Factors That Determine the Adhesive Strength in a Bioinspired Bone Tissue Adhesive

Phosphoserine-modified cements (PMCs) are a family of wet-field tissue adhesives that bond strongly to bone and biomaterials. The present study evaluated variations in the adhesive strength using a scatter plot, failure mode, and a regression analysis of eleven factors. All single-factor, continuous-variable correlations were poor (R2 < 0.25). The linear regression model explained 31.6% of variation in adhesive strength (R2 = 0.316 p < 0.001), with bond thickness predicting an 8.5% reduction in strength per 100 μm increase. Interestingly, PMC adhesive strength was insensitive to surface roughness (Sa 1.27–2.17 μm) and the unevenness (skew) of the adhesive bond (p > 0.167, 0.171, ANOVA). Bone glued in conditions mimicking the operating theatre (e.g., the rapid fixation and minimal fixation force in fluids) produced comparable adhesive strength in laboratory conditions (2.44 vs. 1.96 MPa, p > 0.986). The failure mode correlated strongly with the adhesive strength; low strength PMCs (<1 MPa) failed cohesively, while high strength (>2 MPa) PMCs failed adhesively. Failure occurred at the interface between the amorphous surface layer and the PMC bulk. PMC bonding is sufficient for clinical application, allowing for a wide tolerance in performance conditions while maintaining a minimal bond strength of 1.5–2 MPa to cortical bone and metal surfaces.


