Purpose

4D flow magnetic resonance imaging (MRI) allows for the encoding of complex velocity fields over a cardiac cycle. Post processing of 4D flow MRI datatsets can be time consuming and the identification of ‘problem zones’ such as velocity aliasing or intravoxel dephasing from complex flow can be problematic, especially for large imaging volumes and high vascular density such as in cranial and hepatic scans. The risk of missing corrupt data or misinterpreting results is especially high for less experienced users as 4D flow analysis finds more widespread use. Here we introduce the concept of an automated algorithm to identify suspicious vessel segments using the idea of flow conservation throughout the complete vessel network with adjacency matrices. This method has the potential to identify vessel branches where flow conservation is violated and thereby reduce accidental misinterpretation of 4D flow data.

Methods

Adjacency matrices are commonly used in graph theory to help organize complex graphs into a structured vertices matrix. The adjacency matrix uses binary labeling to encode the connectivity of all the vertices in a simple and efficient manner as shown in Fig 1. The size of the adjacency matrix is a square matrix with a row and column length equal to the number of vertices. By altering the encoding parameter from vertices to vessel branch segments, we encode complex vessel connectivity into a binary matrix. Due to the directionality of flow, the adjacency matrix becomes asymmetric in our adapted version. The parallel between a vertex and vessel branch adjacency matrix approach can be seen in Fig1. The row of the matrix indicates the vessel branch. The 1’s column location in the associated row indicate which branches are connected to the current branch. Five cranial scans were completed for this study after IRB approval and providing consent. Imaging was performed on a clinical 3T scanner using 4D flow MRI with an undersampled radial acquisition, PC VIPR2. A vessel skeleton of the vasculature with labeled branches was automatically generated using a centerline algorithm Fig2. Subsequently, the average flow for each centerline point was calculated by generating an analysis plane perpendicular to the centerline and integrating velocity volumes over the vessel area., all with an in-house software tool (MATLAB 2015a). The average flow for each segment was represented by the mean of centerline flow values along that vessel segment near the center of each branch. Adjacency matrices were generated for the vascular tree and analyzed for flow consistency.

Results

Automatic construction of adjacency matrices was successful in all of the presented cranial cases. Conservation of flow calculations for 3 locations in a single case are presented in Fig3. The percent error increased as the analyzed bifurcation moved from large proximal to smaller distal vessels. Percent errors in flow conservation ranged from ~1-10% for good flow conservation and from 11-55% where flow was not conserved as seen in Fig4. Mislabeled junctions due noisy or incomplete angiograms was minimal in this study. The processing needed to complete all conservation of flow measurements in a single case took less than 2 minutes.

Discussion

We were able to show that quick flow conservation validation for junctions in complex vessel networks is possible using our adapted adjacency method. As the junctions moved from proximal to distal the vessel sizes decreased and the error increased accordingly. The increased error for smaller vessel was expected due to lower SNR and a high influence from the partial volume effect. The highest influence of error for this method is thought to be related primarily to vessel area calculations. Examples of some possible errors from incorrectly defined angiograms are shown in Fig5. Defining tolerance levels for incorrect flow conservation based upon junction location has yet to be completed. A comparison between different subjects was not completed in this study.

Conclusion

We introduced a new scheme for automated consistency checks of flow measures in vascular trees and demonstrated its use in 5 cranial studies. The concept of adjacency matrices coupled with vessel segments can be utilized in 4D flow MRI to quickly provide feedback on data consistency and potential problem zones. Future work utilizing the adjacency matrix and uncertainty values of all vessel segments may allow for corrective flow algorithms to be applied. The levels of tolerable uncertainty related to flow, area, and velocity when applying the corrective flow algorithm will need to be investigated further.

Acknowledgements

No acknowledgement found.

References

1) E. Schrauben, et al J Magn Reson Imaging. 2015 Nov;42(5):1458-64 2) Johnson, K. M. et al Magnetic Resonance in Medicine. 2008; 60(6), 1329-1336.