Research Protocol - Validation of Topological Saturation (v7c Model) as a Predictor of Hemodynamic Collapse and Mortality in Sepsis: A Retrospective Cohort Study in MIMIC‑III

Background Septic shock is preceded by autonomic, microcirculatory, and metabolic derangements that may not be captured by conventional linear monitoring. We hypothesize that a waveform-derived composite state—Topological Saturation—captures early loss of physiologic complexity alongside rising metabolic effort and can anticipate hemodynamic collapse. Methods Retrospective cohort study using MIMIC‑III Clinical Database v1.4 linked to the MIMIC‑III Waveform Database Matched Subset v1.0. Adults meeting Sepsis‑3 criteria will be included if they have continuous ECG lead II and invasive arterial blood pressure (ABP) for ≥ 4 hours preceding the index event (T0: vasopressor initiation or sustained MAP < 65 mmHg for ≥ 15 minutes). In 5‑minute sliding windows we will compute: normalized heart rate energy E(t) = HR/HRmax (HRmax = 208 − 0.7×age), sample entropy C(t) (SampEn, m = 2, r = 0.2×SD) of the R–R series, and the Conatus Effort Index I_v7c = E/C². Short‑term prediction will test whether I_v7c and dI_v7c/dt predict collapse ≥ 30 minutes in advance versus the shock index and baseline lactate. Long‑term outcomes include 28‑day mortality and 24‑hour norepinephrine‑equivalent vasopressor exposure. Expected results and falsifiability: We pre‑specify quantitative targets (e.g., AUC(I_v7c) ≥0.78 at 30 minutes and ΔAUC ≥0.03 vs shock index). Failure to meet discrimination targets, absence of a reproducible MAP–I_v7c plateau in high‑effort ranges, and lack of adjusted association with mortality will be treated as refutation of this operational translation of the v7c saturating-law template in this clinical domain.