- Two measurement and reproduction methods derived from ontology and epistemology
- Autopoiesis speaks for itself, looking for a new gnathology
- On welcoming a “Centric Relation” with a terminal hinge axis to the Cartesian coordinate system
- About the Virtual Kinematic Axis Method
- About the Ideal World
- About Ideal Parts
- About Precision Provisional Restorations for Measurement
- What can you do in an ideal world?
- For dentists interested in dental technology
Two measurement and reproduction methods derived from ontology and epistemology
The method of measurement and reproduction from ontology is the so-called conventional pantograph method. Let us discuss the ontological mandibular movement.
As the mandible opens, it begins a rotational movement near the axis that penetrates the right and left intercondylar axes. As it opens more widely, the left and right mandibular heads slide anteroinferior almost equally as they rotate.
Next, let us consider right and left lateral movements. During right lateral movement, the right condyle head rotates with a small lateral shift within the mandibular fossa. In contrast, the left condyle head slides anteriorly inferiorly medially. The opposite is true for left lateral movement. During left lateral movement, the opposite is true.
This is the method of consideration governed by the determinants of mandibular motion. For the anterior determinant, it is anterior guidance during contact movement. During mouth opening motion, there is no anterior determinant.
These expressions are ontological interpretations of mandibular movement derived from biological mechanisms. No one would dispute this. That is why conventional measurement methods used instruments such as pantographs to explore the position of the condyles under the skin to determine the intercondylar axis. They also examined the movement and rotation of the working and non-working condyles during left and right lateral movements. These measurements are truly “ontology-derived methods.
On the other hand, my proposed method of measuring and reproducing mandibular movement, the virtual kinematic axis method, is a method that does not derive from the biological mechanism of mandibular movement, the left and right condyles or anterior guidance.
What does the virtual kinematic axis method dependent on? It can only depend on how mandibular movement is measured. The mandible can be thought of as a rigid body. However, the mandible is covered by soft tissues such as muscle and skin, and it is not easy to locate the exact position of the mandibular head from the outside.
The mandible is connected to the dentition, which is exposed to the outer skin. The dentition and mandible are tightly integrated by the periodontal ligament. Thus, they can be considered as one rigid body.
In other words, measuring the movement of the mandibular dentition is measuring the movement of the mandible. This method of measurement is independent of the intercondylar distance, which varies from individual to individual. It is truly an epistemological measurement method.
The exact path of motion of the mandible can be obtained by giving the mandible three points on the dentition, which is tightly connected to the mandible by the periodontal ligament. These three points do not have to be set directly on the dentition. As shown in this example, a probe with three points can be rigidly connected to the dentition.
The path of movement of the mandibular cannot be known without mathematical processing of the displacement of three points in three-dimensional space. If we want to know the path of movement of a specific position of the mandible, such as the mandibular head, we need a 3D MRI image. In other words, these two measurement methods are complementary, and we need information from both to know the entire mandibular movement.
A face-bow transfer and a three-point motion pathway are sufficient to use the acquired data in the articulator; MRI three-dimensional images are not required.
The virtual kinematic axis method measures three coordinate points attached to the dentition. This means that mandibular motion must be represented mathematically in three-dimensional space. When it is not necessary to strictly locate the position of the condyles, a face-bow transfer is all that is needed to make the rotational axis of the articulator the intercondylar axis of the organism.
The 3D MRI image data of the mandible can be superimposed on the dentition to view accurate condyle head movement. These methods can be achieved extremely easily with “general-purpose CAD”.
Living organisms have a slightly different mode of motion than human-made machines. Unlike the geometric motion of a robot, the motion of a living body fluctuates. The detailed movement of the mandible can be viewed again and again by accurately extracting the subtle motions and restoring them on the CAD system.
In any three-point measurement, the left and right condyles and the anterior reference point can be likened to the oscillator since they are the determinants of mandibular motion. Any three points can be the transmitter of the position and path of motion of the entire mandible. The camera captures the movement of the dentition and changes in mandibular posture, so the camera and other sensors are the receivers.