Introduction
A number of adhesives have been proposed for tissue reconstruction. Aside from non-degradable adhesives [1], most biocompatible and biodegradable tissue adhesives utilize crosslinking mechanisms inspired by natural (marine) adhesives. The most common approach to creating adhesion is to incorporate a modified amino acid, L-DOPA (e.g., as a pendant group, onto a polymer) [2,3]. Coacervation and nanoscale electrostatic interactions are also sufficient to create relatively strong tissue adhesion [4][5][6][7]. Recently, strong adhesion has been created in biomaterials that are not adhesive (bioceramics) by incorporating a modified amino acid (phosphoserine) [8][9][10]. Phosphoserine-modified cements (PMCs) display a unique microstructure, appearing amorphous rather than crystalline [10], can stabilize bioactive phases and remodel into precursors of hydroxyapatite [11], and display significantly improved healing, compared to unmodified cements [12][13][14][15]. PMCs are particularly suited for hard tissue applications, with a stronger compressive and (adhesive) shear strength than human On the molecular level, the bond strength of an adhesive reflects a compromise between: (a) the adhesive strength, where adhesive failure occurs via load dissipation between the adhesive and adherend surfaces (e.g., deformation of bonds between poly-methyl methacrylate (PMMA) and a metal or tissue surface (physical interlocking and van der Waals' interactions)) [34,35]; and (b) the cohesive strength of the polymeric matrix (e.g., crosslinking density), or between the matrix/binder and other phases (e.g., in asphalt) [36]. In a shear test, the source of adhesive strength, between polymer and metal surfaces, is predominantly adsorption (wetting) and mechanical interlock [34]. Adsorption and mechanical interlock are also likely to explain much of PMC adhesion to biological surfaces, though ionic bonding (chelation and coordination), surface interpenetration, and additional contributions from the ceramic phase are also possible.
The mechanical properties of PMCs have been well described [8,10]. In contrast, PMC adhesive strength has not been investigated under varied test conditions, and in situations mirroring clinical complications (e.g., very uneven adhesive bond thickness). Thus far, no studies have investigated how (PMC) adhesive strength is affected by different curing, and handling conditions (e.g., laboratory testing versus conditions for clinical use). The purpose of this study was to (a) to identify which factors contribute to the adhesive strength of PMCs, (b) to lay the foundation for subsequent exploratory studies into the mechanisms underlying the adhesion of PMCs, and to identify how to increase the adhesive strength by (c) bridging disparate test conditions, thereby allowing for comparisons/predictions on how PMC behaves in both the laboratory and the clinic.
Steel and aluminum cubes (1 cm 3 ) were prepared at the Uppsala University workshop, by cutting steel or aluminum rods to a height of 1.1 mm, and polishing the surface to 1.0 mm, with USA80 grit roughness. Aluminum cubes were fabricated using an identical process, with cube surfaces polished to either US #80, 320, or 1200 grit roughness. Fresh adult bovine bone was obtained from Lovstakott (Uppsala, Sweden), with approval from the department of agriculture. Cortical tissue from bovine humeral diaphyseal shaft was cut into cubes (1 cm 3 ), using a bone band saw (IMEB Inc., USA) and a diamond blade, and stored in phosphate-buffered saline at −20 • C. The surfaces of the cortical cubes were not polished further and were used as obtained from the diamond blade. The surface roughness was not determined for cortical cubes, as this was not the focus for testing on biological/tissue samples.
Metal cube surface roughness was determined with a Zygo Nexview NX2 optical profiler (Middlefield, CT, USA). A 10× magnification lens, 0.5× zoom (field of view), was used in CSI measurement mode, with high dynamic range (HDR) enabled, and signal oversampling. The data were analyzed with Zygo Mx software. Each surface was partitioned into 64 zones (1.68 × 1.68 mm in total), and 4 evenly dispersed zones were selected for testing from 3 cubes, for each group. The following parameters were recorded: S a (arithmetic mean), S q (root-mean square height), S ku (kurtosis, sharpness), and a 2D roughness measurement (R a , arithmetic mean) traversing the diagonal of the 4 zones, for each cube.
Adhesive (shear) samples were prepared by mixing a total sample size of 0.375 g of PMC, comprising (αTCP: phosphoserine): 0.3 g:0.075 g (27% mole); 0.2325 g:0.1425 g (50% mole); 0.1575 g:0.2175 g (70% mole); 0.0563 g:0.3188 g (90% mole); with 75 uL of deionized water (liquid to powder ratio of 0.2 mL·g −1 ). All samples were prepared at 22.1 • C, in 30% relative humidity (ambient conditions). After mixing with a spatula for 25-30 s, or a cap shaker (ESPE Capmix; 3M ESPE AG, Seefeld, Germany) for 2 s, 0.1 g was applied to each cube surface, and the cubes were fixated with an applied force (3 N or 31 N) for 1 min, 5 min, or 24 h. All shear samples were allowed to cure/set for 5 min at ambient conditions before exposure to a defined curing environment (100% relative humidity, water, or phosphate-buffered saline (PBS)) for 24 h, at 37 • C, unless otherwise indicated. PMMA (shear) samples were prepared per the manufacturer instructions; briefly, 400 mg of powder and 200 uL of liquid were mixed manually for 25 s, and 0.15 g was applied to the cube surface. Each sample was fixated with universal grips (31 N) and cured for 5 min in ambient conditions, before transferring to cure in PBS for 24 h, at 37 • C.
The fixation force, during curing, was applied via Cocraft universal spring grips (Clas Ohlson, Uppsala, Sweden) with an average grip force of 31 N, or with 300-g weights (3 N). The average grip force of 16 individual grips was measured with a Futek UB250 button load cell (250 N max load). The average bond thickness was calculated by measuring the height of each four corners of the test cubes with digital calipers. Each metal cube was etched with a cube number for tracking purposes. To determine the average thickness of the adhesive bond (t ave ): the total height of each of the four corners of the glued cube pair (h 1-2 ) was measured and the height of each individual corner was subtracted (e.g., for a pair of glued cubes, 1 (h 1 ) and 2 (h 2 ), the height of the 1st (h 1 ) corner of the top cube, and the opposing 4th (h 4 ) corner of the bottom cube were measured) (Equation (1)).
The sum of the measured bond thicknesses at each corner was averaged. One of the four surfaces, adjacent to the bond line, was etched to orient each cube pair. The bond skew (k) was calculated by normalizing the difference, between the thickest and thinnest bond, to the average bond thickness for a given sample (Equation (2)), where the average thickness is as follows: After testing, each cube surface was cleaned with 0.5 M citric acid (5 min, sonicated), followed by washing with deionized water (5 min, sonicated). All raw data images were rescaled to 600DPI resolution using Gimp software.

Mechanical Testing
Shear testing was conducted on an AGS-X mechanical testing machine (MTS, Shimadzu Europa Gmbh, Duisburg, Germany). The cubes were fixated in a custom designed shear rig, and a shear force was applied at a displacement rate of 1 mm·min −1 , with a 5-kN load cell (Shimadzu Europa Gmbh, Duisburg, Germany). The peak force at failure was recorded for each sample. Since the dimensions of bone cubes varied due to cutting technique, the obtained shear force was normalized to the average surface area, for each group.

