Technical difficulties

During our previous preliminary investigations, we identified two main technical obstacles in our IOS-based protocol: (1) bite alignment inaccuracy of the scanner, and (2) the positioning and post-processing protocol of the IOS, which resulted in misaligned exported STL files. These misalignments rendered the data unsuitable for axis registration, as our method requires identical meshes perfectly aligned through the upper arches. In contrast, the scanner produced inconsistently displaced meshes with altered surfaces, due to the unavoidable post-processing steps required during scanning. For this control study, we used a different IOS with improved performance and more suitable settings: the Medit i600 (Medit, Seoul, South Korea). This scanner allows scanning up to five different bite positions within a single case. Consequently, after post-processing, all five STL sets were perfectly aligned and identical. Moreover, bite alignment accuracy was superior compared to the previous scanner. (This improvement – likely due to the time elapsed since the last trial and the rapid evolution of IOS technology – was the minimal development we had predicted in our earlier publication and the prerequisite we awaited to continue our clinical trials [1].)

Our initial impression of the selected tool was positive, as the built-in multi-bite scan feature seemed suitable for case acquisition. However, the scanner has a limitation in the number of bites that can be scanned, and it became evident that post-processing could not be skipped even if upper and lower scans were cloned before bite registrations. Consequently, the exported STLs were no longer identical and were positioned differently. These properties make the selected IOS suitable only for single-case registration. Large-scale studies involving multiple bite positions and continuous scans exceed its capabilities. Therefore, we had to perform a modified version of the CLVs method we previously described [1]. This is a manual 3D modeling process used to realign mesh sets based on the upper arches and to substitute the differently processed STLs with identical ones. The modifications were necessary because the CLVs were less stable in their 3D positions with the Medit, resulting in inaccurate realignments. To aid this process, we used the ‘Align to Target’ tool in Meshmixer (Autodesk, San Francisco, CA, USA) for an initial alignment step. Since all meshes were derived from the same raw dataset, this method worked reliably. Nevertheless, the scientific team – accustomed to high-precision 3D modelling – regarded this step as a frustrating necessity, as it introduces a theoretical risk of error. Close supervision of the automated process is essential; the ‘Deviation’ tool in Meshmixer was found to be appropriate for this purpose.

A modeling step was also required to derive the coordinates of the Modjaw axes. Cylinder objects representing the calculated axes can be exported from the software, with the center point at each end of the cylinder defining the linear axis. To extract these coordinates, the vertices of the circle at one end were selected, and a free vertex was moved to the ‘center of the selection’ using shortcuts in Blender v2.79 (Shift+S: ‘cursor to selected’; then, after selecting the free vertex, ‘selection to cursor’). The same procedure was repeated at the other end of the cylinder. (The coordinates can be found under “N” menu.) This represents one possible approach, although several alternative methods could be applied to achieve the same result.

Reproducibility warning: Meshmixer alters the vertex order of meshes. Therefore, if vertex-level labelling is needed for subsequent registration, unmanipulated meshes must also be imported and exported accordingly. While the IOS proved technically capable for registration, its limitations remain a significant barrier. Even for a limited number of participants, the required manual 3D work was immense. This makes large-scale studies involving multiple clinical protocols practically impossible. Ironically, the IOS appears technically suitable for clinical use, but is hindered only by the lack of clinical evidence. These findings suggest that further in-house development has reached a technological glass ceiling without corporate collaboration. Another unfortunate consequence is that these stringent technical requirements significantly restrict the testing of multiple scanners from different manufacturers. However, if any interested author finds an IOS that meets these criteria, all necessary materials for reproducing our investigation are available in the Data Repository of the current and previous papers [1,3].

Methodological Dilemmas: 1) Defining axes using pairs of coordinates (x, y, z) poses a significant challenge. At which point along the defined line should the axis be evaluated or validated? In our protocol, we typically defined the start and end points of the axis as being 200 mm apart, measured 100−100 mm from the point on the axis closest to the center of gravity of the given mesh. However, when manipulating multiple meshes, different coordinate sets can occasionally be generated for the same axis. This is an unfortunate but unavoidable consequence of the experimental setup. While this variation typically introduces only minor discrepancies that do not affect the overall conclusions, it remains a technical limitation.

