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A New Method for Simulating Embolic Coils as Heterogeneous Porous Media

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Abstract

Purpose

To gain insight into the influence of coils on aneurysmal hemodynamics, computational fluid dynamics (CFD) can be used. Conventional methods of modeling coils consider the explicit geometry of the deployed devices within the aneurysm and discretize the fluid domain. However, the complex geometry of a coil mass leads to cumbersome domain discretization along with a significant number of mesh elements. These problems have motivated a homogeneous porous medium coil model, whereby the explicit geometry of the coils is greatly simplified, and relevant homogeneous porous medium parameters are approximated. Unfortunately, since the coils are not distributed uniformly in the aneurysm, the homogeneity assumption is no longer valid.

Methods

In this paper, a novel heterogeneous porous medium approach is introduced. To verify the model, we performed CFD simulations to calculate the pressure drop caused by actual deployed coils in a straight cylinder. Next, we considered three different anatomical aneurysm geometries virtually treated with coils and studied the hemodynamics using the presented heterogeneous porous medium model.

Results

We show that the blood kinetic energy predicted by the heterogeneous model is in strong agreement with the conventional approach. The homogeneity assumption, on the other hand, significantly over-predicts the blood kinetic energy within the aneurysmal sac.

Conclusions

These results indicate that the benefits of the porous medium assumption can be retained if a heterogeneous approach is applied. Implementation of the presented method led to a substantial reduction in the total number of mesh elements compared to the conventional method, and greater accuracy was enabled by considering heterogeneity compared to the homogenous approach.

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Acknowledgments

We would like to acknowledge the support from the National Science Foundation (Award #1512553). We would like to thank Endovantage, LLC for providing us with the numerical coil deployments.

Funding

This study was funded by NSF (Award #1512553).

Conflict of interest

Author Hooman Yadollahi-Farsani, Author Marcus Herrmann, Author David Frakes, and Author Brian Chong declare that they have no conflicts of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Author information

Authors and Affiliations

  1. School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA

    Hooman Yadollahi-Farsani & Marcus Herrmann

  2. School of Biological and Health Systems Engineering, Arizona State University, 501 E Tyler Mall, BLDG ECG RM#334, Tempe, AZ, 85287, USA

    Hooman Yadollahi-Farsani, David Frakes & Brian Chong

  3. School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ, USA

    David Frakes

  4. Mayo Clinic Hospital, Phoenix, AZ, USA

    Brian Chong

Authors
  1. Hooman Yadollahi-Farsani
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  2. Marcus Herrmann
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  3. David Frakes
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  4. Brian Chong
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Corresponding author

Correspondence to Hooman Yadollahi-Farsani.

Additional information

Associate Editors Dr. Ajit P. Yoganathan & Dr. Matthew J. Gounis oversaw the review of this article.

Appendices

Appendix A

Algorithm used to generate the porosity and permeability maps:

  1. (1)

    Read in the STL file.

  2. (2)

    Break the domain into a lattice of hexahedra.

  3. (3)

    For each hexahedral, find the colliding surface mesh triangles.

  4. (4)

    Watertight the coil portion which falls within the hexahedral by closing the open faces.

  5. (5)

    Find the porosity (coil volume/sac volume).

  6. (6)

    Use the Carman-Kozeny equation to find permeability.

  7. (7)

    Associate each porosity/permeability to its position in the CFD mesh using a tri-linear interpolation method and generate the map.

  8. (8)

    Use the generated map as an input for the source term in momentum equation.

Appendix B

See Tables 1, 2, 3, 4, 5, and 6.

Table 1 Total number of mesh elements for the cases considered in the study.
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Table 2 Aneurysmal K.E. (kg/ms2) for the anatomical cases considered in the study.
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Table 3 Pressure drop values (mmHg) found numerically across the verification model.
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Table 4 Grid Convergence Index (GCI) analysis for the anatomical models based on aneurysmal K.E. (kg/ms2).
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Table 5 Grid Convergence Index (GCI) analysis for the coiled verification model based on pressure drop values.
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Table 6 Two-norms calculated for different cases in the numerical studies for Mesh 2.
Full size table

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Yadollahi-Farsani, H., Herrmann, M., Frakes, D. et al. A New Method for Simulating Embolic Coils as Heterogeneous Porous Media. Cardiovasc Eng Tech 10, 32–45 (2019). https://doi.org/10.1007/s13239-018-00383-1

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  • DOI: https://doi.org/10.1007/s13239-018-00383-1

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