Automatic 4D Flow MRI Segmentation Using the Standardized Difference of Means Velocity

We present a method to automatically segment 4D flow magnetic resonance imaging (MRI) by identifying net flow effects using the standardized difference of means (SDM) velocity. The SDM velocity quantifies the ratio between the net flow and observed flow pulsatility in each voxel. Vessel segmentation is performed using an F-test, identifying voxels with significantly higher SDM velocity values than background voxels. We compare the SDM segmentation algorithm against pseudo-complex difference (PCD) intensity segmentation of 4D flow measurements in in vitro cerebral aneurysm models and 10 in vitro Circle of Willis (CoW) datasets. We also compared the SDM algorithm to convolutional neural network (CNN) segmentation in 5 thoracic vasculature datasets. The in vitro flow phantom geometry is known, while the ground truth geometries for the CoW and thoracic aortas are derived from high-resolution time-of-flight (TOF) magnetic resonance angiography and manual segmentation, respectively. The SDM algorithm demonstrates greater robustness than PCD and CNN approaches and can be applied to 4D flow data from other vascular territories. The SDM to PCD comparison demonstrated an approximate 48% increase in sensitivity in vitro and 70% increase in the CoW, respectively; the SDM and CNN sensitivities were similar. The vessel surface derived from the SDM method was 46% closer to the in vitro surfaces and 72% closer to the in vitro TOF surfaces than the PCD approach. The SDM and CNN approaches both accurately identify vessel surfaces. The SDM algorithm is a repeatable segmentation method, enabling reliable computation of hemodynamic metrics associated with cardiovascular disease.

Modeling Bias Error in 4D Flow MRI Velocity Measurements

We present a model to estimate the bias error of 4D flow magnetic resonance imaging (MRI) velocity measurements. The local instantaneous bias error is defined as the difference between the expectation of the voxel's measured velocity and actual velocity at the voxel center. The model accounts for bias error introduced by the intra-voxel velocity distribution and partial volume (PV) effects. We assess the intra-voxel velocity distribution using a 3D Taylor Series expansion. PV effects and numerical errors are considered using a Richardson extrapolation. The model is applied to synthetic Womersley flow and in vitro and in vivo 4D flow MRI measurements in a cerebral aneurysm. The bias error model is valid for measurements with at least 3.75 voxels across the vessel diameter and signal-to-noise ratio greater than 5. All test cases exceeded this diameter to voxel size ratio with diameters, isotropic voxel sizes, and velocity ranging from 3-15mm, 0.5-1mm, and 0-60cm/s, respectively. The model accurately estimates the bias error in voxels not affected by PV effects. In PV voxels, the bias error is an order of magnitude higher, and the accuracy of the bias error estimation in PV voxels ranges from 67.3% to 108% relative to the actual bias error. The bias error estimated for in vivo measurements increased two-fold at systole compared to diastole in partial volume and non-partial volume voxels, suggesting the bias error varies over the cardiac cycle. This bias error model quantifies 4D flow MRI measurement accuracy and can help plan 4D flow MRI scans.