2) The second dilemma arises when evaluating mesh-to-mesh distances. We typically used the root mean square (rms) error of all corresponding vertex pairs. This method proved appropriate for calculating derived parameters such as the EcD_ratio or AEcFE. However, it only loosely reflects clinical scenarios, since dental arches do not penetrate one another – in reality, the first point of contact halts or redirects further movement. To address this limitation, we performed double measurements: in addition to the rms_error, we also calculated the maximum distance between all vertex pairs. This secondary metric may prove to be a more clinically relevant indicator in future analyses.

Future note

The presented manual modeling workflow used to overcome alignment- and mesh surface-related issues could, in principle, be automated using optimizer approaches similar to our two-stage axis registration method [1]. The positional changes introduced by multiple translation, rotation, and mesh substitution steps can be adjusted to the specific output characteristics of the scanner’s built-in software and the given experimental setup. However, such automation would require continuous fine-tuning and maintenance.

In routine clinical use with the Medit system, the manual workflow is not required, as the limited number of bite registrations needed per case is already supported by the software. The constraints become relevant primarily in multi-case validation research, where the number of required registrations exceeds the software limits. A major obstacle is that each scanner brand – and in some cases even different models – would require a distinct automation algorithm, which would likely remain functional only until a subsequent software update, where even minor changes in output properties could unintentionally compromise the entire process. Scanner-specific output handling and frequent software updates therefore introduce variability that is difficult to manage without direct corporate assistance.

Notably, this issue could be resolved by the Manufacturers with only minor modifications to the software output, such as aligning exported STL files by the upper arch (defined by mass center and local orientation) and optionally applying post-processing prior to the bite scan, which would effectively replace the need for the current manual workflow.

Registrations

For the IOS-based method, we applied our previously published optimizer-based Iterative Closest Point (ICP) algorithm, utilizing a simplified Euclidean distance metric and the Levenberg-Marquardt optimizer (Shown in Fig 3. of our previous study [1] available at https://doi.org/10.1371/journal.pone.0285162.g003). The open meshes were rotated, while the corresponding closed ‘fixed’ meshes served as the targets of the transformation. The resulting registered axes were named according to the two meshes involved (e.g., CA1:OA1).

The EcD_ratio was calculated by assigning a single theoretical ‘fix’ mesh as the target of two other (e.g., the same closed case CA1 – fix – served as the target for both OA2 and OB3 opened scans, the positional difference between the resulting axes – d_axis of CA1:OA2 and CA1:OB3 axes – was caused by the misalignment of the two opened meshes OA2 and OB3 – quantified as rms_error or max_error; for the purpose of EcD value calculation, open scans were also temporarily designated as theoretical fixed meshes.).

All registered axes were tested through rotational simulations (compared with each other or with the control axes – Modjaw in Setup-2), mimicking their use as primary inputs in a digital articulator. For each participant in Setup-1 Modjaw and Setup-2 the previously ‘selected’ mesh was placed in our virtual articulator and subjected to rotations of 1°, 2°, and 3° (approximately equivalent to 1.3 mm, 2.6 mm, and 3.8 mm of mouth opening) in both positive and negative directions. In Setup-1 Szeged all closed meshes were used. These rotations simulated mandibular autorotation following various clinical interventions, such as surgical maxillary impaction, molar intrusion, or bite elevation etc.

The base unit of the experimental setup was presented in Fig 3. of our previous study [3] available at https://doi.org/10.1371/journal.pone.0329021.g003; with the only difference in the names of the axes of the setup: the registered Szeged- and Modjaw-axes acted as ‘central’ and ‘modified’ axes with different combinations determined by the given Setup).

Intra-group comparisons were conducted to evaluate the reproducibility of our registration method and its clinical reliability, with a focus on the 0.1 mm error threshold. The same reproducibility assessments were also performed on the Modjaw-derived axes. These were labeled as Setup-1 Modjaw and Setup-1 Szeged.

In addition, we compared the performance of the axes derived by the Szeged-method with those produced by Modjaw, designated as Setup-2.

