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

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 | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Method Article 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and Mortality in Sepsis: A Retrospective Cohort Study in MIMIC‑III Vicente Merino Gallardo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8903117/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract 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. Critical Care & Emergency Medicine sepsis septic shock hemodynamic collapse heart rate variability sample entropy complexity microcirculation MIMIC‑III waveform analytics prediction model Figures Figure 1 Figure 2 Figure 3 1. Introduction and justification Sepsis and septic shock remain major causes of morbidity and mortality in critical care, and contemporary management emphasizes early recognition, timely antimicrobials, source control, and hemodynamic resuscitation with vasopressors to maintain adequate perfusion pressure, typically targeting MAP ≥ 65 mmHg [ 1 ]. Yet sustained hypotension and vasopressor requirement often represent a late stage of physiological decompensation. Physiological systems show multiscale variability; during critical illness, complexity can collapse as regulatory degrees of freedom are lost [ 8 , 9 ]. Heart rate variability (HRV) is a key marker of autonomic regulation with standardized measurement guidance [ 10 ]. In sepsis, depressed HRV and reduced entropy have been associated with higher inflammatory burden, declining blood pressure, and worse outcomes [ 14 – 21 ]. Meanwhile, microcirculatory derangements may persist despite apparently adequate macrocirculatory targets, challenging hemodynamic coherence and motivating richer monitoring paradigms [ 2 ]. The CUCE v7c framework introduces a mathematically explicit saturating law in which an effective coupling approaches a bounded ceiling and transitions into a plateau regime as a system nears a critical scale (E*) [ 28 ]. This protocol proposes a strictly operational (non‑literal) translation: when cardiovascular reserve is failing, R–R dynamics may become more regular (lower entropy/complexity) while metabolic effort increases (tachycardia), yielding a composite state—Topological Saturation—that could anticipate hemodynamic collapse earlier than conventional linear markers. 2. Theoretical framework 2.1 Complexity loss and autonomic failure in sepsis Reduced variability and entropy in physiological time series are consistently reported in critical illness and have been proposed as markers of reduced adaptive capacity [ 8 , 9 ]. HRV provides a window into autonomic regulation and has internationally accepted standards for acquisition and interpretation [ 10 ]. Multiple studies have linked depressed HRV and reduced entropy to severity and outcome in sepsis, including emergency department and ICU cohorts [ 14 – 21 ]. 2.2 Sample entropy as an operational complexity metric Sample entropy (SampEn) quantifies the irregularity of time series and is widely used in physiology; canonical methodological formulations specify m = 2 and r scaled to the series SD [ 11 , 12 ]. Artifact characterization and filtering are crucial when working with R–R tachograms [ 13 ]. 2.3 Operational definition of Topological Saturation We operationalize Topological Saturation using (i) metabolic effort via normalized HR energy E(t), (ii) complexity via SampEn C(t), and (iii) a plateau behavior of MAP versus I_v7c in high-effort regions. The Conatus Effort Index is defined as I_v7c = E/C², emphasizing that rising effort combined with shrinking complexity yields disproportionately larger I_v7c. 2.4 v7c saturating-law template as a hypothesis generator CUP‑Ω* v7c implements bounded saturation through a tanh functional calculus that produces plateau-like behavior near a critical scale [ 28 ]. This protocol does not claim mechanistic identity between open‑quantum‑system saturation and cardiovascular physiology. Instead, the v7c saturating form is used as a falsifiable template for detecting plateau-like behavior in a composite physiologic effort index before shock. 2.5 Reporting standards We will report this retrospective observational study following STROBE guidance and the prediction‑model component following TRIPOD recommendations [ 26 , 27 ]. 3. Objectives 3.1 Primary objective To determine whether the Conatus Effort Index (I_v7c) and its time derivative (dI_v7c/dt) predict hemodynamic collapse (MAP < 65 mmHg sustained and/or vasopressor initiation) at least 30 minutes in advance in septic ICU patients. 3.2 Secondary objectives To evaluate the association between Topological Saturation status at shock onset (T0) and 28‑day all‑cause mortality. To correlate pre‑T0 I_v7c trajectory features with total vasopressor exposure in the first 24 hours, expressed as a norepinephrine‑equivalent dose (NED). To test whether I_v7c outperforms the shock index (HR/SBP) and baseline serum lactate in short‑term prediction of collapse. To assess robustness via subgroup and sensitivity analyses (alternative definitions and exclusion criteria). 4. Materials and methods 4.1 Study design and data sources Retrospective, observational cohort study using the MIMIC‑III Clinical Database v1.4 linked to the MIMIC‑III Waveform Database Matched Subset v1.0 [ 5 , 6 ]. PhysioNet provides the waveform infrastructure and distribution for these resources [ 7 ]. 4.2 Target population and sepsis definition (Sepsis‑3) Eligible admissions will be adult ICU stays (≥ 18 years) meeting Sepsis‑3 criteria: suspected infection plus organ dysfunction (SOFA score increase of ≥ 2) [ 3 , 4 ]. Suspected infection will be operationalized as antibiotics and body‑fluid cultures ordered within Sepsis‑3 time windows [ 3 ]. 4.3 Index event (T0) and analytic time windows T0 is the earliest time at which either (i) a continuous vasopressor infusion is initiated (norepinephrine, epinephrine, vasopressin, dopamine), or (ii) MAP < 65 mmHg is sustained for ≥ 15 minutes based on ABP (1‑minute rolling median). Input window: T0 − 4 h to T0, analyzed in 5‑minute sliding windows with 50% overlap. Outcome windows: T0 to day 28 for mortality; T0 to 24 h for vasopressor exposure. 