Improving MRI turbulence quantification by addressing the measurement errors caused by the derivatives of the turbulent velocity field – Sequence development and in-vitro validation

Abstract

Purpose

To improve the current method for MRI turbulence quantification which is the intravoxel phase dispersion (IVPD) method. Turbulence is commonly characterized by the Reynolds stress tensor (RST) which describes the velocity covariance matrix. A major source for systematic errors in MRI is the sequence's sensitivity to the variance of the derivatives of velocity, such as the acceleration variance, which can lead to a substantial measurement bias.

Methods

We developed a Cartesian phase contrast sequence with FAST velocity encoding and two separately measured partial echoes with opposite readout directions. This design aims to reduce the high-order gradient moments that are responsible for the described measurement error. Velocity encoding directions follow the ICOSA6 scheme to capture the full RST. Turbulence data is reconstructed using the intra-voxel phase dispersion (IVPD) technique. We validated this sequence in vitro using a periodic hill flow benchmark with highly anisotropic turbulence. MRI data underwent extensive averaging, with multiple velocity encoding values employed to reduce noise and isolate systematic effects.

Results

The RST data obtained from the new sequence agree well with the ground truth. Compared to a state-of-the-art sequence, the maximum errors were reduced by factor five.

Conclusion

Simple adjustments to current MRI protocols can greatly enhance turbulence measurement accuracy through the reduction of high-order gradient moments. The proposed measures include applying FAST velocity encoding, high readout bandwidth, and a highly asymmetric readout. Ringing artifacts due to the asymmetric readout can be removed via a second, inverted readout.