A further experiment (Setup-3) was conducted in which the ‘selected’ closed meshes were rotated using the Modjaw-derived axes until optimal overlap with the open meshes from the IOS-based acquisition was achieved, defined by the lowest Euclidean distance metric. This procedure was repeated for each open scan.

For all setups, the following metrics were recorded: d_axis, rms_error, maximum_error, angular deviation between compared axes, and derived parameters such as the AEcFE ratio.

IOS bite alignment accuracy, EcD_ratio and d_axis values

All bite positions were scanned three times in quick succession, without any opening movement. Pairwise distance measurements were performed between the three meshes of each bite position (e.g., CA1–CA2, CA2–CA3, and CA1–CA3) using Meshmixer’s Deviation tool to evaluate the maximum distance within each mesh group. The average maximum distance across all four participants was 0.036 ± 0.030 mm in the closed-bite groups, with only one case (Case III: CA2–CA3) exceeding the 0.1 mm clinical limit (S1 Table). The open-bite group showed lower accuracy, with a 0.145 ± 0.066 mm mean maximum deviation, and approximately 75% of cases exceeding the clinical limit. Since IOS performance is likely not optimized for scanning in an open-bite position, the reduced accuracy may be due to untested clinical scenarios from the perspective of the alignment algorithm, or the less stable mandibular position compared to ICP.

For pairwise distance measurements carried out by the automated algorithm (not via Meshmixer) for all closed (CA & CB groups combined) and open cases (OA & OB groups combined), see S2 Table – “rms & max_error values” Sheet Tab. These results show that introducing an opening between the two sets of bite scans, as well as remanufacturing the bite block, slightly increased the measured values. Caution is advised when comparing datasets, as the Meshmixer and automated algorithm measurements are not identical.

The EcD_ratio values indicate how tolerant the Szeged-method registration was to positional error. Here, error is defined as “error from the perspective of pure rotation” with any physiological translational components or technological positioning inaccuracies affecting the final calculated axis of rotation. If such components are present during registration, the resulting axis should technically be defined as the instantaneous center of rotation (ICR), since the motion was not purely rotational but simplified as such (see [1,3] for a detailed discussion). The EcD_ratio can be interpreted as the number of millimeters by which a registered axis would shift in response to 1 mm of registration error (either rms or maximum values can be used for calculation). S2 Table – “EcD_ratio_Szeged_Method” Sheet Tab – lists all EcD_ratio values. The observed ratio 36.69 ± 22.83 (: 1) closely matches our previous clinical registration results (41.83 ± 14.89). Comparisons between cases with the same clinical bite position showed greater error tolerance than “mixed bite” comparisons. (‘same bite’ vs ‘mix bite’ in S2 Table).

Preliminary evaluation of the registered axes revealed no major errors in the IOS-based registrations that would indicate clinical or technological acquisition problems (in our previous study, cases with significant registration errors were excluded). However, two Modjaw registrations produced exceptionally high d_axis values (highlighted in red and crossed in S2 Table – “d_axis Modjaw” Sheet Tab). After excluding these two cases, the average d_axis value was 1.71 ± 0.59 mm (Case I: 1.62 ± 0.61 mm; Case II: 1.72 ± 0.66 mm; Case III: 2.03 ± 0.66 mm; Case IV: 1.56 ± 0.47 mm), compared to 2.78 ± 1.81 mm for Participant I and 4.32 ± 3.02 mm for Participant III without exclusion. These two axes were excluded, as they were considered the result of inadequate registration. For completeness and transparency, all further calculations were also performed with and without these exclusions wherever possible, as shown in the corresponding Supplementary Tables; however, our main conclusions in this paper focus on the datasets with exclusions applied.

