The Effect of an Implanted Filter on Valsalva-Compression and Respiratory-Compression of the Inferior Vena Cava

Abstract

We carry out computational simulations of the Valsalva compression of an inferior vena cava (IVC) with a filter implanted in it. We find that when we treat the IVC wall as simply a boundary between 2 fluids and apply an external pressure on the IVC, the deformation magnitudes and patterns do not agree with data in the literature. We conclude that IVC compression is mainly caused by solid bodies (i.e. tissue and organs) compressing the IVC, and develop a model to simulate this phenomenon. We calibrate our model to data in the literature for Valsalva compression with and without an implanted filter. We then use our approach to predict the area reduction of the IVC during breathing when 2 different types of filters are implanted. Not surprisingly, we find that a compliant filter is less able to resist the compression of the IVC during respiration than a stiffer one, and we quantify the difference. We anticipate that, with further development, our model can be used to make assessments of design and testing parameters that can help to avoid fatigue failure of a filter that is subjected to millions of compressions due to breathing.

Appendices

Appendix A: Mesh Dependency Analyses

The simulation depicted in Fig. 8 is carried out using different meshes for the leg. Five different mesh densities are analyzed. In the coarsest mesh, the global seed size is 4 mm, whereas in the finest case we use a 0.25 mm global seed size. Table 3 contains the number of elements for the primary leg and for the secondary leg. Labels M1 … M5 indicate specific meshes.

Table 3 Number of element numbers for the meshes under investigation for filter legs

We analyze the effect of the mesh density on the applied force and the maximum Mises stress in the leg corresponding to a 10 mm displacement of the rigid wall in Fig. 8. We use the linear elastic materials properties of Conichrome. Figure 15 shows the effect of mesh density on the applied force for both the primary and secondary legs, whereas Fig. 16 presents the variation of the maximum Mises stress versus the global seed size. The maximum Mises stress is located in the cross-section at the fixed end of the legs. As can be seen from the figures, the mesh density does not have a significant effect on the results, an outcome that arises from our use of quadratic beam elements. However, we note that the mesh density can have an effect on the contact formulation, but we see that this is also negligible in this case. The maximum Mises stress is almost identical for both the primary and the secondary legs. The secondary leg has a different shape and a smaller cross-section when compared with the primary leg. Thus, it is coincidental that the maximum Mises stress magnitudes in the 2 legs are almost identical. For the simulations utilized for our results, we have chosen the mesh designated M3, with a global seed size of 1 mm.

Fig. 15

Variation of the leg contact force versus the global seed size

Fig. 16

Variation of the maximum Mises stress in a leg versus the global seed size

The effect of the mesh density was also analyzed for the IVC wall. Figure 17 shows a schematic of the configuration used for this mesh dependency analysis. An oval IVC in its undeformed configuration is shown in grey. Two circular rigid cylinders are used to deform the IVC. The deformed configuration is depicted in black in Fig. 17. A vertical displacement $u=7\text{ mm}$ of the rigid cylinder is prescribed for the calculation. Due to symmetry, we analyze only one quarter of the configuration. Eight-node biquadratic plane strain quadrilateral elements with hybrid formulation are used with uniform thickness of 1 mm. Ten different mesh densities are analyzed. In the coarse case (M1), the global seed size is 1 mm, whereas the finest mesh (M5) contains element having a 0.1 mm global seed size. The details of the meshes are listed in Table 4, whereas Fig. 18 shows three examples of meshes for the purposes of illustration.

Fig. 17

Schematic of the problem used for the mesh dependency analysis of the IVC wall

Fig. 18

Illustration of meshes M1, M5 and M10

Table 4 Investigated meshes

As indicators we compute the reaction force at the circular cylinder and the horizontal displacement, $t$, of the inner point of the IVC wall on the horizontal axis (see Fig. 17). The results are shown in Fig. 19 for the reaction force and in Fig. 20 for the horizontal displacement of the point on the inner surface of the IVC wall. Only the results for meshes M1, M5 and M10 are shown in the plots; the results for the other meshes are bracketed by the curves corresponding to meshes M1 and M10. Very minor differences can be seen among the results. Based on this study we use the mesh M5 in our other computations.

