This study aimed to derive and validate a prediction rule for estimating the central venous pressure (CVP) from the inferior vena cava collapsibility index (IVCCI) in adults. Five hundred forty paired CVP-IVCCI measures were obtained from 180 adults. The CVP was measured via a central venous catheter connected to a pressure transducer, and the IVCCI was estimated by abdominal ultrasound. The dataset was randomly split at the patient level into training (121 patients, 363 observations) and validation (59 patients, 177 observations) samples. A generalized estimating equation for repeated measures was used to fit a prediction rule from the training sample, which was validated on the validation subset. The model showed promising performance with a mean absolute error of 2.13 mmHg and 75.7% of predictions falling within ± 3 mmHg of the true values. The limits of agreement ranged from -6.0 to + 4.3 mmHg, 85.9% of predictions fell within a prespecified maximum accepted difference of ± 4 mmHg, and the direction of change was correctly predicted in 65.3% of instances. Calibration analysis showed the model tended to systematically underestimate high values and vice versa, but recalibration by applying a shrinkage factor worsened the model's performance. The suggested rule exhibits promising performance for most instances, rendering it useful for non-invasive trend monitoring and triaging purposes. However, single-point estimates carry considerable uncertainty that precludes their use for definitive, high-stakes clinical decisions. Validation on larger cohorts and recalibration utilizing more elaborate modeling methods are recommended before it is adopted for regular use. The trial was prospectively registered at the clinicaltrials.gov registry ( https://register. gov/ , registration number: NCT06166875, registration date: 4 December 2023).
Acute aortic syndromes (AAS), including aortic dissection, intramural haematoma (IMH), and penetrating atherosclerotic ulcer (PAU), are uncommon but life-threatening causes of chest pain. Computed tomography angiography (CTA) is highly sensitive for AAS but is increasingly overutilised despite low diagnostic yield, exposing patients to radiation, contrast risk, and healthcare cost. The ADvISED rule-out algorithm, combining the Aortic Dissection Detection Risk Score (ADD-RS) with serum D-dimer, has demonstrated high negative predictive value (NPV) in prospective studies but has limited external validation. We performed a retrospective cohort study of adult emergency department patients within a tertiary cardiothoracic referral network in southern New Zealand who underwent CTA for suspected AAS between January 2018 and January 2024. Clinical records were reviewed to retrospectively calculate ADD-RS and extract D-dimer results prior to imaging. CTA findings served as the reference standard. The primary outcome was the NPV and failure rate of the ADvISED rule-out algorithm (low ADD-RS [0-1] plus negative D-dimer < 500 ng/mL). Of 1392 CTA studies reviewed, 1000 met inclusion criteria. Forty-one patients (4.1%) were diagnosed with AAS. Among patients with low ADD-RS and negative D-dimer (n = 180), one case of AAS (IMH) was identified, yielding an NPV of 99.4% and a failure rate of 0.6%. No Stanford type A AAS were missed. Most non-AAS diagnoses were non-specific chest pain (45%) or cardiac conditions (20%), with fewer than 1% benefiting from alternative angiographic diagnoses. In this regional emergency department cohort, the ADvISED rule-out algorithm demonstrated excellent negative predictive value and safely excluded AAS in low-risk patients. External validation in this population supports its use as a clinical decision aid to reduce unnecessary CTA utilisation without compromising patient safety. Prospective implementation studies are warranted to further assess its impact on imaging stewardship and clinical outcomes.
The ability to acquire new skills is essential throughout the lifespan and allows older adults to maintain independence and quality of life. Age-related declines in learning may stem from impairments in declarative systems supporting rule-based (RB) reasoning, procedural systems supporting associative learning, or their interaction. Prior work has yielded mixed findings regarding which of these specific processes (simple rules, complex rules, or procedural acquisition) is disproportionately affected by aging. Category learning provides a useful paradigm to disentangle these possibilities, as it distinguishes between RB tasks supported by the declarative system and information-integration (II) tasks driven by the procedural system. The present study compared younger (n = 53; aged 17-49 years) and older (n = 30; aged 60-79 years) adults on a one-dimensional (1RB), a two-dimensional (2RB), and an II category learning task. Bayesian survival analyses revealed that older adults reached criterion at approximately 57% of the rate of younger adults in the 1RB task, 78% in the 2RB task, and 75% in the II task. Thus, age-related slowing was greatest in the simplest RB condition and weaker in the more complex 2RB and II tasks. The 1RB effect was also estimated with greater clarity, whereas the 2RB and II effects were directionally similar but more uncertain. These effects may reflect impairments in either or both learning systems or difficulty shifting between them. (PsycInfo Database Record (c) 2026 APA, all rights reserved).
