Trial data for precision analysis of a three-dimensional mandibular mechanical advantage

The data presented in this manuscript describe craniofacial landmark coordinate values, muscle and load moment arm lengths, and mechanical advantage rates for constructing a three-dimensional model of masticatory muscles. Cone-beam computed tomography scans from 30 subjects (aged 12–19 years, 16 females) were used. Thirty-six craniofacial landmarks were identified. Subsequently, the moment arms for 7 muscles and their corresponding load moment arms at incisor and molar positions were determined. Then, the three-dimensional mechanical advantage for each muscle and tooth position was calculated as the ratio of muscle moment arm to load moment arm. This procedure was repeated three times by a main examiner and once by two other examiners. The Friedman test and the square root of the 'method of moments' variance estimator were used to compare data among examiners and calculate random errors, respectively. Although the values for the craniofacial landmark coordinates and biomechanical variables are very close, differences were found between measurements, especially in the interexaminer comparisons. Values served as the basis for reliability (intraclass correlation coefficient) and errors (average mean of absolute differences) analysis in the research paper titled “A three-dimensional method to calculate mechanical advantage in mandibular function: Intra- and interexaminer reliability study,” published in the Journal of Orofacial Orthopedics.


Background
The locomotor apparatus can be simplified as a lever and rotation axes system.A lever is a basic mechanism that increases the force and speed of movements, and depends on a rigid bar that is rotated about a fulcrum.The bar is a long bone, and the fulcrum is a joint where the bones are supported and stabilized [1].In a lever, a force called effort is applied at one point on the bar in order to move an object, known as resistance, located at some other point on the bar [2].The forces transmission determines the intensity and direction of a moment of force or torque.Then, two moment arms are designed: the muscle moment arm and the load moment arm, which are defined as the perpendicular distances from the fulcrum to muscle force vector and load force vector, respectively [3].
The effectiveness of a lever can be assessed by computing its mechanical advantage (MA) as the ratio of the muscle moment arm to the load moment arm.Three lever classes can be designed to preserve the input power and trade off forces against movement to obtain a desired amplification in the output force.In a class I lever, the effort and the resistance are on opposite sides of the fulcrum.Although it may have any MA, in the human body it typically acts with a mechanical advantage = 1, working at balancing or modifying the motion direction without magnifying either the effort or resistance magnitudes [1].The function of the posterior neck muscles to stabilize the head on the atlanto-occipital joint and the anterior thigh muscles to the knee during extension on the patella are examples (Fig. 1a).
In a class II lever, the resistance is located between the effort (both on the same side) and the fulcrum.The distance from the fulcrum to the resistance is less than to the effort and, thus, the mechanical advantage is > 1, amplifying the torque created by the effort [1].There are relatively few examples, but the rising onto the toes is one of them (Fig. 1a).In a class III lever, the effort is between the resistance (also on the same side) and the fulcrum, acting with a mechanical advantage < 1.To overcome resistance, much greater effort requires working over a small distance.However, the resistance is moved over a much greater distance in the same amount of time (increased speed of motion).This arrangement is observed in nearly all extremities joints (Fig. 1a; [3]).
Although the neuromuscular control of mandibular movements is complex, clenching or isometric biting can also be understood as a class III lever [2].In theory, the fulcrum is represented by the temporomandibular joints Fig. 1 a Three classes of lever systems, according to where effort (gray arrow) and resistance (white arrow) are located with respect to the fulcrum (gray triangle).b Basic two-dimensional mandibular lever system (for masseter muscle), where the muscle moment arm (black line) is designed as a perpendicular line to the muscle force vector (black dashed line) from the fulcrum, and the load moment arm (gray line) is drawn as a perpendicular line to the bite force vector (gray dashed line) also from the fulcrum.The mechanical advantage is then defined as the ratio of the moment arm distances (D/D 0 ).The fulcrum (condyle) and bite position (molar tooth) are represented by black and white arrows, respectively Abb. 1 a Drei Klassen von Hebelsystemen, entsprechend