Trefoil has been designed and developed to extend the benefits of osseointegration to a new patient population. In the following article, you are invited to dive deeply into the innovative bioengineering that has made this solution possible.

Even to the casual observer, it’s obvious that Trefoil has a particularly innovative feature. Its prefabricated framework contains a special adaptive fixation mechanism at each implant connection that functions to create a precision fit by compensating for any slight angular (± 4°), horizontal (± 0.4 mm), and/or vertical (± 0.5 mm) misalignment of the implants. (Figures 1A and 1B.)

Figures 1A and B: Here is the first pre-manufactured bar with passive fit. Anatomically designed for the natural arch of the lower jaw, the standardized Trefoil system bar contains adaptive joints that adjust to compensate for horizontal, vertical and angular deviations from the ideal implant position.

As exciting as this feature is, there is so much more to the design of Trefoil. A great deal of biomechanical engineering insight has been incorporated into its design and subsequent clinical application.

Consider the words of Steve Jobs: “Design is a funny word. Some people think design means ‘how it looks.’ But of course, if you dig deeper, it’s really ‘how it works.’ ”

In this article, I hope to explain Trefoil’s biomechanical design in the spirit of this quote. With a nod of appreciation to the late Philip Kapleau and his book, The Three Pillars of Zen, I’d like to introduce you to the “Three Pillars of Trefoil.”

Pillar 1: Teachings

Individualized fit can be provided with a standardized device.

Small deviations in implant placement can greatly influence the strain distribution on the implants, the framework and surrounding anatomy. Ideally, a prosthetic framework should not introduce strain on the supporting implants and surrounding bone in the absence of an external load. This is known as passive fit.

Many studies throughout the scientific literature reveal that, in the past, cast bars and some premanufactured prosthetics experienced unfavorable levels of implant and prosthetic failures. While many factors can contribute to failures, mechanical complications such as implant and prosthetic fractures and screw loosening have been attributed to excess mechanical strain due to a lack of passive fit.

Historically, there have been many approaches to achieve passive fit. This has included cutting prosthetic bars and piecing them back together intraorally. From an engineering perspective, one might worry that this approach could affect the integrity of the prosthetic superstructure. Alternatively, the development of CAD/CAM individualized solutions has made great strides to address the issue of passive fit. However, individualized bars are still subject to deviations in implant placement and they can be expensive for many patients due to the need for multiple clinical visits and the use of a provisional prosthesis while the definitive solution is manufactured.

By contrast, with the Trefoil system, a dental team can deliver—on the day of surgery—a definitive solution that fits like a custom solution.

This is evidenced by a recent in vitro study conducted at Saarland University in which the Trefoil Bar was directly compared to both traditional cast bars and CAD/CAM customized bars. In this study, five replicates of each comparison framework were seated on three NobelParallel CC Tissue Collar RP 5.0 x 13 mm implants placed in resin models representing edentulous jaws using the Trefoil surgical guides and templates. Strain gauges were mounted to each system and recorded the strain development at all three implant sites when the clinical screws were tightened to 35 Ncm.

The results indicated that cast bars show significantly higher levels of misfit and more uneven distributions of strain compared to other comparison groups (Figure 1C). The Trefoil and CAD/CAM bars each had a low level of misfit and more even distribution of strain. The two systems were not statistically different from each other.

Figure 1C: A recent in vitro study conducted at Saarland University in which the Trefoil Bar was directly compared to both traditional cast bars and CAD/CAM individualized bars, cast bars show significantly higher levels of misfit and more uneven distributions of strain compared to other comparison groups. 

The articulating disks of the Trefoil system tackle the issue of misfit at the implant-framework interface while maintaining the integrity of the individual components. While no system showed a strain measurement of 0 μm/m, Trefoil’s innovative compensation mechanism enabled a premanufactured bar to fit as well as a state-of-the-art individualized restoration.

Pillar 2: Practice

A cantilever’s dimensions and loading govern how it’s stressed.

An in-depth stress analysis of Trefoil needs to go beyond the above. A relevant quote from the architect Mies van der Rohe speaks to a key issue: “No design is possible until the materials with which you design are completely understood.”

