Real-Time Vascular Blood Flow Reconstruction Technology Integrating Physics-Informed Neural Networks and 3D Gaussian Splatting

This article introduces an innovative meshless framework that embeds Physics-Informed Neural Networks (PINNs) into 3D Gaussian Splatting technology to achieve real-time reconstruction of 3D hemodynamics from sparse 2D angiography, while solving the Navier-Stokes equations to render blood flow velocity and pressure fields. This technology addresses the limitation of traditional 2D angiography in not being able to intuitively present 3D blood flow characteristics, providing real-time support for cardiovascular disease diagnosis and interventional surgery.

Real-Time Requirements for Medical Imaging

In modern medical diagnosis, angiography is a core method for evaluating cardiovascular diseases. However, traditional 2D angiography cannot intuitively present 3D hemodynamic characteristics, so doctors have to rely on experience for reconstruction, which has spurred an urgent need for real-time 3D blood flow reconstruction.

Key Technical Principles

• Physics-Informed Neural Networks (PINNs): Embed physical laws (such as the Navier-Stokes equations) into neural network training. Ensure results satisfy physical conservation through physical residual terms in the loss function, and handle complex geometric boundaries without mesh division.
• 3D Gaussian Splatting Technology: Represent scenes using millions of anisotropic 3D Gaussian ellipsoids to achieve high-quality real-time rendering. Compared to NeRF, it has advantages of faster training, higher frame rates, and explicit geometric representation, making it suitable for medical image reconstruction.

Core Innovations

This project embeds PINNs into the 3D Gaussian Splatting optimization process to build an end-to-end meshless framework, which simultaneously completes three tasks: reconstructing 3D vascular geometry from sparse 2D projections, solving blood flow velocity fields, and calculating pressure distributions. It avoids the mesh generation step of traditional CFD, enabling real-time clinical applications.

Data Flow and Processing Pipeline

Input: sparse 2D angiography sequence → 3D Gaussian Splatting module optimizes the Gaussian representation of the vascular surface to reconstruct geometry → PINNs module predicts local flow velocity and pressure at Gaussian points and constrains them via physical equations → Both modules are optimized collaboratively, outputting 3D vascular models, flow velocity vectors, and pressure distribution maps.

Network Architecture Design

PINNs use a fully connected network. The input is 3D coordinates and time (time-series data), and the output is three velocity components and pressure values. The loss function includes three parts: data fitting term (matching projection data), physical residual term (satisfying the Navier-Stokes equations), and regularization term (ensuring solution smoothness).

Real-Time Rendering Optimization

A custom Gaussian Splatting rasterization renderer is used to simultaneously render geometric surfaces and color-coded flow velocity/pressure fields. Through CUDA acceleration and memory optimization, interactive frame rates are achieved on consumer GPUs. An incremental update mechanism is implemented to locally update parameters when new angiography frames arrive, reducing latency.

Diagnostic Assistance

Provides real-time navigation for interventional surgeries (such as angioplasty and stent implantation). Doctors can instantly view 3D blood flow changes to evaluate surgical effects, and more accurately identify eddy current regions, abnormal flow velocity points, and pressure gradient changes.

Scientific Research & Teaching

Provides interactive blood flow visualization methods for medical education, helping medical students understand cardiovascular diseases; provides researchers with tools for quantitative analysis of large-scale blood flow data.

Current Challenges

1. Data Quality Dependence: The accuracy of sparse projection reconstruction is limited by the coverage of projection angles; 2. Generalization Ability: The model needs to be tuned for different vascular types.

Future Directions

Introduce time-series modeling to capture pulsatile blood flow characteristics; integrate patient-specific parameters to achieve personalized modeling; explore more efficient neural representation methods.

The integration of Physics-Informed Neural Networks and 3D Gaussian Splatting is an important progress in the AI-driven development of medical imaging. It solves the computational bottleneck of traditional methods and opens up new possibilities for real-time hemodynamic analysis. With algorithm optimization and hardware improvements, this technology is expected to move from research prototypes to routine clinical applications, providing more accurate diagnosis and treatment plans for cardiovascular disease patients.