The position of the condyle head can be reconstructed by superimposing the MRI image in the CAD. A face-bow transfer is sufficient to transfer the data to the articulator; if the only purpose is to know the path of mandibular motion within the CAD, a face-bow transfer is not necessary. This is possible because of the method derived from the measurement method.
Autopoiesis speaks for itself, looking for a new gnathology
The new gnathology, as I see it, begins with the transformation of the real world into the ideal world. The development of the technology of prosthetic dentistry was intended to obtain an indirect environment for the creation of dental prosthetics. In addition, it could be said that it was a history of searching for a kind of norm regarding the alignment of teeth and so on. Specifically, these norms are things like the relationship between the articulator, which is face-bow transferred and fitted with upper and lower dental models, and each reference point on the face, and the rules for how the teeth are aligned.
They ranged from complex to simple. For example, the ideal environment for the creation of dental prosthetics is the articulator. Since we cannot create dental prosthetics directly in the mouth, we need an indirect environment for fabrication. In addition, “Bonwill triangle,” “curve of Spee,” and “Monson’s spherical theory” provide various guidelines for tooth alignment, etc.
Recently I have come to believe that the gnathologists who first devised gnathology asked the people of the world how to interpret centric relation. I propose a way to answer that question using the “virtual kinematic axis” and the “Cartesian coordinate system”. Today, computer technology, as represented by CAD, is well developed. Computer technology allows the dentist to obtain any number of mandibular motion paths if he or she so desires. In addition, the open/close movement of the mandible, which is not directly related to occlusion, can be added to the path of movement. Thus, instead of seeking an ideal environment in an actual “articulator” as in the past, we can consider mandibular motion in a flexible environment by using a new item called CAD.
In my opinion, the term “terminal hinge axis” or “centric relation” in gnathology is actually not of this world, but the ideal world in dentistry, or the central item in a metaphysical narrative. That is to say. In other words, it is not a real world story. There is a gap between the ideal world and the real world. It is not easy for an ideal world entity to appear in the real world. Some procedure is required.
It has been quite some time since the gnathology was published, and the definition of centric relation has changed many times in that time. That is how difficult it is to define. I think the cause of this difficulty lies in the gap between the ideal world and the real world. I feel that this gap has not been resolved for any length of time. In the real world, necessity and chance permeate each other, and one of the reasons is that it is very difficult to confirm only the pure rotational motion of the mandible in the intercondylar axis applied to the centric relation, i.e., the hinge axis alone.
This is not easy to do, no matter how much the patient himself tries to make only open-close movements that do not involve mandibular movement, and no matter how meticulously the dentist tries to guide the patient to make only purely open-close movements. This has been the experience of many dentists historically. However, it is not absolutely impossible.
If the mandibular head were perfectly spherical and the mandible were symmetrical, there might be only one axis of rotation. However, the human mandibular head is not perfectly spherical, and the mandible is not perfectly symmetrical. Furthermore, there may be two or more axes of rotation due to the presence of various buffering tissues as well as bones around the mandible. On the contrary, it may exist as an area. If that is the case, then there could be an infinite number of rotational axes. This is just a consideration, and the actual situation is not clear without careful investigation.
Let us now consider the relationship between the terminal hinge axis and the centric relation. As quoted from the article “Reconsidering the Centric Relation (Theory)” featured in the July 2022 issue of “Shikai Tenbo,” we understand the definition as follows
（Centric relation in the terminal hinge position of the mandible , in which the hinge axis is constant to both the mandible and maxilla.）
Let us again consider the definition of terminal hinge axis or centric relation. The first question is whether the terminal hinge axis is a pure axis of rotation that does not allow even a micron of motion, or whether it allows some motion blur. Currently, there does not seem to be a strict definition of a terminal hinge axis. The latest situation in this area is featured in the July 2022 issue of “Shikai Tenbo,” a dental trade publication, which contains an article titled “Reconsidering the Centric Relation (Theory). It is written by a dentist named Ryushiro Sugita. According to this article, the rotation axis in the centric relation is not “not allowed to blur even one micron,” as defined by metaphysics, but rather “should not blur when visually observed.
