Northeastern University
Associate Professor, Computational Mechanics and Biomechanics Laboratory
So it’s it’s my pleasure to introduce Sinan Müftü to the platform. He’s, the associate professor at Northeastern University Department of Mechanical and Industrial Engineering. He’s been working with Bicon for four years on various projects related to design considerations of different implant abutment connections, and stress distributions on bone of different design implants. He has articles published frequently in respected engineering and biomechanical engineering journals. Dr. Müftü, thank you. Good morning ladies and gentlemen. I would first like to thank the symposium organizers for giving me the opportunity to present our research results. It’s indeed a great pleasure and an honor to talk in front of you this morning. I’m going to talk about, in general, finite element analysis of various implant designs, and I’m going to also touch the results that we found for the five by six millimeter implant. So however, I also would like to overview the recent research that our group has conducted in biomechanics of bone dental implant interactions. I would like to acknowledge my students, Dinçer Bozkaya, John J. Jagodnik, and Hsuan-Yu Chou, who contributed greatly to this research, and of course the support provided by Bicon Dental Implants. And of course my daughter and son who has allowed daddy to do some work during this work. Dr. Morgan yesterday asked me if I had any skiing or fishing pictures. I said no, but this is a picture that we have taken in our last vacation in Turkey, so I thought I would just replace that here. With that in mind, I just want to review in one single slide the overview of our work that we have done in dental implant area. The first thing is we worked on mechanics of the implant abutment attachment methods for dental implants. I’m going to talk about that and also the topic of today’s presentation, evaluation of bone loading characteristics of various dental implant systems. So when it comes to mechanics of the abutment implant attachment methods, we looked at the tapered interference fit or the Morse, the so called Morse taper. We developed some simple formulas to determine the various believe it or not, these are very simple formulas compared to performing finite element analyses and trying to decipher the results of the finite element analyses. So with formulas such as this, one can easily determine the relations between practical parameters such as insertion depth and loosening torque. And of course some other things that I don’t want to go into detail right now. In addition to tapered interference fit, we looked at what I term as taper integrated screwed in abutment attachment methods used by other implant systems. And again, there are some formulas that were developed, and again, we can determine parameters like the effect of tightening torque on loosening torque and parameters of that nature. However, that’s all I want to tell you about this attachment method business. And the next topic of course is the topic of today, biomechanical evaluation characteristics of dental implant systems. Now when we look at this topic, why do we want to study the finite element analysis of bone loading characteristics? Of course the answer is twofold. One of them is to feed back to the implant designers and manufacturers about the bone loading characteristics, whether they load the bone enough or not enough or too much. And the other one is of course to help give feedback to basic scientists who work in bone mechanics area. So analyses like this provide that possibility. With that, I’m going to be talking a lot of mechanical and engineering jargon today and I’m sure you all know these concepts, but I just would like to review briefly mechanical properties of the bone. I’m going to introduce what stress is, strain is and elastic modulus is, so that we are all on the same page. Once that’s done, I’m going to talk about biomechanical evaluation of dental implants. I’m going to do this in three different flavors. Now the first thing I’m going to do is I’m going to compare five different implant systems. Next thing, I’m going to look at the biomechanical evaluation of the five by six Bicon implant and then I’m going look at the evaluation of some implant groove types. Now when I’m doing this, I’m going to increase the complexity of the biomechanical evaluations. First of all, I’m just going to use a criteria of bone overload to compare five implants. This is a fairly straightforward way of looking at things. Next I’m going to look at Bicon implant from a mechanostat point of view, and when we come to it I’ll explain what that means. And then when we are evaluating different implant grooves, I’m going to talk about bone remodeling. So as you know, during mastication complex stress distributions can occur in the bone and the stress is a pointwise quantity, so the stress would change from point to point to point. And a stress at a point can be represented by six different stress components. So but when we look at these we will see that mainly these are normal stresses and shear stresses, we’ll talk about them, and they cause normal strains and shear strains. We are then going to talk about the definitions of elastic and shear moduli, and