Inﬂuence of the Printing Orientation on Parallelism, Distance, and Wall Thickness of Adjacent Cylinders of 3D-Printed Surgical Guides

: This in-vitro study aimed to evaluate the inﬂuence of the printing orientation on parallelism, distance, and thickness between adjacent cylinders of 3D-printed surgical guides. CAD software was used to design a surgical guide with two adjacent parallel cylinders (reference); the design was saved as standard tessellation software (STL) and 63 samples were printed using three different orientations (0, 45, and 90 degrees). A metrology digital microscope was used to measure the distance, the angle and the thickness of the guides cylinders. Afterwards, the printed guides were scanned and cloud comparison software was used to compare STL ﬁles from the printed guides against the reference CAD model. One-way analysis of variance and Tukey test were used for multiple comparisons between groups and signiﬁcance was p < 0.05. The printing orientation affected the distance between cylinders, the parallelism and the wall thickness. In addition, there were global deviations in all printing orientations. Printing with 90 degrees orientation produced almost-parallel cylinders but walls thicker than the reference model; all the cylinders converged toward the coronal but printing at 0 degrees produced the closest distance to the reference value. Within the limitations of this experimental in-vitro study it can be concluded that all the printing orientations inﬂuence the angle, the distance, and the thickness between adjacent cylinders of a surgical guide. Printing at 90 degrees produces the best global correspondence with the master model.


Introduction
Malposition of dental implants is one of the major causes for future prosthetic, and peri-implant hard and soft tissue problems [1]. Improper placement of dental implants can not only result in sub-optimal esthetic outcomes, but also can affect their cleanability, which can result in inflammation of the peri-implant tissues [2]. Several factors such as limited mouth opening, asymmetric bone contours, or clinician's lack of experience may cause deviations in implant positioning [3]. Methods to achieve a more precise implant placement were implemented, and surgical templates became the standard of care [4]. Initially, these templates were fabricated using vacuum forming methods or using acrylic resins based in polymethylmethacrylate (PMMA), and their use demonstrated reduced surgical and prosthetic complications [5].
Computer-aided design and manufacturing (CAD-CAM) surgical templates have been implemented because they provide more precise dental implant placement and minimize positional errors compared to previous surgical guides [6], thus leading to more predictable restorations [7]. Within CAM, methods for the fabrication, milling, and printing offer repeatability and precision [8]. Moreover, guided implant surgery compared to conventional methods of implant surgery have demonstrated fewer deviations, and in general a better positioning of the implants [9][10][11].