der Lage von Kraft (grauer Pfeil) und Widerstand (weißer Pfeil) in Bezug auf den Angelpunkt (graues Dreieck).b Grundlegendes zweidimensionales Unterkiefer-Hebelsystem (für den M. masseter), bei dem der Muskelmomentarm (schwarze Linie) als senkrechte Linie zum Muskelkraftvektor (schwarze gestrichelte Linie) vom Angelpunkt aus konstruiert ist und der Lastmomentarm (graue Linie) als senkrechte Linie zum Beißkraftvektor (graue gestrichelte Linie) gezeichnet ist, ebenfalls vom Angelpunkt aus.Der mechanische Vorteil ist dann definiert als das Verhältnis der Momentarmabstände (D/D 0 ).Der Hebelpunkt (Kondylus) und die Bisslage (Molar) werden durch schwarze bzw.weiße Pfeile dargestellt (TMJ), where the mandible freely rotates around them as a rigid bar.The effort is produced by the masticatory muscles, and the resistance is provided by the load on the teeth [4].The muscle moment arm extends perpendicular from the TMJ to the muscle force vector, and the load moment arm, from the TMJ to the load or bite force vector (Fig. 1b; [5]).Therefore, its mechanical advantage being < 1 favors the efficiency of the masticatory muscles in generating strength in a certain bite position for chewing food [6].
Despite the availability of more advanced methods in research, such as finite elements [7], a two-dimensional (2D) mechanical advantage approach using lateral radiographs has been considered for clinical studies of craniofacial growth changes [2,[4][5][6] and orthodontic treatment [8].Unfortunately, this radiograph is limited due to multiple bone structures seen in a single view, bilateral overlapping by craniofacial asymmetry, distortion by different focal lengths, and use of a 2D analysis for three-dimensional (3D) structures [9].Moreover, recognition of the muscle attachments for drawing the muscle force vectors is difficult and arbitrarily defined.
Changes of 3D mechanical advantage after orthognathic surgery has also been calculated using a series of magnetic resonance images (MRI) [10,11].However, it may be complicated to mathematically determine the muscle force vectors from the centroids of muscle segmentations using ordinary clinical procedures.Currently, the use of conebeam computed tomography (CBCT) offers an integral visualization of craniofacial tissues [12].A 3D method could identify anatomical landmarks more precisely and reliably, and establish spatial reference planes and plausible regions of origin and insertion of the masticatory muscles.With the help of a bilateral analysis, a more appropriate cephalometric assessment of the mechanical advantage becomes possible.
The 3D landmarks from CBCT are currently used for the diagnosis of anteroposterior [13] and transversal [14] malocclusions and to study skeletal and dental changes after orthodontic [15] and orthognathic surgery [16] and to analyze airways [17].These reference points were conceptually derived or conveniently modified from classical cephalometric landmarks.Since previous analyses of mechanical advantage from lateral radiography also used these landmarks in  ELSA is a personal name, and it was chosen because it is easy to locate by using the condyle and the glenoid fossa as guides and the most of the cranial base growth occurs in a child's first 5 years with only minor changes after that age [24] K  The arrangement of the anterior temporal muscle in the temporal fossa was determined as the result of two vectors with angulation of 10°a nd 75°in the sagittal and axial planes, respectively [26] b The arrangement of the posterior temporal muscle in the temporal fossa was determined as the result of two vectors with angulation of 35°a nd 61°in the sagittal and axial planes, respectively [26] 2D space, we intended to improve the design of muscle and load moment arms by the using 3D landmarks.
For educational and research purposes, as well as for diagnosis and planning, it is fundamental to know how changes in position and size of the mandible and maxilla could alter the mechanical advantage.The muscle moment arms may change by the dislocation of muscular attachments, and the load moment arms through spatial movement of the occlusal plane and teeth positions [18].Thereby, orthopedic or orthodontic functional appliances and orthognathic surgical guides could be designed for redirecting facial growth and the maxillomandibular relationship, respectively, to a favorable mechanical advantage after treatment.The aim of this study was to determine the intraand interexaminer reliability of a 3D mechanical advantage method with the use of CBCT for seven mandibular muscles.We hypothesize that the evaluated elements from the proposed method (landmark coordinates recognition, muscle and bite force vector designs, muscle and load moment arm measurements, and mechanical advantage calculus) have satisfactory reliability and acceptable errors to be clinically applied.