4.4 Inclusion criteria Adult ICU admission (≥ 18 years) meeting Sepsis‑3 criteria. Index event (T0) as defined above. Continuous ECG lead II and invasive ABP available for ≥ 4 hours before T0. Minimum clinical variables for adjustment: age, sex, SOFA near infection onset/T0, baseline lactate (± 6 h of T0), and comorbidity proxies. 4.5 Exclusion criteria (signal cleanup and dominant non-autonomic causes) Arrhythmias/pacing: sustained atrial fibrillation/flutter, pacemaker rhythm, or frequent ectopy (> 10% beats per analysis window). Dominant pump failure: known LVEF < 50% or advanced heart failure (NYHA III–IV) when identifiable; planned sensitivity analyses will relax this criterion. Pharmacologic blockade: active β-blockers, non‑DHP calcium channel blockers, or antiarrhythmics within 24 hours when ascertainable. Central dysautonomia: severe traumatic brain injury, acute stroke, or spinal cord injury. Measurement failure: poor signal quality, disconnection, or insufficient waveform coverage. Cohort construction from linked MIMIC‑III clinical and waveform databases. T0 denotes the index event (vasopressor initiation or sustained hypotension). The entry window includes the 4 hours preceding T0 and requires continuous ECG II and ABP. 4.6 Variables and operational definitions 4.6.1 Primary exposure: Conatus Effort Index (I_v7c) Signal processing will be performed in 5‑minute windows (50% overlap). R‑peaks will be detected from ECG lead II; R–R intervals will be cleaned for artifacts and ectopy using HRV standards and tachogram artifact guidance [ 10 , 13 ]. Energy (E): normalized heart rate using an age‑predicted maximal heart rate HRmax = 208 − 0.7×age [ 22 ]. E(t) = HR(t)/HRmax. Complexity (C): sample entropy (SampEn) of the R–R series with parameters m = 2 and r = 0.2×SD [ 11 , 12 ]. Conatus Effort Index: I_v7c(t) = E(t) / (C(t)^2). An epsilon will be added to C in implementation to prevent numerical instability when C→0. 4.6.2 Topological Saturation status (binary state) Primary pre‑specified definition: Topological Saturation is present at T0 if, during the last 60 minutes before T0, the patient meets ≥ 2 of 3 criteria: (1) low complexity: median C < 0.80 (threshold chosen pragmatically and tested in sensitivity analyses; entropy/HRV outcome associations motivate this approach [ 14 – 21 ]); (2) high effort: median E ≥ 0.75 or I_v7c in the top quartile of the cohort; (3) plateau criterion: local slope of MAP versus I_v7c, estimated by robust linear regression in high‑effort windows, satisfies |dMAP/dI_v7c| ≤ 1.0 mmHg per unit I_v7c. Alternative definitions will vary thresholds and use nonparametric local regression for the plateau criterion. 4.6.3 Outcomes Primary short‑term outcome: hemodynamic collapse within 30 minutes (binary), defined as MAP < 65 mmHg sustained ≥ 15 minutes and/or vasopressor initiation. Secondary outcomes: (i) 28‑day all‑cause mortality; (ii) 24‑hour vasopressor exposure quantified as norepinephrine‑equivalent dose (NED) [ 24 ]; (iii) ICU and in‑hospital mortality (exploratory). 4.6.4 Comparator predictors Shock index: HR/SBP, computed in synchronized 5‑minute windows. Baseline lactate: first lactate value within ± 6 hours of T0 (or suspected infection onset if T0 is missing). Table 1 Key variables and definitions. Domain Variable Operational definition Time window Exposure E(t) Normalized HR: HR / (208 − 0.7×age) 5‑min windows, T0 − 4 h to T0 Exposure C(t) Sample entropy of R–R series (m = 2, r = 0.2×SD) 5‑min windows, T0 − 4 h to T0 Exposure I_v7c E / C² (epsilon-stabilized) 5‑min windows, T0 − 4 h to T0 State Topological Saturation ≥ 2/3: low C, high E or high I_v7c, MAP–I_v7c plateau Last 60 min pre‑T0 Outcome Collapse @30 min MAP < 65 for ≥ 15 min and/or vasopressor initiation within next 30 min Prediction horizons 30 & 60 min Outcome 28‑day mortality All-cause death by day 28 from T0 T0 to day 28 Outcome Vasopressor load 24‑h norepinephrine‑equivalent dose (NED) T0 to 24 h Comparator Shock index HR / SBP 5‑min windows, T0 − 4 h to T0 Comparator Baseline lactate First lactate within ± 6 h of T0 Per episode 4.7 Hypotheses Working hypothesis (H1) : I_v7c and/or its short‑term slope (dI_v7c/dt) improves prediction of collapse at 30 minutes compared with the shock index and baseline lactate. Null hypothesis (H0) : I_v7c provides no clinically meaningful improvement in discrimination (ΔAUC < 0.03) over the best comparator for predicting collapse, and shows no reproducible plateau behavior at high effort. 4.8 Data extraction and signal-processing pipeline Waveforms will be retrieved from the matched subset using record identifiers linked to clinical admissions [ 6 ]. Processing steps (per patient/episode): 1) Load ECG II and ABP signals; synchronize timestamps. 2) Detect R‑peaks; compute R–R intervals; filter artifacts/ectopy and exclude arrhythmic windows [, ]. 3) Compute HR, E(t), C(t) (SampEn), and I_v7c per window [, , ]. 4) Derive trajectory features for prediction horizons (current value, 30‑min slope, area-under-trajectory, percentiles). 5) Label outcomes using the T0 definition and subsequent MAP/vasopressor time series. All derived-variable definitions and code will be documented for reproducibility. Synthetic plot illustrating the plateau concept: MAP becomes relatively insensitive to increasing effort (high I_v7c). The analysis will test whether comparable plateau behavior is detectable empirically in MIMIC‑III. Synthetic example showing an increase of I_v7c toward T0. In the study, trajectories will be computed from real waveforms and evaluated for predictive value. 5. Statistical analysis plan 5.1 Descriptive statistics Baseline characteristics and severity will be summarized using mean ± SD or median (IQR); categorical variables as n (%). Between-group comparisons (Saturated vs Not saturated at T0) will use t‑test/Wilcoxon and chi‑square/Fisher as appropriate. 5.2 Predictive analysis (short-term) We will build prediction models for collapse at 30 and 60 minutes using I_v7c features (value, slope, area-under-trajectory, distributional summaries). Primary metrics: AUC with 95% CI via patient-level bootstrap; calibration via Brier score and calibration curves. AUC comparisons will use DeLong’s method for correlated ROC curves when applicable [ 25 ]. Internal validation will use grouped cross‑validation by patient/ICU stay to avoid leakage. Predictive-model reporting will follow TRIPOD [ 27 ]. 