Estimating the Accuracy of Mandible Anatomical Models Manufactured Using Material Extrusion Methods

Along with modern manufacturing methods, more demands are placed on coordinate metrology, which concerns assessing the accuracy of manufacturing 3D models [ 48 51 ]. Most often, in the process of determining the accuracy of a geometry, coordinate measuring machines (CMM) [ 52 54 ] or articulated arm coordinate measuring machines (AACMM) [ 55 ] are used. However, in models with very complex geometry (such as anatomical structures), the measurement using tactile methods is very time-consuming or impossible to carry out. Therefore, in such cases, optical coordinate measuring systems such as structure light (SL) [ 56 58 ], laser scanner (LS) [ 59 60 ], or micro computed tomography (μCT) [ 61 63 ] are used. Accuracy tests of optical measurement systems are mainly carried out by VDI/VDE 2634, ASME B89.4.22, and VDI/VDE 2630 Blatt 1.3 standards [ 64 66 ]. In assessing the accuracy of optical coordinate measuring systems, traditional standards such as ball bar or flat plane are used. Currently, there are no present studies of new solutions of measures that would allow the preparation of measurement procedures to check the optical measurement errors in terms of a specific type of geometry (such as anatomical structures) and the material used. Moreover, no comparative research has been undertaken to select which of the optical systems allows to obtain the most reliable results assessing the mandible’s accuracy of 3D printing models. The knowledge regarding estimating manufacturing errors of melted and extruded methods can help with the controlled preparation of templates and surgical instruments regarding the accuracy expected during operations. It can also provide significant support in the procedures to restore the continuity of the mandible geometry.

In recent years, there has been a rapid increase in 3D printing techniques in manufacturing anatomical structures of the mandible in planning operations, including the reconstruction of continuity of the mandible geometry. Without a precise fixation of the mandible sections after the bone resection process, it may lead to breathing, speech, and swallowing problems. Thanks to the use of 3D printing methods, the procedures significantly improved. Manufactured models are most often used to pre-bend a reconstructive titanium plate before surgery or plan places where the resection process of a bone will be carried out. It is assumed that the accuracy of manufactured anatomical models in the mandible area should be in a range ±0.25 mm [ 38 39 ]. In the process of manufacturing surgical templates of the anatomical structures of the mandible, polyamide and acrylic materials were often used [ 40 43 ]. Due to the high cost of powder bed fusion, vat polymerization, and material jetting processes, new technologies were analyzed that would minimize the cost of surgery preparation. In recent years, there has been an increase in the use of thermoplastic polymer materials such as acrylonitrile butadiene styrene (ABS), polycarbonate (PC), polylactic acid (PLA), polyethylene terephthalate (PET), and polyetheretherketone (PEEK) in the process of planning surgical procedures within the mandibular area [ 44 47 ]. These are a group of thermoplastic materials used in the melted and extruded methods.

Traditional modeling of machine elements and parts is carried out using computer-aided design (CAD) systems [ 1 ], which are also commonly used in the design process of industrial products using reverse engineering (RE) methods [ 2 6 ]. The designer’s concept becomes a reality due to creating a model using computer numerical control (CNC) techniques [ 7 9 ]. However, to minimize costs and increase the efficiency of the prototyping process and testing of new solutions, additive manufacturing (AM) [ 10 14 ] and hybrid methods, e.g., rapid tooling (RT), are used [ 15 18 ]. In the process of manufacturing final models, metallic materials are still the most often used. However, it has now been observed that due to the continuous improvement of mechanical and functional properties, polymeric materials are also used in processes including injection molding [ 19 ], machining [ 20 21 ], electrical discharge machining [ 22 23 ], and plastic working [ 24 ]. The demand for polymers materials results from their many advantages, including low density, high chemical resistance, easy forming of complex shapes and large sizes, good strength, and low production costs. Due to the improvement of mechanical and functional properties, polymeric materials are also used in additive manufacturing. In the process of manufacturing models using 3D printing methods, polymeric materials can take the form of solid [ 25 26 ], liquid [ 27 28 ], or semi-liquid [ 29 31 ]. The manufactured polymeric models are mainly used in the automotive [ 32 ], aviation [ 33 34 ], and medical industries [ 35 37 ].

