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An important input to FEA is material characterization and limit information.  In our laboratory we use  a Bose 3230 test system for achieving test speeds up to 200Hz.   Depending on the project, we may test complete devices, sub-components, coupon samples and/or simple material characterization samples.  Many times, we will test more than one configuration to make sure our data are consistent and ultimately demonstrates the validation of an implantable medical device’s safety and efficacy.

Many factors are involved in deciding what testing would be most efficient to support a product’s validation effort.  Characterization of material properties is typically the first step.  For medical implants that utilize advanced materials, fine geometric features and deliberate metallurgical processing, it is important to capture these in the specimen design.  Fabrication of appropriate samples takes the most effort compared to the relatively short test times and the simplicity of material characterization tests.

After material characterization, testing to validate the performance features of an implant are typically necessary.  These tests may also require the fabrication of appropriate samples but can additionally involve the reproduction of complex in vivo load states.  Besides verifying that the test setup reproduces the desired load state, performance testing is short term and individual samples can be tested in series to study the effect of loading magnitudes, variations in processing, load combinations, etc.  Many times, these studies to quantify the impact of such variables play an important role in a validation strategy and can be efficiently performed since only one or a few cycles of loading are required.

Beyond material characterization and performance testing, material limit properties are the next category of data necessary for input to FEA models.  When the required number of cycles is low, say 10 million or fewer, accelerated testing can be performed on individual samples tested in series or multiple samples tested simultaneously.  The advantage of testing individual samples was mentioned above while testing multiple samples simultaneously produces stronger statistics more quickly.

When the required number of cycles reaches 100 million or more, a balance between testing enough samples for the desired confidence level and testing the samples to run out at the high cycle limit must be reached.  A typical strategy might involve a combination of testing individual samples  to 10 million cycles and then selecting one or more loading conditions/levels for testing multiple samples simultaneously.  Such a scenario takes advantage of the relatively short testing time frame for a 10 million cycle test (on the order of 1-2 days, compared to 4-6 weeks for testing to 400 million cycles) and the statistical advantage of testing multiple samples.

In the photo above, a multiple sample fixture capable of testing 12 fatigue coupon samples in a controlled temperature chamber is shown.  Such a fixture must be fabricated and aligned very carefully to insure identical loading conditions are achieved for all of the samples.  Stroboscopic verification, randomized experimental design, fracture surface investigation and other experimental mechanics techniques also help to build confidence in a validation test methodology.

I just returned from a workshop sponsored by the FDA (and the NHLBI and NSF) on Computer Methods for Cardiovascular Devices.  It was an excellent workshop providing an audience of regulatory, academic and industrial interests a chance to get caught up on the state-of-the-art, trends and, in general, to exchange ideas on the issues of using computational methods to support regulatory filings for medical devices.  A general theme emerged for me during the workshop that I’d like to discuss in this article:

We are not providing the FDA with adequate validation of our computational models!

For years now I’ve been helping companies demonstrate the safety and effectiveness of their products.  I’ve written many FEA reports that have been reviewed and accepted by the agency, including cases where we’ve argued to forgo expensive and time consuming durability testing in lieu of providing computational results to support safety claims.  It has been my experience that the FDA has been very open to such an approach, provided there was an adequate demonstration of the validity of the FEA models.

From what I heard from reviewers at the workshop, however, the typical submission of FEA results does not include adequate validation.  I don’t know if it is because companies don’t know how or what to provide for validation of their FEA models or if they are reluctant to share testing or data that the FDA has not specifically asked for or if they have unreasonable expectations about what computational models can replace in terms of physical testing, but it is clear to me that if we want to leverage FEA to streamline the development and approval process then we need to take a proactive role at demonstrating how well our models describe our products.

It is far less expensive and time consuming to perform carefully designed bench tests to validate computational results than it is to run long term durability tests on our devices and hope they pass.  Not to mention far less risky from a product development perspective.  It was clear in the workshop that the FDA understands this and that they too are motivated to see a better balance between physical testing and computational modeling in a submission.

In my over ten years experience in the field, I have yet to run across a device or a specified test or loading scenario that I could not analyze using Abaqus and achieve excellent agreement between experiment and computer simulation.  Many times the endeavor to match experiment and analysis reveals critical insight into the mechanics of the product involved or nuances associated with the loading conditions that lead to important improvements.  With advanced contact, strong nonlinear capabilities and the extensibility of user subroutines, Abaqus provides a platform to model almost any physical scenario giving the engineer and product designer a more than ample toolkit for validating any device.

Still, as open and receptive as the FDA may be, they are not in a position to advise on how best to perform the appropriate validation. As engineers we need to establish the validity of our computational models and we need to do so BEFORE we submit results to the FDA.  In fact, we need to begin this effort early in the development process before we start making decisions based on our computational data.  Otherwise, how can we expect the FDA to accept that our results have emerged from a rigorous engineering methodology?

How much and what type of validation is necessary in any given case depends on how a model is going to be used.  Conversely, the confidence we have in a computational model depends on how extensively it has been applied and shown to agree with reality.  There are numerous opportunities we have during the development process to establish the validity and range of our computational models.  Radial force testing of different stent designs for example provides an excellent opportunity to confirm our models ability to predict reality.

In summary, the time is right for advancing the use of computational models for demonstrating the safety of our products.  But we need to be proactive and utilize models that are well grounded in experimental data.  How far we are able to leverage these results with the FDA will depend on how good of a job we do at convincing them that they represent actual experience.