Health Technology Assessment (HTA) supports evidence-based decision-making, but integrating economic evaluation within Multi-Criteria Decision Analysis (MCDA) remains challenging in hospital-level HTA. This study developed and preliminarily applied an integrated decision-support framework combining MCDA, economic evaluation, and contextualized evidence assessment to support adoption recommendations. A pragmatic digital framework integrated MCDA with Budget Impact Analysis (BIA) and Cost-Consequence Analysis (CCA) within a rule-based decision matrix. The economic module estimated cost per patient, incremental cost, budget impact, cost-consequence outputs, and, when appropriate, a supportive soft ICER. Evidence was assessed through structured critical appraisal, Summary of Findings tables, and outcome relevance, using a GRADE-informed approach mapped onto the predefined 0-1-3-5-7-9 MCDA evidence scale. Operational robustness was assessed through Failure Mode and Effects Analysis (FMEA) and self-audit controls. In a case study comparing disposable and reusable continence care systems, the disposable option showed a lower MCDA score than the current standard (2.60 vs 4.80; ΔMCDA = -2.20) and a higher cost per patient (€1.00 vs €0.65; incremental cost €0.35). Although the 3-year budget impact was €2,634 and remained within the institutional affordability threshold, the technology was classified as dominated because it generated lower value at a higher cost. The final recommendation was not favorable for routine adoption. The framework supports transparent integration of MCDA and economic evaluation in hospital-level HTA and helps distinguish affordability from overall value. The case study suggests that technologies should not be adopted solely because their budget impact is acceptable when the value-risk profile is unfavorable. Further validation across technologies and settings is required.
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The measurement of the angiogenic biomarkers placental growth factor (PlGF) and soluble fms-like tyrosine kinase-1 (sFlt-1) are increasingly used to support the prediction and diagnosis of preeclampsia (PE) in routine clinical practice. There are an increasing number of methods available for the analysis of these markers but data showing their analytical comparability is limited. The assays for PlGF and sFlt-1 from Revvity were evaluated and compared against Roche methods that are used in current clinical practice in Oxford. Imprecision and paired analytical comparisons studies were undertaken and data evaluated for numeric agreement and concordance relative to manufacturer recommended rule-in and rule-out thresholds for PE. Imprecision estimates for the Revvity PlGF and sFlt-1 methods calculated from quality control material analysed during the evaluation were between 3.2 and 9.0 CV%. Revvity method precision profiles derived from 581 clinical specimens analysed in duplicate had a median CV% for PlGF of 1.8%, IQR 2.3% and for sFlt-1 a median CV% of 1.1%, IQR 1.5%. Comparison against the Roche PlGF and sFlt-1 methods in 437 clinical specimens showed an overall Passing-Bablok regression relationship for PlGF of y = -23.4 + 0.73x (r = 0.983) and for sFlt-1, y = -87.7 + 0.40x (r = 0.971). However, there was statistically significant (p < 0.0001) concentration dependant relative bias for both methods and the calculated ratio. Concordance of the sFlt-1:PlGF ratio relative to manufacturer specific rule-in and rule-out thresholds was 95.2%. The Revvity methods for PlGF and sFlt-1 are precise and correlate with the Roche methods. However, numeric agreement precludes result interchangeability and the use of common rule-in and rule-out thresholds. The manufacturer specific thresholds should be applied in clinical practice. Further work is required to understand how method differences impact clinical outcomes and their causes.