2. Materials and Methods

To develop a methodology of estimating the optical systems’ accuracy, a template geometrically similar to the left side of the mandible was used. The template model was designed ( Figure 1 a) and manufactured from aluminum alloy AW-7075 on the DMU 100monoBLOCK. In the research process, three optical coordinate measuring systems were tested. In the process of reconstructing anatomical models of the 12 left sides of the mandible ( Figure 1 b), the Digital Imaging and Communications in Medicine (DICOM) data from the Siemens Somatom Sensation Open 40 scanner was used. A traditional “Head Routine” scanning protocol was used during the measurement process, intended for the craniofacial area. In the stage of the segmentation process, the threshold value was set above 200 HU. To visualize the 3D models of the left side of the mandible, the isosurface method was used. This method is based on the marching cube (MC) algorithm. The final models were saved to the STereoLitography (STL) format. The reconstructed body and angle of the left side of the mandible were used in the research because it is the most frequently affected by tumors. To this surface, they pre-bend a reconstructive titanium plate before the surgery.

P s ) measurement, the deviation between the measured diameter sphere and the calibrated value was determined using the least-squares fit method by Equation (1):

P s = D m e a s u r e d − D c a l i b r a t e d

(1)

The process of verifying the accuracy of the manufacture of the mandibular template was carried out on a coordinate measuring machine (CMM). As a result of the measurement of the model manufactured on the five-axis machining center, the template errors were estimated. The next step was to measure the template on three types of optical measurement systems: Atos III Triple Scan structure light (SL) system; articulated arm (AA) MCA-II with a laser scanner (LS) MMD × 100; and micro-tomography system (μCT) Benchtop CT160Xi. This process aimed to develop a methodology for estimating manufacturing errors of the mandible anatomical models using these systems. The Atos III Triple Scan system comprises a stand holding the measuring head, fitted with a projector and two cameras. The measuring system also includes a rotating table and a computer workstation for processing the measured data. Evaluating the Atos III Triple Scan system performance was carried out by the VDI/VDE 2634 standards requirements and represents three tests. During the probing error shape () measurement, the deviation between the measured diameter sphere and the calibrated value was determined using the least-squares fit method by Equation (1):

S D ) determines the difference between the estimated and calibrated distance between the centers of the two spheres. The measured distance is derived from the measured values obtained from multiple area-based probing by Equation (2):

S D = L m e a s u r e d − L c a l i b r a t e d

(2)

The sphere distance error () determines the difference between the estimated and calibrated distance between the centers of the two spheres. The measured distance is derived from the measured values obtained from multiple area-based probing by Equation (2):

The flatness measurement error (F) was made on the standard plate and is the range of the signed distances of the measurement point from the best-fit plane calculated according to the least-squares method. In the next stage, tests are performed on the system’s template measurement geometry ( Figure 2 a). In the first step, the outer part of the template was measured ( Figure 2 b); in the second step, the internal part was measured ( Figure 2 c). The Atos III Triple Scan measured each piece every 30 degrees (12 counting steps). The resolution of the data during the measurement was 0.050 mm, and the process was fully automated. Then, two measured geometries representing a cloud point were fitted in GOM Professional software using the best-fit algorithm to present the final template model. To assess the repeatability of the measurement process, it was repeated five times. The difference between the maximum (0.002 mm) and minimum (0.001 mm) value of the standard deviation was around 0.001 mm.

E D P ) test was carried out by probing nine points around specific areas of a mounted gage ball. The routine was completed three times, and the maximum absolute deviation from the certified value of the ball was recorded as the test result. The final deviation between the measured diameter sphere and the calibrated value was determined using the least-squares fit method by Equation (3):

E D P = D m e a s u r e d − D c a l i b r a t e d

(3)

Measurements of the template model were also performed with the Metris MCA II articulated arm with a laser head MMD × 100. Firstly, the accuracy of the arm against the ASME B89.4.22 standard was checked. Under the procedure, three tests were performed to check the arm and one for the laser head. The effective diameter performance () test was carried out by probing nine points around specific areas of a mounted gage ball. The routine was completed three times, and the maximum absolute deviation from the certified value of the ball was recorded as the test result. The final deviation between the measured diameter sphere and the calibrated value was determined using the least-squares fit method by Equation (3):

S P A ) test, the probe is placed within a conical socket. Individual points are measured from multiple approach angles with the maximum articulation of all of the principal joints. Each point measurement is analyzed as a range of deviations about the average value for the point locations by Equation (4):

S P A = R a n g e / 2

(4)

In the single point articulation () test, the probe is placed within a conical socket. Individual points are measured from multiple approach angles with the maximum articulation of all of the principal joints. Each point measurement is analyzed as a range of deviations about the average value for the point locations by Equation (4):