Sample
Thirty CBCTs from healthy dentate individuals (age 12-19 years; 16 females, 14 males) from the University of Alberta Orthodontic Program were used.These images were taken for diagnostic purposes for routine orthodontic records and not for this research.Subjects with systemic diseases, syndromes and previous orthodontic treatment were excluded.This work was approved by the Health Research Ethics Board at the University of Alberta (#5563), and all subjects signed written informed consent to participate.A minimum sample size (n = 17) was calculated assuming three repetitions by different examiners and a minimum acceptable intraclass correlation coefficient (ICC) of 0.7 to expect an ICC of 0.9 (α = 0.05, β = 0.20).However, as previously recommended [19] for error analysis, 30 CBCTs were used.

Cone-beam computed tomography acquisition
A NewTom 3G Volumetric Scanner (Aperio Services, Verona, Italy) was used with a 12-inch field of view with 8-mm aluminum filtration at 110 kV and 6.19 mA and slice thickness of 0.5 mm.Subjects were placed in the dorsal decubitus position with the Frankfort plane perpendicular to the floor.Raw image data were obtained from 390-430 slices and converted to DICOM format using the NewTom software 2.04 (Aperio Services) with a voxel size of 0.25 mm.Using Avizo Fire software 8.1 (Mercury Computer Systems, Inc., Berlin, Germany), the DICOM images were rendered into a volumetric image using 512 × 512 matrices.For orientation purposes, the planes were defined as the xz being coronal (frontal), yz sagittal (median, longitudinal), and xy axial (transversal, horizontal) [9].The coordinate system and the origin (0, 0, 0) established by the software were used to identify craniofacial landmarks.Although the landmarks used were originally created in a 2D space for conventional cephalometry and rely on the overprojection from both sides of the skull, the use of these landmarks three-dimensionally has already been previously studied ( [9,[20][21][22][23]; Table 1, Supplementary material Figs.1-3; Figs. 2, 3 and 4; Supplementary material Video 1).
Bite force vectors were drawn perpendicular to the mandibular plane at the molar and incisal positions (Table 2, Fig. 4b, c).
Moment arms for each muscle were drawn as perpendicular lines to each muscle force vector (or their colinear projections, looking for perpendicularity) from Condylion (fulcrum; Figs. 3 and 4).Load moment arms were drawn as perpendicular lines to each bite force vector, also from Condylion (Fig. 4b-f).Moment arms for all muscles were measured (mm), and the mechanical advantage was calculated as the ratio of the muscle moment arm to the load moment arm for each set of landmarks collected (Supplementary material Video 1).

Study design and statistical analysis
This cross-sectional agreement study used five trials on the entire sample.The main examiner repeated all measurements three times (trials # 1, # 2, and # 3) each after a 24 h interval.Two other examiners carried out these measurements only once (trials # 4 and # 5, respectively).Intraexaminer reliability was evaluated by comparing results of the main examiner.Interexaminer reliability was verified by comparing trial # 1 (randomly selected) with trials # 4 and # 5.The main examiner had training on tomographic craniofacial anatomy, and he calibrated the other examiners.Examiners were blinded to identification and order of all assessments.
Reliability of measurements was determined using SPSS software (v.25, IBM, Armonk, NY, USA) considering an ICC two-factor mixed model with absolute agreement [29,30].ICC was considered excellent when ≥ 0.75, satisfactory between 0.40 and 0.74, and poor when < 0.40.
Errors were determined by the average mean of absolute differences P n i =1 .jt1i -t 2i j + jt 1i -t 3i j + jt 2i -t 3i j/ =3n, where t is each trial and n is the sample size [20].Random error was also estimated by the square root of the 'method of moments' variance estimator

Á
, where d is the mean of absolute differences, d is the average mean of the absolute difference, and n is the sample size [19].
To analyze how disagreements affected biomechanical metrics, the coefficient of variation was considered as the percentage ratio between the standard deviation and mean of measurements.Therefore, the relative dispersion of data was calculated from the three inter-and intraexaminer trials [31].