Materials and Methods
In this in-vitro study, three experimental groups based on the printing orientation were created: (a) 0 degrees, (b) 45 degrees, and (c) 90 degrees. The sample size was determined with the software Raosoft (Raosoft, Inc., Seattle, WA, USA) at the website http://www.raosoft.com/samplesize.html, accessed on 7 July 2022. The following data were inserted in the online formulary, a 5% margin of error, a 95% confidence level, and a standard deviation (SD) of 0.5. The sample size was determined as N = 63. Each experimental sub-group group was set for 21 samples.
Fusion 360 (version October 2022, Autodesk Inc., San Rafael, CA, USA) and AutoCAD 2022 (version 24.1, Autodesk Inc., San Rafael, CA, USA) software were used to design a model simulating a surgical guide with two cylinders for two adjacent implants with the following characteristics: rectangular base (3 mm thickness × 13 mm width × 30 mm length); two adjacent cylinders with an inner diameter of 8 mm, an outer diameter of 9.2 mm and a height of 10 mm. The distance between the walls of two adjacent cylinders was 4 mm. The distance between the center of the cylinder and the width of the rectangular Prosthesis 2023, 5 312 prism was 8.4 mm. The distance between the center of the cylinder and the length of the rectangular prism was 6.5 mm (Figure 1).
Prosthesis 2023, 5, FOR PEER REVIEW 3 length); two adjacent cylinders with an inner diameter of 8 mm, an outer diameter of 9.2 mm and a height of 10 mm. The distance between the walls of two adjacent cylinders was 4 mm. The distance between the center of the cylinder and the width of the rectangular prism was 8.4 mm. The distance between the center of the cylinder and the length of the rectangular prism was 6.5 mm (Figure 1).   The design was exported as a master STL file and transferred to the printing preparation software (Preform Software, version 3.0.1; Formlabs, Somerville, MA, USA); the design was replicated 21 times per each printing angle (0, 45, and 90 degrees) ( Figure 2). Prosthesis 2023, 5, FOR PEER REVIEW 3 length); two adjacent cylinders with an inner diameter of 8 mm, an outer diameter of 9.2 mm and a height of 10 mm. The distance between the walls of two adjacent cylinders was 4 mm. The distance between the center of the cylinder and the width of the rectangular prism was 8.4 mm. The distance between the center of the cylinder and the length of the rectangular prism was 6.5 mm (Figure 1).   Models were arranged so that all samples for a single printing orientation could be printed in one cycle. The support type used was mini rafts with internal supports at a density of 0.50 and a touch size of 0.40 mm. The models were printed using an SLA Form2 3D printer (Formlabs, Somerville, MA, USA) and photopolymerization resin (Dental SG Resin, RS-F2-SGAM-01; Formlabs, Somerville, MA, USA) at a layer thickness of 100µm.
Post-fabrication, the samples were washed following the manufacturers' instructions in 99% isopropyl alcohol for 20 min (Form Wash; Formlabs, Somerville, MA, USA). After washing, the samples were removed from the build platform and transferred to a curing unit (Form Cure; Formlabs, Somerville, MA, USA) and post-cured for 1 h at 50°C. Flush cutters were used to remove the support structures from each sample. All samples were subsequently placed and stored away from ambient light. If a sample was broken during post processing, then the sample was reprinted and cleaned. The primary endpoint of this experimental study was to evaluate the dimensional properties of the cylinders of simulated surgical guides printed with different orientations. The outcomes included measuring the angle and distance between cylinders (expressed in mm), the cylinders' wall thickness (mm), and the global positive and negative deviations (root mean squared error) of the whole printed samples. Two methods used to evaluate the accuracy of the samples were a direct measurement using a digital microscope (Keyence VHX-6000; Keyence, Itasca, MN, USA) and a global evaluation using dimensional inspection software (GeoMagic Design X; 3D Systems, Rock Hill, SC, USA) (version. 2020.0.4).

Direct Measurement
The digital microscope was used at a magnification of 20× to measure the following characteristics: the angle between cylinders (parallelism), the distance between the cylinders, and the thickness of the cylinder walls. The samples were oriented flat to the surface and with the top of the cylinders facing up. The angle between cylinders was measured by tracing lines parallel to the adjacent cylinder walls. The angle formed between both lines was automatically recorded by the microscope (Figure 3). density of 0.50 and a touch size of 0.40 mm. The models were printed using an SLA 3D printer (Formlabs, Somerville, MA, USA) and photopolymerization resin (Den Resin, RS-F2-SGAM-01; Formlabs, Somerville, MA, USA) at a layer thickness of 100 Post-fabrication, the samples were washed following the manufacturers' instru in 99% isopropyl alcohol for 20 min (Form Wash; Formlabs, Somerville, MA, USA) washing, the samples were removed from the build platform and transferred to a unit (Form Cure; Formlabs, Somerville, MA, USA) and post-cured for 1 h at 50 ℃ cutters were used to remove the support structures from each sample. All sample subsequently placed and stored away from ambient light. If a sample was broken d post processing, then the sample was reprinted and cleaned. The primary endpoint experimental study was to evaluate the dimensional properties of the cylind simulated surgical guides printed with different orientations. The outcomes inc measuring the angle and distance between cylinders (expressed in mm), the cyli wall thickness (mm), and the global positive and negative deviations (root mean sq error) of the whole printed samples. Two methods used to evaluate the accuracy samples were a direct measurement using a digital microscope (Keyence VHX Keyence, Itasca, MN, USA) and a global evaluation using dimensional inspection so (GeoMagic Design X; 3D Systems, Rock Hill, SC, USA) (version. 2020.0.4).