Indeed, from a bioengineering perspective, the mechanical success vs. failure of any oral implant system depends not only on how many implants are used and how they are loaded, but also on the sizes of the implants, the bone anchorage area, and the size and rigidity of the framework.

In other words, “size matters” because the ultimate failure limits of materials—such as the ultimate tensile strength and the fatigue strength of commercially pure titanium (CP Ti), Ti-6Al-4V alloy, and bone—are expressed in terms of stress, not force, and stress depends on dimensions. So in this spirit, let’s explore more details of a stress analysis of Trefoil, with a focus on framework design.

A common clinical evaluation of a framework’s design involves measuring the “AP (anterior-posterior) spread”, which is the distance from a line drawn between the posterior aspects of the two most distal abutment interfaces and the midpoint of the most anterior abutment/implant in the arch. Depending on whom you read, the recommended maximum cantilever length of a framework almost always falls between 1.5 and 2.5 times the AP implant spread.

Trefoil’s AP implant spread is 8.7 mm, while the AP bar spread is 14.5 mm. This a ratio of 1.67, which—according to this widely accepted “AP spread rule”—is well below the maximum recommended range for this configuration.

But a calculation based on the AP spread is not a stress analysis; it’s only a guideline, with its predictive value depending upon numerous factors such as strength of bite force, material used in the bar, whether the patient is a bruxer, etc. (see Dr. Steven E. Eckert’s excellent discussion on this topic at researchgate.net).

For more enlightenment about framework design, the required approach involves stress analysis and the consideration of possible mechanical failure (in order to avoid it).

Figure 2A: Illustration of the setup in the 3D finite element modeling of a bar supported by three Trefoil implants. Similar setups were used for the four upright implants and All-on-4® treatment concept implants.

Figure 2B: Overhead views of the bar and implant arrangements (top row) and distributions of tensile stress in the bars for 300 N acting at the right cantilever (bottom row).

Consider three example cases, each of which is formulated in 3D finite element (FE) models. Case 1 involves four upright implants (each 4 mm in diameter); Case 2 involves four All-on-4®implants (each 4 mm in diameter, with the distal two implants tilted); and Case 3 involves three Trefoil implants (each 5 mm in diameter). As can be seen in the top row of Figure 2B, the implants support a metal framework that’s 5.5 mm wide (bucco-lingually) in each case; but 4 mm thick for Cases 1 and 2 vs. 5.5 mm thick for Case 3. Each bar is loaded downward at the right distal end of the cantilever with a force of 300 N. Each case is formulated and analysed using 3D FEA.

These models, like all other idealizations, are subject to the usual list of limitations, of course, such as the fact that the models here neglect the fine geometric details of the wide variety of bars, implants, and bone encountered clinically; but they do provide the analytical advantage of uniformity.

Here all three models have the same setup of materials—apart from implant diameter, location and bar size—so it is a straightforward process to make meaningful comparisons between these three crucial variables. The Young’s elastic modulus of the Ti alloy bars is 115 GPa, the modulus of the commercially pure (CP) Ti implants is 105 GPa, and the modulus of the mandibular bone is that of dense cortical bone ≈20 GPa. As seen in Figures 2A and B, the chosen load at the cantilever is 300 N.

Now we’re ready to answer the question, “What stresses develop in the three bars, and how do those stresses relate to possible failure?”

The results (Figure 2B, bottom row) reveal that the maximum tensile stress (1st principal stress) on the top surface of each bar concentrates at the location expected— near the fixed end of the cantilever region. Case 1 (upright 4) shows the largest stress (398 MPa); Case 2 (All-on-4®) has a lower stress (218 MPa); and Case 3 (Trefoil) has the lowest stress of all (201 MPa).

What this means in terms of a likelihood of bar fracture is as follows: If the bars happened to be made of CP Ti, the ultimate tensile strength of some grades of CP Ti is over 700 MPa, so none of the bars made from such a material would be in danger of fracturing. However, since the fatigue endurance limit of some grades of CP Ti is only 300 MPa—which is less than the stress seen in the Case 1 bar (398 MPa)—a CP Ti bar in Case 1 would be at risk of failing by metallurgical fatigue.

