A comprehensive numerical approach to coil placement in cerebral aneurysms: mathematical modeling and in silico occlusion classification

Endovascular coil embolization is one of the primary treatment techniques for cerebral aneurysms. Although it is a well-established and minimally invasive method, it bears the risk of suboptimal coil placement which can lead to incomplete occlusion of the aneurysm possibly causing recurrence. One of the key features of coils is that they have an imprinted natural shape supporting the fixation within the aneurysm. For the spatial discretization, our mathematical coil model is based on the discrete elastic rod model which results in a dimension-reduced 1D system of differential equations. We include bending and twisting responses to account for the coils natural curvature and allow for the placement of several coils having different material parameters. Collisions between coil segments and the aneurysm wall are handled by an efficient contact algorithm that relies on an octree based collision detection. In time, we use a standard symplectic semi-implicit Euler time stepping method. Our model can be easily incorporated into blood flow simulations of embolized aneurysms. In order to differentiate optimal from suboptimal placements, we employ a suitable in silico Raymond-Roy-type occlusion classification and measure the local packing density in the aneurysm at its neck, wall region and core. We investigate the impact of uncertainties in the coil parameters and embolization procedure. To this end, we vary the position and the angle of insertion of the micro-catheter, and approximate the local packing density distributions by evaluating sample statistics.

Improving the accuracy of computational fluid dynamics simulations of coiled cerebral aneurysms using finite element modeling

Cerebral aneurysms are a serious clinical challenge, with ∼half resulting in death or disability. Treatment via endovascular coiling significantly reduces the chances of rupture, but the techniquehas failure rates of ∼20 %. This presents a pressing need to develop a method fordetermining optimal coildeploymentstrategies. Quantification of the hemodynamics of coiled aneurysms using computational fluid dynamics (CFD) has the potential to predict post-treatment outcomes, but representing the coil mass in CFD simulations remains a challenge. We use the Finite Element Method (FEM) for simulating patient-specific coil deployment for n = 4 ICA aneurysms for which 3D printed in vitro models were also generated, coiled, and scanned using ultra-high resolution synchrotron micro-CT. The physical and virtual coil geometries were voxelized onto a binary structured grid and porosity maps were generated for geometric comparison. The average binary accuracy score is 0.8623 and the average error in porosity map is 4.94 %. We then conduct patient-specific CFD simulations of the aneurysm hemodynamics using virtual coils geometries, micro-CT generated oil geometries, and using the porous medium method to represent the coil mass. Hemodynamic parameters including Neck Inflow Rate (Qneck) and Wall Shear Stress (WSS) were calculated for each of the CFD simulations. The average relative error in Qneck and WSS from CFD using FEM geometry were 6.6 % and 21.8 % respectively, while the error from CFD using a porous media approximation resulted in errors of 55.1 % and 36.3 % respectively; demonstrating a marked improvement in the accuracy of CFD simulations using FEM generated coil geometries.

Fast virtual coiling algorithm for intracranial aneurysms using pre-shape path planning

To aid in predicting and improving treatment outcome of endovascular coiling of intracranial aneurysms, simulation of patient-specific coil deployment should be both accurate and fast. We developed a fast virtual coiling algorithm called Pre-shape Path Planning (P3). It captures the mechanical propensity of a released coil to restore its pre-shape for bending energy minimization, producing coils without unrealistic kinks and bends. A coil is discretized into finite-length segments and extruded from the delivery catheter segment-by-segment following a generic coil pre-shape. With the release of each segment, coil-wall and coil-coil collisions are detected and resolved. Modeling of each case took seconds to minutes. To test the algorithm, we evaluated its output against the literature, experiments, and patient angiograms. The periphery-to-core ratio of coils deployed by P3 decreased with increasing coil packing density, consistent with observations in the literature. Coils deployed by P3 compared well with in vitro experiments, free from unphysical kinks and loops that arose from previous virtual coiling algorithms. Simulations of coiling in four patient-specific aneurysms agreed well with the patient angiograms. To test the influence of coil pre-shape on P3, we performed hemodynamic simulations in aneurysms with coils deployed by P3 using the generic pre-shape, P3 using a coil-specific pre-shape, and full finite-element-method simulation. We found that the generic pre-shape was sufficient to produce results comparable to virtual coiling by finite element modeling. Based on these findings, P3 can rapidly simulate coiling in patient-specific aneurysms with good accuracy and is thus a potential candidate for clinical treatment planning.

