Topological Scission and Dirichlet Boundary Confinement in High-Risk Surgical Resection: A Deterministic Model for Preventing Cascading Organ Failure

Abstract

While current perioperative risk models rely on foundational stochastic probabilities, these classical approaches encounter structural limitations when predicting cascading multi-organ failure during highly coupled, high-risk surgical interventions. This paper introduces a next-generation architecture for computational surgical planning by translating the patient's macroscopic physiological network into the Chrysene Tensor Space, defined as a discrete, fibrated three-dimensional topological manifold. To accurately bound physiological resilience, the framework evolves beyond standard deviation and Z-score metrics, utilizing rigid Dirichlet boundary conditions evaluated via the L-infinity norm. The physical act of surgical resection is formally defined as the Topological Scission Operator, which mathematically decouples the geometric spatial connectivity vector between tissue nodes. The subsequent diffusion of hemodynamic and structural shock is calculated deterministically, elevating the definition of irreversible tissue necrosis from historical morbidity approximations to a state defined strictly by the invariant Dirichlet bornology. We establish that by continuously minimizing spatial Hamiltonian overlap, the surgical pathway rigorously ensures that kinetic strain remains safely bounded below localized Dirichlet capacities. Furthermore, we prove that this preoperative containment methodology is bijectively isomorphic to an H-infinity min-max robust control optimization. Utilizing a next-generation Clinical Decision Support System (CDSS), this framework elevates high-risk surgical intervention from a probabilistic heuristic into a mathematically structured topological phase transition, securing patient survival through absolute spatial and geometric boundaries.