CRITERIOS DE EVALUACIÓN Y ESTÁNDARES DE APRENDIZAJE EVALUABLES

Following model development and validation, a parametric study was undertaken to investigate the expansion and recoiling characteristics as a function of the stent geometry (width, thickness, pitch) and coefficient of friction (COF) between the stent and expansion cylinder. For computational efficiency, a 5-coil stent was used. Results from the middle coil were reported since they were representative of 5-coil or longer stents, as described below.

4.5.1.1 Number of Stent Coils

The effect of coil number, ranging from 3 to 8, on expansion and recoiling was investigated. The stent width (1 mm) and pitch (2 mm) were held constant. The evaluation parameters (foreshortening, uncoiling, pitch change and radial recoiling) were relatively constant for stents with 5 or more coils (Figure 4-18). However, for stents with less than 5 coils, a significant increase in pitch and radial recoiling was predicted. This was attributed to the interaction with end coils in these shorter stents, suggesting that stents with less than 5 coils should not be considered for implantation.

Figure 4-18 Evaluation parameters as a function of number of coil.

4.5.1.2 Effect of Friction Coefficient

Expansion balloons are typically made of polymers such as Nylon, PE, PET, PVC, PTFE and PA, the friction coefficients of which are from approximately 0.04 to 0.2 [Yang, 2010].

Helical stent expansion results in uncoiling as the stent coils slide along the balloon surface. Therefore, in addition to the geometry of the helical stent, the stent-balloon interface can affect both expansion and subsequent recoiling behaviour. These effects were examined in a series of parametric studies on both 5-coil and 8-coil stents with a range of COFs at the stent-cylinder interface. The stent width (1 mm) and pitch (2 mm) were held constant. Coil number was varied from 5 to 8 and, since there was no significant change in the results, only the 5-coil results were reported, consistent with other data provided. As expected, increasing the COF resulted in a significant decrease in pitch change and a corresponding increase in foreshortening, while uncoiling and radial recoiling remained constant (Figure 4-19).

Figure 4-19 Evaluation parameters as a function of COF.

4.5.1.3 Stent Width

The stent width is directly related to the artery coverage area, and is also known to affect drug diffusion patterns from drug eluting stents. The coverage area is important since it is related to the stressed area of the artery during expansion, with larger values being desirable since they result in lower arterial stresses [Rogers, 1999]. A parametric study was undertaken to evaluate a 5-coil helical stent with a 2 mm pitch and varying widths between 0.5 - 1.2 mm.

Increasing the stent width (Figure 4-20), increased both the uncoiling and pitch change, and reduced foreshortening due to increased frictional effects. However, radial recoiling (Figure 4- 20) was not significantly affected by the stent width.

Figure 4-20 Evaluation parameters as a function of stent width.

4.5.1.4 Stent Thickness

Common stent thickness ranges from 0.1 to 0.2 mm. Therefore, in a 2-layer stent with a constant total thickness (here 0.2 mm), the share for the PLGA layer can be increased by reducing the thickness of the PLLA layer. Since the PLGA layer is typically the drug-carrying layer, changing its thickness could affect the amount and pattern of drug diffusion. Multiple layers of PLGA can also be included, each containing a different drug. The effect of thicknesses ranging from 0.06 to 0.16 mm was evaluated using a 5-coil stent with constant width (1mm) and pitch (2 mm). The pitch change (Figure 4-21) was predicted to increase with increasing thickness, and produce a corresponding decrease in foreshortening and small decrease in radial recoiling and uncoiling behaviour. In general, thicker stents showed larger plastic deformation, which is ideal for fixing the stent inside the artery.

Figure 4-21 Evaluation parameters as a function of stent thickness.

4.5.1.5 Stent Pitch

Stent pitch is relatively easy to modify in the stent manufacturing process, and was investigated for a 5-coil stent with a constant width (1 mm) and thickness (0.12 mm). When the pitch value was varied from 1.1 to 2.0 mm, the pitch change decreased significantly (Figure 4- 22). Uncoiling also decreased while foreshortening increased. Radial recoiling, however, remained almost constant with increasing stent pitch.