Direct Measurement
The digital microscope was used at a magnification of 20× to measure the foll characteristics: the angle between cylinders (parallelism), the distance betwe cylinders, and the thickness of the cylinder walls. The samples were oriented flat surface and with the top of the cylinders facing up. The angle between cylinde measured by tracing lines parallel to the adjacent cylinder walls. The angle f between both lines was automatically recorded by the microscope (Figure 3). The distance between cylinders was evaluated from a lateral view. Lines were at the adjacent walls of the cylinders and the distances at the coronal and at th between the walls of the cylinders were recorded. In addition, the distance betwe cylinder walls at the top (DC) was evaluated by tracing a line perpendicular to the c of the cylinders; the site where the line intersects the edge of each cylinder was m and the distance between the cylinder walls was measured ( Figure 4). The distance between cylinders was evaluated from a lateral view. Lines were traced at the adjacent walls of the cylinders and the distances at the coronal and at the base between the walls of the cylinders were recorded. In addition, the distance between the cylinder walls at the top (DC) was evaluated by tracing a line perpendicular to the centers of the cylinders; the site where the line intersects the edge of each cylinder was marked and the distance between the cylinder walls was measured ( Figure 4). The thickness of the cylinder walls was measured by tracing two lines that divided each cylinder in four segments. The wall thickness was measured at the four points where the lines intersect the cylinder walls. The measures were obtained in microns ( Figure 5).

Global Evaluations
For the evaluation of the global dimensions, the printed samples were covered with a thin, non-reflective layer of zirconium powder prior to scanning. Then each sample was placed in a holder supporting 3 mm of the rectangular base and inserted into a laboratory scanner (E3, 3Shape, Copenhagen, Denmark). The scanning was completed in detail mode; afterward, the scanned files were digitally trimmed using the 3Shape TRIOS Design Studio (E3, 3Shape, Copenhagen, Denmark) to remove the contours of the sample holder. Cloud comparisons between original master design and each scanned guide were completed by superimposing the master STL file to the scanned STL files.
The global evaluations were completed by using surface-matching (cloud comparison) software (GeoMagic Design X; 3D Systems, Rock Hill, SC, USA) (version 2020.0.4). The master STL file was imported and moved to reference data. The resegment, split, and merge tools were used to segment the reference model into 5 separate regions: the base, left hollow cylinder, right hollow cylinder, base inside left cylinder, and base inside right cylinder ( Figure 6). The thickness of the cylinder walls was measured by tracing two lines that divided each cylinder in four segments. The wall thickness was measured at the four points where the lines intersect the cylinder walls. The measures were obtained in microns ( Figure 5).

Global Evaluations
For the evaluation of the global dimensions, the printed samples were covered w a thin, non-reflective layer of zirconium powder prior to scanning. Then each sample w placed in a holder supporting 3 mm of the rectangular base and inserted into a laborato scanner (E3, 3Shape, Copenhagen, Denmark). The scanning was completed in de mode; afterward, the scanned files were digitally trimmed using the 3Shape TRIOS Des Studio (E3, 3Shape, Copenhagen, Denmark) to remove the contours of the sample hold Cloud comparisons between original master design and each scanned guide w completed by superimposing the master STL file to the scanned STL files.
The global evaluations were completed by using surface-matching (clo comparison) software (GeoMagic Design X; 3D Systems, Rock Hill, SC, USA) (vers 2020.0.4). The master STL file was imported and moved to reference data. The resegme split, and merge tools were used to segment the reference model into 5 separate regio the base, left hollow cylinder, right hollow cylinder, base inside left cylinder, and b inside right cylinder ( Figure 6).

