Judging Valve Assessment

• Judging Valve is an evaluative framework combining mechanical modeling, imaging analysis, and data-driven algorithms to assess valve integrity and performance in diverse applications.
• It integrates quantitative indices from physical, hydraulic, and biomedical measurements to diagnose faults, predict failures, and guide interventions.
• Hybrid methods merging physics-based models with machine learning empower robust, real-time and retrospective evaluations of valve function across industrial and clinical domains.

A judging valve is any device, algorithm, or set of criteria intended to determine the status, integrity, or suitability of a valve—mechanical, hydraulic, or biological—for its intended function. Within the engineering, medical, and industrial domains, “judging” a valve encompasses multidimensional quantitative evaluations of dynamic response, structural integrity, functional competence, or the presence of faults or failure modes. This assessment draws upon mechanical modeling, imaging analysis, flow measurement, statistical learning, and diagnostic algorithms for robust, real-time, or retrospective categorization of valve performance and health across settings ranging from industrial control systems to biomedical prostheses.

1. Physical Principles and Modeling Frameworks

Valve judgment in technical and clinical settings relies on accurate physical modeling to capture the relevant mechanical and fluid-dynamic phenomena. In biological valves (e.g., mitral or aortic), the tissue is modeled as an inelastic, anisotropic, viscoelastic membrane governed by continuum-mechanics equations. The leaflet position $$\mathbf{x} = \mathbf{X} + \mathbf{u}(\mathbf{X}, t)$$ is a function of the material coordinate $\mathbf{X}$ and the displacement field $\mathbf{u}$, from which the deformation gradient $$\mathbf{F} = \frac{\partial \mathbf{x}}{\partial \mathbf{X}}$$ and Green–Lagrange strain tensor $$\mathbf{E} = \frac{1}{2}(\mathbf{F}^T \mathbf{F} - \mathbf{I})$$ are constructed. Constitutive relations typically combine an isotropic ground matrix, anisotropic fiber reinforcement, and inelastic (viscous) flow rules, with stresses described by the second Piola–Kirchhoff tensor $$S = 2 \frac{\partial W}{\partial C} + S_{\text{viscous}}$$ (Karvandi et al., 2015).

In engineered systems such as hydraulic or control valves, orifice flow equations model the pressure-flow relationship: $$Q = C \epsilon A \sqrt{\frac{2(p_1 - p_c)}{\rho_1}}$$ where $Q$ is volumetric flow rate, $C$ and $\epsilon$ are empirical coefficients, $A$ is area, $p_1$ and $p_c$ are upstream and vena contracta pressures, and $\rho_1$ is fluid density. Parameters like pressure-recovery $F_L$, choked-flow coefficients $F_F$, and loss coefficients $K_y$ further specify dynamic response (Chi et al., 2020). Fault-detection modeling in digital hydraulics uses detailed balance equations for mass, flow, and force, augmented by sparse error variables to identify anomalies (Ersfolk et al., 2018).

2. Quantitative Indices of Valve Function and Failure

Robust judgment requires extraction of quantitative indices that characterize normal versus faulty or pathological operation. In patient-specific mitral valves, indices include:

• Maximum leaflet tip displacement (systole): Normal 12–18 mm; <10 mm = restricted; >20 mm = prolapse.
• Peak fiber strain / strain-rate: Normal $0.10$–$0.20$ (strain), $1.0$–$1.5$ $s^{-1}$ (strain-rate); elevated in myxomatous disease.
• Coaptation length: <5 mm predicts significant regurgitation.
• Principal stress extrema: Local $S_2 > 200$ kPa suggests rupture risk (Karvandi et al., 2015).

In bileaflet mechanical heart valves, indices include:

Dysfunction (%)	$U_\mathrm{max}$ (m/s)	$\Delta P_\mathrm{max}$ (mmHg)	$\tau_{w,\mathrm{peak}}$ (Pa)	max $|\omega|$ (s$^{-1}$)
0	2.53	20	241.7	$2.09 \times 10^3$
50	3.89	35	448.9	$5.94 \times 10^3$
100	4.90	63	952.8	$9.79 \times 10^3$

Shear at hinge regions above 500 Pa, $\Delta P_\mathrm{max} > 40$ mmHg, or $U_\mathrm{max} > 4$ m/s indicate severe dysfunction (Khalili et al., 2017).

In control valve applications, root mean squared error (RMSE), mean absolute percentage error (MAPE), and parameter estimates from hybrid models—e.g., discharge and recovery coefficients—serve as quantitative criteria (Chi et al., 2020). In hydraulic systems, residuals from steady-state flow-balance models and the evolution of continuous error variables (e.g., $x^o_i$, $x^c_i$) indicate the presence and location of faults (Ersfolk et al., 2018).

3. Judgment via Imaging, Data-Driven, and Hybrid Methods

Judging valve function encompasses both model-based and data-driven pipelines, depending on the source and nature of available signals.

Medical Imaging: Deep-learning pipelines exploit cine MR or echo images to localize annular and leaflet landmarks, enabling automated extraction of kinematic and strain-based judgment indices with accuracy near (and sometimes exceeding) expert manual tracing. Long-axis strain, strain rate, and diastolic filling velocities are computed directly from landmark trajectories (Kerfoot et al., 2020).

Finite Element and Continuum-Mechanics Models: Multi-plane echocardiography data are mapped onto 3D finite element meshes governed by inelastic balance laws, with model parameters calibrated against ex vivo and in vivo measurements, and validated by comparing predicted and echo-measured displacements and strains (Karvandi et al., 2015).

Hybrid (Physics + Machine Learning) Models: Series hybrid models combine mechanistic orifice flow laws with data-driven residual modeling using unbiased LSSVM, providing robust flow/pressure prediction and fault diagnosis. State parameters—upstream/downstream pressure, stem position, and temperature—are tracked, and deviations in fitted parameters signal transitions to faulty states (Chi et al., 2020).

