TITLE:
A Graph-Theoretical and MRS-Based Mathematical Model of Glutamatergic Dysfunction in Schizophrenia
AUTHORS:
Duygu Gülşah Başaran Çevik, Mehmet Enver Analan, Şerife Büyükköse
KEYWORDS:
Schizophrenia, Glutamate, NMDA Receptor, GABA, Dopamine, Magnetic Resonance Spectroscopy, Graph Theory, Mathematical Modeling
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.16 No.3,
August
31,
2026
ABSTRACT: In this study, the effects of glutamatergic dysfunction on the dopaminergic system in schizophrenia are investigated using a graph-theoretical framework integrated with magnetic resonance spectroscopy (MRS) data. The classical dopamine hypothesis associates positive symptoms with increased mesolimbic dopamine activity and negative as well as cognitive symptoms with reduced mesocortical dopamine transmission. However, this hypothesis alone does not fully explain the upstream mechanisms responsible for dopaminergic dysregulation. Consequently, the glutamate hypothesis has emerged as a complementary framework emphasizing NMDA receptor hypofunction and impaired GABAergic inhibition. The proposed model represents cortical pyramidal neurons, GABAergic interneurons, the ventral tegmental area, the nucleus accumbens, and the prefrontal cortex as nodes of a directed weighted graph. Furthermore, glutamate, GABA, and total N-acetylaspartate (tNAA) measurements reported in ultra-high-field 7 Tesla MRS studies are incorporated into the mathematical framework. Based on these biomarkers, a schizophrenia connectivity index is introduced to quantify excitatory-inhibitory imbalance and neuronal integrity loss simultaneously. The obtained results suggest that reductions in glutamate and tNAA levels may contribute substantially to network instability and functional dysregulation in schizophrenia.