5.3 Vasopressor exposure (24 h) Total vasopressor exposure will be computed as 24‑hour norepinephrine‑equivalent dose (NED) using a standardized conversion [ 24 ]. Associations with I_v7c trajectory features will be assessed using Spearman correlation and multivariable regression adjusting for age, SOFA, baseline lactate, ventilation, and sedation level (RASS) [ 23 ]. 5.4 Survival analysis (28 days) Patients will be stratified by Topological Saturation status at T0. Kaplan–Meier curves will be compared via log‑rank testing. Multivariable Cox proportional hazards models will estimate hazard ratios for 28‑day mortality, adjusting for age, SOFA, baseline lactate, ventilation, and sedation level (RASS) [ 23 ]. Proportional hazards assumptions will be evaluated using Schoenfeld residuals. 5.5 Missing data and sensitivity analyses We will quantify missingness for covariates. Where feasible, multiple imputation will be applied for covariates under a missing‑at‑random assumption. Sensitivity analyses include: alternative T0 definitions, alternative SampEn thresholds and plateau criteria, relaxing exclusion criteria (e.g., advanced HF), and restricting to high-quality waveform segments. 6. Sample and sampling strategy This is a retrospective consecutive-sampling study: all eligible ICU admissions in the linked MIMIC‑III cohort will be included. We will report achieved sample size and event counts. For multivariable modeling, we will limit covariate complexity and report model stability per TRIPOD [ 27 ]. 7. Limitations and risk of bias Limitations include residual confounding, selection bias from requiring high-quality ECG + ABP signals, incomplete ascertainment of outpatient medications and LVEF, and single-center historical data limiting generalizability. We will document exclusions and signal-quality filtering rates and perform sensitivity analyses to assess robustness. 8. Ethical considerations MIMIC‑III is de‑identified and access requires training and adherence to a data use agreement [ 5 – 7 ]. This study involves secondary analysis of de‑identified data and is expected to pose minimal risk. Local institutional review should confirm exemption or expedited review as applicable. 8.1 Confidentiality No attempt will be made to re-identify individuals. Only de-identified identifiers will be used; results will be reported in aggregate with no patient‑level releases. 8.2 Value of the research question Earlier detection of loss of autonomic and microcirculatory reserve could support earlier escalation and improved risk stratification in sepsis. 8.3 Risk/benefit and non-maleficence Direct risk is negligible due to de-identification; potential benefit is societal, by enabling development of earlier and more informative monitoring signals. 8.4 Independent review and informed consent Independent ethical review is recommended to confirm regulatory status. Individual informed consent is not required for de‑identified secondary data use, subject to local regulations and MIMIC agreements. 9. Quantitative predictions, expected results, and falsifiability criteria We pre‑specify the following falsifiability targets: Prediction 1 (30‑min discrimination): AUC(I_v7c) ≥ 0.78 and absolute superiority ΔAUC ≥ 0.03 over the shock index. Prediction 2 (adjusted association): Adjusted odds ratio ≥ 1.8 for 30‑min collapse per 1 SD increase in I_v7c (adjusted for age and SOFA). Prediction 3 (mortality): Adjusted hazard ratio ≥ 1.5 for Topological Saturation at T0 versus not saturated for 28‑day mortality. Prediction 4 (vasopressors): |Spearman ρ| ≥ 0.35 between pre‑T0 I_v7c trajectory summary and 24‑h NED. Refutation criteria (pre‑specified): This operational v7c translation will be considered not supported if: (i) AUC(I_v7c) fails to exceed the best comparator by ≥ 0.03 and the difference is not statistically significant; (ii) no plateau behavior is detected in MAP versus I_v7c in the high‑effort range across pre‑specified analyses; or (iii) the adjusted association with mortality is absent under pre‑specified models. References Evans L, Rhodes A, Alhazzani W et al (2021) Surviving Sepsis Campaign: International Guidelines for Management of Sepsis and Septic Shock 2021. Intensive Care Med 47(11):1181–1247 Ince C (2015) Hemodynamic coherence and the rationale for monitoring the microcirculation. Crit Care 19(Suppl 3):S8 Singer M, Deutschman CS, Seymour CW et al (2016) The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis–3). JAMA 315(8):801–810 Vincent JL, Moreno R, Takala J et al (1996) The SOFA (Sepsis–related Organ Failure Assessment) score to describe organ dysfunction/failure. Intensive Care Med 22(7):707–710 Johnson AEW, Pollard TJ, Shen L et al (2016) MIMIC–III, a freely accessible critical care database. Sci Data 3:160035 Moody B, Moody G, Villarroel M, Clifford GD, Silva I (2020) MIMIC–III Waveform Database Matched Subset (version 1.0). PhysioNet. 10.13026/c2294b Goldberger AL, Amaral LAN, Glass L et al (2000) PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals. 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Am J Respir Crit Care Med 166(10):1338–1344. 10.1164/rccm.2107138 Kotani Y, Di Gioia A, Landoni G et al (2023) An updated norepinephrine equivalent score in intensive care as a marker of shock severity. Crit Care 27(1):29. 10.1186/s13054-023-04322-y DeLong ER, DeLong DM, Clarke–Pearson DL (1988) Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. Biometrics 44(3):837–845 von Elm E, Altman DG, Egger M et al (2007) The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement: guidelines for reporting observational studies. Lancet 370(9596):1453–1457 Moons KGM, Altman DG, Reitsma JB et al (2015) Transparent Reporting of a multivariable prediction model for Individual Prognosis Or Diagnosis (TRIPOD): explanation and elaboration. Ann Intern Med 162:W1–W73. 10.7326/M14-0698 Merino Gallardo V (2026) CUP–Ω* v7c (Closed Topological Formulation): A Completely Positive Local Evolution Law for the CUCE/Spinoza/Hilbert Programme Based on the Hilbert Hermetic Seal (Squared–Circle). Res Square. 10.21203/rs.3.rs-8673041/v1 Zenodo record: 10.5281/zenodo.18344963 Additional Declarations The authors declare potential competing interests as follows: No conflict of interest Supplementary Files AppendixA.