Global Evaluations
For the evaluation of the global dimensions, the printed samples were covered with a thin, non-reflective layer of zirconium powder prior to scanning. Then each sample was placed in a holder supporting 3 mm of the rectangular base and inserted into a laboratory scanner (E3, 3Shape, Copenhagen, Denmark). The scanning was completed in detail mode; afterward, the scanned files were digitally trimmed using the 3Shape TRIOS Design Studio (E3, 3Shape, Copenhagen, Denmark) to remove the contours of the sample holder. Cloud comparisons between original master design and each scanned guide were completed by superimposing the master STL file to the scanned STL files.
The global evaluations were completed by using surface-matching (cloud comparison) software (GeoMagic Design X; 3D Systems, Rock Hill, SC, USA) (version 2020.0.4). The master STL file was imported and moved to reference data. The resegment, split, and merge tools were used to segment the reference model into 5 separate regions: the base, left hollow cylinder, right hollow cylinder, base inside left cylinder, and base inside right cylinder ( Figure 6). The STL files from the printed samples were imported one by one. Each sample wa first aligned using the transform alignment; then, the N points method was used to superimpose the two files. The reference and the superimposed STL files were indicated in two windows where 10 points were placed on each model for alignment. Five point were placed at the top of each cylinder and 5 points were placed using the crosshairs o the cursor at each corner and/or middle of the base. The 3D comparison was conducted using the shape method with a 100% sampling ratio, shortest projection direction, and maximum deviation of 1 mm. Reports generated for each superposition included the roo mean square error (RMSE), mean negative, and mean positive deviations.
Given that printing at different angles may affect angulation, parallelism (cylinder may diverge or converge in a coronal and apical direction) and thickness, positive and negative global deviations were considered. The positive average deviations indicate the mean of all the positive gap distances between superimposed clouds of points, and the negative average deviations indicate the mean of all the negative gap distances between superimposed clouds of points. The root means square error values were measured to determine the magnitude of all deviation values at the cylinders and at the base.
Statistical analyses were performed using the web application Minitab. The normality of the samples was evaluated with the Kolmogorov-Smirnoff test. One-way analysis of variance (ANOVA) was completed, and differences between groups were evaluated with Tukey post-test. T-test was used to determine differences between the global, positive, and negative deviations. The level of significance for all analyses was se to p < 0.05.

Results
Printing at different orientations affected the angulation between cylinders, distance between cylinders, and thickness of cylinders of 3D printed surgical guides as confirmed with direct digital measurements and cloud comparisons of the mesh structures. In the next subsections the results for each variable are described. Supportive figures, tables and graphics are included for each subsection (Figure 7). The STL files from the printed samples were imported one by one. Each sample was first aligned using the transform alignment; then, the N points method was used to superimpose the two files. The reference and the superimposed STL files were indicated in two windows where 10 points were placed on each model for alignment. Five points were placed at the top of each cylinder and 5 points were placed using the crosshairs of the cursor at each corner and/or middle of the base. The 3D comparison was conducted using the shape method with a 100% sampling ratio, shortest projection direction, and maximum deviation of 1 mm. Reports generated for each superposition included the root mean square error (RMSE), mean negative, and mean positive deviations.
Given that printing at different angles may affect angulation, parallelism (cylinders may diverge or converge in a coronal and apical direction) and thickness, positive and negative global deviations were considered. The positive average deviations indicate the mean of all the positive gap distances between superimposed clouds of points, and the negative average deviations indicate the mean of all the negative gap distances between superimposed clouds of points. The root means square error values were measured to determine the magnitude of all deviation values at the cylinders and at the base.
Statistical analyses were performed using the web application Minitab. The normality of the samples was evaluated with the Kolmogorov-Smirnoff test. One-way analysis of variance (ANOVA) was completed, and differences between groups were evaluated with Tukey post-test. T-test was used to determine differences between the global, positive, and negative deviations. The level of significance for all analyses was set to p < 0.05.

Results
Printing at different orientations affected the angulation between cylinders, distance between cylinders, and thickness of cylinders of 3D printed surgical guides as confirmed with direct digital measurements and cloud comparisons of the mesh structures. In the next subsections the results for each variable are described. Supportive figures, tables and graphics are included for each subsection (Figure 7).

Angle between Cylinders
None of the 3D printing orientations resulted in perfect parallelism between cylinders. The 90 degrees printing orientation group had the closest angle to 0 degrees (best for parallelism) (0.4143 ± 0.2435 degrees) p < 0.001 compared to the other printing orientation, 45 degrees (1.4571 ± 0.2378 degrees) p < 0.001 and 0 degrees (worst for parallelism) (2.7429 ± 0.1886 degrees) p < 0.001 ( Figure 8, Table 1). The statistical comparison showed significant differences between the three groups ( Table 2).