then we’ll talk about the multiaxial stress just a little bit. So normal stress, typically it’s very easy to visualize it in the tensile testing. For example, if we were to test an aluminum piece or even maybe a piece of bone, we would prepare a sample, a cylindrical sample, put it into a tensile tester, and we would impose an elongation and measure the force. And in engineering it turns out that force and elongation are not scalable to generic laws but stress and strain are scalable to generic laws. So when we plot the results of such a test, on the vertical axis we get the normal stress, on the horizontal axis we get the normal strain, and the proportionality constant for this normal stress normal strain relation is known as the elastic modulus. Now, when we look at the shear strain, our shear stress, again shear stress develops when two surfaces which, for example, were glued over here in this footprint area were made to slide with respect to each other and a shear force develops, a resultant shear force develops over here, and shear stress is defined as the ratio of the shear force to the cross sectional area. And this is an average quantity of course, for this definition. And shear strain causes some angular changes with respect to a rectangular configuration, and shear stress, shear strain curve would look something like this. And so if things were very simple, we would have a very simple linear axial tension test, and stress would be related to normal stress would be related to normal strain with Hooke’s law, and shear stress would be related to shear strain through a shear modulus. Now before going into more complicated methods, let me just show you some pictures about the internal structure of the bone. As everybody knows, inside the bone is typically cancellous bone and outside cortex is the cortical bone with a higher density. And a typical elongation test for cancellous bone looks like this, where over here we have the ultimate stress but we really want to load the bone in here in this regime somewhere. As I said, due to mastication a complex stress distribution occurs in the bone, and there are six stress components and correspondingly six strain components that develop in general. And they are connected through a generalized Hooke’s Law where this C is a compliance matrix. Now, in reality, bone is an orthotropic material, so we actually get nine different independent parameters to represent the stress strain behavior. But often, as was done in our finite element analysis, the bone is assumed to be isotropic, in that case we can get away with two independent parameters. In that case for the bone, for the cortical bone, the elastic modulus is typically thirteen gigapascals. For the trabecular bone it’s one gigapascal. And the Poisson’s ratio is point three. Now there is ample experimental and theoretical evidence that shows that there is a relationship between the density of the bone and the elastic modulus. And when I say elastic modulus, I’m talking about the mean elastic modulus that we see at the macro level. So this relationship is in this general form where mean elastic modulus is proportional to a constant times the density of the bone to a power n. Now for cancellous bone this power is almost two and for cortical bone it’s about three. Now on to the topic of today. I’m going to talk about biomechanical evaluation of dental implants and the first we will talk about comparison of five dental implant systems and the comparison criteria is going to be bone overload. So the implant systems that we are considering are these five listed over here, and the dimensions and the implant surface area in the bone are as given. Now the comparison criteria is the maximum stress criteria. And it just, as I said at the beginning, it’s a simple criteria. We are just looking at the bone failure, whether bone failure occurs or not. So to do that we need to determine the maximum stress that occurs in the bone due to the loading and compare that to the ultimate stress that the bone can take. Now it turns out that experimental measurements show that the ultimate tensile stress in cortical bone is 170 MPa in tension but 100 MPa in compression. And in cancellous bone this is in the range of two to five MPa. Now, again, just a little bit of more engineering jargon, but it’s necessary. As I said, principal stresses or the maximum stresses are necessary to calculate to make this failure criteria. So the maximum stresses that occur in the bone are the principal stresses and they are found by solving this cubic equation and the constants that occur, i1, i2, i3, that occur for this cubic equation are actually the stresses that are given by the finite element method. So when this cubic equation is found, it gives three roots. When solved it gives three roots. The first one is the first principal stress, second principal stress, third principal stress. And in general, you would get a tensile behavior here and a compressive behavior here. It’s not necessary, but in these analyses that’s what ends up happening. So we just check these conditions. So this is a summary slide. These are the systems that we considered and what we are looking at is just the area at the intersection of the implant and the cortical bone in these five graphs over here. The