Results of Setup-1 Szeged and Setup-1 Modjaw

Many authors of the last century set the clinical goal of articulation such that the registered axis should be within 3–5 mm (in some cases up to 6 mm) of the ‘true axis’ – usually determined by axiography – resulting in less than 0.1 mm clinical error at the level of the occlusal surfaces [4,11,12] – or at least claimed/ expected to be less (later discussed). Conventional analogue, facebow-based articulation methods meet these criteria in 20–98% of cases (Walker: 20%; Piehslinger: 23%; Lauritzen and Bodner: 33%; Teteruck and Lundeen: 56.4%; Beyron: 87%; Schallhorn: 98%) according to these authors [4,13–17]. The IOS-based method’s reproducibility meets ‘similar’ (The digital variant of these investigations, which could be interpreted as applying the ‘same’ rather than merely ‘similar’ criteria, can be found under Setup-2 – practically the digital version of the analogue facebow- and axiography- based setups.) criteria in approximately 65.1% of cases, if maximum error – rather than the rms_error value – is considered clinically relevant (Table 1). However, the mesh surface sites producing the maximum error may be located at the extremities of the scan, e.g., on the gingival parts. This makes the criterion somewhat too strict, whereas rms_error would be too lenient.

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Table 1. The registered parameters of Setup-1 Szeged.

https://doi.org/10.1371/journal.pone.0342893.t001

Reproducibility issues increased with greater amounts of opening. While 1° of opening produced maximum error values below 0.1 mm in 97% of cases, this proportion decreased gradually with greater rotation, ~ 62% in the 2° group and ~34–37% in the 3° group (Table 2). This can be explained by the different AEcFE values of these groups: the 1° group tolerated positional differences of the axes well (~120 mm distance between axes would produce 1 mm maximum error at the scan level), whereas this ratio decreased to ~60:1 and then to ~40:1 with increased rotation angles. The participants produced similar mean AEcFE values (Table 3), indicating that the level of error tolerance was relatively constant.

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Table 2. The different mean error and AEcFE values of all four participants divided by the amounts of rotation.

https://doi.org/10.1371/journal.pone.0342893.t002

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Table 3. The different AEcFE values of the four participants.

https://doi.org/10.1371/journal.pone.0342893.t003

The Modjaw’s reproducibility was, as expected, far superior. The majority of cases met the 0.1 mm maximum error criterion in our virtual articulator model, and the axes were distributed within a ~ 2 mm radius (Table 4). We therefore accepted our Modjaw protocol as a sufficient clinical control tool for rotation axis registration. It is important to note that a perfect registration tool is unlikely to exist, as minimal translational components or other ‘errors’ will probably compromise the stability of axis position acquired by pathographic methods, as noted by Mehl [2]. All other relevant information on Setup-1 Modjaw is available in Table 4 and S4 Table.

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Table 4. The registered parameters of Setup-1 Modjaw.

https://doi.org/10.1371/journal.pone.0342893.t004

Visual inspection of the axes of each participant (IOS based and Modjaw) reveals many details on the core logic of the system acting behind the surface. For 3D display.obj files are available in the data repository (.obj files are oriented “Forward: -Z & Up: Y” manner, some software import settings may alter this. For example, Blender should be set to ‘Y Forward’ and ‘Z Up’ import option). The coordinates of the registered ICRs can also be found in the respective supporting tables. S2–S5 Video briefly presents each case: black axes are from IOS-based registrations, while coloured axes were acquired by Modjaw. (the position of the excluded Modjaw axes – Case I: Modjaw-3 and Case II: Modjaw-2 – support our decision as they are clearly located further from the main distribution site of the Modjaw axes). The most important visual finding is that the Szeged-axes appear aligned with the previously described “parallel error direction”, see Fig 4 (The different directions are shown in Fig 2. of our previous study [3] available at https://doi.org/10.1371/journal.pone.0329021.g002). This was not the result of investigator intervention; the same optimizer algorithm was used as before, without fine-tuning. The only changes to the IOS-based registration experimental setup were: the improved bite alignment accuracy and a modified closed bite registration protocol. Seeing the axes distributed along a line was initially a surprising ‘pinch me’ moment for the authors – but it is entirely logical: the parallel error direction was proven to be the least error-sensitive of all directions (producing the highest AEcFE values in digital in-vitro settings [3]). It is therefore a ‘natural’ phenomenon that an optimizer algorithm minimizing error would find axes along the direction of least sensitivity. This serves as a clear example of fundamental research findings recurring in clinical settings.