Angle between Cylinders
None of the 3D printing orientations resulted in perfect parallelism between cylinders. The 90 degrees printing orientation group had the closest angle to 0 degrees (best for parallelism) (0.4143 ± 0.2435 degrees) p < 0.001 compared to the other printing orientation, 45 degrees (1.4571 ± 0.2378 degrees) p < 0.001 and 0 degrees (worst for parallelism) (2.7429 ± 0.1886 degrees) p < 0.001 ( Figure 8, Table 1). The statistical comparison showed significant differences between the three groups ( Table 2).

Angle between Cylinders
None of the 3D printing orientations resulted in perfect parallelism between cylinders. The 90 degrees printing orientation group had the closest angle to 0 degrees (best for parallelism) (0.4143 ± 0.2435 degrees) p < 0.001 compared to the other printing orientation, 45 degrees (1.4571 ± 0.2378 degrees) p < 0.001 and 0 degrees (worst for parallelism) (2.7429 ± 0.1886 degrees) p < 0.001 ( Figure 8, Table 1). The statistical comparison showed significant differences between the three groups ( Table 2).

Distance between Cylinders (Lateral View Top)
None of the groups had the distance of 4 mm between cylinders established in the reference STL model. The top of the cylinders converged to the center and the distances were shorter. The 45-degree printing orientation was closest to the reference of 4 mm (3733.05 ± 40.82 µm) compared to the other printing orientations (Figure 9, Table 3). The smallest distance was observed at 90-degree printing orientation (3537.53 ± 38.25 µm). The statistical comparison demonstrated significant differences between the means between all the groups (Table 4).

Distance between Cylinders (Lateral View Top)
None of the groups had the distance of 4 mm between cylinders established in th reference STL model. The top of the cylinders converged to the center and the distanc were shorter. The 45-degree printing orientation was closest to the reference of 4 m (3733.05 ± 40.82 µm) compared to the other printing orientations (Figure 9, Table 3). Th smallest distance was observed at 90-degree printing orientation (3537.53 ± 38.25 µm). Th statistical comparison demonstrated significant differences between the means betwee all the groups (Table 4).

Distance between Cylinders (Lateral View Base)
None of the distances recorded at the base of the cylinder maintained the 4 mm distance of the STL reference model. The cylinders converged towards the center and the distances were shorter. The 90-degrees printing orientation group was closest to the reference of 4 mm (3873.2 ± 110.5 µm) compared to the other printing orientations ( Figure 10, Table 5). The smallest distance was observed at 0 degrees printing orientation (3548.363 ± 39.39 µm). Group comparisons showed that the distances between cylinders at the base were different among all groups (Table 6).

Distance between Cylinders (Lateral View Base)
None of the distances recorded at the base of the cylinder maintained the 4 m distance of the STL reference model. The cylinders converged towards the center and t distances were shorter. The 90-degrees printing orientation group was closest to t reference of 4 mm (3873.2 ± 110.5 µm) compared to the other printing orientations (Figu 10, Table 5). The smallest distance was observed at 0 degrees printing orientation (3548.3 ± 39.39 µm). Group comparisons showed that the distances between cylinders at the ba were different among all groups (Table 6).

Thickness of Cylinder Wall
Printing at 0 degrees provided the most values close to the 600 microns of the standard model. Printing at 45 degrees orientation produced a slight increment of the wall thickness ( Figure 11). The 90-degrees group experienced the most discrepancy in the thickness of the wall of the cylinders (Figure 11). Printing at 90 degrees orientation showed thicker walls exceeding the standard by 400-500 microns (Figure 11).

Thickness of Cylinder Wall
Printing at 0 degrees provided the most values close to the 600 microns of the standard model. Printing at 45 degrees orientation produced a slight increment of the wall thickness ( Figure 11). The 90-degrees group experienced the most discrepancy in the thickness of the wall of the cylinders (Figure 11). Printing at 90 degrees orientation showed thicker walls exceeding the standard by 400-500 microns ( Figure 11).