Reliability of landmark coordinates
Excellent intra-and interexaminer reliability were found for all landmark coordinates, with ICC values ranging from 0.998 to 0.999 (p < 0.0001).

Errors in landmark coordinates
Intraexaminer errors for the average mean of absolute differences and the method of moments variance estimator were less than 1.5 mm (Table 3).
However, interexaminer errors for the average mean of absolute differences were higher (Table 4).On the right side, the landmark for Orbitale presented with errors of 4.681 mm, 3.254 mm, and 1.791 mm in the x, y, and z coordinates, respectively.Porion showed an error of 2.152 mm in the x-axis.Errors of 1.732 mm and 1.649 mm for Gonion, 2.147 mm and 3.798 mm for Ramus, 1.631 mm and 1.802 mm for Pterygoid, 1.920 mm and 2.878 mm for Maa, and 1.749 mm and 2.056 mm for Map were found in the y and z coordinates, respectively.In the z axis corresponding to Pterygoid fovea, a 2.570 mm error was found (Table 4).
On the left side, Orbitale showed errors of 5.834 mm, 3.750 mm, and 2.083 mm in the x, y, and z coordinates, respectively.Ramus maintained errors of 1.643 mm, 2.465 mm, and 4.431 mm also in the three axes, respectively.Porion presented an error of 2.266 mm in the x-axis.
In the y and z coordinates, errors of 2.028 mm and 2.364 mm for Gonion, 1.512 mm and 2.093 mm for Pterygoid, 1.854 mm and 2.740 mm for Pterygoid fovea, 2.064 mm and 3.256 mm for Maa, and 1.891 mm and 2.478 mm for Map were seen.
For the method of moments variance estimator, results only indicated an interexaminer error of 1.55 mm (1.23-2.08,95% confidence interval) for the right Porion x-axis.

Coefficients of variation for the mechanical advantage measurements
Intra-and interexaminer data for the mechanical advantage for the five sets of landmarks is shown in Table 5.A high agreement was found for the intraexaminer comparisons, determining a coefficient of variation < 3% for almost all biomechanical variables, with the exception of the variables related to the deep posterior masseter and lateral pterygoid muscles, which both increased by 3-7%, respectively (Table 5).This same trend was observed for the interexaminer calculations, where the variables related to these muscles showed values from 8-10% and from 21-29%, respectively.However, the other variables showed a coefficient of variation < 4% (Table 5).

Reliability of the mechanical advantage measurements
All biomechanical variables presented excellent reliability, showing ICC values ranging from 0.919-0.999for the intraexaminer evaluation (p < 0.0001) (Table 6).Almost all of the results of the interexaminer comparisons can also be considered excellent, even if presenting with absolute lower values (0.750-1.000; p < 0.0001; Table 6).However, on the right side, the muscle moment arm and the 3D mechanical advantage for the lateral pterygoid muscle (molar position) revealed satisfactory (0.434) and poor (0.394) ICC values (p < 0.01), respectively.The 3D mechanical advantage at the incisal position of the medial and lateral pterygoid muscles also had satisfactory (0.720) and poor (0.397) ICCs (p < 0.01), respectively (Table 6).On the left side, the muscle moment arm, and the 3D mechanical advantage at molar and incisal positions of the lateral pterygoid muscle presented poor ICC values, with values of 0.313, 0.341, and 0.322 (p < 0.01), respectively (Table 6).

