How might Flow Vortex Analysis Help in Characterization

How might Flow Vortex Analysis Help in Characterization of ICA Aneurismal Flow: A Case Study Using Siemens CFD Prototype Software and VTK Jingfneg Jiang 1, Kevin Sunderland 1, Gouthami Chintalapani 2, Kevin Royalty 2 and Charles M Strother 3 1 Michigan Technological University 2 Siemens Medical Solutions (USA), Inc. 3 University of Wisconsin-Madison ASNR 2015

Disclosure 1. 2. J. Jiang and K. Sunderland are supported by a research contract from Siemens Medical Solution (USA), Inc. G. Chintalapani and K. Royalty are employed by Siemens Medical Solution (USA), Inc.

Introduction l Hemodynamics plays a vital role in the origin, growth and rupture of aneurysms l A growing body of literature indicates computational fluid dynamics (CFD) simulations could potentially provide insight into clinical management of cerebral aneurysms 1, 2

What is CFD? l CFD produces results of mathematical models (i. e. Navier-Stokes equations) that researchers postulate capture the basic laws governing the physics of fluid flows. l Widely used and valued for industrial applications such as airplane design l Image-based CFD simulations 3 are under a rapid development l l “Patient-specific” vessel geometry is currently used Patient-specific physiological data could potentially further enhance the predictions

Clinical Utility of CFD? l Significant anatomical and hemodynamic variations make interpretation of aneurismal dynamics difficulty l Viewing time-resolved 3 D hemodynamic (hundreds of) images may become a timeconsuming and difficult task for physicians Jiang and Strother, ICS, 2009

Purpose Objective: To improve potential clinical utility of CFD, automated flow analysis may be useful l l Vortex core may provide relevant information related to flow physics The usefulness of vortex core analysis was demonstrated through a pilot study using 5 sets of ICA tandem (closely-space) aneurysms Study Design: Design • 10 lateral ICA aneurysms in 5 patients; two closely spaced aneurysms in each patients • CFD simulations of those six aneurysms were performed using Siemens CFD prototype software • Automated vortex core analysis was performed using in-house software derived from Visualization Tool. Kit (VTK, Kitware Inc. , NY)

Workflow

Step 1: CFD Simulations

CFD Simulation Conditions l Typical waveforms (transient flow rates) were selected based on averaged Phase-contrast MR measurements 6, 7 l For instance, averaged flow rate at the ICA was 280 ml/min l Transient CFD simulations were performed for 2 cardiac cycles l A voxel-based method 8 (i. e. Siemens CFD prototype solver) was used to solve the Navier-Stokes equations l Time steps were sufficiently fine and were adaptively chosen by the Siemens CFD solver l 18 phases/steps of the second cardiac cycles were analyzed

Step 2: Isolate Aneurismal Flow This algorithm was based on an published aneurysm extraction algorithm 10 and implemented in the VTK

Vortex Analysis l The well-known Lambda 2 method by Jeong and Hussain 9 was used to define the vortex core areas l l Two negative eigenvalues from a matrix derived from local velocity gradients A simple Marching-cube algorithm was used to segment out the vortex core volumes l Implemented in the VMTK 5

Temporal Flow Stability l Flow stability was assessed by tracking changes of the vortex core(s) over time l l Calculate a temporally –averaged velocity field Calculate the time-averaged vortex core(s) from the timeaverage velocity field (purple colored vortex core below) Compare the (volume) overlap between the time-averaged vortex core(s) and the instantaneous vortex core(s) The (temporal) flow stability assessment is between 0 and 1 and there, is easy to interpret l Low overlap means low (temporal) flow stability

Results The extracted vortex cores were visually consistent with velocity Vector plot Vortex Cores Velocity Plot Purple and green colors represent two vortex cores of the proximal and distal aneurysms, respectively

Results The calculate overlap value was consistent with visual assessments of temporal flow stability Overlap = 0. 57 Overlap = 0. 87

Summary Results Mean Overlap of Vortex Cores Proximal Aneurysms 0. 90 ± 0. 06 Distal Aneurysms 0. 78 ± 0. 08 • Temporal flow stability in proximal aneurysms were greater as compared to that in distal aneurysms (p = 0. 03 [rank-sum test]) in data investigated • Flow instability in the distal aneurysm might be induced by disturbed flow coming out from the proximal aneurysm

Study Limitations l Vortex analysis results are yet to be verified with imaging measurements (e. g. Phase-contrast MR angiography) l Only 10 aneurysms were studied

Conclusion and Future Work l Preliminary results demonstrate that vortexcore analysis can potentially provide relevant information to characterize aneurismal hemodynamics l l Assessment of temporal flow stability through vortex core analysis might be an independent variable Future work is to verify results and explore its use in a clinical setting

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References [7]M. Zhao, S. Amin-Hanjani, S. Ruland, A. P. Curcio, L. Ostergren, and F. T. Charbel, "Regional cerebral blood flow using quantitative MR angiography, " AJNR Am J Neuroradiol, vol. 28, pp. 1470 -3, Sep 2007. [8] V. Mihalef, P. Sharma, A. Kamen, and T. Redel, “An immersed porous boundary method for computational fluid dynamics of blood flow in aneurysms with flow diverters, ” in Proceedings of the ASME Summer Bioengineering Conference, 2012. [9] J. Jeong and E. Hussain, “On the identification of a vortex”, J. of Fluid Mechanics, vol. 285, pp. 6995, 1995. [10] J. Jiang and C. M. Strother, "Interactive decomposition and mapping of saccular cerebral aneurysms using harmonic functions: its first application with "patient-specific" computational fluid dynamics (CFD) simulations, " IEEE Trans Med Imaging, vol. 32, pp. 153 -64, Feb 2013.