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8903117","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":592884368,"identity":"3443ae45-f3a0-41d7-9902-ec66d3f42054","order_by":0,"name":"Vicente Merino Gallardo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYBACgxv5zz/+bLOR52dgfADkMxOh5c4bNonEY2mGMxuYDRuI03IfpOXZ4QSDA8RqkZydA9FifCOZ/QFDhXViA2Et+cc/JG47nGB2I5mxgeFMOjFactgPALUkb7uRf7CBse0wYS38EjlsCYnzDidungG0hfEfkVoMEvsOJ26QAGlpIEILmwTI+31phjPOPGackXAs3ZgILfnPJMFR2Z7M8OFDjbUsQS2oIIE05aNgFIyCUTAKcAEA1l9J/2iLwoYAAAAASUVORK5CYII=","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Vicente","middleName":"Merino","lastName":"Gallardo","suffix":""}],"badges":[],"createdAt":"2026-02-17 16:59:36","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":false,"conflictsOfInterestStatement":true,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8903117/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8903117/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102982221,"identity":"a5db290b-dcdd-49b7-a845-df1432f2ed00","added_by":"auto","created_at":"2026-02-19 09:12:56","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":227498,"visible":true,"origin":"","legend":"\u003cp\u003eCohort flow and analytic windows.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8903117/v1/69e4b67444f6a6c23cf07479.png"},{"id":102982218,"identity":"08bf4dc6-8621-406c-b8d4-1da1c9c3c51c","added_by":"auto","created_at":"2026-02-19 09:12:56","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":76737,"visible":true,"origin":"","legend":"\u003cp\u003eIllustrative saturation (plateau) of MAP versus I_v7c (synthetic).\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8903117/v1/486750c34007c8e790050120.png"},{"id":103049316,"identity":"4305c870-0d00-4a15-997d-ab0290c75742","added_by":"auto","created_at":"2026-02-20 07:39:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":68317,"visible":true,"origin":"","legend":"\u003cp\u003eIllustrative pre‑T0 trajectory of I_v7c (synthetic).\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8903117/v1/a1e3348cea1776e1a192339b.png"},{"id":103051419,"identity":"8303d4e4-186e-4391-b49b-08173cf7f08b","added_by":"auto","created_at":"2026-02-20 08:00:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1353837,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8903117/v1/6e078696-51bc-47db-a246-f0cea558865d.pdf"},{"id":103049684,"identity":"7447f760-d207-42a0-8f1b-ec664fa8fd85","added_by":"auto","created_at":"2026-02-20 07:44:45","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":15138,"visible":true,"origin":"","legend":"","description":"","filename":"AppendixA.docx","url":"https://assets-eu.researchsquare.com/files/rs-8903117/v1/4a67cf08a457dffdc96d9003.docx"}],"financialInterests":"The authors declare potential competing interests as follows: No conflict of interest","formattedTitle":"\u003cp\u003e\u003cstrong\u003eResearch Protocol - Validation of Topological Saturation (v7c Model) as a Predictor of Hemodynamic Collapse and Mortality in Sepsis:\u003cbr\u003e\nA Retrospective Cohort Study in MIMIC‑III\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction and justification","content":"\u003cp\u003eSepsis and septic shock remain major causes of morbidity and mortality in critical care, and contemporary management emphasizes early recognition, timely antimicrobials, source control, and hemodynamic resuscitation with vasopressors to maintain adequate perfusion pressure, typically targeting MAP\u0026thinsp;\u0026ge;\u0026thinsp;65 mmHg [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Yet sustained hypotension and vasopressor requirement often represent a late stage of physiological decompensation.\u003c/p\u003e \u003cp\u003ePhysiological systems show multiscale variability; during critical illness, complexity can collapse as regulatory degrees of freedom are lost [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Heart rate variability (HRV) is a key marker of autonomic regulation with standardized measurement guidance [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. In sepsis, depressed HRV and reduced entropy have been associated with higher inflammatory burden, declining blood pressure, and worse outcomes [\u003cspan additionalcitationids=\"CR15 CR16 CR17 CR18 CR19 CR20\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Meanwhile, microcirculatory derangements may persist despite apparently adequate macrocirculatory targets, challenging hemodynamic coherence and motivating richer monitoring paradigms [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe CUCE v7c framework introduces a mathematically explicit saturating law in which an effective coupling approaches a bounded ceiling and transitions into a plateau regime as a system nears a critical scale (E*) [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. This protocol proposes a strictly operational (non‑literal) translation: when cardiovascular reserve is failing, R\u0026ndash;R dynamics may become more regular (lower entropy/complexity) while metabolic effort increases (tachycardia), yielding a composite state\u0026mdash;Topological Saturation\u0026mdash;that could anticipate hemodynamic collapse earlier than conventional linear markers.\u003c/p\u003e"},{"header":"2. Theoretical framework","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Complexity loss and autonomic failure in sepsis\u003c/h2\u003e \u003cp\u003eReduced variability and entropy in physiological time series are consistently reported in critical illness and have been proposed as markers of reduced adaptive capacity [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. HRV provides a window into autonomic regulation and has internationally accepted standards for acquisition and interpretation [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Multiple studies have linked depressed HRV and reduced entropy to severity and outcome in sepsis, including emergency department and ICU cohorts [\u003cspan additionalcitationids=\"CR15 CR16 CR17 CR18 CR19 CR20\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Sample entropy as an operational complexity metric\u003c/h2\u003e \u003cp\u003eSample entropy (SampEn) quantifies the irregularity of time series and is widely used in physiology; canonical methodological formulations specify m\u0026thinsp;=\u0026thinsp;2 and r scaled to the series SD [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Artifact characterization and filtering are crucial when working with R\u0026ndash;R tachograms [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Operational definition of Topological Saturation\u003c/h2\u003e \u003cp\u003eWe operationalize Topological Saturation using (i) metabolic effort via normalized HR energy E(t), (ii) complexity via SampEn C(t), and (iii) a plateau behavior of MAP versus I_v7c in high-effort regions. The Conatus Effort Index is defined as I_v7c\u0026thinsp;=\u0026thinsp;E/C\u0026sup2;, emphasizing that rising effort combined with shrinking complexity yields disproportionately larger I_v7c.