Ultrasonography is the standard for diagnosing steatotic liver disease (SLD), but its use in population-based health screening is often limited by resource and workflow constraints. We evaluated alanine aminotransferase (ALT) and two non-imaging indices, the Fatty Liver Index (FLI) and Hepatic Steatosis Index (HSI), for screening attenuation imaging (ATT)-defined steatosis. We retrospectively analyzed 2,394 adults who underwent health checkups. Abdominal ultrasonography with ATT was optional and performed in participants who elected to undergo it. Steatosis grades were defined using ATT cutoffs (S0-S3), with SLD defined as S1-S3. Diagnostic performance was assessed using area under the receiver operating characteristic curve (AUROC), and screening-oriented thresholds were examined using prespecified rule-out (sensitivity ≥90%) and rule-in (specificity ≥90%) criteria. SLD prevalence was 35.5% (850/2,394). For detecting SLD, AUROCs were 0.653 for ALT, 0.692 for FLI, and 0.703 for HSI (both vs ALT, p < 0.001). Screening-oriented thresholds showed negative predictive values of 79.1%-82.3% and positive predictive values of 60.2%-67.4%, indicating modest but clinically useful rule-out and rule-in performance. In lean participants, HSI showed higher discrimination than ALT (AUROC 0.651 vs 0.561), and HSI also remained favorable in women. The advantage of FLI and HSI over ALT was more apparent at earlier steatosis stages than at severe stages. Using ATT as a quantitative reference, FLI and HSI discriminated ATT-defined SLD better than ALT, supporting their use as practical non-imaging tools for initial screening in routine health screening and primary care settings when ultrasonography is not readily available.
Self-renewing divisions of stem cells at the growing tip universally govern plant development. In basal land plants, a single apical stem cell (AC) undergoes successive 120-degree rotational divisions while maintaining a self-similar tetrahedral geometry with three division walls, recapitulating the helically symmetric body architecture. The mechanisms by which AC geometry and mechanics determine the division axis and its rotation are largely unknown. Here, we develop two 3D multicellular mathematical models to address these questions. Our geometrical model reveals that the least area rule, coordinated with the AC surface curvature, is sufficient to drive rotational divisions by rotating the geometric proportion of the AC. Furthermore, by incorporating biologically plausible cell growth mechanics, we show that the tetrahedral AC and its rotational division spontaneously emerge from a spherical cell. Notably, the maximal tension rule confers superior robustness against stochastic fluctuations in division orientation compared to the least area rule, because the sequential formation of division walls continuously updates the tension distribution to guide subsequent orientation. These results suggest that the tetrahedral AC and the helically symmetric body plan are natural consequences of self-renewing cell divisions, imposed by 3D geometry and/or mechanics.
Large language models (LLMs) show promise for text-based pathology tasks, yet most reported applications remain experimental, lack formal clinical validation, or operate outside secure, health system-approved environments. We developed and clinically validated a rule-guided, agent-based LLM that assists gastrointestinal (GI) biopsy reporting by automating report structuring while preserving full diagnostic authority with the pathologist. The AI agent (Microsoft 365 Copilot) ran within an enterprise-approved, HIPAA-compliant Microsoft 365 environment, configured with a fixed rule-based system configuration prompt and a quick-text knowledge base. In a prospective validation, 94 GI biopsy cases were evaluated by subspecialty GI pathologists using specimen container labels extracted from the laboratory information system and pathologist-entered shorthand diagnoses. Agent outputs were reviewed for formatting accuracy, organ and procedure identification, shorthand expansion fidelity, blank diagnosis enforcement, and diagnostic safety. The agent preserved specimen part structure and correctly identified organ, sub-organ, and procedure context in 100% of cases; shorthand expansion was accurate in all applicable cases. Minor formatting deviations occurred in 8 cases (8.5%) without affecting diagnostic meaning. Two cases (2%) showed minor diagnostic misinterpretation, in which descriptive container-label terms (e.g., "ulcer," "erosion") were incorporated into diagnostic text; no hallucinated diagnoses were identified. Repeatability testing on cases enriched for descriptive labels showed 81% identical outputs across 105 runs (19% variability), with non-reproducible semantic leakage in 3% of runs. A comparative time study showed faster AI-assisted reporting (mean 39 vs 72 seconds for speech-to-text and 76 seconds for manual typing; ∼33-37 second reductions, p < 0.05), measured across the full workflow through sign-out, with lower variability. By restricting this end-to-end, production-embedded agent to rule-guided structuring, formatting, and controlled shorthand expansion while prohibiting diagnostic inference, the system achieved high efficiency, consistency, and seamless workflow integration on real GI biopsy cases. Low-frequency, stochastic errors and minor variability remain inherent to LLMs despite strict constraints; although infrequent, they indicate such systems are best suited for non-diagnostic, clerical augmentation rather than autonomous use. All output therefore requires pathologist careful review before sign-out. These findings support constrained, agent-based LLMs to safely enhance reporting efficiency while preserving diagnostic responsibility and human oversight.