Model-Based + Sparse Optimization in Hydraulics: Online detection of digital hydraulic valve faults utilizes quantile regression ($\ell_1$ minimization) to identify sparse faults using only three pressure sensors and command logs, automatically discriminating between open/closed faults via thresholded, filtered error variables (Ersfolk et al., 2018).

Image-Based Defect Detection: High-resolution two-step segmentation networks (FaultNet) with geometric computer vision rules deliver pixel-level valve shape and robust integrity judgments for railway valves, surpassing convolutional classifier baselines in recall and accuracy (Pahwa et al., 2019).

Machine Learning Prescription in Valve Replacement: For TAVR, doubly robust counterfactual risk estimation and optimal policy trees integrate heterogeneous patient data sources to construct interpretable rulesets for device selection, achieving statistically significant reductions in permanent pacemaker rates by refining valve judgment criteria (Paschalidis et al., 9 Dec 2025).

4. Experimental Validation and Performance Metrics

Judging frameworks are validated by direct comparison of predicted indices and classifications to gold standard experimental or clinical measurements.

Biomechanical and Hemodynamic Verification: Patient-specific finite element models show echo-aligned displacement residuals within a few percent and strain-rate errors <0.05 s$^{-1}$ across population studies (Karvandi et al., 2015). Mechanical valve studies calibrated via micro-PIV and micro-pillar WSS sensors quantitatively resolve spatiotemporal wall shear stress fields, identifying absolute magnitude and impact region differences between competing prosthetic designs, such as BMHV vs. TMHV (peak $\tau_w$ 10.23 vs. 5.15 Pa, respectively) (Li et al., 2018).

Hydraulic System Evaluation: Hardware-in-the-loop test rigs with controlled valve faults consistently yield correct fault identification within 1–2 s; false-positive error variables in healthy systems are suppressed below 0.12 by EWMA filtering, achieving near-zero false-alarm rates (Ersfolk et al., 2018).

Image-Based Fault Detection: FaultNet achieves 97.3% accuracy and 100% recall on 73 rail-valve images, a $>4\%$ gain over the best ResNet/DenseNet baselines, due to precise segmentation and robust geometric judgment (Pahwa et al., 2019).

Clinical Risk and Outcome Reduction: In TAVR, rule-based model-guided device prescription reduces permanent pacemaker implantation rates by 26.5% and 16.6% in internal and external cohorts, respectively, with 95% confidence intervals demonstrating statistical robustness (Paschalidis et al., 9 Dec 2025).

5. Practical Implementation Guidelines and Limitations

Best practices for valve judgment implementers are defined by sensor placement, data acquisition, calibration, and system maintenance.

• Material Parameter Calibration: Use ex vivo or in situ step tests to calibrate mechanical properties, valve area and loss coefficients before deploying inferential models (Karvandi et al., 2015, Chi et al., 2020).
• Data Preprocessing: High-frequency transients and rapid task reversals should be filtered or omitted to preserve steady-state or quasi-static model validity (Ersfolk et al., 2018).
• Computational Performance: Embedded CPUs and GPUs suffice for real-time solutions to LSSVM or quantile regression problems of moderate dimensionality (e.g., 100x40 LPs solved in <500 ms) (Pahwa et al., 2019, Ersfolk et al., 2018).
• Diagnostic Thresholds: Establish operational alert thresholds on quantitative indices by statistical analysis of baseline runs, ROC analysis on labeled cohorts, or cross-validation in clinical/systematic trials (Khalili et al., 2017, Paschalidis et al., 9 Dec 2025).
• Known Limitations: Material coefficients may not fully capture in vivo mechanical properties. Imaging-based analyses are sensitive to registration errors and limited spatial resolution, and meshing strategies may miss local stress gradients or out-of-plane signal. Automated geometric rules may need retraining for edge cases or generalized anatomy (Pahwa et al., 2019, Karvandi et al., 2015).

6. Emerging Trends and Research Directions

Judging valves is increasingly a multimodal, cross-disciplinary endeavor.

• Integration of Deep Learning with Physics: Future methodologies aim to combine temporally regularized networks (e.g., ConvLSTM) or hybrid uncertainty-aware models with established balance-law frameworks for enhanced accuracy and stability (Kerfoot et al., 2020).
• Quantitative Imaging Cross-validation: Further work is needed to translate in vitro discriminators—such as normalized velocity profile shape $S$ and asymmetry $A$—to clinical imaging (e.g., 4D PC-MRI) and noninvasive diagnostics, with expected accuracy >90% for major dysfunction (Darwish et al., 2019).
• Generalization to Multivalve and Multiclass Systems: Automated segmentation and classification approaches are being extended to simultaneous detection of multiple valves, multi-fault scenarios, and real-time embedded implementations for safety-critical environments (Pahwa et al., 2019).
• Personalized and Causal Effect Modeling: Patient-specific prescription frameworks for valve devices increasingly exploit causal inference and policy-optimization, with explicit counterfactual estimation and evaluation against global and leaf-level metrics (Paschalidis et al., 9 Dec 2025).
• Mechanism-informed Fault Detection: Series hybrid models demonstrate promise for online adaptation and diagnosis, leveraging physically meaningful residuals and parameter evolution for early-warning and root-cause attribution (Chi et al., 2020, Ersfolk et al., 2018).

In summary, the judging valve paradigm encompasses a spectrum of physically grounded, algorithmically sophisticated, and clinically or industrially validated approaches for assessing valve function, structural integrity, and failure modes. Technical rigor, quantitative standards, and cross-domain model integration are foundational to objective, high-accuracy valve judgment.