On welcoming a “Centric Relation” with a terminal hinge axis to the Cartesian coordinate system
It will allow us to explore whether or not the initial pure mandibular intercondylar axis rotational movement, i.e., the initial rotational movement of the hinge axis only, is possible during the opening movement. It would also show, for example, the possibility that there is more than one. Any number of opening and closing motion paths can be taken, and any number of lateral movement, etc., can be added.
Applying the 3D Cartesian coordinate system to the analysis of the motion of artificial objects such as robots is easily accomplished. However, precisely analyzing the motion of living organisms is a difficult task because of the complex rotational and translational motions involved, which are difficult to reproduce exactly. If we introduce the 3D Cartesian coordinate system, which is the ideal world of computer-aided CAD for analyzing centric relations, we will be able to perform various analyses and verifications.
In CAD, the 3D Cartesian coordinate system allows for easy coordinate transformation. Even if the position where the mandible motion is measured on the body and the position of the drive unit of the articulator are different, the coordinate data of the measurement position can be converted to the coordinate data of the drive unit of the articulator. By using the coordinate conversion, it is possible to reproduce the motion of the mandible model on the articulator as it has been in the past. Also, by introducing the equation of motion, the mandible position can be managed in time because the equation of relationship between the mandible position and time is created on the CAD.
As a procedure to achieve this, it would be good to introduce the dynamical systems theory, as detailed in the autopoiesis theory, to the dental field. In the history of gnathology, we read, “In 1921 McCollum devised the hinge-axis locator and demonstrated the existence of a terminal hinge-axis.” However, this would only be at the visual level. No matter which dentist guides the mandible, there will always be a blur at the micron level. In the real world, it is not easy to find a pure terminal hinge axis that can be reproduced.
When the centric latch of the articulator is activated, the mandibular part of the articulator can only perform pure rotational motion without any blurring. I do not think it is possible to make the mandible move in the real world in a similar way. It would be quite difficult even if dentists applied manual restraints. In the real world, all or several of the “six degrees of freedom of motion” are intricately bound together by the body; in an ideal world using a three-dimensional Cartesian coordinate system, the intricately combined “six degrees of freedom of motion” of the mandible could be broken down to display each component.
About the Virtual Kinematic Axis Method
Why is it necessary to align the axis of rotation of the articulator with the hinge axis of the organism? Rather than a necessity, I believe it stems from the conventional method of measuring mandibular motion. The axis for opening the mandible set in the articulator would have had to be set in a position similar to that of the biological jaw. The July 2022 issue of “Shikai Tenbo,” a dental trade publication, features the following article, “Reconsidering the Centric Relation (Theory),” which also states the following.
The terminal hinge axis is the central tenet of gnathology. The supreme goal of gnathology was to reproduce the patient’s open/closed mouth motion on the articulator by identifying the terminal hinge axis and aligning it with the open/closed axis of the articulator. Once this is done accurately, the clinical benefits are immeasurable, as a dental prosthetic device fabricated with a modified occlusal vertical dimension on the articulator can be placed in the patient’s mouth with minimal adjustment.”
This is how the purpose of gnathology is described. As a matter of fact, the relationship between the terminal hinge axis and the centric relation in many people is such that in the centric occlusion, few people have the centric relation and terminal hinge axes coincide. The fact that these are misaligned does not seem to cause or predispose to TMJ disorder. While there are operational advantages for the dentist in the above statements, there does not seem to be a health reason for the purpose of gnathology. After all, gnathology is a concept derived from structuralism in accordance with the fundamentalist theory of biomechanics.