Fig. 19

Computed reaction force at the circular cylinder for meshes M1, M5 and M10

Fig. 20

Computed horizontal displacement $t$ for meshes M1, M5 and M10

Appendix B: Effect of the Larger Radial Displacement on the Stiffness Values of the Legs

Before implantation, a filter is compressed to fit within a catheter or sheath of narrow diameter that is then passed through the vasculature to position the filter at the desired location within the IVC, usually the infrarenal position. This process involves significant deformation of the filter legs that might lead to permanent deformation or phase transition in the material. Our computational model for the Valsalva maneuver and for normal breathing neglects these deformations as we used only linear elastic behavior for the filter legs. In this appendix, we demonstrate that this is an acceptable approach for the analysis.

We repeat the calculation shown in Fig. 8 but with the following loading history: i) In the 1st step, the leg is compressed radially by the rigid wall until it is 1 mm above the fixed end of the leg. This configuration simulates a filter confined in a sheath or catheter with a representative value of 2 mm for the sheath inner diameter. ii) In the second step, the rigid wall is raised and the leg is allowed to relax back to a configuration, where the rigid wall is 8 mm above the fixed end of the leg. This configuration represents a filter implanted in the IVC. iii) Finally, in the third step, the leg is compressed radially again by the rigid wall being brought down again until it is 6 mm above the fixed end of the leg.

For the legs of a Celect filter we use a linear elastic – perfectly plastic material model with yield stress of 1.93 GPa according to [39, 41]. The legs of the alternative Nitinol filter with the same shape as a Celect filter is modelled using the fitted superelastic material model, with parameters given in Table 1 [54].

The resulting forces applied by the legs to the rigid wall during the entire loading are shown in Fig. 21-Fig. 24, where the radial coordinate is defined as the vertical distance of the rigid wall from the fixed end of the leg in Fig. 8.

Fig. 21

Reaction force for the secondary leg of the Celect filter

Celect filter: The stress in the secondary leg remains below the yield stress and, therefore, the material deforms pure elastically. The loading-unloading-reloading curves are on the same curve in the plot (Fig. 21). The stress in the primary leg reaches the yield stress of the material and, therefore, plastic deformation initiates. However, the resulting permanent deformation is minor and, therefore, only a small amount of hysteresis is visible in the force-displacement plot in Fig. 22. The slope of the curve in the re-loading phase is practically the same as during initial loading. Thus, the deformations of the legs during a Valsalva maneuver and during normal breathing are in the range where only elastic deformation occurs. We note also that we include no work hardening during plastic deformation. Including work hardening during yielding would reduce the hysteresis in the plot.

Fig. 22

Reaction force for the primary leg of the Celect filter. Dashed rectangle shows the magnified region

Alternative Nitinol Filter: A very tiny amount of hysteresis can be seen in the force result for the secondary leg (Fig. 23). This implies that phase transformation occurred during the loading, but had negligible effect on the stiffness of the leg. The primary leg experiences much more phase transformation, as can be seen clearly in Fig. 24. It can be seen that the prior phase transformation that the leg has experienced reduces the radial force applied by the leg to the IVC wall by a small amount in the radial coordinate range from 6 mm to 8 mm compared to that prevailing during the loading phase prior to the martensitic phase transformation. However, it is important to emphasize that in the reloading phase the prior transformation has little effect and the stiffness of the leg is then nearly identical to the stiffness prevailing during initial loading. Similar to the Celect filter, the deformations of the legs during a Valsalva maneuver and during normal breathing are in the range where only linear elastic deformation occurs.

Fig. 23

Reaction force for the secondary leg of the Alternative filter

Fig. 24

Reaction force for the primary leg of the Alternative filter. Dashed rectangle shows the magnified region

Therefore, the significant deformation that occurs during delivery of these 2 filters in a sheath or catheter, given their mechanical properties, has no major effect thereafter on the stiffness of the filters in the range of deformations corresponding to a Valsalva maneuver and normal breathing. From this we conclude that neglecting nonlinear material behavior during our study of the interaction of the filter with the IVC and surrounding tissue and organs is an appropriate approach.