[Paper Review] Physics-informed neural networks for improving cerebral hemodynamics predictions

Mohammad Sarabian, Hessam Babaee+1 more|arXiv (Cornell University)|Aug 25, 2021

Advanced MRI Techniques and Applications44 references4 citations

TL;DR

This paper introduces a physics-informed neural network (PINN) framework that fuses sparse transcranial Doppler (TCD) ultrasound measurements with 3D angiography data to predict high-resolution, physically consistent cerebral hemodynamics, including velocity, vessel area, and pressure. The model significantly improves hemodynamic predictions over purely physics-based simulations by reducing errors from boundary condition uncertainties and modeling inaccuracies, achieving strong agreement with 4D flow MRI and enabling accurate diagnosis of cerebral vasospasm.

ABSTRACT

Determining brain hemodynamics plays a critical role in the diagnosis and treatment of various cerebrovascular diseases. In this work, we put forth a physics-informed deep learning framework that augments sparse clinical measurements with fast computational fluid dynamics (CFD) simulations to generate physically consistent and high spatiotemporal resolution of brain hemodynamic parameters. Transcranial Doppler (TCD) ultrasound is one of the most common techniques in the current clinical workflow that enables noninvasive and instantaneous evaluation of blood flow velocity within the cerebral arteries. However, it is spatially limited to only a handful of locations across the cerebrovasculature due to the constrained accessibility through the skull's acoustic windows. Our deep learning framework employs in-vivo real-time TCD velocity measurements at several locations in the brain and the baseline vessel cross-sectional areas acquired from 3D angiography images, and provides high-resolution maps of velocity, area, and pressure in the entire vasculature. We validated the predictions of our model against in-vivo velocity measurements obtained via 4D flow MRI scans. We then showcased the clinical significance of this technique in diagnosing the cerebral vasospasm (CVS) by successfully predicting the changes in vasospastic local vessel diameters based on corresponding sparse velocities measurements. The key finding here is that the combined effects of uncertainties in outlet boundary condition subscription and modeling physics deficiencies render the conventional purely physics-based computational models unsuccessful in recovering accurate brain hemodynamics. Nonetheless, fusing these models with clinical measurements through a data-driven approach ameliorates predictions of brain hemodynamic variables.

Motivation & Objective

• To address the limitations of purely physics-based computational models in predicting accurate cerebral hemodynamics due to uncertainties in boundary conditions and modeling errors.
• To develop a data-driven framework that integrates sparse clinical measurements (TCD) with computational fluid dynamics (CFD) to enhance hemodynamic predictions.
• To generate high spatiotemporal resolution maps of velocity, vessel area, and pressure across the entire cerebrovasculature.
• To validate the model against in-vivo 4D flow MRI data and demonstrate clinical utility in diagnosing cerebral vasospasm.
• To reduce reliance on idealized assumptions in hemodynamic modeling by embedding physical laws into a neural network architecture.

Proposed method

• The framework employs a physics-informed neural network (PINN) that enforces the conservation of mass and momentum via the Navier-Stokes equations within the loss function.
• Input features include real-time TCD velocity measurements at multiple intracranial locations and baseline vessel cross-sectional areas from 3D angiography.
• The PINN is trained to predict full 3D velocity, area, and pressure fields across the cerebrovasculature while satisfying physical constraints.
• The model is optimized using a loss function combining data fidelity (TCD measurements) and physics consistency (Navier-Stokes residuals).
• The architecture is designed to generalize across subjects and handle sparse, noisy clinical data while maintaining physical plausibility.
• Validation is performed against in-vivo 4D flow MRI scans to assess accuracy in hemodynamic parameter estimation.

Experimental results

Research questions

• RQ1 Can a physics-informed neural network effectively improve hemodynamic predictions when combined with sparse clinical measurements?
• RQ2 How does the integration of TCD data and 3D angiography enhance the accuracy of cerebral hemodynamic maps compared to purely physics-based models?
• RQ3 To what extent can the model predict local vessel diameter changes associated with cerebral vasospasm from limited velocity measurements?
• RQ4 Does embedding physical laws into the neural network loss function lead to more reliable and physically consistent hemodynamic predictions?
• RQ5 Can the model achieve high-resolution hemodynamic mapping across the entire cerebrovasculature using only a few clinical measurements?

Key findings

• The PINN framework significantly outperformed purely physics-based CFD simulations in predicting hemodynamic parameters due to reduced sensitivity to boundary condition uncertainties.
• The model achieved strong agreement with in-vivo 4D flow MRI measurements, validating its predictive accuracy across the cerebrovasculature.
• The framework successfully predicted local vessel diameter changes associated with cerebral vasospasm using only sparse TCD velocity measurements.
• Incorporating physical laws into the neural network loss function led to more physically consistent and reliable hemodynamic predictions.
• The model demonstrated robustness in generating high-resolution velocity, area, and pressure maps from limited clinical data, enabling comprehensive hemodynamic assessment.
• The approach enables noninvasive, real-time, and whole-vasculature hemodynamic evaluation, enhancing diagnostic potential for cerebrovascular diseases.