Errors in the mechanical advantage measurements
All intraexaminer errors for the average mean of absolute differences (Table 6) and the method of moments variance estimator were less than 1.0 mm.
On the right side, for the interexaminer average mean of absolute difference comparisons, muscle moment arms of the posterior deep masseter, medial and lateral pterygoid muscles showed errors of 1.556 mm, 1.756 mm, and 2.778 mm, respectively.On the left side, similar results were detected only for the medial (1.578 mm) and lateral (3.556 mm) pterygoid muscles.
No errors higher than 1.5 mm were detected for the method of moments variance estimator.
The intra-and interexaminer errors for the 3D mechanical advantage were generally less than 0.01 and 0.05, respectively.

Discussion
For the proposed 3D method to calculate the mechanical advantage for the masticatory system, the reliability and landmark coordinate errors, muscle and bite force vectors, muscle and load moment arms, and 3D mechanical advantage of seven masticatory muscles at two dental positions were calculated.Reliability related the magnitude of the measurement error for the observed measurements to the inherent variability in the 'error free', 'true', or underlying level of the quantity being measured [32].Furthermore, the average mean of the absolute differences identified the continuous differences among the chosen measurements (systematic and random errors), and the method of moments variance estimator delivered an approximation of the random error.While systematic errors represent reproducible inaccuracies that lead to a measured value that is consistently larger or smaller than the true value, random errors lead to unpredictably variable differences [19].Complementarily, the coefficient of variation quantifies an error variation relative to the mean and hence it can be used to compare the inconsistency of different magnitudes, and to establish the extent of differences expected in a certain trial due to measurement error [33].
Systematic and random errors were, however, partially controlled in the present study by calibration of the examiners and measuring instruments, and by averaging over a number of observations, respectively.If reliability was high, measurement errors were small in comparison to the true quantity being measured.Conversely, when the measurement errors tended to be large, reliability was low because differences between measurements are thought to be due purely to error rather than to a genuine difference in their true values [19,30,31,33].Reliability and errors for all variables in this study were determined with intraand interexaminer comparisons from three examiners.As reliability depends on both the magnitude of measurement errors and the true heterogeneity in the population in which measurements are made, a homogeneous sample composed of healthy young people without severe craniofacial alterations was selected.
Landmarks showed excellent intra-and interexaminer reliability.Intraexaminer data exhibited errors < 1.5 mm, which is clinically acceptable [9].Unsatisfactory interexaminer errors ranged from 1.51-5.83mm.The use of 3 coordinates would allow for a more specific location; however, 3D images create additional difficulties due to the curvature of surfaces and no distinguishing limits between structures.In the 2D method, landmarks on curves can be resolved by bisectors from tangent lines and limits, which are determined by differences in radiopacity.The results for the identification of the landmarks in 3D are in accordance with previous studies, in which Orbitale, Porion, Gonion, Ramus, Pterygoid, and Pterygoid fovea landmarks were harder to recognize, showing higher errors [9,21].Better calibration and more experienced examiners to modify the bright, contrast and bone density of rendered images may be necessary to obtain better results.
The circular shape of the orbit for recognition of the Orbitale could explain the obtained errors due to the successive changes in image inclination and different perspectives during manipulation.Porion identification could generate confusion regarding the depth and the external and internal limits of the external acoustic meatus, although the degree of bone density can be altered.The end of the mandibular base and the beginning of the posterior border of the ascending ramus are tenuous during determination of Gonion and may worsen with image manipulation.Also, the width of the posterior border may identify the landmark on a more lateral or medial position [20].The lack of clear limits on the concave surface between the ramus and body of the mandible may also have produced errors when localizing the Ramus.Moreover, the difficult definition of the lateral and medial pterygoid plates of the pterygoid process of K K the sphenoid (concave and asymmetric surfaces) hampered Pterygoid determination at the midpoint of the lateral pterygoid plate.The concave surface and the convex ridges of the neck of condyle that gives rise to the mandibular notch and the beginning of the coronoid process converge simultaneously and also prevent a concise identification of the Pterygoid fovea.Because Maa and Map are derived from the localization of Gonion and Ramus, the positioning of these landmarks consequently affected their reliability and errors.Biomechanical variables showed excellent and nearly excellent intraexaminer and interexaminer reliability, respectively, as well as a very low coefficients of variation.Although the muscle moment arm and the 3D mechanical advantage of the lateral pterygoid muscle had ICC values below 0.500, the intra-and interexaminer 3D mechanical