# Design of Reliable Remobilisation Finger Implants with Geometry Elements of a Triple Periodic Minimal Surface Structure via Additive Manufacturing of Silicon Nitride

^{1}

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*J*in 2022)

## Abstract

**:**

## 1. Introduction

_{3}N

_{4}implant material for a representative example. For comparison, ATZ, Ti-alloys, and steel were also investigated in the same setting, but results are omitted.

#### 1.1. Biomechanical Simulation and Imaging

#### 1.2. AI-Based Reconstruction of the Joint and Implant Generation

#### 1.3. Materials and Processes for Implant Manufacturing

_{2}O

_{3}, have been successfully approved and used in medicine for many years. In endoprosthetics, the mixed ceramic Zirconia-Toughened-Alumina is used for hip, knee and shoulder endoprosthetics. In the field of implantology, Yttria stabilized zirconoxide ceramics have become established for crown and bridge frameworks. The implants are manufactured using a conventional ceramic shaping technology consisting of powder conditioning, densification, thermal treatment and hard machining. Silicon nitride was found to show a decreased bacteria activity on the surface [22] and to be an ideal ceramic for medical applications [23]. A broader overview of its benefits was already given by [24]. Due to the excellent mechanical properties of silicon nitride, investigations of tribological behaviour are being extended. The main activities in the field of silicon nitride for implants are currently in the spine area and are being pushed by a US company [25].

_{2}[29], HA [30], SiC [31], and others, but Si

_{3}N

_{4}still has yet to be attempted.

_{3}N

_{4}ceramics, a circular gradient structure for finger implants, and reliability calculation will be demonstrated in this paper.

## 2. Materials and Methods

#### 2.1. 3D Model Generation from 2D Medical Images

#### 2.2. Design Process

#### 2.3. CerAMfacturing of Test Components

_{3}N

_{4}is particularly suitable for being used as material of patient specific ceramic implants [39,40,41], since it offers a suitable surface chemistry and high mechanical properties. Therefore, a Si

_{3}N

_{4}composition suitable for biomedical applications was used for investigations and the development of a new photoreactive suspension that can be used within a lithography-based additive manufacturing (AM) process, especially with the CerAM VPP technology. Lithography-based Ceramic Manufacturing (LCM, Lithoz GmbH, 1060 Wien, Austria) is one example of this technology and used for the manufacturing of all test components presented in this study. A detailed description of the process can be found in [42] and the development of the Si

_{3}N

_{4}suspension is described in [24].

_{3}N

_{4}suspension of [24] with a solid content of approx. 40 vol%.

#### 2.4. Mechanical Strength

_{3}N

_{4}) was determined via ball-on-three-balls (B3B) and compression tests.

_{c}, characteristic strength σ

_{0}, and the Weibull modulus m. Danzer et al. and Nohut et al. [43,44] described the limitations and the application of the B3B tests based on ISO 14704. A total of 10 Constant stress-rate (CSR) tests were executed at 20 °C (denoted by RT) at a load rate of 100 N/s. Cyclic fatigue tests were conducted in phosphate buffered solution at 37 °C up to 5 times 10

^{6}cycles based on ISO 13356 with a frequency of 15 Hz and an R-ratio of 0.1. A total of 14 specimens were tested using a maximal stress of the cyclic load at 80% (5 specimens), 70% (4 specimens) and 60% (5 specimens) of the characteristic strength σ

_{0}. The geometry of the B3B setup is defined by 4 ceramic spheres with radius 12mm and 3 spheres positioned at the backside 15 mm from the center of the 4th sphere and the center of the disc. A biaxial tensile stress is formed at the centre. The calculation of the stress can be done using a geometric function f, the applied force F, and the thickness of the disc.

^{3}and machined according to DIN EN 843-1 [48]. The tests were also conducted according to DIN EN 843-1. Constant stress-rate (CSR) tests were performed on 4-point bend bars at 20 °C at load rates of 200 N/s. Cyclic fatigue tests were carried out in lab air at 20 °C. For each combination of load rate and temperature 30 samples were characterized as in [49].

_{eff}

_{,comp}), and this is given analytically or by finite element representation as:

_{0}) can now be calculated using the effective volume of a component (V

_{eff}

_{,comp}), by means of the scaling volume (V

_{0}). These parameters can be estimated from the strength results of CSR-tests and by characteristic Weibull strength from the tests (comp: B3B and 4PB):

_{I}, and the fracture toughness K

_{IC}, are needed in addition of two parameters, namely, a material parameter A and the crack-growth exponent n [51]. For a description:

_{f}) by:

_{f}plot.

