Physics-Informed Neural Networks for 4D Flow MRI Enhancement: Towards Super-Resolution, Denoising, and Flow Rate Consistency

다국어 초록 (Multilingual Abstract)

Four-dimensional flow magnetic resonance imaging (4D Flow MRI) provides time- resolved, three-dimensional visualization of cardiovascular hemodynamics, but its accuracy is limited by noise, low resolution, and phase artifacts. These deficiencies hinder reliable estimation of critical biomarkers such as wall shear stress and volumetric flow rate. This study presents Physics-Informed Neural Networks (PINNs) for reconstructing high-fidelity, physically consistent velocity fields from degraded 4D flow MRI data. The network integrates the Navier–Stokes, continuity equations, and flow rate constraints into a composite loss function that enforces data fidelity and physical constraints. Loss normalization and projecting conflicting gradient (PCGrad) optimization maintain balance among multiple objectives, while a learnable turbulent viscosity term improves stability in turbulent flows. Validation across synthetic, in-vitro, and in-vivo datasets—including aortic stenosis and regurgitation cases—demonstrated substantial improvements in flow rate consistency and velocity reconstruction accuracy. By embedding physical laws into deep learning optimization, the proposed PINNs achieve simultaneous denoising, super-resolution, and physiological coherence. This physics-constrained paradigm bridges computational fluid dynamics and medical imaging, advancing 4D flow MRI toward robust and clinically reliable hemodynamic assessment.

국문 초록 (Abstract)

4차원 유동 자기공명영상(4D Flow MRI)은 시간에 따른 3차원 심혈관 혈류역학을 시각화할 수 있으나, 잡음, 낮은 공간 해상도, 위상(phase) 아티팩트로 인해 정확도가 제한된다. 이러한 결함은 벽전단응력(wall shear stress)과 체적 유량(volumetric flow rate)과 같은 핵심 바이오마커를 신뢰성 있게 추정하는 데 장애가 된다. 본 연구는 열화된 4D Flow MRI 데이터로부터 고충실도이면서 물리적으로 일관된 속도장을 재구성하기 위해 물리 정보 신경망(Physics-Informed Neural Networks, PINNs)을 제안한다. 제안한 네트워크는 Navier–Stokes 방정식, 연속방정식, 그리고 유량 제약을 복합 손실함수에 통합하여 데이터 적합성과 물리 제약을 동시에 만족하도록 한다. 손실 정규화와 상충 그래디언트 투영(PCGrad) 최적화를 통해 다중 목적 간 균형을 유지하며, 학습 가능한 난류 점성 항을 도입하여 난류 유동에서의 학습 안정성을 향상시킨다. 합성(synthetic), in-vitro, in-vivo 데이터셋(대동맥 협착 및 역류 사례 포함) 전반에 대한 검증 결과, 유량 일관성과 속도 재구성 정확도가 유의미하게 개선됨을 확인하였다. 물리 법칙을 딥러닝 최적화 과정에 내재화함으로써, 제안한 PINNs는 잡음 제거, 초해상도, 생리학적 정합성을 동시에 달성한다. 이러한 물리 제약 기반 패러다임은 전산유체역학(CFD)과 의료영상의 간극을 연결하여, 4D Flow MRI가 보다 견고하고 임상적으로 신뢰 가능한 혈류역학 평가로 발전하는 데 기여한다.

목차 (Table of Contents)