V L A ) test is the most appropriate test for determining machine accuracy and repeatability. It involves measuring a certified length standard many times in several locations and orientations and compares the resultant measurements to the actual length—Equation (5):

V L A = L m e a s u r e d − L c a l i b r a t e d

(5)

The volumetric length accuracy () test is the most appropriate test for determining machine accuracy and repeatability. It involves measuring a certified length standard many times in several locations and orientations and compares the resultant measurements to the actual length—Equation (5):

In the case of a laser scanner, an accuracy test is determined by scanning a plane from various directions. The result is the maximum standard deviation of the scan data to fitted plane features. The best-fit plane is calculated according to the least-squares method. The measurement procedure of the template used three measuring steps. The first step focused on measuring the outer part ( Figure 3 a) and the second on the internal part ( Figure 3 b). The third step was to measure the places on the external and internal surfaces that could not be measured in the first and second steps ( Figure 3 c). The resolution of the data during the measurement of the template model was 0.050 mm. Then, three measured geometries representing a cloud point were fitted in Focus Inspection software using the best-fit algorithm to present the final template model. The measurement process was repeated five times to assess the repeatability. The difference between the maximum (0.020 mm) and minimum (0.015 mm) value of the standard deviation was approximately 0.005 mm.

P S ) is calculated as the difference between the measured diameter and the calibrated diameter by Equation (6):

P S = D m e a s u r e d − D c a l i b r a t e d

(6)

The Benchtop CT160Xi (Nikon) tomography used in the research is not calibrated and does not have a maximum permissible error (MPE). Before each measurement, one must check it separately. This scanning error process is mainly carried out on the ball-bar standard. The probing error of size () is calculated as the difference between the measured diameter and the calibrated diameter by Equation (6):

E ) error were performed on reference standards (ball plates). During the procedure, the deviation between the measured length and the calibrated value was determined by Equation (7):

E = L m e a s u r e d − L c a l i b r a t e d

(7)

The length measurement () error were performed on reference standards (ball plates). During the procedure, the deviation between the measured length and the calibrated value was determined by Equation (7):

The template of the mandibular ( Figure 4 ) also verified the Benchtop CT160Xi (Nikon) system. The structure of the iso-voxel during measurements was characterized by the size of the pixel 0.050 mm × 0.050 mm and the layer thickness 0.050 mm. The geometry of the model was reconstructed using ITK-Snap software. The segmentation process was carried out using the region growing method. The 3D model was visualized using the isosurface method. Measurement of the template was carried out five times while maintaining the repeatability conditions. The difference between the maximum (0.050 mm) and minimum (0.030 mm) value of the standard deviation was approximately 0.020 mm.

In the next step, the template and the 12 anatomical models of the left side of the mandible were manufactured using fused deposition modeling (FDM), melted and extruded modeling (MEM), and fused filament fabrication (FFF) techniques. During the manufacture of the models, comparable layer thickness was used ( Table 1 ). Additionally, each model during the manufacturing process was oriented in the same way in the 3D printer space ( Figure 5 a). This procedure aimed to ensure that the side surface of the mandible models was as accurately manufactured as possible. This is because these surfaces are most often pre-bended surgical plates before the operation. Based on the development of measurement procedures, it was implemented in the perspective of the template and the 12 anatomical models of the left side of the mandible, manufactured using melted and extruded methods ( Figure 5 b,c).

The process of verifying the accuracy of manufacturing models was carried out in the Focus Inspection software. The fitting process of the nominal model obtained at the RE/CAD design stage and the reference model created at the measurement stage using the optical systems were carried out using the best-fit algorithm with an accuracy of 0.001 mm. Evaluation of the quality of manufacture geometry was carried out using:

• Calculate the arithmetic mean (mean deviation) by Equation (8):

y ¯ = 1 n ∑ i = 1 n x i

(8)

• Sample standard deviation—sigma (σ) by Equation (9):

σ = 1 ( n − 1 ) ∑ i = 1 n ( x i − x ¯ ) 2

(9)

• Calculate the skewness value by Equation (10):

s k e w n e s s = ∑ i = 1 n ( x i − x ¯ ) 3 σ 3

(10)

• Calculate the kurtosis value by Equation (11):

k u r t o s i s = ∑ i = 1 n ( x i − x ¯ ) 4 σ 4

(11)

n

—the number of measurements, x i —

i

-th measured value, x ¯ —mean value.

where—the number of measurements,-th measured value,—mean value.