load that we applied was an occlusal load at an oblique angle applied a little bit off center to the implant for all the cases and we varied the magnitude of this load. Now the good news is for moderate levels of mastication loads there are no differences and no failure occurs in any of these implants. But when we go to very high loads, which can occur in patients which have grinding problems or in catastrophic situations when somebody tries to eat something that they are not supposed to eat too hard or something like that, the loads can go up to a thousand. I’ve read numbers of two thousand newtons on individual implants or teeth. So when that happens, some differentiation starts to happen between the implant systems. The results are here and I think we have a poster so I’ll be happy to talk about the specifics of the results. But since we are here for Bicon, I think Bicon fares fairly well in these so called catastrophic situations. Now, actually let’s go back here. I’m just going to say something. Now, for a very high occlusal load of sixteen thirty two newtons it’s one hundred and sixty two kilograms roughly we find that this system, Ankylos and Bicon, have a failure area marked by this little off mark color, and that failure happens due to tension. So this area is in tension, this area is in tension. So are these. The other implant systems, in addition to that, have failures at the top region. So if you look at why the ankylosing implant and Bicon don’t have failure due to compression in this region, we immediately notice that this sloping shoulder business. So yesterday Tom Driskell explained very well why there are advantages to using the sloping shoulder and I thought I would just present a back of the envelope calculation, an explanation of what that is. So if we turn the envelope and we look at the statics equilibrium of what might be happening in this interface, so this is the sloping shoulder of a Bicon implant, and this is the occlusal load coming down, and I’m making a gross assumption over here. I’m saying that all the load coming due to this force is perhaps shared only in the cortical region, and it causes this normal force and the shear force. So when we look at the forces, these depend on the external force by these cosine and sine relationships, and when we calculate the maximum stresses that are really generated by this, without going into too much details. If you look at the shoulder angle in the horizontal axis, and the maximum normal stress that’s developed on the surface, we see that actually right around over here, the maximum stresses are reduced considerably. So that may be an explanation why the sloping shoulder system works quite well. And that’s what Mr. Driskell was explaining so nicely yesterday. So I think I talked enough about this. Let me go to the next topic. I’m going to next talk about, again, another biomechanical evaluation, so I’m going to increase the level of complexity just a little bit from a biomechanic standpoint. I’m going to change from bone overload criteria to what’s known as mechanostat, and I’m going to explain what that is. And we are going to look at the effect of this in the five by six millimeter Bicon implant. So this mechanostat theory is introduced by Dr. Frost, And as you know, bone remodeling produces and maintains bone that is biomechanically and metabolically competent, and bone tissue adapts to mechanical usage. And the mechanostat hypothesis of Dr. Frost states that the bone remodeling response depends on the strain level it experiences. Now, what are the effects of different strain levels? This is a diagram a ninety degree version, ninety degree twisted version of this was presented by Dr. Lemons yesterday. So this hypothesis essentially says that if the local strains are below two hundred microstrain, this trigger a response which will eventually cause net bone loss. So this is this region, and we will have net bone loss. This is the strain, this is the bone mass. If the strains that the bone encounters are in the mid range, that is two hundred to fifteen hundred microstrain, this will evoke no response. This region is also known as the lazy region sometimes, lazy bone. So nothing happens, bone mass is conserved. And strains in the range of fifteen hundred to three thousand microstrain will cause net increase in bone mass. So fifteen hundred to three thousand actually is probably something that we would like an implant to impose on the bone. And if we go beyond three thousand or four thousand some catastrophic events start to happen. So we really don’t want to move beyond four thousand microstrain. Now I’m going to analyze the implant by using finite element method, but what type of assumptions do I need to make in terms of the bone quality and implantation depth and so on and so forth? So over here I have some slides and in practice it’s very obvious that the bone quality and insertion depth are patient and site specific. And you know this much better than me of course. In certain cases the implant can be inserted all the way down into the bone and with very fine growth of bone around it. And in certain cases this looks like cortical bone, very good cortical bone coverage. Whereas in certain cases, you know, there may be some non integrated components over here, such as