## 3. Results and Discussion

#### 3.1. 3D Model Generation from 2D Medical Images

#### 3.2. Individual Implant Design

#### Creation of Implant Design

#### 3.3. Additive Manufacturing of Silicon Nitride Specimen

_{3}N

_{4}test samples created by additive manufacturing via vat photopolymerization (CerAM VPP) were discs for biaxial bending test via ball-on-three-balls method. Afterwards, cylindrical SplitP-type TPMS components with a base plate were successfully generated via 3D-printing followed by the manufacturing of a first complex finger implant also based on a SplitP design. The various test samples are presented in the following in sintered state (Figure 6).

#### 3.4. Fracture Test of Silicon Nitride Specimen

#### 3.4.1. Discs for Ball-On-Three-Balls Test in Comparison to 4-Point Bending Results

_{3}N

_{4}ceramics were tested in B3B or standardized 4-point bending test geometry. VPP (via vat photopolymerization) S

_{3}N

_{4}is the ceramic optimized for the additive manufacturing process via photopolymerization of a binder suspension; CIP (cold isostatic pressed) S

_{3}N

_{4}is the ceramic based on the same Si

_{3}N

_{4}granules as VPP with 6 wt% alumina and 5 wt% yttria [24]; and Si

_{3}N

_{4}-E10 SC [49] is a high temperature resistant benchmark that was gas pressure sintered at 1800 °C under 50 bar nitrogen atmosphere based on the same Si

_{3}N

_{4}powder but 1.5 wt% alumina and 8.1 wt% yttria.

^{3}in the test, and thus silicon nitride. Two steps are required in the application: to apply surface sensitive testing with the B3B method for surface dominated structures, and to compare test results from the B3B method and 4-point bending. The methodical verification of the comparison of the B3B test and 4-point bending was shown by Danzer. An applicability of the distribution assumption for critical errors is checked via a Weibull plot (Figure 7) of the individual strength results. A high applicability was proven for the materials and test types since a high linear correlation was found. In detail, minor deviations from linearity are visible, representing high and low strength cases. The Weibull parameter m can be obtained from the slope in this diagram, and is high in all cases.

_{3}N

_{4}and Si

_{3}N

_{4}-E10 have revealed that the evolution of cyclic fatigue is similar (Figure 8), and therefore a similar resistance against crack growth is obtained. This can be concluded by the very parallel slope of strength reduction at increasing cycles. But VPP Si

_{3}N

_{4}shows a broader distribution of underlying critical defects due to the additive process, and obviously has larger defects in comparison to the optimized Si

_{3}N

_{4}E10 SC.

_{3}N

_{4}, which possibly could be the result of these larger defects, but the results are promising for the use in an innovative structured design.

#### 3.4.2. Mechanical Behavior of Cylinder with SplitP TPMS

_{3}N

_{4}ceramics) to that of the bone by structuring. The achieved strength of this structure of 90 MPa is sufficiently high in comparison with biological material. To what extent the calculated loads can be compared with the actual physiological loads cannot yet be answered. For these reasons, a comparison will be sought via load simulations of each structure, shape, implant and loading scenario.

#### 3.5. Finite-Element-Modeling and Reliability Calculations

#### 3.5.1. Discs for Ball-on-Three-Balls Test and Calculation of Weibull-Parameter

_{eff}

_{,B3B}= 0.02 mm

^{3}, and using the characteristic fracture stress σ

_{0,B3B°}= 847 MPa for the B3B test, the reference volume based parameters V

_{0}= 1 mm

^{3}und σ

_{0,B3B°}= 681 MPa can now be calculated.

^{2}for the specific geometry (Figure 12).

#### 3.5.2. Cylinder with Cylindrical SplitP TPMS in Comparison to Experimental Results

_{eff}

_{,cylinder}= 11.4 mm

^{3}and a characteristic stress σ

_{0, cylinder°}= 595 MPa in the structure valid for the geometry can be calculated (Figure 13). The strength parameters determined from the experiments of the B3B test for the case with the assumed optimised load application through a mounting plate (top) could be almost identical in value as well as a converted standard deviation.

#### 3.5.3. Calculation of Implant Load with Gradient SplitP TPMS for a Diagonal Joint Load

_{eff}

_{,implant}= 1.23 × 10

^{−4}mm

^{3}and a characteristic stress σ

_{0,implant45°}= 1123 MPa are calculated. The used subroutine creates an output field parameter probability of survival for each element.

