiber tracts identified for more difficult (red) and easier (blue) mental arithmetic.
Panel A gives a detailed view on the course of the fiber tracts in axial orientation. Two largely anatomically distinct dorsal vs. ventral fiber pathway profiles for the processing of more difficult (magnitude-related) and the easier (fact retrieval related) problems can be observed. Importantly, difficult mental arithmetic (depicted in red) and easier mental arithmetic (depicted in blue) seems to involve two largely separate networks differing not only in localization of activation but also in the connections between associated cortex areas. Additionally, the connection between the visual number form area (VNF) and the number magnitude representation (IPS/pIPS) is displayed in red. Panel B again reflects the identified pathways in a 3D volume rendering with PIBI values>0.0148. Finally, Panel C depicts a detailed view on the course of the fiber tracts in coronal orientation, illustrating that easier mental arithmetic encompasses the EC/EmC system more superiorly and medially (depicted in blue), whereas more difficult mental arithmetic recruits more inferior and lateral components of the EC/EmC system (depicted in red).Abbreviations: AG = angular gyrus; IPS = intraparietal sulcus; pIPS = posterior intraparietal sulcus; VNF = visual number form.
Figure 4.
Inter-hemispheric tracking of the connection of the bi-hemispheric representation of number magnitude in intraparietal cortices.
Panel A depicts the transcallosal bundle of fibers directly connecting left and right intraparietal cortices in a 3D volume rendering with PIBI values>0.0148. Panel B gives a detailed view on the course of the fiber tracts in coronal orientation.Abbreviations: IPS = intraparietal sulcus; pIPS = posterior intraparietal sulcus; PSPL = posterior superior parietale lobule.
Figure 5.
Hypothetical model capturing the interplay between magnitude-related processing and arithmetic fact retrieval.
The figure depicts an interaction model: Basic fact retrieval related processing is assumed to be involved even in difficult arithmetic, for instance to retrieve partial results from long term memory. However, in easier tasks a larger variable component of fact retrieval may be recruited, whereas in more difficult tasks more and more magnitude-related processing is assumed.