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 v7c saturating-law template as a hypothesis generator\u003c/h2\u003e \u003cp\u003eCUP‑Ω* v7c implements bounded saturation through a tanh functional calculus that produces plateau-like behavior near a critical scale [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. This protocol does not claim mechanistic identity between open‑quantum‑system saturation and cardiovascular physiology. Instead, the v7c saturating form is used as a falsifiable template for detecting plateau-like behavior in a composite physiologic effort index before shock.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Reporting standards\u003c/h2\u003e \u003cp\u003eWe will report this retrospective observational study following STROBE guidance and the prediction‑model component following TRIPOD recommendations [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Objectives","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Primary objective\u003c/h2\u003e \u003cp\u003eTo determine whether the Conatus Effort Index (I_v7c) and its time derivative (dI_v7c/dt) predict hemodynamic collapse (MAP\u0026thinsp;\u0026lt;\u0026thinsp;65 mmHg sustained and/or vasopressor initiation) at least 30 minutes in advance in septic ICU patients.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Secondary objectives\u003c/h2\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eTo evaluate the association between Topological Saturation status at shock onset (T0) and 28‑day all‑cause mortality.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTo correlate pre‑T0 I_v7c trajectory features with total vasopressor exposure in the first 24 hours, expressed as a norepinephrine‑equivalent dose (NED).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTo test whether I_v7c outperforms the shock index (HR/SBP) and baseline serum lactate in short‑term prediction of collapse.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTo assess robustness via subgroup and sensitivity analyses (alternative definitions and exclusion criteria).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Materials and methods","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n\u003ch2\u003e4.1 Study design and data sources\u003c/h2\u003e\n\u003cp\u003eRetrospective, observational cohort study using the MIMIC‑III Clinical Database v1.4 linked to the MIMIC‑III Waveform Database Matched Subset v1.0 [\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e]. PhysioNet provides the waveform infrastructure and distribution for these resources [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n\u003ch2\u003e4.2 Target population and sepsis definition (Sepsis‑3)\u003c/h2\u003e\n\u003cp\u003eEligible admissions will be adult ICU stays (\u0026ge;\u0026thinsp;18 years) meeting Sepsis‑3 criteria: suspected infection plus organ dysfunction (SOFA score increase of \u0026ge;\u0026thinsp;2) [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e]. Suspected infection will be operationalized as antibiotics and body‑fluid cultures ordered within Sepsis‑3 time windows [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n\u003ch2\u003e4.3 Index event (T0) and analytic time windows\u003c/h2\u003e\n\u003cp\u003eT0 is the earliest time at which either (i) a continuous vasopressor infusion is initiated (norepinephrine, epinephrine, vasopressin, dopamine), or (ii) MAP\u0026thinsp;\u0026lt;\u0026thinsp;65 mmHg is sustained for \u0026ge;\u0026thinsp;15 minutes based on ABP (1‑minute rolling median). Input window: T0\u0026thinsp;\u0026minus;\u0026thinsp;4 h to T0, analyzed in 5‑minute sliding windows with 50% overlap. Outcome windows: T0 to day 28 for mortality; T0 to 24 h for vasopressor exposure.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n\u003ch2\u003e4.4 Inclusion criteria\u003c/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eAdult ICU admission (\u0026ge;\u0026thinsp;18 years) meeting Sepsis‑3 criteria.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eIndex event (T0) as defined above.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eContinuous ECG lead II and invasive ABP available for \u0026ge;\u0026thinsp;4 hours before T0.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eMinimum clinical variables for adjustment: age, sex, SOFA near infection onset/T0, baseline lactate (\u0026plusmn;\u0026thinsp;6 h of T0), and comorbidity proxies.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\n\u003ch2\u003e4.5 Exclusion criteria (signal cleanup and dominant non-autonomic causes)\u003c/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eArrhythmias/pacing: sustained atrial fibrillation/flutter, pacemaker rhythm, or frequent ectopy (\u0026gt;\u0026thinsp;10% beats per analysis window).\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eDominant pump failure: known LVEF\u0026thinsp;\u0026lt;\u0026thinsp;50% or advanced heart failure (NYHA III\u0026ndash;IV) when identifiable; planned sensitivity analyses will relax this criterion.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003ePharmacologic blockade: active \u0026beta;-blockers, non‑DHP calcium channel blockers, or antiarrhythmics within 24 hours when ascertainable.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eCentral dysautonomia: severe traumatic brain injury, acute stroke, or spinal cord injury.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eMeasurement failure: poor signal quality, disconnection, or insufficient waveform coverage.