Root Mean Square Error of the Cylinders (RMSE)
The root mean square differs slightly between all groups. The 90-degrees group had the lowest RMS error values (0.6158 ± 0.0511 mm) compared to the other printing orientations ( Figure 12, Table 7).

Root Mean Square Error of the Cylinders (RMSE)
The root mean square differs slightly between all groups. The 90-degrees group had the lowest RMS error values (0.6158 ± 0.0511 mm) compared to the other printing orientations ( Figure 12, Table 7).

Thickness of Cylinder Wall
Printing at 0 degrees provided the most values close to the 600 microns of the standard model. Printing at 45 degrees orientation produced a slight increment of the wall thickness ( Figure 11). The 90-degrees group experienced the most discrepancy in the thickness of the wall of the cylinders (Figure 11). Printing at 90 degrees orientation showed thicker walls exceeding the standard by 400-500 microns ( Figure 11).

Root Mean Square Error of the Cylinders (RMSE)
The root mean square differs slightly between all groups. The 90-degrees group had the lowest RMS error values (0.6158 ± 0.0511 mm) compared to the other printing orientations ( Figure 12, Table 7).   The statistical comparison showed differences between the means between the 0degrees group and 90-degrees group (p = 0.015), as well as between the 45-degrees group and 90-degrees group (p = 0.022). (Table 8). No difference was observed for the RMS values among the 0-degrees group and 45-degrees group (p = 0.392).

Negative Mean Deviations
The negative mean deviations differ slightly between the three groups. The 90-degrees group had the lowest negative average deviations (−0.5747 ± 0.0665 mm) compared to the other printing orientations ( Figure 13, Table 9). The statistical comparison showed differences between the means between the 0degrees group and 90-degrees group (p = 0.015), as well as between the 45-degrees group and 90-degrees group (p = 0.022). (Table 8). No difference was observed for the RMS values among the 0-degrees group and 45-degrees group (p = 0.392). The negative mean deviations differ slightly between the three groups. The 90degrees group had the lowest negative average deviations (−0.5747 ± 0.0665 mm) compared to the other printing orientations ( Figure 13, Table 9).   The statistical comparison showed differences between the means between the 0degrees group and 90-degrees group (p = 0.006) and between the 45-degrees group and 90-degrees group (p = 0.035) ( Table 10). No difference was observed for the negative average deviations among the 0-degrees group and 45-degrees group (p = 0.947) ( Table 10).

Positive Mean Deviations
The positive mean deviations differed greatly between all groups. The 90-degrees group had the lowest positive average deviations (0.3795 ± 0.2176 mm) compared to the other printing orientations ( Figure 14, Table 11). The statistical comparison showed significant differences between the means between all the groups (Table 12).

Positive Mean Deviations
The positive mean deviations differed greatly between all groups. The 90-degr group had the lowest positive average deviations (0.3795 ± 0.2176 mm) compared to other printing orientations ( Figure 14, Table 11). The statistical comparison show significant differences between the means between all the groups (Table 12).

Global Deviations at the Base Level
The bases presented similar root mean square errors (RMSEs) without differences among the different printing orientations. The statistical comparisons did not show differences between groups (p > 0.05). (Figure 15, Tables 13-15). The bases presented similar root mean square errors (RMSEs) without differences among the different printing orientations. The statistical comparisons did not show differences between groups (p > 0.05). (Figure 15, Tables 13-15).

