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Numerical simulation of endovascular treatment options for cerebral aneurysms

Martin Frank, Fabian Holzberger, Medeea Horvat, Jan Kirschke, Matthias Mayr, Markus Muhr, Natalia Nebulishvili, Alexander Popp, Julian Schwarting, Barbara Wohlmuth

TL;DR

This work develops a patient specific computational framework to evaluate endovascular treatment options for cerebral aneurysms by representing coils, WEB and flow diverters with geometric and mechanical models and by predicting immediate postinterventional blood flow. It combines fully resolved lattice Boltzmann simulations of incompressible flow with a complementary poro elastic homogenized approach to capture device effects without resolving every microstructure. The study provides a complete preprocessing and meshing pipeline from imaging to geometry, presents detailed device models including discrete elastic rods for coils and parametric thread based WEB and stent designs, and demonstrates numerical experiments that show flow reduction and WSS attenuation after intervention. The framework paves the way for patient specific planning and opens avenues for predicting thrombus formation and long term occlusion, with practical impact on planning and outcome assessment in intracranial aneurysm treatments.

Abstract

Predicting the long-term success of endovascular interventions in the clinical management of cerebral aneurysms requires detailed insight into the patient-specific physiological conditions. In this work, we not only propose numerical representations of endovascular medical devices such as coils, flow diverters or Woven EndoBridge but also outline numerical models for the prediction of blood flow patterns in the aneurysm cavity right after a surgical intervention. Detailed knowledge about the post-surgical state then lays the basis to assess the chances of a stable occlusion of the aneurysm required for a long-term treatment success. To this end, we propose mathematical and mechanical models of endovascular medical devices made out of thin metal wires. These can then be used for fully resolved flow simulations of the post-surgical blood flow, which in this work will be performed by means of a Lattice Boltzmann method applied to the incompressible Navier-Stokes equations and patient-specific geometries. To probe the suitability of homogenized models, we also investigate poro-elastic models to represent such medical devices. In particular, we examine the validity of this modeling approach for flow diverter placement across the opening of the aneurysm cavity. For both approaches, physiologically meaningful boundary conditions are provided from reduced-order models of the vascular system. The present study demonstrates our capabilities to predict the post-surgical state and lays a solid foundation to tackle the prediction of thrombus formation and, thus, the aneurysm occlusion in a next step.

Numerical simulation of endovascular treatment options for cerebral aneurysms

TL;DR

This work develops a patient specific computational framework to evaluate endovascular treatment options for cerebral aneurysms by representing coils, WEB and flow diverters with geometric and mechanical models and by predicting immediate postinterventional blood flow. It combines fully resolved lattice Boltzmann simulations of incompressible flow with a complementary poro elastic homogenized approach to capture device effects without resolving every microstructure. The study provides a complete preprocessing and meshing pipeline from imaging to geometry, presents detailed device models including discrete elastic rods for coils and parametric thread based WEB and stent designs, and demonstrates numerical experiments that show flow reduction and WSS attenuation after intervention. The framework paves the way for patient specific planning and opens avenues for predicting thrombus formation and long term occlusion, with practical impact on planning and outcome assessment in intracranial aneurysm treatments.

Abstract

Predicting the long-term success of endovascular interventions in the clinical management of cerebral aneurysms requires detailed insight into the patient-specific physiological conditions. In this work, we not only propose numerical representations of endovascular medical devices such as coils, flow diverters or Woven EndoBridge but also outline numerical models for the prediction of blood flow patterns in the aneurysm cavity right after a surgical intervention. Detailed knowledge about the post-surgical state then lays the basis to assess the chances of a stable occlusion of the aneurysm required for a long-term treatment success. To this end, we propose mathematical and mechanical models of endovascular medical devices made out of thin metal wires. These can then be used for fully resolved flow simulations of the post-surgical blood flow, which in this work will be performed by means of a Lattice Boltzmann method applied to the incompressible Navier-Stokes equations and patient-specific geometries. To probe the suitability of homogenized models, we also investigate poro-elastic models to represent such medical devices. In particular, we examine the validity of this modeling approach for flow diverter placement across the opening of the aneurysm cavity. For both approaches, physiologically meaningful boundary conditions are provided from reduced-order models of the vascular system. The present study demonstrates our capabilities to predict the post-surgical state and lays a solid foundation to tackle the prediction of thrombus formation and, thus, the aneurysm occlusion in a next step.
Paper Structure (35 sections, 1 theorem, 40 equations, 16 figures, 2 tables)

This paper contains 35 sections, 1 theorem, 40 equations, 16 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Medical Relevance & Challenges
  3. Coiling
  4. Flow diversion
  5. Flow disruption devices
  6. From imaging data to computational geometries
  7. Case selection, medical imaging and segmentation
  8. 3D Geometry preprocessing & meshing
  9. Geometry extraction, adaption and alignment
  10. Geometric measures of vessel and aneurysm
  11. Meshing
  12. Calculation of surface normals
  13. Continuum-mechanics & numerics of flow in aneurysms
  14. Free-flow fluid model w/o fully resolved endovascular devices
  15. Governing equations
  16. ...and 20 more sections

Key Result

Theorem 1

Let $\boldsymbol{a},\boldsymbol{b}\in\mathds{R}^3$ be two unit-vectors enclosing the angle $\vartheta=\angle(\Vec{a},\Vec{b})\in(0,\pi)$ between them. Defining the matrix representation $\boldsymbol{R}$ of the rotation by the angle $\vartheta$ around the rotational axis $\hat{\Vec{w}}$ that maps $\boldsymbol{a}$ onto $\Vec{b}$ is given by: For the special cases $\vartheta=0$ (iff $c=1$) and $\va

Figures (16)

  • Figure 1: Pre- and post-operative angiography for different options of endovascular aneurysm occlusion with injected contrast medium (Images taken from our data collection described in Section \ref{['subsec:MedicalSelectionAndSegmentation']})
  • Figure 2: Pre-processing of vessel geometries: After extraction of the domain of interest, the inflow surface is extruded to create a flow extension with a circular inflow cross section. For the perception of the used colors we refer the reader to the online version of the article.
  • Figure 3: Left: Cartesian grid used for an -simulation (left sector: voxel-based geometry, right sector: outward unit normal field depicted by green arrows). Right: Zoom into the red marked region of \ref{['fig:LBMMesh']} to showcase the staircase approximation of curved boundaries. Sector I shows the grid constructed inside the (orange) triangulation of the vessel surface. Sector II. illustrates normal vectors originating from lattice- cells and surface mesh intersections, while Sector III. depicts the (continuous to mesh resolution) field of normal vectors without the surface mesh. Note: For an improved visualization, only a random selection of cell normal vectors is shown.
  • Figure 4: Time-dependent pulsatile velocity amplitude profiles $v^{(t)}(t)$ and vessel radius pulsation $r(t)$ from the 0D-1D model fritz20221d over one heart cycle in the basilar artery (vessel # 22 in Figure 1 in alastruey2007modelling).
  • Figure 5: Virtual model examples for the three classes of endovascular devices
  • ...and 11 more figures

Theorems & Definitions (1)

  • Theorem 1