4D Flow MRI Wall Shear Stress Estimation via Pressure Gradient Correction
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Solution Overview
Problem
Current methods for estimating wall shear stress (WSS) using 4D flow MRI suffer from inaccuracies due to limited spatial resolution and measurement noise, leading to underestimation of WSS magnitudes and inconsistencies with other modalities like CFD and PIV.
Innovation Solution
The proposed method, pressure-gradient induced velocity-gradient correction (PG-VGC), corrects velocity gradients using a reconstructed pressure field and flow physics constraints, specifically incorporating conservation laws of mass and linear momentum to improve WSS estimation accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If 4D flow MRI is used to estimate WSS, then WSS information can be obtained from in vivo blood flow data, but the estimated WSS magnitude is inaccurate and underestimates true WSS values
Solution Approach 1:
The method uses conservation laws of mass and linear momentum as feedback constraints to correct the velocity gradient estimation. The pressure gradient derived from momentum conservation is fed back to adjust the velocity field, ensuring the corrected velocity gradient satisfies both continuity and momentum equations, thereby improving WSS accuracy and consistency with CFD/PIV results
Solution Approach 2:
The method changes the parameter used for WSS calculation by introducing a corrected velocity gradient that incorporates pressure gradient information. Instead of using only the raw velocity gradient from 4D flow MRI, the method computes a corrected velocity gradient that accounts for pressure variations, leading to more accurate WSS magnitudes
2Ease of operation
If limited spatial resolution 4D flow data is used, then in vivo measurements can be obtained, but WSS estimation is significantly underestimated compared to high-resolution modalities
Solution Approach 1:
The pressure gradient acts as an intermediary that bridges the gap between low-resolution velocity measurements and accurate WSS estimation. By introducing the pressure gradient field as an intermediate variable that satisfies conservation laws, the method recovers accurate velocity gradients and WSS values even from limited-resolution 4D flow data
Solution Approach 2:
The method performs preliminary correction of the velocity gradient using conservation laws before computing WSS. By pre-correcting the velocity field to satisfy mass and momentum conservation, the method ensures that subsequent WSS calculations are accurate, effectively compensating for the limited spatial resolution of the original 4D flow data
3Ease of manufacture
If conventional WSS estimation methods are used, then processing can be performed with standard 4D flow data, but the results show large discrepancies (0-2 Pa vs 0-30 Pa) compared to CFD and PIV
Solution Approach 1:
The method incorporates feedback from conservation laws to correct the velocity gradient. By using the continuity equation (mass conservation) and momentum equation as feedback constraints, the method systematically corrects the velocity field to produce physically consistent results that match CFD and PIV measurements, eliminating the large discrepancy in WSS magnitudes
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
PG-VGC enhances WSS estimation accuracy by up to 100% for synthetic data and reduces underestimation by 39-50% for aneurysmal flows, with predicted mean WSS being 31-50% higher than prior methods, aligning with CFD results and improving correlation with vortical flow structures.
Implementation Method 1
The conservation laws of mass and linear momentum are incorporated to formulate a linear system
Implementation Method 2
The conservation laws of mass and linear momentum are incorporated to formulate a linear system
Data Source
AI summary
The invention generally relates to systems and methods that employ a novel wall shear stress (WSS) estimation method for 4D flow MRI. In certain embodiments, the invention provides systems and methods for determining Wall Shear Stress (WSS) with 4D flow Magnetic Resonance Imaging (MRI), that involve receiving 4D MRI flow data; calculating a velocity gradient (and optionally calculating the pressure field) from the 4D MRI flow data; correcting the velocity gradient (such as by using a spatial gradient of the pressure field to correct the velocity gradient), thereby producing a corrected velocity gradient; and determining a WSS from the corrected velocity gradient.