Failure Analysis
The failure mode was assessed semi-quantitatively by manual scoring, and qualitatively by scanning electron microscopy (SEM). Failure scoring was based upon the percentage of the cube surface coverage, with the least amount of adhesive remaining attached after testing [19]: 0% surface coverage scored as "1" (adhesive failure-the adhesive layer remained unbroken, attached to only 1 surface); 0% < x < 100% surface coverage (mixed mode failure involving adhesive failure at the adhesive/cube interface (adhesive zone) and cohesive failure within the adhesive layer) scored as "2"; a combination of adhesive and cohesive failure, where these failure types occupied distinct regions, hereafter referred to as "combined mode" failure, scored as "3", or 100% (purely cohesive failure-the adhesive layer failed leaving adhesive on both surfaces, while adhesive failure was not observed) scored as "4". The selected samples from each group were investigated with SEM (Merlin field emission microscope, AB Carl Zeiss, Stockholm, Sweden), with a secondary electron in-lens detector, an acceleration voltage of 3 keV, and a 195-pA current. The SEM samples were dried for 24 h in ambient conditions, and were not sputter coated.
Linear regression was evaluated using the linear regression and general linear model procedure in SPSS. In the first linear regression, all samples were repetitions of a single formulation of 27% PMC, tested under varied curing and handling conditions (groups #1-13). The dependent variable was "shear strength", and the fixed factors were "cure type", "grip force", "grip time", and "mix method". The following factors were added as covariates, stepwise, to evaluate whether their inclusion improved the linear regression: "average thickness", "unevenness (abbreviated as "skew")", "failure mode", and "application time". A second linear regression was conducted on different formulations (27-90% PMC, groups #3, 13-21), with the dependent variable "shear strength", and the fixed factors "cure type", "grip time", and "formulation". The following factors were added as covariates, stepwise, to evaluate whether their inclusion improved the linear regression: "average thickness", "unevenness (skew)", "failure mode", and "application time". The significance criteria were set at p = 0.05. Heteroskedasticity was evaluated with White's test.

Results
An overview of the experimental design is shown in Figure 1. Preliminary testing identified a number of factors, and covariates, that could contribute to the adhesive strength after curing for 24 h ( Table 1). The assignment of each factor or covariate, for each group, is shown in Table A1.

Material Characterization
The average particle size and composition of synthesized αTCP is shown in Table 2. The average particle size and purity were comparable to materials used in prior PMC studies [9].

Surface Roughness of Test Cubes
Two different types of cubes were used for shear testing: steel cubes (US #80 grit) were used for linear regression modeling, and aluminum cubes polished with different grit silicon carbide (US #80, 320, or 1200 grit) were used to evaluate how surface roughness affected shear strength. Preliminary testing revealed that identical values for roughness were obtained for high (50x lens) and medium (10x lens) magnification profilometer surface measurements (n = 6, p = 0.803, T-test). All subsequent measurements were made using a wide field of view (10x lens and 0.5x field of view). Representative 3D roughness profiles are shown for steel cubes in Figure 2A, and for aluminum cubes in Figure 2B-D (images A-D, F, and G represent the total field of view of 1.681 mm × 1.681 mm). A macroscale and profilometer light image of a steel cube surface is shown in Figure 2E,F. The two-dimensional roughness measurement (R a ) of a single field, from each group, is shown in Figure 2G (note that the absolute values of each aluminum R a have been shifted, consecutively, by 15 µm to allow for comparison). The average surface roughness (S a ; R a ) of four regions, from three separate steel or aluminum cubes in each group, is shown in Table 3. The difference in roughness between each aluminum group was statistically significant (ANOVA p < 0.001; Steel 80 g vs. Aluminum 80 g and 320 g, Games-Howell p < 0.001; Aluminum 80 g vs. 32 0 g vs. 1200 g, Games-Howell p < 0.024; Levene's test p = 0.005), while the intragroup differences between the average surface roughness within the steel cube group were not significant (ANOVA p = 0.882; Levene's test p = 0.886).