# Structuralism is one of the modern philosophies of the 20th century. In a broad sense, the term has been extended from modern thought to refer to a methodology for extracting the latent structure of any phenomenon and using that structure to understand and, in some cases, control the phenomenon. Adapted from Wikipedia
If there are many teeth that have nothing to do with the treatment, the standard of occlusion is the centric occlusion. Usually, the tooth shape of a dental prosthesis is formed based on this position for both anterior teeth and molars. In the real world, if the centric relation of the living body and the axis of rotation of the articulator can truly be aligned, the centric occlusion can be freely determined on the articulator. This means that the height of the occlusion can be changed. This can be done simply by adjusting the incisal pin of the articulator. However, this can only be used in practice when creating dental prosthetics for the entire upper and lower dentition. It is useful, for example, when fabricating occlusal surfaces in ceramic.
In my opinion, in the real world, it is very likely that there is no pure axis of rotation of the mandible in a living organism. If there is even a micron of deviation, it is not the pure axis of rotation of the mandible. The pure axis of rotation of the mandible definitely exists in the ideal world. There is a gap between the ideal world and the real world, and they do not easily overlap. It is necessary to eliminate the gap or bridge the gap between the two. How can we bridge the gap between the ideal world and the real world?
One idea is the virtual kinematic axis method. What is the virtual kinematic axis method? In a few words, it can be described as follows. When the maxillary model is mounted on the articulator, the intercondylar axis of the articulator automatically becomes the kinematic axis of the mandibular model. When the maxillary dental model is mounted on the articulator by means of the face-bow transfer, the intercondylar axis of the mandible is set at the average position of the body. If done by eye, it will be set in a reasonable position. This is the virtual kinematic axis method.
The opening and closing motion of the biological mandible is different from the opening and closing motion of the articulator. Even if they are different, I do not think it is a problem. When making dental prosthetics, differences in the position of the axes in simple open-close motion have no effect on the tooth shape and do not cause any problems in the work. The virtual kinematic axis method is based on the idea that in the real world it is very difficult to find a purely rotational axis in the centric relation with a terminal hinge axis. In cases where only the centric occlusion is at issue, the coincidence of axes is irrelevant, so the virtual kinematic axis method is sufficient. We believe that the terminal hinge axis exists in an ideal world. I just haven’t found a way to make that position appear in the real world.
The virtual kinematic axis method does not measure the amount of movement of the axis of rotation when the patient moves the mandible open and closed. Nor does it have a method to reproduce it. Therefore, when the incisal pin of the articulator is adjusted to change the occlusal vertical dimension, an error will always occur. Whenever it is necessary to change the occlusal vertical dimension, in other words, to change the centric occlusion, it is necessary to obtain a mush bite for confirmation in vivo. The mandibular model must be reattached to the articulator using the mush bite.
If we want to know the true axis of open/closed mandibular motion, we need to load the MRI 3D image of the mandible into an environment where the upper and lower dental models are attached to the articulator on the CAD. When the 3D MRI image of the mandible is loaded and superimposed on the mandibular model, the left and right condyle heads of the organism are displayed. It will probably be slightly off from the intercondylar axis of the articulator. If you use the measured data to move the mandible, you can see on the CAD how the condylar part of the MRI 3D image of the mandible moves.
Dentists have probably never seen a video of the mandibular head moving in three dimensions because they have been measuring mandibular motion using conventional methods. In the conventional method, the three-dimensional movement of the mandibular head is determined based on the projected trajectory on a two-dimensional plane. It is also impossible to reproduce the opening and closing movements of the mandible on an actual articulator.
About the Ideal World
Let us invite the “centric relation with terminal hinge axis” to the ideal world. In the ideal world, there is no error. Even at the micron level, there is zero motion of the axis of rotation. In the ideal world, the “six degrees of freedom of rigid body motion” can be driven individually. It is also possible to combine multiple elements of motion and rotation. In the ideal world, time can move forward or backward. Objects can overlap, touch, or move away from each other, collide, or pass through each other. The ideal world may be the equivalent of the world described by mathematics, for example, theory or physics.
There is no error in the ideal world; there is error in the real world. This error refers to dimensional differences that occur unexpectedly due to chance and necessity. Even in the ideal world, depending on the setting, there can be a very large number of mathematical decimal places in the setting.