Discussion
The goal of the present study was to evaluate the influence of the printing angles on the parallelism, distance, and thickness of two adjacent cylinders on a simulated surgical guide. The results of this study showed that the printing angles significantly affected all these parameters.
The printing orientation and the orientation of the objects in the printing platform can influence the number of objects that can fit in the build platform, the number of supports, the accuracy, and the waste of material [32,34]. Specifically in implant surgical guides, the printing orientation affects the accuracy and level of distortion [32]. However, the isolated effects of the printing angle on the cylinders that guide the drilling and implant placement procedures has not been evaluated.
The results of the present study showed that the best parallelism between cylinders was achieved by printing at 90 degrees (0.4143 ± 0.2435 degrees). Meanwhile, printing at 45 and 0 degrees produced deviations between 1.5 and 3 degrees, respectively. These results suggest that if the number of cylinders increases, then printing at 0 and 45 degrees can potentially increase the disparallelism between cylinders in a summative manner.
The distance between cylinders is measured from a lateral view (CA) and coronal view (DC). None of the distances recorded maintained the 4 mm distance of the STL reference model and the majority of distances recorded were less than 4 mm. The 45degrees group (3733.05 ± 40.82 µm) was closest to the reference when measured from a side view (CA) and the 90-degrees group (3873.2 ± 110.5 µm) was closest to the reference when measured from the coronal view (DC). However, the 90-degrees group (3537.53 ± 38.25 µm) produced the smallest distance when measured from the lateral view (CA), indicating a significant convergence of cylinders. The 45-degrees group recorded the most similar means when measured from the lateral (CA) view and top view (DC), indicating less convergence compared to the 0-degrees group and 90-degrees group. Therefore, the present results indicate that printing at 45 degrees will result in the most consistent distances between cylinders.
When analyzing the thickness of the cylinder walls, the 0-degrees and 45-degrees groups achieved values closer to the 600 microns of the STL reference model. The 90degrees group had the greatest variation in the thickness of the wall in the cylinders, with the thickness at the right and left of both cylinders around 900 to 1000 microns. An increase in the thickness of the cylinder walls can influence the parallelism and the distance between cylinders.
The 90-degrees group had the lowest RMS values, negative mean deviations, positive mean deviations, and highest standard deviations compared to the other printing orientations. The global mesh comparisons indicate that the 90-degrees group had greater accuracy and fewer errors to the reference STL in comparison to the printing angles; however, all RMS values are comparable.
The surgical guide allows for the application of a virtually planned implant position into a clinical environment [35]. Any deviations between the planned and actual implant positioning are based upon the cumulative sum of errors during guide fabrication, post processing, intraoral or extraoral scans, data acquisition, and actual implant placement [35,36]. Based on the result of the present study, it can be observed that an increase in the number of cylinders may result in an increase in the cumulative errors between the initially planned position and the printed cylinders.
Multiple factors might lead to the seat distortion for 3D-printed surgical guides. For example, the curing process of each layer during 3D printing leads to the shrinkage of each layer during the polymerization process [37]. As each additional layer is cured, internal stresses and distortions may occur leading to a systematic deviation resulting in a guide smaller than intended [37]. In addition, further post-printing processes such as support struts, cleaning, and curing may potentially introduce an increase in dimensional errors and influence the seating of the guide [37,38].
In the present study, the printing orientation did not affect the global deviations of the cylinders' bases, which is probably related to the base thickness (3 mm) and the lack of complexity of the geometrical form of the base (rectangle). However, in conventional surgical guides prepared on teeth and considering the arch curvatures and other patient factors, the influence of the base design can't be overlooked. Additionally, the present report evaluated the accuracy of the 3D-printed bases. Future research with the same materials is needed to test mechanical properties such as flexural strength and hardness to achieve a complete overview of the materials tested [39,40]. Alternative materials with better optical and mechanical properties may produce better outcomes when manufacturing with different printing orientations.
Within the limitations of the present study should be noted the in-vitro nature of the experiment, that a single SLA printer was used, and that only three printing orientations were tested. The strengths of this work lie in the following aspects: a simple geometric form with two parallel cylinders excluded the variability of a guide fabricated with the curvature of a dental arch; the calibration of the procedures resulted in reduced variability; in addition, the known dimensions of the reference model allowed a precise comparison with the multiple printed samples.
The practical and clinical implications of this work are that perfect surgical guides (equal to the design) do not exist, and surgical guides with multiple cylinders will have increased positional discrepancies produced by the sum of erroneous distances and angles between cylinders.

Conclusions
Within the limitations of this experimental in-vitro study it can be concluded that the printing orientation influences the angle, the distance, and the thickness between adjacent cylinders of a surgical guide. The printed objects differ from the reference model and the 90-degree orientation produces the highest variability in cylinder thickness, the best parallelism, and the best global concordance with the reference model. Data Availability Statement: Data will be available upon request to the corresponding authors.