these. Although all of these look pretty good. So in order to consider all the possibilities, this is what I did. We looked at, first of all, cortical bone thickness of one and two millimeters. We looked at different implant insertion depths, which I’m going to explain next. And we looked at extent of the cortical bone, how much cortical bone exists at the apical region of the bone. So this gives a total of thirty two combinations. So we looked at all different combinations. For example, in terms of insertion depths we looked at four different scenarios, as seen over here. And Dr. Grippo yesterday actually was talking about what happens if the implant for some reason gets exposed like this. It’s not a desirable situation, but what happens? And you know, different bone depths. And we also looked at the thickness of the cortical bone, one millimeter or two millimeters, although two millimeter I realize is a very thick bone to be found in the apical region. And we also looked at the amount of cortical bone coverage. Now let me explain what I mean by this. So this purple shell over here is the cortical bone, and in this region when I say full coverage, is full cortical bone. When I say two thirds coverage, the faraway regions, two thirds of the faraway regions is covered by cortical bone, but right around the implant there is cancellous bone. One third coverage has more cancellous bone, and no coverage has no cancellous bone. So we looked at all those thirty two cases but we are only going to present to you just a few of them, just to give you a flavor, but the results are pretty much similar. So over here we are looking at the results of the five by six Bicon implant, the so called fat boy. And so we are looking at the effect of insertion depth for two thirds cortical bone coverage. So around the implant actually we assumed that the bone is cancellous up to that region. So as we put the implant, or the implant is implanted deeper and deeper, the events that take shape, place are as follows. When the sloping shoulder starts to engage the bone, we start to see a reduction in strains. However, before I say that, let’s just look at the strain levels. So the strain levels generated in all of these cases this case, this case, and this case are actually, and in fact also this case, are in the when we look at the problem from a mechanostat point of view, are in the range where we would actually have bone growth. So this design creates favorable strain situation in the bone, for all of the cases. Most of the strains we found are around the tips of the fins or the plateaus, and as we implant deeper and deeper into the cancellous bone, the levels of strains drop. However, they either still remain in the bone growth region or in the lazy zone. So we don’t go down to less than two hundred microstrain regions. So in all of these cases there is healthy, expectations of healthy bone situation. Now when I look at the effect of cortical coverage on stress distribution for a submerged implant. So all of these are submerged, but we are looking at the effects of cortical coverage. Now this is fully cortical bone. What happens in this case is the stresses are highest in the cortical bone. This is a known result. Cortical bone has a higher elastic modulus and carries most of the load. When we have two thirds coverage, cortical bone ends here, there is cancellous bone here, and the sloping shoulder in this particular case is creating the strain levels, the stress levels over here. In the next slide I’m going to show the stress levels and you will see that they are pretty good. And as we go down, as we go to different coverage, we see that the response really doesn’t change. So this figure and this figure are pretty much the same. So that means the cancellous bone, the coverage level of it really doesn’t matter that much, as long as there is cancellous bone. But if we can develop cortical bone here, then that makes a difference. Now again coming back to the strain, which is the mechanostat approach, we see that, as I was saying before, in the case of cancellous bone developing over here, the strain levels are in the bone growth range, so we would probably have development of strong bone development activity in this range. So in summary of this part, the strains for the five by six Bicon implant were found to be in the healthy range. The peak strains in the cancellous bone are reduced as the implant is placed deeper in the bone. The peak strains in the cancellous bone increase in case there is less cortical bone coverage. For totally submerged case the sloping shoulder of the implant resists the loading provided that the osseointegration took place. So with that, again I’m going to increase the complexity of the analysis one more notch and we are going to look at the bone remodeling. Now the mechanostat theory by Frost tells us that we expect that bone resorption or growth or no change in bone to occur as a function of strain in the bone. But it does not tell us how it will grow and what densities it will take. So the bone remodeling models, mechanical or mathematic, they are mathematical models of bone remodeling that tell us that. So I’m going to talk about that a little bit next. In his famous observations, Julius Wolf observed that every change in the function