Advertisement

Information Theoretic Measurement of Blood Flow Complexity in Vessels and Aneurysms: Interlacing Complexity Index

  • Jose M. PozoEmail author
  • Arjan J. Geers
  • Alejandro F. Frangi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10434)

Abstract

Haemodynamics is believed to be a crucial factor in the aneurysm formation, evolution and eventual rupture. The 3D blood flow is typically derived by computational fluid dynamics (CFD) from patient-specific models obtained from angiographic images. Typical quantitative haemodynamic indices are local. Some qualitative classifications of global haemodynamic features have been proposed. However these classifications are subjective, depending on the operator visual inspection.

In this work we introduce an information theoretic measurement of the blood flow complexity, based on Shannon’s Mutual Information, named Interlacing Complexity Index (ICI). ICI is an objective quantification of the flow complexity from aneurysm inlet to aneurysm outlets. It measures how unpredictable is the location of the streamlines at the outlets from knowing the location at the inlet, relative to the scale of observation.

We selected from the @neurIST database a set of 49 cerebral vasculatures with aneurysms in the middle cerebral artery. Surface models of patient-specific vascular geometries were obtained by geodesic active region segmentation and manual correction, and unsteady flow simulations were performed imposing physiological flow boundary conditions. The obtained ICI has been compared to several qualitative classifications performed by an expert, revealing high correlations.

Keywords

Aneurysms CFD Haemodynamics Flow complexity Mutual information 

Notes

Acknowledgments

The work has been partially supported by the project OCEAN (EP/M006328/1) funded by the Engineering and Physical Sciences Research Council.

References

  1. 1.
    Aref, H., Blake, J.R., Budišić, M., Cartwright, J.H.E., Clercx, H.J.H., Feudel, U., Golestanian, R., Gouillart, E., Guer, Y.L., van Heijst, G.F., et al.: Frontiers of chaotic advection. arXiv preprint arXiv:1403.2953 (2014)
  2. 2.
    Bogunović, H., Pozo, J.M., Villa-Uriol, M.C., Majoie, C.B.L.M., van den Berg, R., Gratama van Andel, H.A.F., Macho, J.M., Blasco, J., San Román, L., Frangi, A.F.: Automated segmentation of cerebral vasculature with aneurysms in 3DRA and TOF-MRA using geodesic active regions: an evaluation study. Med. Phys. 38, 210 (2011)CrossRefGoogle Scholar
  3. 3.
    Cebral, J.R., Mut, F., Weir, J., Putman, C.M.: Association of hemodynamic characteristics and cerebral aneurysm rupture. Am. J. Neuroradiol. 32(2), 264–270 (2011)CrossRefGoogle Scholar
  4. 4.
    Geers, A.J., Larrabide, I., Radaelli, A.G., Bogunovic, H., Kim, M., van Andel, H.A.F.G., Majoie, C.B., VanBavel, E., Frangi, A.F.: Patient-specific computational hemodynamics of intracranial aneurysms from 3D rotational angiography and CT angiography: an in vivo reproducibility study. Am. J. Neuroradiol. 32(3), 581–586 (2011)CrossRefGoogle Scholar
  5. 5.
    Jang, B., Funakoshi, M.: Chaotic mixing in a helix-like pipe with periodic variations in curvature and torsion. Fluid Dyn. Res. 42(3), 035506 (2010)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Lin, Z., Thiffeault, J.L., Doering, C.R.: Optimal stirring strategies for passive scalar mixing. J. Fluid Mech. 675, 465–476 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Mathew, G., Mezić, I.: Metrics for ergodicity and design of ergodic dynamics for multi-agent systems. Physica D 240(4), 432–442 (2011)CrossRefGoogle Scholar
  8. 8.
    McDaid, A.F., Greene, D., Hurley, N.: Normalized mutual information to evaluate overlapping community finding algorithms. arXiv preprint arXiv:1110.2515 (2011)
  9. 9.
    Meng, H., Tutino, V., Xiang, J., Siddiqui, A.: High WSS or low WSS? Complex interactions of hemodynamics with intracranial aneurysm initiation, growth, and rupture: toward a unifying hypothesis. Am. J. Neuroradiol. 35(7), 1254–1262 (2014)CrossRefGoogle Scholar
  10. 10.
    Millan, R.D., Dempere-Marco, L., Pozo, J.M., Cebral, J.R., Frangi, A.F.: Morphological characterization of intracranial aneurysms using 3-D moment invariants. IEEE Trans. Med. Imaging 26(9), 1270–1282 (2007)CrossRefGoogle Scholar
  11. 11.
    Reymond, P., Merenda, F., Perren, F., Rüfenacht, D., Stergiopulos, N.: Validation of a one-dimensional model of the systemic arterial tree. Am. J. Physiol.-Heart Circulatory Physiol. 297(1), H208–H222 (2009)CrossRefGoogle Scholar
  12. 12.
    Rinkel, G.J.E., Djibuti, M., Algra, A., Van Gijn, J.: Prevalence and risk of rupture of intracranial aneurysms a systematic review. Stroke 29(1), 251–256 (1998)CrossRefGoogle Scholar
  13. 13.
    Robert, C., Casella, G.: Monte Carlo Statistical Methods. Springer Science & Business Media, Heidelberg (2013)zbMATHGoogle Scholar
  14. 14.
    Sforza, D.M., Kono, K., Tateshima, S., Viñuela, F., Putman, C., Cebral, J.R.: Hemodynamics in growing and stable cerebral aneurysms. J. Neurointerventional Surg. 8(4), 407–412 (2016)CrossRefGoogle Scholar
  15. 15.
    Shannon, C.E., Weaver, W.: The Mathematical Theory of Information. University of Illinois Press, Urbana (1949)zbMATHGoogle Scholar
  16. 16.
    Thiffeault, J.L.: Using multiscale norms to quantify mixing and transport. Nonlinearity 25(2), R1 (2012). http://stacks.iop.org/0951-7715/25/i=2/a=R1MathSciNetCrossRefGoogle Scholar
  17. 17.
    Villa-Uriol, M.C., Berti, G., Hose, D.R., Marzo, A., Chiarini, A., Penrose, J., Pozo, J.M., Schmidt, J.G., Singh, P., Lycett, R., Larrabide, I., Frangi, A.F.: @neurIST complex information processing toolchain for the integrated management of cerebral aneurysms. Interface Focus 1(3), 308–319 (2011)CrossRefGoogle Scholar
  18. 18.
    VTK community: VTK visualization toolkit (2014). http://www.vtk.org
  19. 19.
    Wiggins, S., Ottino, J.M.: Foundations of chaotic mixing. Philos. Trans. R. Soc. A 362(1818), 937–970 (2004)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Xia, H.M., Shu, C., Chew, Y.T., Wang, Z.P.: Approximate mapping method for prediction of chaotic mixing in spatial-periodic microchannel. Chem. Eng. Res. Des. 88(10), 1419–1426 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Jose M. Pozo
    • 1
    Email author
  • Arjan J. Geers
    • 2
  • Alejandro F. Frangi
    • 1
  1. 1.Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB), Department of Electronic and Electrical EngineeringThe University of SheffieldSheffieldUK
  2. 2.CISTIB, Department of Information and Communication TechnologiesUniversitat Pompeu FabraBarcelonaSpain

Personalised recommendations