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eCohort construction from linked MIMIC‑III clinical and waveform databases. T0 denotes the index event (vasopressor initiation or sustained hypotension). The entry window includes the 4 hours preceding T0 and requires continuous ECG II and ABP.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\n\u003ch2\u003e4.6 Variables and operational definitions\u003c/h2\u003e\n\u003cdiv id=\"Sec18\" class=\"Section3\"\u003e\n\u003ch2\u003e4.6.1 Primary exposure: Conatus Effort Index (I_v7c)\u003c/h2\u003e\n\u003cp\u003eSignal processing will be performed in 5‑minute windows (50% overlap). R‑peaks will be detected from ECG lead II; R\u0026ndash;R intervals will be cleaned for artifacts and ectopy using HRV standards and tachogram artifact guidance [\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eEnergy (E): normalized heart rate using an age‑predicted maximal heart rate HRmax\u0026thinsp;=\u0026thinsp;208\u0026thinsp;\u0026minus;\u0026thinsp;0.7\u0026times;age [\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e]. E(t)\u0026thinsp;=\u0026thinsp;HR(t)/HRmax.\u003c/p\u003e\n\u003cp\u003eComplexity (C): sample entropy (SampEn) of the R\u0026ndash;R series with parameters m\u0026thinsp;=\u0026thinsp;2 and r\u0026thinsp;=\u0026thinsp;0.2\u0026times;SD [\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eConatus Effort Index: I_v7c(t)\u0026thinsp;=\u0026thinsp;E(t) / (C(t)^2). An epsilon will be added to C in implementation to prevent numerical instability when C\u0026rarr;0.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec19\" class=\"Section3\"\u003e\n\u003ch2\u003e4.6.2 Topological Saturation status (binary state)\u003c/h2\u003e\n\u003cp\u003ePrimary pre‑specified definition: Topological Saturation is present at T0 if, during the last 60 minutes before T0, the patient meets\u0026thinsp;\u0026ge;\u0026thinsp;2 of 3 criteria:\u003c/p\u003e\n\u003cp\u003e(1) low complexity: median C\u0026thinsp;\u0026lt;\u0026thinsp;0.80 (threshold chosen pragmatically and tested in sensitivity analyses; entropy/HRV outcome associations motivate this approach [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e]);\u003c/p\u003e\n\u003cp\u003e(2) high effort: median E\u0026thinsp;\u0026ge;\u0026thinsp;0.75 or I_v7c in the top quartile of the cohort;\u003c/p\u003e\n\u003cp\u003e(3) plateau criterion: local slope of MAP versus I_v7c, estimated by robust linear regression in high‑effort windows, satisfies |dMAP/dI_v7c| \u0026le; 1.0 mmHg per unit I_v7c.\u003c/p\u003e\n\u003cp\u003eAlternative definitions will vary thresholds and use nonparametric local regression for the plateau criterion.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec20\" class=\"Section3\"\u003e\n\u003ch2\u003e4.6.3 Outcomes\u003c/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003ePrimary short‑term outcome: hemodynamic collapse within 30 minutes (binary), defined as MAP\u0026thinsp;\u0026lt;\u0026thinsp;65 mmHg sustained\u0026thinsp;\u0026ge;\u0026thinsp;15 minutes and/or vasopressor initiation.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eSecondary outcomes: (i) 28‑day all‑cause mortality; (ii) 24‑hour vasopressor exposure quantified as norepinephrine‑equivalent dose (NED) [\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e]; (iii) ICU and in‑hospital mortality (exploratory).\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec21\" class=\"Section3\"\u003e\n\u003ch2\u003e4.6.4 Comparator predictors\u003c/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eShock index: HR/SBP, computed in synchronized 5‑minute windows.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eBaseline lactate: first lactate value within \u0026plusmn;\u0026thinsp;6 hours of T0 (or suspected infection onset if T0 is missing).\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eKey variables and definitions.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eDomain\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eVariable\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eOperational definition\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eTime window\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eExposure\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eE(t)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNormalized HR: HR / (208\u0026thinsp;\u0026minus;\u0026thinsp;0.7\u0026times;age)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5‑min windows, T0\u0026thinsp;\u0026minus;\u0026thinsp;4 h to T0\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eExposure\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eC(t)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSample entropy of R\u0026ndash;R series (m\u0026thinsp;=\u0026thinsp;2, r\u0026thinsp;=\u0026thinsp;0.2\u0026times;SD)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5‑min windows, T0\u0026thinsp;\u0026minus;\u0026thinsp;4 h to T0\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eExposure\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eI_v7c\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eE / C\u0026sup2; (epsilon-stabilized)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5‑min windows, T0\u0026thinsp;\u0026minus;\u0026thinsp;4 h to T0\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eState\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eTopological Saturation\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026ge;\u0026thinsp;2/3: low C, high E or high I_v7c, MAP\u0026ndash;I_v7c plateau\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eLast 60 min pre‑T0\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eOutcome\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCollapse @30 min\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eMAP\u0026thinsp;\u0026lt;\u0026thinsp;65 for \u0026ge;\u0026thinsp;15 min and/or vasopressor initiation within next 30 min\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePrediction horizons 30 \u0026amp; 60 min\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eOutcome\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e28‑day mortality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAll-cause death by day 28 from T0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eT0 to day 28\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eOutcome\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eVasopressor