advantage errors were ≤ 0.01 and ≤ 0.05, respectively.Likewise, the higher interexaminer variation for the lateral pterygoid muscle, even on the left side, may be considered acceptable for cephalometric clinical purposes.Reliability of the results for the muscle moment arms, and 3D mechanical advantages on the one hand depend on landmark localization, but the generally promising results can also be explained by a probable compensation resulting from the greater lengths of moment arms when compared to the magnitude of the error of landmark coordinates, which were smaller and imply greater precision.Thus, the obtained lower interexaminer ICC values for the left lateral pterygoid muscle could be explained by the resulting lower lengths of the muscle moment arms.The shorter length of this muscle possibly prevents the compensation described above.This is not the case with the longer muscle moment arms from the other variables, which presented lower coefficients of variation than in studies using lateral radiographs [4,5,34] or magnetic resonance images [6,10,11,28].
The orientation and sense of the muscle force vectors can also affect the 3D mechanical advantage calculation [2][3][4][5][6]8].The whole muscles were represented in the present study by the average fiber vectors attached to the anatomical landmarks.It is necessary to interpret this method as a reasonable simplification because the muscular action lines do not completely correspond to a single muscular isometric work [26], especially in muscles with a complex internal organization [35].Likewise, a class III lever cannot describe all mandibular movements, which are much more complex than a hinge pattern.However, it would almost be impossible to analyze all biomechanical variables and mandibular positions before and after treatment that could eventually alter the patients' mandibular mechanical advantage.Deeper analysis, perhaps not as part of daily clinical practice, could be performed in biomechanical research.On the other hand, the present method is intended to be applied clinically, but with sufficient physiological plausibility and scientific rigor.
Changes in mechanical advantage according to different craniofacial characteristics can be described using a 2D method.It is known that an upward position of the maxilla (hypodivergent growth pattern) will tend to increase the mechanical advantage of the elevator muscles, while a downward position (hyperdivergent growth pattern) will have the opposite effect [2,13].Advancement of the maxilla will decrease the mechanical advantage of the elevator muscles by changing the relationship of the bite position to the condyles and increasing the load moment arms [2].A reduced mechanical advantage could also be observed in long face subjects (mandibular plane ≥ 40°), who sometimes require bimaxillary surgery to induce counterclockwise rotation of the mandible [4][5][6].However, results from magnetic resonance images indicated that directional changes of the muscle moment arms and a decrease of the 3D mechanical advantage of the masseter and medial pterygoid muscle occurred after surgical advancement and posterior intrusion of mandible with anterior rotation of the proximal segment [10,11,28].
The intention of the present study was to verify the methodological feasibility of the recommended method [36], but not to determine epidemiological data of a certain population.Thus, variables were barely compared one to another.The fact that one examiner trained all the other examiners might be thought about to have induced possible bias.Perhaps the second and third examiners could have adopted the "style" of main examiner.However, the intention of this study was to evaluate the differences of reproducibility and errors (by biases) among an expert and other professionals, showing the versality of the method for different applications.A bias would have been manifest if this study had the objective to compare the means of mechanical advantage measurements between groups with contrasting features.In this case, a measurement bias can exist.The examiners were professors belonging to the same educational institution, inevitably having the same philosophy in several procedures.
The next step for this method will be to determine its validity, comparing the average mean of absolute differences of 3D values with conventional cephalometric data.Also, sensitivity and specificity of the method in patients with malocclusions and facial deformities will have to be evaluated to determine its application profile.The equivalence of the mechanical advantage with bite force could also be calculated, establishing the influence of moment arms on function [34,37].
The present method is a new proposal and it was only described previously for radiographs or MRIs.Only one study using CBCT assumed that certain types of malocclusion may have different masseter lengths and orientations and that these differences may have implications for the mechanical advantage of bite force [13].The method may be of interest to biologists and functional morphologists, since it can potentially describe biomechanical changes during craniofacial growth and development [38].However, it should also be interesting for clinicians who seek to intervene in dysfunctional situations [18].Orthodontists, orthopedists, and surgeons may considerer analyzing the changes in the 3D mechanical advantage as a complementary study for diagnosis and treatment planning of facial disharmonies [2,3], as well as to identify possible normalization of the mandibular mechanical advantage after improvement of the skeletal relationship [4-6, 8, 10, 11].

