We use a second generation semi-adjustable articulator, semi-adjustable because of its ability to adjust several determinants (the condylar slope, the immediate mandibular lateral movement and the Bennett angle); as a consequence, it is not a fully adjustable one or a non-adjustable one (occludator).

The two parts (upper and lower) that compose it are movable to one another, and allow a contact via the incisal pin. They bear plaster keys to fix dental casts (Fig. 2a).

Fig. (2). Second generation semi-adjustable articulator: a. general sagittal view, b. condylar guide (sagittal view), c. Bennett insert (straight or curved) in the condylar guide (bottom view), d. dental mouldings in place.

The upper part represents the middle part of the face, especially the Axis-Orbital Plane (AOP). It bears condylar guides representing the mandibular (glenoid) fossae of the temporal bones. Anatomically, they are cavities on the outer surface of these bones, where the mandibular condyles are articulated, thus forming the TMJ. By programming, that is to say by adjusting the condylar guides settings, it is aimed to closer reproduce the anatomy of the mandibular fossae, and get an idea of the condylar kinematic of the patient.

A condylar guide bears a protrusion screw and an anterior stop including a spring. This one allows sticking the condylar bowls (representing the mandibular condyle) to the bottom of their box (Fig. 2b). NWLM is then reproducible. The Bennett angle can be replicated by inserting straight Bennett inserts (angle equal to 0°, 10°, 15° or 20°) and the immediate lateral movement can be replicated by inserting curved Bennett inserts (displacement equal to 0.5 mm, 1 mm or 1.5mm) (Fig. 2c).

The condylar slope can also be programmed on the lateral part of the condylar guides by a setting wheel adjusting the inclination from 0 to 70° by an increment of 5° (Fig. 2a).

The lower (double) part corresponds to the mandible. The condylar bowls on the vertical part, corresponding to the mandibular condyles, articulate with the condylar guides on the upper part. The horizontal part bears the plaster key and an incisal table (on which the incisal pin is placed) steerable so representative of the incisal guidance angle (angulation of the maxillary central incisors’ inner part).

On such an articulator, the upper part is movable and the lower one is fixed, (Fig. 2d) contrary to the anatomical reality, where the mandible is movable. Depending on the manufacturer, the setting modes of determinants are different, by changing the Bennett inserts as above noticed (for instance the articulator Quick Master^®, Fag) or by tilting the condylar guides sides (for instance the articulators Perfect ^®, Fag or Mark II ^®, Denar).

Determinants are required to programme an articulator. These data are issued from a recording system drawing the displacements of the mandibular condyles: the axiograph (Fig. 3a-c). The condylar slope and the Bennett angle or the immediate lateral displacement are so identified, allowing replicating the NWLM. Nevertheless two major disadvantages have to be underlined.

Fig. (3). Axiograph (Fag, France): a. on a patient, b. on a semi-physiological articulator, c. standard results.

On the one hand, the axiography is a non-invasive but time consuming act. It requires a substantial patient involvement, which can lead to uncertain results in case of a non-optimal understanding.

On the other hand, despite the accuracy of the axiographic data, the Bennett inserts only allow to approximate the physiology, as different angulations can match with one insert. Various mandibular movements are not accurately reproduced and they are just an approximation of the real trajectory. This brings up questions about the accuracy of teeth contacts on dental mouldings placed on the articulator (Fig. 2d).

The standard articulator used in our study is the Quick Master ^® by Fag company (and its corresponding axiograph). Indeed, it is commonly used within French dental offices because of its programming level and its ease of implementation. Consequently, we use it as a basis for the modified articulator and as a comparative model.

The replacement of the condylar bowls, the Bennett inserts and other devices of adjustment aims to get rid of both the metrology on the patient and the approximation due to the technology of the articulator. It aims to obtain a physiological articulator by adapting on the device a replica of the patient’s condylar guides processed through an additive manufacturing technique from medical imaging data. Therefore, a CT scan replaces the axiography and a rapid prototyped replica of the TMJ replaces the machined condylar guides and bowls.

The CT scan [10] aims to anatomically define the base of the skull and the mandible (head in hyperextension and maximal intercuspidation, that is to say in dental occlusion). The obtained slices are 0.6mm thick (247 slices on the average). As the lower jaw is connected to the base of the skull by the TMJ, density filters contribute to the elimination of the dental arches and the surrounding tissues of this joint. The same process leads to isolate the very TMJ, although it is more difficult because the ligament capsule and the cartilaginous articular disc have densities closed to the one of the bone. Moreover, numerous muscle attachments encompass it. The DICOM3 digital files are modified and converted to the STL format through a dedicated software package (Mimics ^®, Materialise, Belgium).

The fused deposition modelling (FDM) [11] is chosen to manufacture the anatomical part. This rapid prototyping technique is current, reliable, relatively cheap and able to process complex shaped parts. The machine (Dimension^® BST 768, Stratasys, USA) operates a fused deposition of ABS resin filament (acrylonitrile butadiene styrene, 256 µm diameter). The piloting software (Catalyst ^®, Stratasys, USA) ensures the 3D file slicing (STL version) in 0.256 mm thick sections.

In order to position the replica, the standard articulator is modified. The modification must enable to simply replace the TMJ elements of the machined articulator by the prototyped parts. There is no modification of the position, only the feasibility is studied. The condylar bowls are cut from the lower part, in order to position the physiological condyles at the same height than the condylar bowls. It aims to precisely substitute the prototyped condyles to the machined ones. The height is calculated so the centre of the condyle accurately corresponds to the centre of the replaced machined condylar bowl. The standard condylar guides are removed from the upper part. The part allowing the condylar guides coherence is cut.