• I. Introduction 1
• 1.1 Clinical Significance and Current Challenges in Aortic Valve Disease 1
• 1.2 Limitations in Acquiring Comprehensive Hemodynamic Information 4
• 1.3 4D Flow MRI: Assessment of Hemodynamics 5
• 1.4. Technical Limitations of 4D Flow MRI 7
• 1.5. Quantitative Illustration of 4D Flow MRI Artifacts 9
• 1.6 Data-Driven Deep Learning: Advancements and Limitations 11
• 1.7 Physics-Informed Neural Networks (PINNs) 13
• 1.7.1 Generalization Through Physics Information 13
• 1.7.2 Underexplored Gap in PINNs Research 14
• 1.8 Research Objectives 18
• II. Methods 20
• 2.1 Dataset Configurations and Pre-Processing 20
• 2.1.1 CFD 2D Dataset 20
• 2.1.2 In-vitro Experimental Flow Phantom Dataset 21
• 2.1.3 In-vivo Patient Dataset (AS and AR) 24
• 2.2 PINNs for 4D Flow MRI Hemodynamic Reconstruction 28
• 2.2.1 PINNs as Mesh-Free PDE Solvers and Constrained Optimization 28
• 2.2.2 PINNs as Continuous Regression of Physical Fields 29
• 2.2.3 Loss Functions for Data, Physics, and Flow-Rate Constraints 31
• 2.3 Optimization Strategies 37
• 2.3.1 Turbulence Modeling for Stable Optimization 37
• 2.3.2 Loss Normalization 38
• 2.3.3 Projecting Conflicting Gradients (PCGrad) 39
• 2.4 Training Stabilization and Scaling Strategies 41
• 2.4.1 Input Normalization and Coordinate Scaling Layer 41
• 2.4.2 Output Rescaling and Physical Layer 41
• 2.4.3 Learnable Turbulent Viscosity Parameterization 42
• 2.5 Numerical Implementation and Network Architecture 44
• 2.5.1 Network Architecture 44
• 2.5.2 Dataset-Specific Training and Hyperparameter Configurations 45
• 2.5.3 Sampling and Shuffle Strategy for PINNs Training 46
• 2.5.4 Hyperparameter Settings and Computational Environment 47
• 2.6 Physics Consistency Score 55
• 2.6.1 Physics Fidelity (PF): Local Continuity Compliance 55
• 2.6.2 Stroke Volume Fidelity (SVF): Global Volumetric Coherence 56
• 2.6.3 Score Mapping: Converting Error Indices to a Unified 0100 Scale 56
• 2.6.4 Physics Consistency Score (PCS): Composite Summary Measure 57
• III. Results 58
• 3.1 Performance Verification using CFD Dataset 58
• 3.1.1 Analysis of Velocity Field and Flow Rate under Ideal Conditions 58
• 3.1.2 Qualitative Comparison of Velocity Fields for Displacement Error 59
• 3.1.3 Quantitative Flow Rate Analysis of Displacement Error 60
• 3.2 Validation of Feasibility with In-vitro Phantom Data 65
• 3.2.1 TAV Phantom Analysis under Steady-Flow Conditions 65
• 3.2.2 Analysis of the Stenotic Model under Pulsatile Flow Conditions 66
• 3.3 Validation Feasibility with Clinical Data 72
• 3.3.1 Analysis of Clinical Data from AS Patients 72
• 3.3.2 Analysis of AR Patient Data 74
• 3.3.3 Physics Consistency Scores in Aortic Regurgitation 77
• 3.3.4 Physics Consistency Scores in Aortic Stenosis 79
• 3.3.5 Quantitative Performance Evaluation Using Score-Based Metrics 80
• IV. Discussion 93
• 4.1 Conceptual Overview and Significance of the Proposed Framework 93
• 4.2 Mechanistic Interpretation of the Proposed PINN Framework 95
• 4.2.1 Loss Normalization for Scale-Consistent Optimization 95
• 4.2.2 PCGrad for Dynamic Balancing of Competing Objectives 96
• 4.2.3 Turbulent Viscosity as Physics-Guided Regularization 97
• 4.2.4 Synergistic Interaction and Adaptive Learning Dynamics 97
• 4.3 Functional Strengths in 4D Flow MRI Reconstruction 100
• 4.3.1 Physics-Constrained Noise Suppression and Flow Plausibility 100
• 4.3.2 Flow Rate and Stroke Volume Consistency under Data Defect 100
• 4.3.3 Physics-Guided Super-Resolution via Continuous Representation 102
• 4.3.4 Validation with External Flow-Rate Constraints 103
• 4.4 Clinical and Physiological Implications 112
• 4.4.1 Clinical Evaluation in AS And AR Cohorts 112
• 4.4.2 Dimensionless Indices for Assessing Volumetric Consistency 112
• 4.4.3 Clinical Impact on Diagnostic Stability and Decision Confidence 113
• 4.6 Limitations 115
• 4.7 Future Works 119
• V. Conclusion 122
• References 125
• Summary in Korean 131
• Acknowledgement 132