4D Flow MRI Helicity Index (HI): Explanation and Clinical Context Helicity quantifies the local alignment between velocity and vorticity in a flow field. In cardiovascular 4D Flow MRI, the helicity density is the dot product of the velocity vector and vorticity (the curl of velocity), and its normalized form—Local Normalized Helicity (LNH)—is defined as LNH = (v · ω) / (|v||ω|), ranging from −1 (left-handed) to +1 (right-handed) helical flow. The Helicity Index (HI) implemented here follows the volumetric absolute LNH approach: it reports the fraction of the segmented ROI volume where |LNH| exceeds a chosen threshold, commonly 0.60. This thresholded volume fraction has been shown to distinguish healthy aortas from bicuspid aortic valve (BAV) phenotypes and to track relationships with aortic size, peak velocity, and valve effective orifice area. Plane- or pathline-based helicity quantification exists (historically termed Helical Flow Index, HFI) and is conceptually related; for users adhering to plane/pathline workflows, a weighted segmental proxy is also provided for practicality.
How to obtain inputs: After standard 4D Flow MRI preprocessing (phase unwrapping/anti-aliasing, noise masking, eddy-current correction), segment the vessel lumen for the ROI (e.g., entire thoracic aorta or sub-territories). Compute LNH voxel-wise from the velocity field and its vorticity, then measure: (1) total ROI volume and (2) the subset volume where |LNH| ≥ threshold (default 0.60). If your software provides the mean |LNH|, include it for context. Keep all volumes in consistent units (e.g., voxels or mL).
Clinical significance: Elevated helical content is a reproducible feature in BAV aortopathy and other flow-altering conditions. Volumetric |LNH|-based metrics can differentiate cohorts and associate with disease markers (e.g., aortic diameter, stenosis severity). Helicity analysis complements wall shear stress, turbulent kinetic energy, and flow eccentricity, contributing to a more comprehensive, mechanism-aware hemodynamic profile. However, universal “normal ranges” are not established; values should be interpreted using internal references or published cohort percentiles, with attention to acquisition resolution, noise, and segmentation quality.
Methodological notes: This calculator mirrors the publication-aligned volumetric |LNH| paradigm (absolute LNH thresholding, frequently 0.60) and exposes a plane/pathline proxy acknowledging the earlier helical quantification framework. For risk studies, report HI alongside imaging parameters (VENC, spatial/temporal resolution), segmentation strategy, chosen threshold, and—when possible—segmental breakdown (AAo, arch, DAo) to aid comparability across centers.
References
Stankovic Z, et al. 4D flow imaging with MRI: methods, visualization, and quantification in cardiovascular disease. Cardiovasc Diagn Ther. 2014. (Overview of 4D Flow MRI and advanced hemodynamic metrics, including helicity).
Morbiducci U, et al. In vivo quantification of helical blood flow in human aorta by time-resolved 3D cine PC-MRI. Ann Biomed Eng. 2009. (Introduced Lagrangian helical flow quantification / HFI using pathlines).
García J, et al. Volumetric quantification of absolute local normalized helicity in BAV and aortic dilatation. Magn Reson Med. 2016/2017. (Established voxel-wise absolute LNH and thresholded volumetric analysis; commonly |LNH| ≥ 0.60).
Gustafsson F, ISMRM 2017. Quantification of helical flow and aortic tortuosity using 4D Flow MRI. (Explicit definition of LNH = (v·ω)/(|v||ω|)).
Moffatt HK. Helicity and singular structures in fluid dynamics. PNAS. 2014. (Fluid dynamics foundation: helicity as velocity–vorticity correlation).