On the other hand, the fatigue endurance limit of specially cold- worked Grade 4 CP Ti is ≈430 MPa; and the comparable value for the Ti-6Al-4V alloy used in the Trefoil Bar is ≈620 MPa—both of which provide ample margins above maximum stress. Bars made of these materials, used in cases like these, would not be expected to fail in fatigue.

Figures 3A and 3B. During the design stage of Trefoil, Nobel Biocare’s stress analysis of the detailed geometry of Trefoil’s bar went beyond the author’s FE examples depicted in Figure 2B. Nobel Biocare’s more detailed analysis of the bar (using its actual geometry instead of the simple U-shape depicted in Figures 2A and 2B) showed that under large cantilever loading, “hot spots” of high stress developed at the base of the cantilever (Figure 3B). Such agreement between FE predictions and experimental test data gives validity to the FE analysis, and confidence in the safety and efficacy of the final bar.

Pillar 3: Enlightenment

Thanks to proper design, the Trefoil framework works nicely.

During the design stage of Trefoil, Nobel Biocare’s stress analysis of the detailed geometry of Trefoil’s bar (see Figure 3A) went beyond my FEA examples above; Nobel’s more detailed analysis of the bar (using its actual geometry instead of the simple U-shape assumed for FEA) showed that under large cantilever loading, “hot spots” of high stress developed at the base of the cantilever (Figure 3B). Notably, those hot spots of stress matched well with the locations of fatigue fractures seen in laboratory fatigue testing of bars in saline solution. Such agreement between FEA predictions and experimental test data gives validity to the FEA and confidence in the safety and efficacy of the final bar.

The thoroughness of Trefoil’s design emerges more fully when considering Nobel Biocare’s fatigue comparative testing on bars supported by aligned vs. misaligned implants (Figure 4A). That is, tests were run on bars that fit perfectly on aligned implants (i.e., on implants placed according to the ideal surgical plan) and bars in which the compensation mechanism became “active” in accommodating a passive fit of the bar to misaligned Trefoil implants (i.e., a situation where two of the implants were misaligned to their maximum angular and lateral shifts).

Figures 4A and 4B. Trefoil’s exemplary design became clearly evident when tests were run on bars that fit perfectly on aligned implants (i.e., on implants placed according to the ideal surgical plan, left column above) and bars in which the compensation mechanism became “active” in accommodating a passive fit of the bar to misaligned Trefoil implants (i.e., a situation where two of the implants were purposely misaligned by known angular and lateral shifts, a.k.a. the “Trefoil Worst Case,” depicted in the column to the right).

A typical fatigue test was conducted by applying a known cyclic force—say 300 N—at 1 cycle/sec to the end of the cantilever, and then allowing the test to keep running until either “runout” occurred (no bar failure at 2 million cycles) or fatigue failure occurred (e.g., cracks formed) at a specific number of cycles.

The fatigue tests revealed no difference in fatigue performance between the ideal and worst cases (Figure 4B); the mean fatigue limit (here quoted in terms of force, since these were tests on whole bars) was statistically the same for both cases, at about 313 N.

What these data show is that the compensation mechanism supports reliable and predictable resistance to mechanical fatigue within its full compensation range.

While fatigue tests are usually designed to compare different systems with each other, to gain insight into the role of various material characteristics on fatigue life, it is enlightening nevertheless to consider how we can estimate a practical in vivo lifetime of a Trefoil Bar.

For instance, since it’s known from the tests that the bar can withstand at least 300 N of cyclic bite force at the cantilever without failing after 2 million cycles (the point at which the testing was stopped for practical reasons), how long—in days or years—does this mean that the bar will last? An approximate answer can be based on estimates in the literature of a typical chewing rate in humans—60 to 80 cycles per minute—and a typical length of time spent chewing each day— about 9 to 17 minutes per day.

Assuming 60 chewing cycles/min during 10 minutes/day of chewing, this produces 600 chewing cycles per day. We know from fatigue tests that the Trefoil Bar can withstand at least two million cycles with 300 N on the cantilever. So this translates into a minimum survival time for the Trefoil Bar of at least 9 years—and it could very well last much longer.

There has really been nothing like this to emerge from the lab to the clinic before!

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Posted by John Brunski