load\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e24‑h norepinephrine‑equivalent dose (NED)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eT0 to 24 h\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eComparator\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eShock index\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eHR / SBP\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5‑min windows, T0\u0026thinsp;\u0026minus;\u0026thinsp;4 h to T0\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eComparator\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBaseline lactate\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eFirst lactate within \u0026plusmn;\u0026thinsp;6 h of T0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePer episode\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec22\" class=\"Section2\"\u003e\n\u003ch2\u003e4.7 Hypotheses\u003c/h2\u003e\n\u003cp\u003e\u003cstrong\u003eWorking hypothesis (H1)\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eI_v7c and/or its short‑term slope (dI_v7c/dt) improves prediction of collapse at 30 minutes compared with the shock index and baseline lactate.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNull hypothesis (H0)\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eI_v7c provides no clinically meaningful improvement in discrimination (\u0026Delta;AUC\u0026thinsp;\u0026lt;\u0026thinsp;0.03) over the best comparator for predicting collapse, and shows no reproducible plateau behavior at high effort.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec23\" class=\"Section2\"\u003e\n\u003ch2\u003e4.8 Data extraction and signal-processing pipeline\u003c/h2\u003e\n\u003cp\u003eWaveforms will be retrieved from the matched subset using record identifiers linked to clinical admissions [\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e]. Processing steps (per patient/episode):\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003e1) Load ECG II and ABP signals; synchronize timestamps.\u003c/p\u003e\n\u003cp\u003e2) Detect R‑peaks; compute R\u0026ndash;R intervals; filter artifacts/ectopy and exclude arrhythmic windows [, ].\u003c/p\u003e\n\u003cp\u003e3) Compute HR, E(t), C(t) (SampEn), and I_v7c per window [, , ].\u003c/p\u003e\n\u003cp\u003e4) Derive trajectory features for prediction horizons (current value, 30‑min slope, area-under-trajectory, percentiles).\u003c/p\u003e\n\u003cp\u003e5) Label outcomes using the T0 definition and subsequent MAP/vasopressor time series.\u003c/p\u003e\n\u003cp\u003eAll derived-variable definitions and code will be documented for reproducibility.\u003c/p\u003e\n\u003cp\u003eSynthetic plot illustrating the plateau concept: MAP becomes relatively insensitive to increasing effort (high I_v7c). The analysis will test whether comparable plateau behavior is detectable empirically in MIMIC‑III.\u003c/p\u003e\n\u003cp\u003eSynthetic example showing an increase of I_v7c toward T0. In the study, trajectories will be computed from real waveforms and evaluated for predictive value.\u003c/p\u003e"},{"header":"5. Statistical analysis plan","content":"\u003cdiv id=\"Sec30\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Descriptive statistics\u003c/h2\u003e \u003cp\u003eBaseline characteristics and severity will be summarized using mean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD or median (IQR); categorical variables as n (%). Between-group comparisons (Saturated vs Not saturated at T0) will use t‑test/Wilcoxon and chi‑square/Fisher as appropriate.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec31\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Predictive analysis (short-term)\u003c/h2\u003e \u003cp\u003eWe will build prediction models for collapse at 30 and 60 minutes using I_v7c features (value, slope, area-under-trajectory, distributional summaries). Primary metrics: AUC with 95% CI via patient-level bootstrap; calibration via Brier score and calibration curves. AUC comparisons will use DeLong\u0026rsquo;s method for correlated ROC curves when applicable [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Internal validation will use grouped cross‑validation by patient/ICU stay to avoid leakage. Predictive-model reporting will follow TRIPOD [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec32\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Vasopressor exposure (24 h)\u003c/h2\u003e \u003cp\u003eTotal vasopressor exposure will be computed as 24‑hour norepinephrine‑equivalent dose (NED) using a standardized conversion [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Associations with I_v7c trajectory features will be assessed using Spearman correlation and multivariable regression adjusting for age, SOFA, baseline lactate, ventilation, and sedation level (RASS) [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec33\" class=\"Section2\"\u003e \u003ch2\u003e5.4 Survival analysis (28 days)\u003c/h2\u003e \u003cp\u003ePatients will be stratified by Topological Saturation status at T0. Kaplan\u0026ndash;Meier curves will be compared via log‑rank testing. Multivariable Cox proportional hazards models will estimate hazard ratios for 28‑day mortality, adjusting for age, SOFA, baseline lactate, ventilation, and sedation level (RASS) [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Proportional hazards assumptions will be evaluated using Schoenfeld residuals.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec34\" class=\"Section2\"\u003e \u003ch2\u003e5.5 Missing data and sensitivity analyses\u003c/h2\u003e \u003cp\u003eWe will quantify missingness for covariates. Where feasible, multiple imputation will be applied for covariates under a missing‑at‑random assumption. Sensitivity analyses include: alternative T0 definitions, alternative SampEn thresholds and plateau criteria, relaxing exclusion criteria (e.g., advanced HF), and restricting to high-quality waveform segments.