mean ± standard deviation (SD).

Young's modulus (Figure 10b) was estimated from the initial slope of stress–strain curves (Figure 10a) in the elastic region. Compressive strength (Figure 10c) was evaluated from stress–strain curves (Figure 10a). The results showed that the energy absorptions of the sinus lift scaffold and onlay B are comparable, while onlay A showed a higher energy absorption. Nevertheless, all investigated scaffolds, independently from their shape, showed a higher energy absorption and strength in comparison with the control group (BioOss®).

≤ ≤ ≤ ≤ **Figure 10.** Mechanical properties of individual scaffolds in comparison with BioOss®. (**a**) Representative compressive stress–strain curves. (**b**) Young's modulus and (**c**) compressive strength determined from the curves (\* *p* ≤ 0.05, \*\*\* *p* ≤ 0.001, \*\*\*\* *p* ≤ 0.0001, mean ± standard deviation, n = 5).

#### **4. Discussion**

This study aimed to determine the optimal porosity of CPC scaffolds for bone augmentation in maxillofacial surgery according to specific indications. Regarding stability and cell infiltration, the data presented suggest that pore sizes of 750 µm allow for a significantly higher increase in cell colonization compared to smaller pores after 12 weeks (see Figure 3). Furthermore, the stability of the CPC cubes increases up to a pore size of 100 µm with an observed compressive strength of 31.3 ± 6.8 MPa and a Young's Modulus of 870 ± 117 MPa (see Figure 2). Nevertheless, individual CPC scaffolds, which are closer to clinical conditions, have shown a much lower compressive strength resistance depending on the respective site of destination. Thus, in certain cases, the porosity of individual scaffolds in maxillofacial surgery needs to be adapted with an acceptance of the concomitant decrease of cell infiltration.

Bone augmentation is performed when bony defects compromise the function and aesthetics of the orofacial system [25–28]. One of its main functions is to grind food as the first step of digestion. This is conducted by frequently repeated contraction of the chewing muscles. The chewing muscles belong to the strongest muscles in the human body. During the chewing process, forces beyond 200 N emerge depending on the region within the oral cavity [20,21]. The highest pressure can be measured in the lateral region of the jaws since this is the chewing center [20]. In other sites, such as the sinus floor, the anterior parts of the jaws or parts of the facial bone, the pressure is much lower [20]. Assuming a full dentition with an average chewing surface of approx. 6 cm<sup>2</sup> , this corresponds to a pressure of approx. 0.4 MPa per tooth.

By Zwick universal testing, uniaxial compression can be applied to the test object. This makes it an appropriate testing procedure to resemble the in vivo situation, as teeth and the adjacent bone are stressed in a similar way. By testing standardized CPC cubes, 32 MPa was measured as the highest compressive strength withstood by scaffold A, which had a strand-to-strand distance of 430 µm and a pore size of 100 µm. This easily exceeds the essential requirements (0.4 MPa) for an in vivo application. Compared to the control group (BioOss®), which is commonly used for bone substitution, the applicable compressive strength of scaffold A was 60 times higher.

Nevertheless, the colonization experiments have shown that pore sizes of 100 µm (scaffold A) are too small to let cells quickly migrate into the scaffold. Due to the small pores, instead of infiltrating, cells instead colonized the scaffold's outer surface.

As depicted in Figure 3, in our case, a porosity of 750 µm (scaffold F) seems to be the best for cell infiltration. Nevertheless, cell numbers observed in the control group (BioOss®) were still superior from week 4 onwards. The reason for this could be the surface of BioOss®, which mimics the surface of natural bone better than CPC does (Figure 11). As seen in Figure 11, the CPC's surface is smooth, whereas the surfaces of BioOss® and natural bone have many micro irregularities. These irregularities lead to an enhanced attachment area for cells.

**Figure 11.** SEM imaging of CPC scaffold D (**a**,**b**), BioOss ® (**c**,**d**) and natural bone (**e**,**f**).

However, this advantage seems to decrease over time. Up to week 12, the difference in cell numbers between BioOss® and the CPC scaffolds with high porosity decreases continuously until they are nearly the same after week 12 (Figure 3). The influence of surface roughness on cell adhesion and function has been discussed in several studies [29,30]. The observed micro irregularities not only offer more surface for cell binding, but they also strengthen the adsorption of proteins and the extracellular matrix, which enhances the cells' adhesion and function. This effect was observed for different biomaterials and cells [31–33]. To improve the early cell adhesion on CPC scaffolds, the CPC could be enriched with nanoparticles such as bioactive glass, as shown by Richter et al. [34]. Thereby, the CPC's surface could be enriched with irregularities to better resemble natural bone.

