30 Apr 4D flow MRI pressure estimation using velocity measurement-error based weighted least-squares
Pressure measured from the cardiovascular system is widely used to diagnose disease. Pressure reconstruction methods are increasingly of interest with the development of 4D flow magnetic resonance imaging (MRI) which noninvasively measures time-resolved velocity fields in-vivo. However, several error sources and limitations inherent to in vivo 4D flow MRI result in unreliable pressure fields.
This work introduces a robust pressure reconstruction method which employs weighted least-squares (WLS) for pressure integration. Pressure gradients are calculated from the velocity fields, and velocity errors are estimated from the velocity divergence for incompressible flow. Pressure gradient errors are estimated by propagating the velocity errors through Navier-Stokes momentum equation. A weight matrix is generated based on the pressure gradient errors, then employed for pressure reconstruction. Error analysis indicated that the proposed method is more robust to velocity measurement errors. Improvement on pressure results was found to be more significant for the cases with spatially-varying velocity error level, with reductions in error ranging from 50% to over 200%. Finally, the method was applied to flow in patient-specific cerebral aneurysms.
Pressure calculated by WLS, as opposed to the Poisson equation, was more consistent with the flow structures and showed better agreement between the in vivo and in vitro data. These results suggest the utility of WLS method to obtain reliable pressure field from clinical flow measurement data.
The proposed WLS pressure reconstruction method employs weights based on velocity errors estimated from velocity-divergence to enhance the pressure accuracy. The methods were applied to in vivo 4D flow MRI measurements in basilar tip and internal carotid artery aneurysms
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