Also, in the ideal world, elements can exist individually, whereas in the real world, multiple elements exist in connection. This arises from the idea of interpenetration. They cannot be easily separated by humans. Therefore, there must be an interface between the real world and the ideal world, and trying to directly superimpose or connect the ideal world and the real world will not work. To access the ideal world from the real world requires error resolution and interpretation of the ideal world from the real world.
It is the dentist who actually operates the mandibular measurements. Dentists and dental technologists operate CAD and other equipment, but the operation must be within the scope of their daily work. Equipment that is too expensive or time-consuming to operate is not acceptable for practical use.
About Ideal Parts
The component-related elements for mandibular movement that are indirectly represented are fabricated as “ideal parts” in CAD. For example, the length of the left-right intercondylar axis in the ideal world is the same for all, 110mm. In the conventional method, the inter-condylar distance would have to be changed. In the ideal world, the shape of the left and right condyles of the mandible are perfectly spherical and perfectly symmetrical in position with the midsagittal plane. There is only one axis of rotation. The reason for this is that the focus is on accurately reproducing the motion of the dentition rather than the mandible. These were made possible by performing a “coordinate transformation” in a three-dimensional Cartesian coordinate system.
If the maxillary dental model is mounted on the articulator without face-bow transfer, the maxillary dental model will be mounted off the reference plane of the articulator. Even in such a case, the virtual kinematic axis method does not cause any error in the motion data of the mandible. There is only an error between the reference plane of the organism and the reference plane set in the articulator. If no face-bow transfer is used, the Bennet angle and Condylar guidance inclination and the Angle of incisal path may deviate from the average values.
In the virtual kinematic axis method, the length of the left and right intercondylar axis is fixed at 110 mm. There is no difference between men and women, no difference in age, and no difference in ethnicity. It is constant in all. If for some reason we want to know the true left-right condylar motion, we can do so by showing the positional relationship between the mandibular dentition and the left-right condylar regions of the organism on CAD. The length of the left-right intercondylar axis is 110 mm, which is the length currently employed in articulators of similar size to the living body. The technique of “coordinate transformation” in a three-dimensional Cartesian coordinate system makes this possible.
The left and right condylar areas of the articulator are the reference for manipulating the movement of the mandibular portion of the articulator. The length of the axis between the left and right condyles in a living body differs from person to person. In addition, the three-dimensional position of the condyles in a living body is not perfectly symmetrical about the median plane. What is important in this virtual kinematic axis method is the change in the three-dimensional position of the mandibular dentition in relation to the maxillary dentition.
Three-dimensional positional changes of the mandibular dentition are collected using the “pre-labial measurement method”. This data is used to reproduce the displacement of the mandibular model position on the articulator in the CAD. The data collected in front of the lips is converted into the motion of the condylar ball and the tip of the incisal pin on a virtual kinematic axis with a left-right intercondylar axis length of 110 mm. It is not a reproduction of the specific positional motion pathways of the left and right mandibular heads that exist in the organism.
About Precision Provisional Restorations for Measurement
When fabricating a dental prosthesis with a large number of teeth, a precise provisional restoration will probably be needed to measure the positioning of the maxillary and mandibular dentition. Its anterior tooth county portion has anatomical morphology and is given accurate anterior guidance. The molars have a occlusal vertical dimension that the centric occlusion is maintained and reproduced. It would be even better if the molars also had an anatomical form. A 3D printer could be used.
What can you do in an ideal world?
There are ideas from the categories of coincidence and inevitability, but suddenly something interferes or leads to something else, and this was a story that works among those who look only at the real world. When we stick to the real world in this way, there is nothing definite about the future. There is always uncertainty.
Also, the term “ideal world” does not mean a world of convenience. In the ideal world, the future is already determined, and there is no such thing as a future based on ideas of chance and inevitability. In the ideal world, the past, the future, and everything else is already known. Even if you hide in the shadows, you will be found. Everything is in full view. It is like the world of Adam and Eve in the Old Testament book of Genesis.