In contrast, due to a decreased surface and increased strand-to-strand distance, a higher porosity goes along with a significant decrease of the compressive strength resistance and Young's Modulus. As depicted in Figure 2, scaffold F (pore size 750 µm) shows a compressive strength of 5.2 ± 0.6 MPa, which is much higher compared to that of the control group (0.5 ± 0.007 MPa). In Figure 5, it is shown that the porosity of scaffold D seems to be similar to that of BioOss®. Nevertheless, scaffold D is much more stable. This superior stability of the CPC scaffolds compared with BioOss® may be caused by the differences in their architecture. Microscopically, a natural spongious bone, similar to the architecture of BioOss®, can be observed. As shown in Figure 6, the spongious trabeculae are arranged irregularly in contrast to the strands of the CPC scaffolds. This regular arrangement of the CPC strands may be the reason for the higher compressive strength resistance. The pressure can be evenly deviated above the whole surface.

The Young's Modulus of the observed CPC cubes ranged from 444 ± 44 MPa to 870 ± 117 MPa. Human bone has a Young's Modulus of about 4.42 MPa as shown by Boughton et al. [35]. It is worth noting that Boughton et al. investigated cortical bone samples from femoral necks, the mechanical properties of which may differ from jaw and facial bone. Furthermore, the donors from which the bone was harvested had a mean age of 69 years. Due to the fact that age and chronic diseases have a significant impact on bone density, architecture and mechanical properties [36], these values may not be comparable to the jaw bones of patients undergoing maxillofacial surgery.

Nevertheless, the Young's Modulus of natural human bone seems to be much lower in comparison to the observed CPC scaffolds. The orofacial system is in permanent motion and underlies continuous dynamics. In such dynamic systems, differences of the Young's modulus can be crucial. They could lead to micro movements between scaffold and bone and thereby compromise the scaffold's integration. Here, BioOss® is much closer to natural bone, due to its natural origin and closely mimics natural bone tissue. In contrast to this,

the CPC scaffolds consist of artificial tri-calcium phosphate and are manufactured by using amorphous paste. This may be why they are more brittle and less elastic. Besides the differences in the Young's Modulus, a high brittleness could compromise the intraoperative handling since the scaffolds have to be fixed with titanium screws. If the scaffolds are too brittle, they may break when the screw is inserted. This could probably be avoided by integrating a screw channel preliminarily and thereby decreasing the stress in the CPC while inserting the screw (as shown in Figure 9). Nevertheless, a pore size of 750 µm seems to be adequate for facilitating a high infiltration of cells and still meeting the mechanical requirements in the orofacial system. These findings were, however, observed in regularly shaped, cubic CPC scaffolds.

Knowing that this design might fail in simulating in situ settings with complex shaped defects, we additionally investigated clinical cases. Three cases were selected that displayed typical intraoral regions with mechanical requirements different to those of a bone scaffold (Figure 8): sinus floor elevation, onlay osteoplasty located posterior to the remaining teeth (onlay A) and onlay osteoplasty embraced by remaining teeth (onlay B).

Sinus floor elevation is a procedure that is used to create a sufficient base for dental implants in the posterior maxilla [37–39]. This is realized by inserting the bone substitution material through a bony window that has to be cut into the lateral wall of the maxillary sinus. During the healing period prior to implant insertion, it is not affected by pressure or movement. Due to these highly protected conditions during the healing period, a CPC scaffold for sinus floor elevation does not need to withstand a high compressive strength. Therefore, in such cases it could be advantageous to choose large pore sizes to gain the maximum cell infiltration. According to our findings, 750 µm would be the appropriate pore size in this case. Nevertheless, due to its pyramidal and compact geometry, the scaffold reaches high compressive strength resistance (1.7 ± 0.3 MPa) and therefore exceeds the essential requirements of the maxillary sinus. Considering this, even larger pore sizes could be assumed for such cases. The control group also seems to be a good choice for sinus floor elevation. As discussed above, the low compressive strength resistance of BioOss® can be neglected. According to Figure 3, BioOss® would even allow for a faster and larger increase of cell colonization on its surface compared to CPC scaffolds. This advantage of BioOss® could probably be compensated for by coating the CPC scaffolds with collagen as shown by Lee et al. [40]. Moreover, there are several advantages that favor CPC scaffolds. In contrast to BioOss®, CPC scaffolds can be individually designed based on a CBCT scan. Patient-specific geometries can be printed [24,41,42], thus they will fit perfectly to the defect site. The surgeon saves time during surgery since there is no need to prepare or adapt the scaffold intraoperatively. The planning of the augmentation is conducted before the surgery, which minimizes the risk of over- or under treatment. Additionally, CPC scaffolds can be printed with a graded porosity. Thus, the outer "soft tissue facing side" of the scaffold can be printed densely so that fibroblasts are not able to immigrate. Usually for this purpose additional membranes need to be placed to cover the defect site [43–45]. These membranes always come with the risk of early dehiscences and inflammation [46]. To summarize, for sinus floor elevation, CPC scaffolds with a pore size of 750 µm seem to be a sufficient tool.

