Hybrid Ornstein-Uhlenbeck-Branching Modeling of Pediatric Leukemia Evolution: A Computational Extension and Cohort-Level Application

Pediatric cancers evolve under developmental constraints that limit mutational diversity yet preserve adaptive potential. A computational extension of the Hybrid Ornstein-Uhlenbeck (OU)-Branching framework was developed to model clonal diversification and phenotypic stabilization in pediatric leukemia. The OU component captures mean-reverting dynamics representing developmental homeostasis, while the branching component introduces stochastic lineage bifurcation and extinction. Using de-identified clinical metadata from Ahlgren et al. (Nature Communications, 2025; 16:8964), the model simulates patient-specific evolutionary trajectories across relapse categories and disease subtypes (B-ALL, T-ALL, MPAL, AML). Simulations reproduce observed clinical trends--rapid relapse and limited diversification in early or refractory KMT2A-r ALL, and slower, therapy-resistant relapses in AML. Group- and patient-level analyses demonstrate how the balance between stabilizing selection ({theta}) and diversification rate ({lambda}) determines clonal persistence and phenotypic drift. This computational implementation provides a quantitative framework for linking developmental constraint, clonal diversity, and therapeutic response in pediatric malignancies and establishes a tractable platform for model-driven hypothesis testing and translational oncology. Statement of Relationship to Prior WorkThis preprint represents a computational and cohort-level extension of the hybrid OU-Branching framework introduced in the authors manuscript currently under review at Frontiers in Oncology ("A hybrid Ornstein-Uhlenbeck-branching framework unifies microbial and pediatric tumor evolution," Manuscript ID 1727973). The Frontiers paper focuses on experimental validation and cross-domain analogies between microbial long-term evolution experiments (LTEE) and pediatric tumor evolution, emphasizing biological interpretation. In contrast, this preprint focuses on clinical modeling, patient specific simulations, and computational methods applied to pediatric KMT2A-rearranged leukemia. No data, text, or figures are duplicated from the in-review article. All code and simulations presented here are novel and will be released upon publication.