\u003c/p\u003e \u003c/div\u003e"},{"header":"6. Sample and sampling strategy","content":"\u003cp\u003eThis is a retrospective consecutive-sampling study: all eligible ICU admissions in the linked MIMIC‑III cohort will be included. We will report achieved sample size and event counts. For multivariable modeling, we will limit covariate complexity and report model stability per TRIPOD [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e"},{"header":"7. Limitations and risk of bias","content":"\u003cp\u003eLimitations include residual confounding, selection bias from requiring high-quality ECG\u0026thinsp;+\u0026thinsp;ABP signals, incomplete ascertainment of outpatient medications and LVEF, and single-center historical data limiting generalizability. We will document exclusions and signal-quality filtering rates and perform sensitivity analyses to assess robustness.\u003c/p\u003e"},{"header":"8. Ethical considerations","content":"\u003cp\u003eMIMIC‑III is de‑identified and access requires training and adherence to a data use agreement [\u003cspan additionalcitationids=\"CR6\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. This study involves secondary analysis of de‑identified data and is expected to pose minimal risk. Local institutional review should confirm exemption or expedited review as applicable.\u003c/p\u003e \u003cdiv id=\"Sec38\" class=\"Section2\"\u003e \u003ch2\u003e8.1 Confidentiality\u003c/h2\u003e \u003cp\u003eNo attempt will be made to re-identify individuals. Only de-identified identifiers will be used; results will be reported in aggregate with no patient‑level releases.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec39\" class=\"Section2\"\u003e \u003ch2\u003e8.2 Value of the research question\u003c/h2\u003e \u003cp\u003eEarlier detection of loss of autonomic and microcirculatory reserve could support earlier escalation and improved risk stratification in sepsis.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec40\" class=\"Section2\"\u003e \u003ch2\u003e8.3 Risk/benefit and non-maleficence\u003c/h2\u003e \u003cp\u003eDirect risk is negligible due to de-identification; potential benefit is societal, by enabling development of earlier and more informative monitoring signals.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec41\" class=\"Section2\"\u003e \u003ch2\u003e8.4 Independent review and informed consent\u003c/h2\u003e \u003cp\u003eIndependent ethical review is recommended to confirm regulatory status. Individual informed consent is not required for de‑identified secondary data use, subject to local regulations and MIMIC agreements.\u003c/p\u003e \u003c/div\u003e"},{"header":"9. Quantitative predictions, expected results, and falsifiability criteria","content":"\u003cp\u003eWe pre‑specify the following falsifiability targets:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003ePrediction 1 (30‑min discrimination): AUC(I_v7c)\u0026thinsp;\u0026ge;\u0026thinsp;0.78 and absolute superiority ΔAUC\u0026thinsp;\u0026ge;\u0026thinsp;0.03 over the shock index.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePrediction 2 (adjusted association): Adjusted odds ratio\u0026thinsp;\u0026ge;\u0026thinsp;1.8 for 30‑min collapse per 1 SD increase in I_v7c (adjusted for age and SOFA).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePrediction 3 (mortality): Adjusted hazard ratio\u0026thinsp;\u0026ge;\u0026thinsp;1.5 for Topological Saturation at T0 versus not saturated for 28‑day mortality.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePrediction 4 (vasopressors): |Spearman ρ| \u0026ge; 0.35 between pre‑T0 I_v7c trajectory summary and 24‑h NED.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eRefutation criteria (pre‑specified): This operational v7c translation will be considered not supported if: (i) AUC(I_v7c) fails to exceed the best comparator by \u0026ge;\u0026thinsp;0.03 and the difference is not statistically significant; (ii) no plateau behavior is detected in MAP versus I_v7c in the high‑effort range across pre‑specified analyses; or (iii) the adjusted association with mortality is absent under pre‑specified models.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eEvans L, Rhodes A, Alhazzani W et al (2021) Surviving Sepsis Campaign: International Guidelines for Management of Sepsis and Septic Shock 2021. 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Ann Intern Med 162:W1\u0026ndash;W73. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.7326/M14-0698\u003c/span\u003e\u003cspan address=\"10.7326/M14-0698\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMerino Gallardo V (2026) CUP\u0026ndash;Ω* v7c (Closed Topological Formulation): A Completely Positive Local Evolution Law for the CUCE/Spinoza/Hilbert Programme Based on the Hilbert Hermetic Seal (Squared\u0026ndash;Circle). Res Square. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.21203/rs.3.rs-8673041/v1\u003c/span\u003e\u003cspan address=\"10.21203/rs.3.rs-8673041/v1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZenodo record: 10.5281/zenodo.18344963\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Finis Terrae University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"sepsis, septic shock, hemodynamic collapse, heart rate variability, sample entropy, complexity, microcirculation, MIMIC‑III, waveform analytics, prediction model","lastPublishedDoi":"10.21203/rs.3.rs-8903117/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8903117/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSeptic 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.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eRetrospective 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 \u0026lt; 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.\u003c/p\u003e\n\u003cp\u003eExpected 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.\u003c/p\u003e","manuscriptTitle":"Research Protocol - Validation of Topological Saturation (v7c Model) as a Predictor of Hemodynamic Collapse and Mortality in Sepsis:\nA Retrospective Cohort Study in MIMIC‑III","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-19 09:12:51","doi":"10.21203/rs.3.rs-8903117/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"95c112c2-a453-41a1-bde6-0cfc61fa374d","owner":[],"postedDate":"February 19th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":63086552,"name":"Critical Care \u0026 Emergency Medicine"}],"tags":[],"updatedAt":"2026-02-19T09:12:52+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-19 09:12:51","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8903117","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8903117","identity":"rs-8903117","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}