Onlay osteoplasty in combination with dental implants is a standard procedure for the functional rehabilitation of highly atrophic jaws [27]. For onlay osteoplasty, the surgeon prepares a mucoperiosteal flap and fixes the bone substitution material directly to the defect site. In these cases, the bone scaffold is located submucosally. Hence, it is exposed to motions and forces directly after surgery. In this study, we simulated two clinical cases: region of teeth 46 and 47 (onlay A: Figure 9D–F) and region 36 (onlay B: Figure 10G–I). Both sites are under permanent pressure due to their location in the chewing center. Remarkably, there is an important difference between both cases. Onlay A covers an area of two teeth and there are no teeth posterior to the defect. Therefore, it needs to hold those forces that emerge in the chewing center on its own. In contrast, onlay B covers the area of one tooth and is embraced by teeth, anteriorly and posteriorly. The adjacent teeth may protect the

scaffold from high compressive strength. Nevertheless, both scaffolds need to resist a higher compressive strength compared to that resisted by the sinus floor scaffold. Zwick testing of onlay A and onlay B revealed that the favored pore size of 750 µm is not stable enough to withstand the forces during the chewing process. The same effect was shown with a pore size of 620 µm (data not shown).

The pore size that was found to be strong enough to withstand the forces in the chewing center and also showed excellent colonization data was 490 µm with a compressive strength resistance of at least 1.0 ± 0.2 MPa. The individual scaffolds with pores of 490 µm have a Young's Modulus of 239 ± 45 MPa and 127 ± 22 MPa for onlay A and onlay B, respectively. As mentioned above, the Young's Modulus of human bone is approx. 4.42 MPa [35]. The mandible, especially, is known to be flexible and moved by different surrounding muscles. Unfortunately, the mechanical testing has shown that even very wide pore sizes, such as 750 µm, cannot affect the Young's Modulus to the extent that it would be comparable to human bone (Figure 2B). Nevertheless, CPC scaffolds with pore sizes of 490 µm seem to be a solid option for onlay osteoplasty in the lower lateral jaw. The superior compressive strength resistance compared to the control group especially makes CPC scaffolds an appropriate alternative to autologous bone, which is mostly used for onlay osteoplasty. Nevertheless, this study has certain limitations. The outer soft tissue facing layer was printed as densely as possible to prevent the migration of mucosal cells. Our experimental setting does not clarify whether our scaffold design fulfills this requirement properly. Furthermore, there are various other patient specific aspects that influence the integration of the scaffolds, such as certain comorbidities or lifestyle habits. Moreover, the degradation time of scaffolds is of high clinical relevance and it could be hypothesized that pore size also affects degradation time. To answer this question, an in vivo study would have to be conducted.

#### **5. Conclusions**

Our findings suggest that the pore size of CPC scaffolds for bone augmentation in maxillofacial surgery should be adapted for the planned site. CPC scaffolds for augmentation sites that are not exposed to high forces, such as the sinus floor, could be printed with a pore size of 750 µm to benefit from the enhanced cell infiltration. In contrast, CPC scaffolds for bone augmentation in areas exposed to high pressures, such as the lateral mandible, should be planned with a pore size of 490 µm. This pore size facilitates adequate cell infiltration and simultaneously meets the mechanical requirements in these highly stressed areas.

**Author Contributions:** Conceptualization, M.C.S.; methodology, L.M.K., D.M., P.S., S.H., H.M.; software, L.M.K., P.S., S.H.; validation D.M., L.M.K.; formal analysis L.M.K., P.S., S.H.; investigation, L.M.K., D.M., P.S., S.H., H.M.; resources, G.L.; data curation, D.M., L.M.K., P.S., S.H.; writing original draft preparation, D.M., L.M.K.; writing—review and editing, D.M., P.S., S.H., A.H., M.C.S., G.L., L.M.K., H.M.; visualization, D.M., L.M.K.; supervision, L.M.K., G.L.; project administration, G.L.; funding acquisition, M.C.S., S.H., P.S., A.H., D.E., A.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the German Federal Ministry for Economic Affairs and Energy (BMWi), grant number ZF4379203MC8.

**Institutional Review Board Statement:** The use of patient data was approved by the local ethical review board (IRB00001473; file reference: EK1450420019).

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study. Written informed consent has been obtained from the patient(s) to publish this paper.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy restrictions.

**Acknowledgments:** The authors thank Diana Jünger (Department of Oral and Maxillofacial Surgery, University Hospital "Carl Gustav Carus", Technische Universität Dresden) for their excellent technical assistance.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**


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