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Fig 4. Orientation of the parallel error direction relative to the skull and the registered digital data.

https://doi.org/10.1371/journal.pone.0342893.g004

Results of Setup-2 – Modjaw control of the Szeged-method

If we accept the superior reproducibility of Modjaw registration as sufficient validation for use as a standard, we can compare IOS-based axes against them to assess the clinical applicability of the novel method. At this stage, the goal is not to prove clinical applicability – case numbers are too low – but to establish a viable workflow for control investigations if manufacturers were to implement the necessary IOS setting modifications. Unfortunately, comparison of the two methods was less promising (Table 5 and S5 Table). The registered maximum error was approximately 2.5 times higher than the 0.1 mm clinical goal, with only ~10% of cases within the limit. This indicates a protocol issue that needs to be addressed. However, the results remain within potential reach of the clinical target. With further improvements, achieving the goal seems feasible, though this would require testing multiple clinical protocols with large case numbers – practically impossible with the available IOS settings. Moreover, enhanced bite alignment performance of the IOS in the open mandibular position could significantly influence the overall results. Just two years ago, such results were unattainable due to technological limitations. Recent advances in closed-bite alignment have shifted the protocol from a theoretical concept to one that is nearly applicable. If similar improvements could be achieved for the remaining half of the protocol, comparable progress might be possible; however, with our current knowledge, it is impossible to assess this prospect.

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Table 5. The registered parameters of Setup-2.

https://doi.org/10.1371/journal.pone.0342893.t005

Results of Setup-3 – Reversed control setup

Setup-3 was a highly theoretical investigation: As pre-defined centres of rotation are not available in a clinical setting, the exact location of each participant’s rotation axis is unknown; indeed, such an axis may not exist in real biological circumstances. From a clinical perspective this is irrelevant – what matters is a modelling method that can mimic a patient’s lower jaw motion acceptably. Since we cannot determine the absolute truth of our registrations, we cannot exclude the theoretical possibility that our control tool (Modjaw) has a technical flaw that consistently produces similar but biologically inaccurate outputs. Based on more than a century of analogue axiography experience, we reject this as a general concern, but adopting a contrarian, critical perspective may still yield insights. This was the case in Setup-3, which compelled the ‘clinical’ side of our team to reassess their firm opposition to what they initially saw as an ‘unrealistic’ and ‘unnecessary’ control setup “that only makes us look unprofessional”, as the results proved otherwise. The ‘selected’ mesh of each participant was used for Modjaw registrations, and we performed rotations of these ‘selected’ closed meshes around the registered Modjaw axes. The target meshes were those obtained during open IOS-based registrations. These rotations produced highly consistent maximum error values of about 0.5 mm on average (S6 Table, All: 0.508 ± 0.132; Case I: 0.555 ± 0.071; Case II: 0.584 ± 0.175; Case III: 0.367 ± 0.044; Case IV: 0.507 ± 0.062) – five times the clinical goal. Such results, by themselves, have limited value. However, the standard deviation values were far more revealing: they were highly stable – often around or even below the 0.1 mm threshold – contrasting with the positional error. Visual inspection of these meshes (the STLs are available through the data repository, S6–S9 Video present an example of each participants: in each video bright scan shows the Modjaw rotated case, dark the original IOS based open scan) clearly showed that the Modjaw axes rotated the scans into a more forward position (except Case II, which showed more of a lateral shift) than the position defined by our bite block protocol. This positional difference was practically the same in 100% of cases for each participant. It led to an important conclusion regarding our protocol: the bite block registration step in our clinical workflow caused the systematic misalignment of the IOS-based registration (the acquired mesh positions and the related values) in Setup-2’s control investigation. While this protocol-induced deviation seems straightforward here, the methodological situation may be more complex, raising well-known clinical dilemmas that require further discussion and resolution.

To facilitate interpretation of the extensive dataset presented above, a comprehensive summary table is provided below (Table 6). This table consolidates some of the key findings into an accessible form, supporting a clearer overview of the study’s comparative results.

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Table 6. Overview table of Results. Simplified overview table of the results highlighting and summarizing some of the key findings.

https://doi.org/10.1371/journal.pone.0342893.t006