Accurate preoperative characterization of solitary pulmonary nodules (SPNs), particularly differentiation of benign from malignant lesions and assessment of adenocarcinoma invasiveness, remains challenging based on morphological features alone. We investigated whether integrating 1024-matrix ultra-high-resolution computed tomography (UHRCT) with two liquid-biopsy signals, urinary cellular energy metabolism (CEM) and a seven tumor-associated autoantibody (7-TAAb) panel, could improve diagnostic performance in surgically treated patients with SPNs. In this single-center prospective study, consecutive adults with SPNs (≤3 cm) scheduled for video-assisted thoracoscopic surgery between January 2022 and December 2024 were enrolled (n = 183). All patients underwent preoperative UHRCT (1024×1024), urinary CEM testing, and 7-TAAb testing. A paired subgroup (n = 85) additionally underwent conventional HRCT (512×512) within 1 month before surgery. Postoperative histopathology served as the reference standard. Diagnostic performance metrics were calculated for each modality, parallel-rule combined strategies, and probability-based logistic regression models. Among 183 patients, 164 (89.6%) had malignant nodules. UHRCT achieved the best single-modality discrimination (AUC, 0.831; sensitivity, 87.2%; specificity, 78.9%), outperforming CEM (AUC, 0.605) and 7-TAAbs (AUC, 0.558). Under the parallel-rule strategy, multimodal testing increased sensitivity but markedly reduced specificity (sensitivity 98.8%, specificity 9.5%). The probability-based fully integrated model achieved the highest AUC (0.946). At the Youden-index threshold of 0.816, this model yielded sensitivity of 92.7%, specificity of 84.2%, PPV of 98.1%, NPV of 57.1%, and accuracy of 91.8%. In the paired comparison (n = 85), UHRCT showed higher sensitivity (92.0% vs. 68.0%) and specificity (90.0% vs. 73.3%) than HRCT. For invasiveness assessment, positivity rates of both urinary CEM (57.6% vs. 31.6%) and 7-TAAbs (53.8% vs. 31.0%) were higher in invasive adenocarcinoma than in pre-invasive lesions. In surgically selected patients with SPNs, 1024-matrix UHRCT provided the strongest single-modality diagnostic information, while urinary CEM and 7-TAAbs offered complementary biological signals associated with invasive adenocarcinoma pathology. Probability-based integration provided a more balanced diagnostic framework than a simple parallel-rule strategy. Given the high prevalence of malignancy and the limited number of benign lesions, these findings should be considered exploratory and require external validation in broader outpatient and screening cohorts.
Indocyanine green (ICG) is the most widely used fluorophore in fluorescence-guided surgery (FGS), and its microenvironment-dependent spectral response is relevant for system design, intersystem comparisons, and phantom development. To characterize ICG with excitation-emission matrices (EEMs) in the microenvironments of dimethyl sulfoxide (DMSO), bovine serum albumin (BSA) solutions, and 3D-printed (3DP) resin and assess excitation-dependent emission, including red-edge excitation shifts (REES) and departures from Kasha's rule of excitation-independent emission. EEMs and absorbance spectra were acquired with extracted excitation spectra, emission spectra, emission peaks, centroids, and integrated emission areas under the curves (AUCs). Concentration-dependent behavior was examined in DMSO, and albumin concentration dependence was assessed from 5 to 100    mg / mL . Data processing employed robust local regression to mitigate excitation scattering artifacts. ICG in DMSO exhibited excitation-independent emission consistent with Kasha-Vavilov behavior. By contrast, ICG in BSA solution and 3DP resin displayed excitation-dependent emission with pronounced REES and additional nonlinear departures from Kasha's rule. To our knowledge, this represents the first documentation of REES and broader anti-Kasha effects for ICG or any FGS fluorophore. Within the excitation range most relevant to ICG-FGS ( ∼ 760 to 805 nm), emission spectra of the BSA solution and 3DP resin overlapped closely, with similar AUC-based comparisons, suggesting that ICG in 3DP resin can serve as a suitable surrogate reference for albumin-bound ICG. The EEM characterization shows that excitation-dependent behavior is a defining feature of ICG in biologically relevant environments, demonstrating that emission cannot be assumed to follow classical Kasha-Vavilov behavior. Reliable comparisons and imaging system design therefore require spectra acquired at defined excitation wavelengths with AUC integration within the emission detection band. Excitation-specific spectra from EEMs establish a consistent framework for intersystem comparisons and phantom standards, whereas the resulting datasets provide a practical spectroscopic reference for addressing excitation-dependent behavior in ICG sensing applications.
