Comments on the Effect of an Orthogonal Locking Plate and Primary Plate Working Length on Construct Stiffness and Plate Strain in an In Vitro Fracture-Gap Model

Christos Nikolaou
Nov 13
6 min read

My Comments on the Article

You can find my letter to the editor here. The authors' reply can be found here.

This study demonstrates significant effort by the researchers, whose primary concern was whether the working length of an implant affects its stress/strain. For this, they used constructs with different working lengths and measured the strain at the middle part of the plate. They stated that they chose four-point bending to ensure a constant bending moment along the length of the construct. The bending moment is the "force" that generates stress/strain in four-point bending. So if you generate the same bending "force" and you measure the stress/strain in a part of the construct that has the same dimensions and is made of the same material, you must not expect any differences. Indeed, the researchers measured strain at the part of the implant between the innermost screw holes. So, same material, same dimensions, same bending force (according to the researchers). So, why would we not expect the same strain?

The researchers answered that they did not expect the same strain because the construct is composite. It is made of the plate and the bone. The overall stiffness of the constructs with the large working length would be less (this sounds correct), which means that the constructs with the large working length will bend more. This is the tricky part. What do we mean by "bend more"? If we mean the overall deflection of the construct, then, yes, the longer construct will deflect more. Imagine you have a long and a short beam. You apply a constant bending force along each cross-section of the beam. Now, imagine that the beam consists of small, equal-sized parts. Each part will be subjected to the same bending force (a constant bending moment across the beam, according to the authors), so each part will be bent the same as the others, say, by 5°. Say the larger beam consists of 10 parts. So, the overall bent will be 50°. The smaller beam consists of one part. So, its overall bent will be 5°. However, the strain will be the same in all parts of the large and small beams. All parts bent by 5°!

So, the question is: Did this experiment achieve the same bending moment across the constructs as the researchers state? Because if it did not, then this is why a difference in strain was found. And, if this is the case, then the working length was not the causal factor of the difference, but the fact that different moments were achieved between the different constructs examined.

To me, this is a typical study where correlation should not imply causation, and where this has not been sufficiently highlighted. My letter might seem technical, but the main ideas are straightforward. Here is a simple summary of my points.

1. The Main Point: A Four-point Bending Test

Many of my comments are about a specific lab test used to check an implant's strength, called a "four-point bending test."

How it works: Imagine holding a ruler with both hands and bending it by pushing down with your thumbs. The test in question is a precise, machine-controlled version of this.
The Key Rule: In this specific test, the amount of "bending force" the implant "feels"
does not change based on how long the implant is. All other things kept equal, the bending force only depends on the distance between the support fingers and the thumbs (pushing fingers). This force is transferred to the middle part of the beam, and it is constant along its length. This is why four-point bending is also called pure bending. It generates a single force throughout the construct.
Conclusion: This means making an implant longer cannot make it stronger or weaker in this particular lab test. This is a fundamental rule of physics, like gravity. And this is why the current impression that long working lengths protect the implant from breaking does not hold up under four-point bending (contrary to what the book says -> strain distribution theory).

Here's what the idea behind a four-point bending test looks like:

2. So, What If a Study Shows a Difference?

This is the central issue. If an experiment finds that longer implants did perform differently in this test, it points to a problem. The difference is likely caused by one of three things:

A Mistake in the Method: The experiment may have been set up incorrectly, or something else changed without the researchers noticing.
Random Chance & Flaws: This is very likely. Think of it like a chain: a longer chain has more links that could have a hidden crack or weak spot. A longer implant has more "room" for a tiny, random material flaw that could cause it to fail. The length itself didn't make it weaker; it just increased the odds of finding a random weak spot.
The transfer of the “push” from your hands to the central part of the beam was different between your experiment setups. Imagine that the part of the ruler where your hands are is made of a different material than the part of the ruler where the bend happens. Say, that in one setup, the part of the ruler around your fingers is made of metal, and in the other setup, it is made of rubber, and that in both setups, the middle part is made of the same plastic material. In the rubber setup, your fingers will bend the rubber, but this “push” will not be transferred efficiently to the middle part of the ruler. Most of the bending will happen at the rubber, which is much more elastic than the plastic material in the middle. The plastic may not bend at all because very little bending force was transmitted to it. Now, imagine that in the rubber setup you chose to have a shorter working length. If you ignored the fact that your “push” did not transfer efficiently in the middle part of the ruler, you would notice that your ruler bent less, and you may conclude that “a shorter working length resulted in less strain in the ruler”. Imagine that the ruler is a bone, and that you have anchored a plate to it. The plate is anchored to the ends of the bone, and not in the middle part where the bend happens. Now say that in one setup, you have anchored more plate to the bone, meaning that the length of the plate anchored to the bone at the ends is larger. You have achieved this by spacing your screws farther apart. Your “push” happens at the ends of the bone/implant construct. In one setup, the length of the plate used to transfer your “push” (part of the plate between the screw closest to the bone end and the screw closest to the middle part of the bone) is larger. So, it is more elastic (like rubber). Because you used different plate lengths to transfer your bend at the middle of the implant, you have introduced a confounding factor —an additional parameter that can affect your results. You think you are comparing two different working lengths, but you are not.

To claim otherwise would be like claiming to have broken a basic law of physics, which would be a Nobel Prize-level discovery!

3. A Critical Warning: Don't Compare Apples 🍎 and Oranges 🍊

A major part of my critique is about comparing different types of tests.

A test that bends an implant is completely different from a test that pushes on its end (like a pogo stick).
In the "pushing" test, the implant's length is very important. Because the longer implant will have a greater overall bend (50°), the point where the "pushing" force is applied will move further away from the centre of rotation (the area where the bend happens), generating a larger bending moment. So, the bending moment changes. This is very different from the four-point-bending, where the bending moment is assumed to be constant.
You cannot take the results from the "bending" test and compare them to the results of the "pushing" test. They are testing two different things.

4. The Big Takeaway: Why This Matters

Science must be built on a solid foundation. If the starting question is flawed, the answer doesn't matter, no matter how much data you have.

My Example:

You could run a massive, complex statistical study to see if the colour of one's t-shirt affects the quality of one's work. You might find a "statistically significant" result (like, "people in red t-shirts made 2% more typos"). But the result is meaningless because the original question doesn't make scientific sense. There is no scientific theory that can link the colour of someone's t-shirt to the number of typos they make causally. The same is true here. We must ensure our research hypotheses are scientifically sound before we start testing.

This does not mean that the correlations found can be ignored. But causality effects based on correlations must be supported by a theory. If such a theory does not exist, or even worse, it seems like you have broken the existing mathematically proven theory, then you may want to start looking for errors or confounding factors. You can still report your results, but the Discussion part needs to be objective and thorough.