Noninvasive Assessment of Arterial Compliance and Lumen Pressure in Human Carotid Arteries Using Physics-Informed Neural Networks and Ultrasound Imaging: A Clinical Feasibility Study

Technical Summary: Noninvasive Assessment of Arterial Compliance and Lumen Pressure Using PINNs and Ultrasound

Problem Statement
Cardiovascular disease remains a leading cause of global mortality, with arterial stiffness serving as a critical independent predictor of adverse outcomes. While global measures like carotid-femoral Pulse Wave Velocity (PWV) are valuable for risk stratification, they provide only spatially averaged estimates. Many vascular pathologies, such as atherosclerotic plaques and carotid stenosis, induce localized, heterogeneous changes in mechanical properties that global metrics miss. Traditional imaging modalities face limitations: MRI offers high resolution for plaque composition but is constrained by cost, time, and spatial resolution (~0.7 mm); ultrasound elastography (shear wave) struggles in stenotic or calcified arteries due to low signal-to-noise ratios and complex wave interactions. Furthermore, translating ultrasound measurements (wall motion and flow) into quantitative, spatially resolved estimates of arterial compliance and lumen pressure remains a significant challenge, particularly because analytical models (e.g., Moens-Korteweg) assume homogeneity and infinite geometry, which are violated in diseased vessels. Existing inverse methods often require precise, non-invasive boundary conditions that are difficult to obtain clinically.

Methodology
This study evaluates a Physics-Informed Neural Network (PINN) framework designed to solve the inverse problem of estimating spatially varying arterial compliance and lumen pressure from high-frame-rate ultrasound data.

• Data Acquisition: High-frame-rate ultrasound data (3 kHz effective frame rate) were acquired from five human subjects (one healthy, four with carotid stenosis) using a Verasonics Vantage 256 system and a Philips L7-4 transducer. The protocol utilized Plane Wave Imaging with coherent compounding.
• Signal Processing:
  • Pulse Wave Imaging (PWI): Extracted arterial wall motion (displacement and velocity) via normalized cross-correlation (NCC) on beamformed RF data.
  • Vector Flow Imaging (VFI): Estimated 2D blood flow velocity using 2D NCC and Singular Value Decomposition (SVD) filtering to separate flow from wall motion. In stenotic cases, where turbulent flow degraded VFI data, the framework relied solely on wall motion data.
• PINN Architecture:
  • Governing Equations: The model is based on linearized 1D partial differential equations (PDEs) describing pulse wave propagation in compliant, heterogeneous vessels, incorporating the Bramwell-Hill relation to link lumen area changes to pressure via compliance ($k_p$).
  • Network Structure: A fully connected feedforward network with multiscale Fourier feature mapping (to handle disparate spatiotemporal scales) and three hidden layers (64 neurons, tanh activation). Inputs are space ($x$) and time ($t$); outputs are lumen area ($A$), axial flow velocity ($u$), and pressure ($P$).
  • Loss Function: A composite loss function minimizes the mismatch between network predictions and measured data (data fidelity) while enforcing adherence to the governing PDEs (physics residual). The model is mesh-free and does not require explicit boundary condition specification.
• Training: The network was trained using the Adam optimizer for 20,000 iterations. For healthy subjects, data were downsampled (16 elements) to reduce computation time; stenotic cases utilized full resolution (128 elements) to capture localized heterogeneity.

Key Contributions

1. Clinical Feasibility of PINNs: This study demonstrates the first application of the previously validated PINN framework to in vivo human carotid arteries, moving beyond in silico and phantom studies.
2. Robustness to Data Scarcity: The framework successfully adapted to clinical challenges, specifically the unreliability of flow data in stenotic regions. By relying on wall motion data alone in stenotic cases, the model maintained convergence and accuracy without requiring explicit boundary conditions.
3. Spatially Resolved Estimation: Unlike global PWV, the model generates spatially varying maps of arterial compliance and lumen pressure, directly correlating mechanical property changes with anatomical features visible on B-mode ultrasound.
4. Non-Invasive Pressure Reconstruction: The model reconstructed luminal pressure waveforms without invasive catheterization or explicit boundary condition inputs, producing waveforms consistent with physiological expectations.

Results

• Healthy Subject: The model achieved high accuracy with normalized differences of <0.2% for both wall motion and flow velocity. The estimated compliance map was uniform, consistent with the healthy anatomy. The global average compliance derived from PINN ($2.98 \times 10^{-9} \text{ m}^2/\text{Pa}$) differed from the Moens-Korteweg estimate ($1.3 \times 10^{-9} \text{ m}^2/\text{Pa}$), attributed to the PINN's integration of flow and anatomical effects versus the analytical model's simplifying assumptions.
• Stenotic Subjects:
  • Accuracy: Wall motion reconstruction errors remained low (<0.48% maximum difference), even in complex geometries like bifurcations.
  • Compliance Mapping: The model successfully identified focal compliance variations (stiffening) that spatially correlated with atherosclerotic plaques and anatomical transitions (e.g., carotid bulb) observed in B-mode images. In cases with acoustic shadowing (indicating calcification), the model correctly estimated reduced compliance.
  • Flow Data Handling: In stenotic cases, VFI data were noisy or missing due to turbulence. The model successfully converged using wall motion data only, demonstrating adaptability to incomplete clinical data.
• Computational Performance: Training times ranged from 20 minutes (healthy, downsampled) to 1.5 hours (stenotic, full resolution) on a standard desktop GPU (NVIDIA Quadro RTX 5000), indicating clinical feasibility for offline analysis.

Significance and Claims
The paper claims that this work establishes the clinical feasibility of using PINNs for non-invasive, patient-specific mapping of localized arterial compliance and luminal pressure. The findings support the potential for this technology to be translated into clinical workflows for:

• Risk Stratification: Identifying "vulnerable" plaques based on localized mechanical properties rather than just stenosis degree.
• Personalized Assessment: Providing detailed vascular health profiles without invasive procedures.
• Complementary Diagnostics: Serving as a pre-screening tool to identify high-risk patients for further investigation via MRI or IVUS, or as a longitudinal monitoring tool.

The authors modestly note that while the results are promising, absolute accuracy validation against invasive pressure measurements was not performed in this feasibility study. They emphasize that the approach currently functions as an offline analysis tool and that future work must address model dimensionality (moving to 2D/3D), nonlinear tissue properties, and larger, diverse patient cohorts to fully realize clinical adoption.