For medical devices, rarely does “one size fit all”.  The human body is extremely variable and patient populations, especially those with disease present a wide range of differences that the medical device design engineer must consider.

Identifying the worst case size for a product family is an important part of the validation process for implantable medical devices.  Understanding your product and especially the in vivo loading conditions are essential for engineering the structure and material specifications for each size over the intended product range.

Typically, there are numerous sources of nonlinearity associated with implantable medical device design.  The materials we use, the geometries and especially the physiology we treat all respond in ways that are difficult to describe in simple terms.  It is tempting to design a product by considering an idealized patient population and then simply “scale” that design to smaller and larger sizes.  But this approach can can result in a poorly optimized product family.  Furthermore, when one considers device/lumen ineraction and teh resulting compliance under physiological loads, identifying the worst case loading condition is not a straightforward activity.

The figure above illustrates how the alternating fatigue strain for a stent-like product can vary for deployment to different diameters.  It is based on an analytic model of lumen compliance and finite element analysis models of the two device sizes.  Clearly, the results indicate a highly nonlinear system that precludes the selection of a single worst case device size and implant condition based on the “four corners” approach.  Assuming that the largest device put into the smallest lumen will result in the most challenged loading condition is niave.

When it is possible, it is preferred to model ALL device sizes to determine the worst case size. It is also advantageous to develop and validate a simulated model of the intended physiology for the implant and use this model to verify the performance of each size in a design family.  Parameters such as radial force, anchoringg, dynamic compliance, vessel tortuosity and fatigue loading conditions can then all be evaluated for each device size and safety established for the complete instructions for use (IFU) for the product.

Finite Element Analysis (FEA) is routinely used to perform fatigue analyses of cardiovascular stents.  For the case of balloon expandable stents, this means modeling the crimping of the stent onto the delivery balloon, the expansion and recoil of the stent as would occur during deployment and finally the simulation of fatigue deformations.  Fatigue deformations typically involve uniform radial pulsatile loading and/or bending of the stent between two different radii of curvature.  A safety factor is determined by computing the alternating and mean stresses for the given cyclic loading conditions and comparing them to allowable material limits using a Goodman-type approach.

A simple method for determining the safety factor is to compute the alternating and mean stresses from the principle stress components for the minimum and maximum extremes of the cyclic loading conditions.  The ratios of the alternating stress  and endurance limit and the mean stress and the ultimate strength are combined and equated to the reciprocal of the safety factor, N.

This equation is evaluated for each integration point in the model.  But as was discussed in our most recent ASTM F04.30.06 Fatigue to Fracture task group, this approach has several shortcomings.

An alternative approach is to use the individual stress components with respect to the global coordinate system for the two fatigue conditions and compute the individual alternating and mean stress components according to

These individual alternating and mean stress components are used to compute an effective alternating and an effective mean stress using

Subsequently, the effective alternating and mean stress values are used to compute a safety factor according to

An alternative approach would be to use the three principle stress components and compute the three alternating and mean principle stresses and then compute the effective stress according to the Gough–Pollard model; however, this approach still does not account for the effect of rotations in stress space on the mean and effective stress.

The exact approach would be to compute the alternating and mean stress components from the six stress components according to an element local coordinate system.  However, in the case of the small fatigue motion associated with a cardiovascular stent, the element rotations between the two fatigue locations are small and therefore the effects are assumed to be negligible.

But now let’s put all of this in perspective.

For balloon expandable stents: The maximum stresses in a stent subjected to characteristic radial fatigue deformations typically occurs near the inner apexes of struts and even under the largest of deformations, there is often very little rotation. Therefore, it is anticipated that the effort to account for the individual stress components will  not make a significant difference.  In fact, for a typical coronary stent, the difference between the standard approach and an approached based on an updated coordinate frame as described above will at most be on the order of a few percent.

For self expanding Nitinol stents, the situation is a bit different because there can exist a shear strain component to the strain tensor which can reverse orientation and thus it’s effect can be cancelled by neglecting to look at the full strain tensor on an individual component level.  Significant differences in predicted alternating strains can be obtained for load-controlled scenarios where the stent undergoes cyclic loading/unloading

In both of these cases, however, we need to keep things in persepctive.  All this effort in considering the multiaxial state of stress may end up secondary when we consider that we generally only have UNIAXIAL material limit data available.  The extension from uniaxial observations to multiaxial predictions is still the subject of much debate even for what are considered to be relatively well understood concepts such as plasticity. This point is important to keep in mind as we move forward with our Fatigue to Fracture initiative.  Whether we take the extra effort to compute fatigue stresses according to the method described here, or by other approaches, we are still basing our predictions on material information and fatigue theories that come with their own inherent limitations.  The best we can do is be consistent, conservative and use our observations and experience to improve our knowledge and condfidence in making lifetime predictions.

Follow this link to the ASTM website and find the long awaited for “Standard Guide for Finite Element Analysis of Metallic Vascular Stents Subjected to Uniform Radial Loading”.

This guide establishes general requirements and considerations for using finite element analysis techniques for the numerical simulation of metallic stents subjected to uniform radial loading. These stents are intended for use within the human vascular system.

It was developed in the F04.30.06 subcommittee for Cardiovascular Device Standards.  The co-chairs of the group are Ken Cavanaugh and Eitan Konstantino and we have about 40 active members with two face to face meetings per year.  There are numerous work items under way and new members are always welcome.  Please contact me for more information on joining our group.