Figure 4-22 Evaluation parameters as a function of stent pitch.

Trends in expansion and recoiling behaviour derived from the parametric study are shown in Table 4-2, where a change in magnitude of more than 5 % was identified as significant.

Table 4-2 Parametric study results for helical stent uniform expansion.

Increased Parameter

Foreshortening Uncoiling

Pitch change

Radial

recoiling

Number of coils

_{3-5 ↑}

5-8 ~

3-5 ↓

5-8 ~

3-5↓

5-8 ~

3-5 ↓

5-8 ~

COF at the stent-

cylinder interface

↑

~

↓

~

Width

_↓

_↑

_↑

_~

Thickness

_↓

_↓

_↑

_~

data. Predicted results were generally within 10% of the experimental values, where differences were attributed to non-uniform expansion along the stent and interactions with the balloon used in the experiments.

The uniform expansion model results showed that helical stents exhibit a uniform stress distribution after expansion, which is important for controlled degradation when using biodegradable materials. The results indicated that increasing stent width, pitch value and coil thickness resulted in a larger diameter after recoiling, which would improve fixation in the artery. It was also noted that a helical stent should have more than 5 coils to ensure stability after uncoiling.

Helical stent expansion occurs by uncoiling and sliding the coils over the surface of the expander (i.e., the cylinder in this study), where uncoiling primarily generates bending stresses and strains. During expansion, the stent length decreases during uncoiling resulting in longitudinal movement, which is resisted by interface friction and interaction with adjacent coils. These effects can cause a tensile stress in the coils and an increase in pitch (Figure 4-10). The ultimate challenge with these sliding motions in practice (expansion inside an artery) is that they can cause small but significant shear stresses on the delicate artery wall. The evaluation parameters used in this study included traditional measures (such as foreshortening and recoiling) and two proposed parameters (uncoiling and pitch change) to evaluate geometric changes to the stent following expansion and recoiling.

In general, factors that affect the motion of the stent over the expansion cylinder or its bending stiffness will affect the final geometry. Increasing the number of stent coils as well as increasing the friction coefficient at the interface limited stent sliding, which was observed through decreased pitch change (Figure 4-18 and Figure 4-19). Changes in stent length were found to be very sensitive to uncoiling, and the values of foreshortening and pitch change were relatively constant for stents with 5 or more coils. Increasing the stent width increased uncoiling and most significantly affected pitch change (Figure 4-20). Increasing the thickness of stent directly increased the bending stiffness and limited uncoiling (Figure 4-21). As expected, increased thickness resulted in higher plastic strain during expansion and reduced recoiling. Decreasing the pitch value somewhat reduced the stent foreshortening (Figure 4-22). The stent design considered in this study showed 10 % recoiling. It is recommended that the stent should expand up to 10% of the artery’s inner diameter to ensure fixation.

Based on the above results, polymer helical stent designs exhibit some benefits over traditional materials and stent geometries. Specifically, the helical stent showed a relatively uniform stress distribution, which is favorable for uniform and controlled biodegradation. This also means the amount of permanent deformation and the stent’s final geometry can be controlled by the initial stent geometry. In particular, increased thickness was found to increase plastic deformation and therefore fixation in the artery; however, this parameter and the expansion rate must be controlled to avoid excessive strain in the material during deployment. The proposed change in pitch parameter was found to provide a sensitive measure to changes in geometry and should be used for evaluation of proposed helical designs.

Limitations of this model include the need to investigate the effects of transient non-uniform balloon and stent expansion.

The uniform expansion of a 3-coil helical stent was investigated with both implicit and explicit codes. This study revealed that, in a simple uniform helical stent expansion, the results from of implicit and explicit codes are identical. The explicit code, however, takes a long time to run and requires scaling. Thus, different scaling levels were applied on the model; a comparison of the produced energy error and resultant mechanical outputs showed that just observing the error levels is not sufficient to capture the effects of contact with mass and time scaling. Therefore, to avoid inaccurate results, implicit modeling should be used whenever possible. Explicit code is essential to solving models that include contact interfaces and nonlinearities. Experimental verification and validation should also be undertaken in these cases.