of bone is followed by certain definite changes in internal architecture and external conformation in accordance with mathematical laws. Now modern theory does not like Wolff very much anymore, but this doesn’t mean that there’s no mechanical effects. The observations that are said that Wolff made was a comparison between a bone and a crane shaft. And he noticed, or it was pointed out to him, that the principal stress directions in a structure that looks like this are very similar to the cancellous bone orientation. So, in fact, this is a cancellous bone. So based on observations like this, not only this one but a long years of observations, he stated his Wolff’s Law. Now modern explanation of this divides this bone remodeling into two major sections. Surface remodeling is thought to change the thickness and or location of the cortical bone. So this layer either grows or its thickness changes. On the other hand, internal remodeling changes the density and the orientation of the cancellous bone. And there are new theories related to, relatively new theories, related to wound healing and tissue differentiation. And these can not only talk about these two, but also predict the generation of different types of tissues. So we are going to talk about the internal remodeling. I think I’m going to skip this view of time and I’m going to come here a little bit more mathematics. We used the model of Weinans, Huiskes, and Grootenboer. There are many other models. This is the one that we chose. You will recall that elastic modulus depends on the bone density. Now this model tracks the changes of the bone density as a function of time, and it uses a property in mechanics known as strain energy density. So if the strain energy density is greater than a certain limit, it predicts a positive rate for density increase. If it’s in the lazy zone, the strain energy density in the lazy zone, the bone density doesn’t change. And as you can imagine, if it’s lower than a threshold it predicts a negative rate of change. And once we can find the density we can calculate the elastic modulus. And this is all thrown into a complicated finite element program. I’m not going to go into the details of that, but first I’m going to look at the results of this type of bone regeneration models around the V shaped groove that you may find in a situation like this. So the model starts with this is the titanium part. This is a V shaped groove. It starts with cancellous bone all around it. It’s loaded radially and axially. So this is the radial direction, this is the axial direction. And for simplicity we only so far have looked only in one groove. So for the low loading case, the model predicts that some cancellous bone structure happens. For example, the radial load in this case is four megapascals and the axial load is one megapascal. And you see that the darker colors are the different higher elastic moduli, and the lower I’m sorry, the red and orange colors like that are the higher elastic moduli and the blues are the lower elastic moduli. And the bone finds an equilibrium state where it can find equilibrium, stay steady, and develop this. So what happened is, it was not loaded perhaps well, and it developed this structure. When we increase the load to twelve megapascals radially and three megapascals axially, actually we get much more cortical bone generation and some cancellous bone. However, we also see that this bullet shape starts to take place. In mechanics it’s known that arched shapes, arch shapes carry load very well, and actually nature, at least these equations seem to find that. And if we increase it even further, the results are as shown over here. So next I’m going to show what happens when we have a square shaped groove. Again, I’m putting this this is not square shaped by any means, just as a representation. We will also look in this case. We haven’t looked at it yet. These models take a long time to run on the computer. But the load ranges are seen over here. So I’m just going to go to the final punch. This is the low loading creates something like this. And as we increase it, actually in this case we seem to be developing more bone as compared to the previous case. So there seems to be some advantages. So these results all need to be analyzed and all need to be compared to histological data, and I look forward to doing those studies. So this is the last slide of my presentation. We used a bone regeneration model to predict bone density variation around a V groove, a rectangular groove for axisymmetric loading. This showed that both cancellous and cortical bone types can be obtained around both types of grooves. Reduced stresses around the grooves result in less cortical bone quality, like Wolf could have told us about one hundred years ago. Some reality checks over here. Model considers only the effect of mechanical loads. Physiological effects, the connection between titanium oxide and bone, are only indirectly included in models like this. And we are going to do some more work on the equilibrium value of the strain energy density. We are going to look at different implant grooves. We are going to study a full implant, and we are going to implement a wound healing model for some technical reasons. So thank you very much for your attention and thank you.