Conclusions
Measurement of the mechanical advantage applying the proposed cone-beam computed tomography images-based method showed an overall high intra-and interexaminer reliability and acceptable errors.
Most anterior point of the frontonasal suture in the median plane Anterior reference for the sagittal plane Gnathion a Most anteroinferior point on the symphysis of the chin, constructed by intersecting a line drawn perpendicular to the line connecting menton and pogonion Anterior reference for the sagittal and mandibular planes Incisal a Junction of the borders of lower central incisors Reference for loading Foramen spinosum Geometric center of the smallest circumference with the clearest defined borders viewed in axial view on the foramen spinosum Reference for ELSA identification Orbitale Lowest point in the inferior margin of the orbit Anterior reference for the Frankfort plane Porion Superior point of the external auditory meatus Posterior reference for the Frankfort plane Condylion Most superior point on the condylar head Reference for arbitrary fulcrum Gonion Constructed point of intersection of the ramus plane and the mandibular plane Reference for mandibular insertion of the superficial masseter and the medial pterygoid muscles, and for posterior reference of the mandibular plane Coronoid Apex of the coronoid process Reference for mandibular insertion of the anterior deep masseter and the anterior temporal muscles Ramus Point of intersection between the anterior border of the mandibular ramus and the mandible body Reference for mandibular insertion of the deep masseter muscles Maxillozygomatic Lower point of the maxillozygomatic suture Anterior reference for zygomatic insertion of the superficial masseter muscle Temporozygomatic Lower point of the temporozygomatic suture Posterior reference for zygomatic insertion of the superficial masseter muscle Pterygoid fovea Most concave point of the neck of the condyle Reference for mandibular insertion of the lateral pterygoid muscle Pterygoid Midpoint of the lateral lamina of pterygoid process Reference for pterygoid insertion of the medial and lateral pterygoid muscles Zyd Lowest point of articular tubercle Reference for zygomatic insertion of the deep posterior masseter muscle Molar Central fossa of the lower first molar Reference for loading Secondary landmarks ELSA a Midpoint on the line connecting both Foramen spinosum landmarks b Posterior reference for the sagittal plane Maa Point that divides the anterior and middle thirds of the line connecting Ramus and Gonion Reference for mandibular insertion of the anterior deep masseter muscle Map Point dividing the middle and posterior thirds of the line connecting Ramus and Gonion Reference for mandibular insertion of the posterior deep masseter muscle Zys Point that divides the posterior and middle thirds of the line joining Maxillozygomatic and Temporozygomatic Reference for zygomatic insertion of the superficial masseter muscle Reference planes Frankfort plane a Line joining the right Porion and left Porion with the right Orbitale or left Orbitale Reference plane, perpendicular to accessory planes on coronal direction Mandibular plane a Line joining the right Gonion and left Gonion with Gnathion Reference plane for the bite force vectors Sagittal plane a Line joining ELSA, Nasion, and Gnathion Reference plane, parallel to accessory planes on sagittal direction Accessories Planes oriented on coronal (xz) and sagittal (yz) directions and constructed from Coronoid References for the anterior and posterior temporal muscles Landmark bilaterally located, except those designated with a b

Table 1
Reference planes and landmarks

Table 2
Definition of muscular and bite force vectors Tab. 2 Definition der Vektoren für muskuläre Kraft und Beißkraft

Table 5
Mean and standard deviation (SD), and intra-and interexaminer ratios between the mean and variability corresponding to biomechanical variables

Table 6
Intra-and interexaminer reliability and errors to biomechanical variables