## 4. Conclusions

- The ceramics created by VPP can be reliably applied to filigree structures.
- The TPMS structures of the implant can be created in a graded form along the curvature of the complex implant. A full workflow for a specific gradient generation of a TPMS to solid structure was achieved in a CAD-nTopology loop for individual implants and bones.
- SplitP TPMS structures have been validated for brittle materials as excellent elasticity-mitigating structures (3.6%) with low stress factor (6.4).
- The ball-on-three-ball test is predestined for the brittle materials of submilimetre VPP ceramic structure.
- A full workflow converts joint bone models, matches and aligns them to implants.
- The submilimetre accuracy of the AI-based 3D shape construction of 2D real data is expected to be good, as it was validated on artificial reconstruction loop 3Dto2Dto3D.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**3D model reconstruction pipeline: (

**a**) original X-ray with automatically segmented 2D thumb metacarpal bone (green overlay); (

**b**) 3D reconstructed shape (orange) generated by fitting the shape model projection (orange contour) to the 2D segmentation.

**Figure 3.**Statistics of Hausdorff distance [mm] for each finger bone summarized for all five reference configurations.

**Figure 6.**Sintered part of silicon nitride manufactured via CerAM VPP: (

**a**) discs for biaxial bending tests; (

**b**) a cylindrical TPMS (SplitP design) component on base-plate; (

**c**) example of on finger implant with inner dense core, outer porous SplitP structure, and a polished glide surface.

**Figure 7.**Weibull diagram for via vat photopolymerization manufactured (VPP) and cold isostatic pressed (CIP) binder based Si3N4 (adapted and redrawn from Ref. [24] 2022 Elsevier Ltd.), in comparison to gas pressure sintered (GPS) high strength Si3N4 (adapted and redrawn from Ref. [49] 2020 Elsevier Ltd.).

**Figure 8.**Cyclic fatigue-adjusted S-N data and normalized stress amplitude to critical stress for via vat photopolymerization manufactured (VPP) binder based Si3N4 (adapted and redrawn from Ref. [24] 2022 Elsevier Ltd.), in comparison to gas pressure sintered (GPS) high strength Si3N4 (adapted and redrawn from Ref. [49] 2020 Elsevier Ltd.).

**Figure 9.**Uniaxial compression of a Si

_{3}N

_{4}-cylinder with SplitP TPMS structure: (

**a**) manufactured specimen with and without loading plate; (

**b**) specimen inside the uniaxial test setup.

**Figure 10.**Results of uniaxial compression of a Si

_{3}N

_{4}-cylinder with SplitP TPMS structure: (

**a**) homogenized true stresses of the cross section and uniaxial mean strain by means of the dimensions; (

**b**) fitted elasticity to stress-strain results.

**Figure 11.**Ball-on-three-balls test: (

**a**) test geometry for cylindric plates with and without top layer; (

**b**) maximal principal stress for cut view of loaded cylinder.

**Figure 12.**Ball-on-three-balls test: dependence of effective volume on Weibull module and loading parameter F/t

^{2}.

**Figure 13.**Uniaxial compression test of SplitP TPMS structure: (

**a**) maximal principal stress at 8 kN; (

**b**) the comparison of calculated fracture stress in comparison to the experimental results.

**Figure 14.**Index finger implant in proximal bone: (

**a**) maximal principal stress when implant is loaded with 45° to bone axis with 2.5 times of 100N reference load; (

**b**) probability of survival for each finite element of a defined region.

**Figure 15.**Index finger implant in proximal bone: (

**a**) cut view of maximal principal stress in the implant; (

**b**) Cut view of von Mises equivalent stress in the bone.

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## Share and Cite

**MDPI and ACS Style**

Koplin, C.; Schwarzer-Fischer, E.; Zschippang, E.; Löw, Y.M.; Czekalla, M.; Seibel, A.; Rörich, A.; Georgii, J.; Güttler, F.; Yarar-Schlickewei, S.;
et al. Design of Reliable Remobilisation Finger Implants with Geometry Elements of a Triple Periodic Minimal Surface Structure via Additive Manufacturing of Silicon Nitride. *J* **2023**, *6*, 180-197.
https://doi.org/10.3390/j6010014

**AMA Style**

Koplin C, Schwarzer-Fischer E, Zschippang E, Löw YM, Czekalla M, Seibel A, Rörich A, Georgii J, Güttler F, Yarar-Schlickewei S,
et al. Design of Reliable Remobilisation Finger Implants with Geometry Elements of a Triple Periodic Minimal Surface Structure via Additive Manufacturing of Silicon Nitride. *J*. 2023; 6(1):180-197.
https://doi.org/10.3390/j6010014

**Chicago/Turabian Style**

Koplin, Christof, Eric Schwarzer-Fischer, Eveline Zschippang, Yannick Marian Löw, Martin Czekalla, Arthur Seibel, Anna Rörich, Joachim Georgii, Felix Güttler, Sinef Yarar-Schlickewei,
and et al. 2023. "Design of Reliable Remobilisation Finger Implants with Geometry Elements of a Triple Periodic Minimal Surface Structure via Additive Manufacturing of Silicon Nitride" *J* 6, no. 1: 180-197.
https://doi.org/10.3390/j6010014