Evaluation of Contact Force between Aneurysm Model and Coil for Embolization of Intracranial Aneurysms

Objective

To ensure safe coil embolization for intracranial aneurysms, it is important to investigate the contact force between the coil and the aneurysm wall. However, it is unclear how the catheter tip position and the diameter of the secondary loop of the coil influence the contact force. In this study, we measured the contact force between a coil and an aneurysm biomodel under different conditions.

Methods

A commercially available coil was inserted through a microcatheter into a silicone rubber aneurysm model at a constant speed (1 mm/s) using an automatic stage, and the contact force between the coil and the aneurysm wall was measured by a force sensor attached on the aneurysm model. The inner diameter of the spherical aneurysm was 5 mm. The effects of varying the position of the catheter tip (near dome, center, near neck) and the diameter of the secondary coil (4.5 mm) were evaluated.

Results

When the catheter tip was inserted more deeply into the aneurysm (especially near the dome), the contact force increased. The contact force also increased as the secondary coil diameter was increased with the catheter tip near and in the center of the dome.

Conclusion

These results suggest that the catheter tip position and the secondary coil diameter affect the contact force. In particular, the contact force should be considered large with the catheter tip near the dome to ensure safe coil deployment.

Improving accuracy for finite element modeling of endovascular coiling of intracranial aneurysm

BACKGROUND

Computer modeling of endovascular coiling intervention for intracranial aneurysm could enable a priori patient-specific treatment evaluation. To that end, we previously developed a finite element method (FEM) coiling technique, which incorporated simplified assumptions. To improve accuracy in capturing real-life coiling, we aimed to enhance the modeling strategies and experimentally test whether improvements lead to more accurate coiling simulations.

METHODS

We previously modeled coils using a pre-shape based on mathematical curves and mechanical properties based on those of platinum wires. In the improved version, to better represent the physical properties of coils, we model coil pre-shapes based on how they are manufactured, and their mechanical properties based on their spring-like geometric structures. To enhance the deployment mechanics, we include coil advancement to the aneurysm in FEM simulations. To test if these new strategies produce more accurate coil deployments, we fabricated silicone phantoms of 2 patient-specific aneurysms in duplicate, deployed coils in each, and quantified coil distributions from intra-aneurysmal cross-sections using coil density (CD) and lacunarity (L). These deployments were simulated 9 times each using the original and improved techniques, and CD and L were calculated for cross-sections matching those in the experiments. To compare the 2 simulation techniques, Euclidean distances (dMin, dMax, and dAvg) between experimental and simulation points in standardized CD-L space were evaluated. Univariate tests were performed to determine if these distances were significantly different between the 2 simulations.

RESULTS

Coil deployments using the improved technique agreed better with experiments than the original technique. All dMin, dMax, and dAvg values were smaller for the improved technique, and the average values across all simulations for the improved technique were significantly smaller than those from the original technique (dMin: p = 0.014, dMax: p = 0.013, dAvg: p = 0.045).

CONCLUSION

Incorporating coil-specific physical properties and mechanics improves accuracy of FEM simulations of endovascular intracranial aneurysm coiling.

Hemodynamics and coil distribution with changing coil stiffness and length in intracranial aneurysms

Purpose

The purpose of this study was to investigate hemodynamics and coil distribution with changing coil stiffness and length using the finite element method (FEM) and computational fluid dynamics (CFD) analysis.

Methods

Basic side-wall and bifurcation type aneurysm models were used. Six types of coil models were generated by changing the coil stiffness and length, based on commercially available embolic coils. Coil embolization was simulated using FEM. CFD was performed to characterize the hemodynamics in the aneurysms after embolization. Coil distribution and velocity reduction in the aneurysms were evaluated.

Results

The median value of radial coil distribution was shifted from the center to the outer side of the aneurysmal dome by changing coil stiffness: harder coils entered the outer side of the aneurysmal dome more easily. Short coils were more distributed at the neck region, since their small size made it easy for them to enter the tighter area. CFD results also indicated that velocity in the aneurysm was effectively reduced when the coils were more distributed at the neck region and the outer side of the aneurysmal dome because of the disturbance in blood inflow.

Conclusions

It is easier for coils to enter the outer side of the aneurysmal sphere when they are harder. If coils are short, they can enter tighter areas more easily. In addition, high coil density at the outer side of the aneurysmal dome and at the neck region is important to achieve effective velocity reduction.