*3.5. The Magnitude of Interfacial Strain is a Key Influence on Whether an Implant will Undergo Fibrous Encapsulation or Osseointegration*

Why did these round occlusal implants fail? The key to answering this question lies in the observation that the same round implants can osseointegrate, provided they are placed sub-occlusally to reduce loading (Figure 3). Thus, the round implants failed because they lacked sufficient primary stability (Figure 1Q). We sought to link this observation about stiffness at PID0 with the fates of the implants on PID20, and to do so, we turned again to FE modeling.

Implant stability is a function of the elastic modulus of peri-implant tissue; in other words, the stiffer the tissue, the less the implant will move under loading. FE modeling was used to back-calculate the peri-implant bone modulus that corresponded to the experimentally-measured lateral stability (see Materials and methods). At PID0 and PID3, the peri-implant tissues surrounding trioval implants were 3.5 times stiffer than those surrounding round implants. Using these modulus values, FE models demonstrated that peri-implant strains at PID0 and PID3 were significantly higher around the round occlusal implant (Figure 4F). For example, at the crestal thread tips of an occlusally-loaded round implant, principal compressive strain magnitudes reached >50% (Figure 4F). On the other hand, identically-loaded tri-oval implants were surrounded by stiffer peri-implant tissue and the resulting strains at PID0 and PID3 were less than 10% (Figure 4H). Collectively, these data provide critical insights as to why a round implant with significantly less primary stability underwent fibrous encapsulation when subjected to immediate loading (Figure 4G), whereas a tri-oval implant, with statistically higher primary stability, underwent osseointegration when subjected to the same immediate loading conditions (Figure 4I).

#### **4. Discussion**

We coupled mechanical testing with computational studies and histologic/immunohistologic analyses to assess how altering an implant's geometry affected its ability to osseointegrate. We tested implants that were placed below the level of the occlusal plane, and those placed in function. In both scenarios, the tri-oval implants out-performed the round implants. Evidence supporting this conclusion came from mechanical, computational, and biological analyses.

#### *4.1. The Maxima of a Tri-Oval Implant aid in Mechanical Stability*

Compared to round implants, the tri-oval implants exhibited better primary stability, which was achieved without using a higher IT (Figure 1). The larger stability was achieved because the maxima of the tri-oval implant penetrated a greater distance into bone than did the threads of the round implant (Figure 2). Based on our data, one might legitimately ask if the novel tri-oval implant design would be negated simply by undersizing the osteotomy for the round implant. In this thought experiment, the threads of the round implant would penetrate deeper into bone and as a result the implant would presumably demonstrate better initial stability. But just as reliably, this scenario would also increase IT [8], peri-implant strain [11], and its associated micro-damage [8,15,33]. In turn, this micro-damage would increase the spatial extent of peri-implant bone resorption (Figure 3) during the early post-operative stages of bone remodeling, which would lower the net modulus of the peri-implant bone and result in a transient decrease of initial stability–as seen for example at PID 3 (Figure 4B).

Clinical observations are consistent with this line of reasoning: in multiple studies, sub-occlusal implants showed a decline in mean ISQ values between weeks 1-4 [34–36]. Friberg also reported a decrease in stability for a majority of sub-occlusal implants [37,38]. Our preclinical study appears to be the first to provide direct molecular, cellular, histologic, and mechanical data to explain how this transient "dip" in implant stability actually occurs.

### *4.2. The Minima of a Tri-Oval Implant Create a Pro-Osteogenic Environment*

Fifty percent of the peri-tri-oval implant environment had very low/no strain (Figure 2E), where damage to the mineralized matrix is minimized, osteocyte death is minimal, and bone resorption is reduced [8,15,33]. Together these events culminated in significantly more new bone around the tri-oval implants (Figures 2 and 3). A similar finding has been reported using a canine implant model, where investigators demonstrated that new woven bone forms first in regions where there is a gap in the bone-implant contact [12]. We find that areas of low/no strain strongly support osteoblast differentiation and new mineralized matrix deposition, provided the osteogenic potential of the bone is good [22].

### *4.3. Clinical Implications of this Study*

Round-shaped implants can osseointegrate, even when subjected to loading immediately after placement. Why, then, did we observe that round implants failed to undergo osseointegration? The answer is straightforward: in those cases where round implants became encapsulated in fibrous tissue it was because loading was allowed on an implant that lacked sufficient primary stability (Figure 1). If the same implant—with the same degree of instability—was buried, then by PID20 it was surrounded by new bone (Figure 3). These data indicate the importance of an "unloaded" healing period proposed by Branemark [39]. What if the healing period is eliminated? Our data predict that healing periods between implant placement and loading could be shortenedor eliminated—without jeopardizing long-term implant success if osteocyte death was minimized during site preparation, and the implant had a geometry that provided both mechanical stability and a pro-osteogenic environment.

#### **5. Conclusions**

These multiscale biomechanical analyses demonstrated that the novel tri-oval implant design provided mechanically and biologically favorable environment for peri-implant bone formation and promoted osseointegration.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2077-0383/8/4/427/s1, Figure S1. Method to determine the distribution of apoptotic osteocytes. (**A**) Using differential interference contrast (DIC), the peri-implant environment of round implants was visualized. (**B**) DAPI staining identified viable osteocytes in four zones circumscribing the implant. (**C**) Co-staining with TUNEL identified apoptotic osteocytes in four zones circumscribing the implant. (**D**–**F**) The same procedure was used to analyze the minima regions of tri-oval implants. Abbreviations: imp, implant. Scale bars = 50 μm.; Table S1. Osteotomy and implant parameters; Table S2. Osteotomy and implant parameters.

**Author Contributions:** Conceptualization: X.Y. and J.A.H.; methodology: X.Y. and J.A.H.; validation: X.Y., J.L., and J.A.H.; data curation: X.Y., J.L., and J.A.H.; formal analysis: X.Y., J.L., W.H., A.G., and J.B.B.; investigation: X.Y. and J.L.; writing—original draft preparation: X.Y. and J.A.H; writing—review and editing: X.Y., J.L., W.H., A.G., J.B.B., and J.A.H.; funding acquisition: X.Y., J.B.B., and J.A.H. All authors gave final approval and agree to be accountable for all aspects of the work.

**Funding:** This research project was supported by grants from National Natural Science Foundation of China (81801019), China Postdoctoral Science Foundation (2018M640929) and Sichuan Science and Technology Program (2019JDRC0099) to X.Y. and National Institutes of Health (DE 024000) to J.B.B. and J.A.H. In addition, funds from Nobel Biocare Services AG (Kloten, Switzerland) were used to support this research (2015-1400).

**Conflicts of Interest:** The authors declare no conflict of interest. J.B.B. and J.A.H. are paid consultants for Nobel Biocare. All other authors declare no potential conflicts of interest with respect to the authorship and/or publication of this article.