However, not everything about the ideal world is revealed to humans. And although humans are trying, they still do not have full access to the ideal world. The categories of chance and inevitability cannot describe, explain, or access the ideal world because they belong to different worlds. Thus, we cannot interact with the ideal world from the categories of chance and necessity.
To access the ideal world, we need to think from uniqueness and diversity. Thinking in terms of uniqueness and diversity, we think of convergence to one reality out of many possibilities. In the ideal world there are all possibilities, but not all can be realized in the real world. This is because there is a consistency problem. The ideal world is a higher concept than the real world, and by sharing the ideal world with the real world, the real world can be brought closer to the ideal world. The ideal world may be paraphrased as dealing with the abstract world from the perspective of the real world.
The term symmetry is used as a means of explaining or expressing the connection between the ideal world and the real world. Symmetry has a slightly different meaning depending on the academic discipline with which it deals. In general, symmetry refers to operations that do not change appearance, such as symmetric transformations. Also, in physics, symmetry is the symmetry of a physical system, that is, the invariance of the appearance of the system under a particular transformation. In mathematics, there are issues such as the solvability of equations, as in Galois theory, and the representation of constructive methods of algebraic structure, as revealed by the exercise of group theory.
Symmetry is the property that “moving it does not change its appearance”. Therefore, it is inversely related to “movement” or “change”. This property could be used to analyze the change of space between occlusal surfaces. I believe that the study of the proximity relationship between the occlusal surfaces of the maxillary and mandibular molars and the mechanism of mastication has not been the subject of much research or has been done. I believe that symmetry is the key to solving the problem of changes in the space between the occlusal surfaces. The shape of the occlusal surfaces of the maxillary and mandibular molars may change, but what remains the same is the occlusal vertical dimension at the centric occlusion. What shape of the occlusal surface should be used for a good bite? In addition, there are many factors to be studied, such as the shape of the occlusal surface that is physiologically reasonable when considering the load on the roots of the teeth.
No matter how good a tooth is, it is impossible to talk about function without considering the opposing teeth. In other words, analysis of the shape of the occlusal surfaces of the molars is meaningless without taking into account the opposing teeth. Function is largely a function of the movement of the mandible. This means analyzing the proximity of the occlusal surfaces of the upper and lower molars, or to put it another way, looking at the shape of the occlusal surfaces in terms of symmetry. In summary, I believe that rather than studying the occlusal surfaces of the teeth themselves, we should now study the changes in the space they create, which will lead to the discovery of new functions.
It is true that the concavity and convexity of the occlusal surfaces of molars exist in response to the concavity and convexity of the opposing teeth, but why are they shaped the way they are? We don’t know what is the purpose of the shape of the occlusal surfaces. I don’t think it is just a random unevenness, but I don’t know why. Of course, I think it is shaped based on the presence of the opposing teeth and the movement of the mandible.。
In dentistry, symmetry is the study of how the space between the occlusal surfaces changes with the opposing teeth. The use of finite element methods and fluid analysis is important. Symmetry is the mechanism of the natural world, which is made up of structure and energy. Symmetry allows us to know the whole from one part or half of things, based on relationships, etc. By abstracting things, idealizing things, and using mathematical models, we can create a depth and breadth that has never been seen before. Humans extracted the abstract world from the real world, but I believe that the ideal world actually preceded the real world, and the real world was created by the fruition of the abstract world.
For dentists interested in dental technology
One reason for the decline of gnathology is that dental technology has been transferred to dental technologists over time. Dental technology has become less involved with dentists. To fully and freely design a dental prosthesis requires 100% discretion over the treatment. I believe that dentists who embrace and practice gnathology have an extraordinary interest in dental technology. This is evident in the history of dentistry. The history of the construction of the occlusal appliance, an ideal environment that simulates the living body, was intended to produce an ideal dental prosthesis, and I think there is a strong recognition that dentists should be actively involved in dental technology as well. Today, we have entered an era in which the use of artificial intelligence is becoming possible in earnest. I believe that many dentists would like to design their own dental prosthetics. I would like to see the “design of dental prosthetics” put back in the hands of dentists with the help of artificial intelligence.