A Unified Bio-Electro-Immuno-Ontogenic-Pathome Framework for the Pathogenesis of Tourette Syndrome: Mathematical Modeling, Bayesian Evidence Synthesis, and Falsifiability Analysis

Tourette syndrome (TS) is a complex neurodevelopmental disorder clinically characterized by persistent motor and vocal tics. Despite decades of intense neurobiological research, the precise etiology remains elusive, with multiple, often disparate, causal pathways postulated. This paper presents a rigorous conceptual and mathematical synthesis of thirteen potential causal factors, ranging from dopaminergic-serotonergic imbalances and microscopic white-matter deformities to sympathetic-immune cross-talk and prion-like proteinopathy. We formulate a unified Bio-Electro-Immuno-Ontogenic-Pathome (BIEOP) framework, conceptualizing the cortico-basal ganglia-thalamo-cortical (CBGTC) loop as a stochastic dynamical system perturbed by these diverse factors. Exact Langevin equations are derived, parameterized utilizing published clinical and neuroimaging data, and simulated via custom algorithms. Bayesian hierarchical modeling is subsequently employed to systematically quantify the posterior probability of each causal hypothesis, conditioned on multi-modal biomarkers and simulated tic severity. Global sensitivity analysis, via Sobol' indices, reveals that dopaminergic gain and microstructural impedance mismatch dictate the system's dynamics, jointly accounting for over 70% of output variance. To ensure scientific rigor, explicit falsification criteria are established for each mechanistic hypothesis, enabling prospective empirical testing. All code and synthetic data utilized in this work are provided to ensure complete reproducibility. Ultimately, this framework successfully aligns disparate etiologies, offering a cohesive roadmap for personalized diagnostic evaluation and targeted intervention strategies.