To examine whether a transparent, rule-based cardiorenal-metabolic classification distinguished mortality and cardiovascular outcome patterns among adults with type 2 diabetes (T2D). This retrospective cohort included 61,250 adults with T2D from Hong Kong DM2016. Three phenotypes were defined from baseline cardiorenal burden and hypertension: lower-risk metabolic, hypertensive metabolic, and cardiorenal disease. Outcomes were all-cause and cardiovascular mortality, myocardial infarction, stroke, heart failure, and atrial fibrillation. Because individual follow-up times were unavailable in the public dataset, cardiovascular event outcomes were evaluated in outcome-specific at-risk cohorts. Modified Poisson regression estimated risk ratios (RRs). The phenotypes comprised 29.4%, 20.9%, and 49.8% of participants, respectively. Compared with the lower-risk metabolic phenotype, the cardiorenal disease phenotype was associated with higher risks of all six outcomes; adjusted RRs ranged from 2.59 (95% CI, 2.36-2.84) for all-cause mortality to 9.17 (95% CI, 6.50-12.94) for myocardial infarction. The hypertensive metabolic phenotype was associated with myocardial infarction (RR, 1.56; 95% CI, 1.02-2.39), stroke (RR, 7.63; 95% CI, 5.27-11.06), and atrial fibrillation (RR, 1.76; 95% CI, 1.30-2.38), but not heart failure. This transparent, rule-based classification summarized differences in recorded mortality and cardiovascular outcomes in T2D but should be interpreted as a descriptive framework rather than a validated prediction tool.
Lupus nephritis (LN) is a major complication of systemic lupus erythematosus (SLE). This study evaluated the association of C1q-circulating immune complexes (C1q CIC) with LN and their potential adjunctive rule-out value compared with conventional biomarkers. We conducted a retrospective analysis of 883 SLE patients from the Asia Pacific Lupus Collaboration (APLC) cohort in Taiwan. C1q CIC was assessed for its association with disease activity and compared to anti-dsDNA, C3, and C4. Logistic regression and ROC analysis were performed. C1q CIC levels were significantly elevated in active SLE and in non-renal manifestations, including cutaneous involvement, serositis, and hematologic abnormalities. In patients with LN, C1q CIC levels were significantly higher than in those without LN, whereas anti-dsDNA, C3, and C4 showed no significant differences. Overall discriminative performance was modest, and C1q CIC is not suitable as a diagnostic or screening tool for LN. At a cutoff of 5.31 μg Eq/mL, C1q CIC showed a high negative predictive value (NPV = 86.04%) but low positive predictive value (PPV = 29.51%). In stratified analysis, discriminative ability was limited in patients with low disease activity (SLEDAI-2K < 4; AUC = 0.55), whereas NPV remained high (97.15%). C1q CIC may serve as an adjunctive rule-out biomarker for LN, particularly when levels are low or in patients with low disease activity. Although not suitable for diagnosis or screening, its relatively high NPV may help identify patients at lower risk of LN. Results should be interpreted in conjunction with clinical and laboratory assessment.
Physical activities can be divided into indoor and outdoor activities. While outdoor activities offer enjoyable fitness opportunities, they are often limited by weather conditions. Unfavorable weather conditions such as cold, rain, fog, or snow can significantly re-duce physical activity levels, posing risks such as heat stress, dehydration, or cold-related injuries. To address these challenges, we have developed the concept of an automated eCoaching system that provides personalized activity recommendations based on real-time weather data. Our system uses an algorithm to annotate, process, and classify the collected data, generating tailored suggestions for indoor or outdoor exercise. This information is semantically represented using an Ontology framework. We have conducted a comprehensive study by collecting weather data for 18 months from thirteen cities in southern Norway. Furthermore, we have developed rules to determine the appropriate activity types corresponding to different weather conditions. The classification performance of the system has been rigorously evaluated using metrics such as accuracy, precision, recall, F1 score, and Matthews correlation coefficient (MCC). Remarkably, the decision tree classifier achieved an accuracy of 99.1%. To increase interpretability, we used local model-independent interpretable explanations (LIME) to explain individual predictions. The consistency of the Ontology model has been verified using inference, providing a reliable semantic representation and efficient rule-based recommendation modeling. In addition, we have developed various test cases of the system to evaluate eCoaching recommendations under different weather scenarios. This approach provides users with accurate and contextually relevant guidance, promoting continuous physical activity regardless of external weather conditions.