The prototyped part is modified to adjust the articulator. The condyles are cut to ensure the exact substitution of the condylar bowls. Both condyles are first joined to keep the distance between them to ensure their placement in the mandibular fossae.

The base of the skull must be centred to the frontal and sagittal planes in order to join the upper part; it must match the AOP. This plane is chosen because it is easily identifiable both on the medical imaging, the prototyped base and the reference for the orientation of the upper part on several standard articulators. A parallelepiped hole centred to the anterior nasal spine is generated in the base of the skull. A virtual axis passing through the centre of the mandibular fossae defines the depth and its height that matches the AOP.

A 2 mm thick polymethyl methacrylate plate is positioned on the cut lower part. The joined condyles are glued on it, ensuring a perfect horizontal position, placed in the middle of the frontal and sagittal planes.

The upper part is then positioned thanks to a fast set plaster (Snow White^®, Kerr). It is placed in the centre of the frontal plane relative to the anterior nasal spine and the sagittal plane relative to the AOP. This latter is located on the prototyped base of the skull thanks to the anatomical elements visible on this latter: the hinge axis and the infraorbital foramen.

The horizontal part is positioned, oriented as on the previously defined plans.

The second generation semi-adjustable articulator is now a semi-physiological articulator.

On the Standard Articulator (SA), in the rest position, the condyle bowl lies against the posterior wall of the condylar guide. During the protrusion, the condylar bowl slides along the ceiling of the condyle guide, along a fully straight linear trajectory; only its angulation is adjustable (Fig. 2a).

On the Semi-Physiological Articulator (SPA), in the rest position, the condyle is located on the highest part of the mandibular fossa. During the protrusion, the condyle naturally follows the shape of the ceiling of the fossa. So the trajectory is curved (Fig. 4b). So there is no more choice of the condylar slope angulation to make.

It is clear that the protrusion trajectory on the SA is only a straight linear representation of the real physiological trajectory (Fig. 5).

Fig. (5). Representation of the condylar trajectory during protrusion on the standard articulator and on the semi-physiological articulator.

The movement of the non-working condyle (NWLM) is studied in the horizontal plane in order to decompose its trajectory. In rest position the condylar bowl is urged, backward, against the posterior wall of the condylar guide and, inside, against the insert. During the movement, the condylar bowl slides along the shape of the insert, the angle being imposed by this one. Thus, to simulate the NWLM relative to the Bennett angle, a straight insert is positioned (Fig. 2c). Finally, to simulate an immediate lateral movement, a curved insert is positioned.

On the SPA, the condylar trajectory is directly related to the anatomy of the internal wall of the mandibular fossa. So, the choice of inserts becomes unnecessary because the condyle naturally slides along this wall (Fig. 4c), from the back to the front and from the outside to the inside, respecting the anatomy of the mandibular fossa.

The working lateral movement is also studied in the horizontal plane. In rest position, the condylar bowl is in the same position as during the NWLM, that is to say backward on the posterior wall of the condylar guide and inside on the insert. During the lateral movement, the condyle makes a transverse displacement of a few millimetres.

On the SPA the condyle makes a slight twisting movement (Fig. 4d).

The study of the reproduction of the movements on the SPA highlights two important points. On the one hand the quality of the movements realised with the replica of the anatomical elements is logically in accordance with the physiology of the patient. The trajectories, which are directly linked to it, are improved and they look like the real ones. On the other hand, the axiography is no more needed because the prototyped anatomical elements positioned on the articulator do not require determinants to be positioned. Nor do they require programming. So the first source of error, axiography, and the second one, programming, disappear.

The reproducibility of the mandibular movements on the SPA is studied through the axiography. This study enables the representation of the trajectories on which it is possible to measure the angle of the protrusion, of the opening movement and of the NWLM relative to the AOP [12]. Two axiographies are carried out: on the patient and on the articulator (Figs. 3a-b).

The results are graphically collected in situ and they are then transferred on a graph paper to facilitate the measures (Fig. 3c). In order to calculate the angulation of the different trajectories relative to the AOP, their secants are drawn. The starting point of the three trajectories is the same and it corresponds to the centric relation point. However, the trajectories do not have the same length; it leads to define a point 10 mm from the starting point, which is used to draw the secants. The angulation of each secant is measured and the value reported in a Table 1 as for the axiographies on the SPA and on the patient, for the right and left sides.

The axiographic plots on the articulator show no aberration relative to the trajectories drawn from the patient. Indeed, when comparing the axiographies the first step consists in a global study of the shape and of the angle of each one. It allows us to check the plottings match before a comprehensive study. In this study the shapes and the orientations are similar. Only the opening movement is less important. This is explained by the fact that there is no elevator muscle on the articulator. By comparing the angulation plots relative to the AOP we can notice that those corresponding to the articulator are less important. This can be explained by the absence of articular discs on the SPA. Indeed, the condyle being highest in the mandibular fossa, in direct bone contact, the angle relative to the AOP is naturally lower. Moreover, the difference between these two types of axiography is generally homothetic, with a loss ranging from 3° to 7.5°, meaning no outlier. It is important to notice that this angulation difference is found both on the left and right recordings. The axiographies show that the reproducibility of the mandibular movements on the SPA is satisfactory. The homothetic decrease of the values ​​is understandable. In fact, this homothety allows validating our results. An aberrant difference between the two sides of the articulator would have been significant of a problem of registration, reproduction or designing of the SPA. The absence of the articular discs cannot be considered as a new gap, since the current standard articulators do not reproduce it either, especially when used without previous programming. The angulation difference will not influence the movements made by our dental casts positioned on the SPA. Thus our aim, which was to overcome the programming of the articulator, can be considered as achieved.