To design and validate a Spanish-language artificial intelligence-based application to support the diagnosis of primary headaches by non-expert physicians. Retrospective observational study for diagnostic development and validation based on clinical records. Neurology outpatient clinics receiving patients referred from primary care (level 2 headache care). A total of 1,029 adult patients with a diagnosis of 17 types of primary headache confirmed by an expert neurologist according to the criteria of the International Classification of Headache Disorders, 3rd edition (ICHD-3), treated at two hospital centers between 2022 and 2024 were included. Sensitivity, specificity, F1-score and accuracy of the rule-based diagnostic algorithm and the supervised learning model. The application integrates a structured clinical questionnaire that includes most primary headache diagnoses defined in the ICHD-3. The rule-based algorithm achieved a sensitivity of 89.8% (95% CI: 87.9-91.5), specificity of 99.4% (95% CI: 99.2-99.5), F1-score of 91.8% (95% CI: 90.3-93.1), and accuracy of 93.3% (95% CI: 91.5-94.8). The supervised learning model showed a sensitivity of 88.1% (95% CI: 84.0-91.8), specificity of 99.1% (95% CI: 98.6-99.5), F1-score of 88.5% (95% CI: 84.6-92.0), and accuracy of 85.5% (95% CI: 79.3-91.4). Cefalytics (https://cefalytics.com/) shows high diagnostic performance and may represent a useful support tool for non-expert physicians, particularly in primary care, facilitating greater diagnostic accuracy and earlier therapeutic optimization. These results require external validation in an independent cohort within this setting.
To evaluate 68Ga-pentixafor PET/CT in the surgical management of primary aldosteronism (PA), with emphasis on its relationship with adrenal venous sampling (AVS), KCNJ5 mutation status, tracer uptake, and postoperative outcomes. This retrospective single-center cohort screened 929 consecutive patients with suspected PA from November 2021 to February 2025. The final cohort included 162 patients who underwent unilateral adrenalectomy and 6-month follow-up; 83 also underwent AVS. Patients treated before September 2024 followed an AVS-guided pathway, and those treated thereafter followed a PET/CT-guided pathway. Outcomes were assessed by PASO criteria. Firth logistic regression, overlap weighting, paired PET/CT-versus-AVS analysis, and genotype-stratified analyses were performed. Clinical and biochemical complete success did not differ significantly between the PET-guided and AVS-guided groups. Among patients with both tests, unilateral PET/CT showed high positive predictive value versus AVS (56/57, 98.2%), but 26 of 82 AVS-confirmed unilateral PA cases had negative or bilateral PET findings. All KCNJ5-mutated patients in the PET-status cohort were PET-positive, whereas 22 of 52 KCNJ5-nonmutated patients were PET-negative. KCNJ5 mutation and CT lesion size were independently associated with PET positivity. SUVmax LI was associated with biochemical complete success, including within KCNJ5-nonmutated patients. 68Ga-pentixafor PET/CT provides strong rule-in information when uptake is clearly unilateral. Negative or bilateral PET/CT, especially in small or KCNJ5-nonmutated lesions, should be interpreted cautiously and should not preclude AVS-based evaluation.
Interpretability remains a central challenge in the deployment of deep neural networks, particularly in safety-critical and decision-sensitive fields. This work proposes a unified framework for post-hoc global interpretability by transforming general neural network architectures-including the Residual Network and Transformer-into equivalent decision diagrams over real-valued inputs and multi-class outputs. These decision diagrams provide a transparent, structured view of the neural network's overall behavior, where each path encodes a tractable and interpretable decision rule. We identify a counterintuitive yet effective modification in the node merging process during diagram construction, which leads to faster entropy reduction and smaller equivalent intervals, thereby significantly reducing the diagram size while maintaining equivalence with the original network. The resulting representations not only support the exploration of logical properties, such as decision boundary tracing, equivalence checking, robustness analysis, and model counting, but also serve as globally interpretable surrogates for the original neural networks. Experiments validate the effectiveness and scalability of the proposed methods, highlighting their potential for reliable neural network analysis and verification.