Effect of Curing/Handling Conditions on PMC Adhesive Strength
The curing environment did not affect the adhesive strength of PMC. The average shear strength after 24 h was comparable in humid, aqueous, and saline conditions ( Figure 3A, groups #1-6 means: 2.44, 2.77, 3.00, 2.63, 2.71, 2.75 MPa; p = 0.475 ANOVA; Levine p = 0.046), regardless of whether samples were held together with universal grips (31 N) for 5 min before curing (red box) or for the entire cure period (24 h, blue box). The applied grip (fixation) force (31 N vs. 3 N), the duration of gripping (1 min, 5 min, or 24 h), and the mixing method (manual mixing or high speed mixing) only significantly affected the adhesive strength when comparing the conditions that produced optimal strength (e.g., group #3, PBS, 24-h grip at 30 N, manual mixing), to lower grip force, or to shorter grip duration ( Figure 3B   (A) Different curing environments (phosphate-buffered saline (PBS), water, or 100% humidity) and grip duration (24 h, blue box; or 5 min, red box) before curing did not affect the adhesive strength of 27% PMC (from left to right: groups #1, 4, 2, 5, 3, 6). (B) When the grip duration was shortened and the grip force reduced to mimic clinical conditions, comparable adhesive strength was observed in all samples except the automated mixing sample (red border) and low grip force (3 N) samples gripped for 5 min (from left to right: groups #3, 9,6,10,7,11,8,12,33,34; the red border indicates high speed mixing; green border indicates bone samples). (C) Different mole ratios of phosphoserine to αTCP, and cure conditions, affected adhesive strengths (from left to right: groups #3, 14, 15; 19-21; 13, 16-18) (100% humidity samples were gripped for 1 min). (D) Adhesive strength of PMMA, 27%, or 90% PMC, to aluminum cubes with different surface roughness (gripped 1 min). All samples were prepared by hand mixing, gripped (31 N) for 24 h in PBS, using 27% PMC, unless otherwise indicated. Box plots represent the mean (midline), 75th (top box), and 25th percentile (bottom box), while whiskers represent the highest and lowest values in each group. Statistical comparisons made in 3C between different formulations, with an identical cure condition, are indicated by black brackets; while comparisons made between different cure conditions with identical formulation are indicated by colored brackets matching the group color in the legend (e.g., 70% PMC compared between PBS vs. PBS + H3PO4 vs. humid, pink bracket). In Figure 3C, within each cure condition, comparisons were made between the mean of 50% PMC and all other formulations. Comparison between group means were conducted with ANOVA (Tukey or Games-Howell post hoc analysis, for samples with homogeneous, or inhomogeneous variance), with * indicating p-values below 0.05, and ** indicating p-value below 0.01. These results are in good agreement with prior studies on PMC [9][10][11], where universal grips (a 31-N applied load) were applied for 24 h to achieve a consistent, thin adhesive layer. In contrast, a 3-N applied load, particularly for short times (less than 5 min), represents the approximate force applied by a surgeon during an actual reconstructive surgery. Considering the varied test conditions, there was no clear trend indicating that higher grip force, grip duration, curing method, or mixing method consistently altered the adhesive strength. Interestingly, identical adhesive shear strength was obtained on polished steel surfaces and unpolished bone ( Figure 3B,  Since the group means were comparable regardless of test conditions ( Figure 3B), the molar ratio of the amino acid to calcium phosphate was varied to produce PMCs with a range of adhesive strengths [10]. When cured in PBS, the adhesive strength declined sharply for formulations with >50% mole % ( Figure 3C, red box and brackets). The failure mode included cohesive failure (Section 3.4) and granular, which suggested an incomplete curing reaction, or washout of phase(s) containing the amino acid. The setting time was determined by the amino acid content, with 27% PMC curing within 4 min, and >50% PMCs taking >15 min to set. It should be noted that the "initial setting time" (Gilmore needle) may not be the most appropriate measure of PMC curing. Since PMCs display properties of both ceramics and polymeric adhesives, it is unclear which method should be used to determine the curing time. In order to distinguish between poor adhesive strength due to setting related effects (e.g., washout or incomplete curing), or due to a true reduction in adhesiveness (e.g., altered wetting properties, or chemistry), the sample formulations were retested with an accelerator (25% wt% H 3 PO 4 in place of the liquid). The setting time was reduced, and this second set of samples was cured in ambient conditions for 15 min, rather than 5 min to prevent washout, before exposure to PBS.  These results suggest that the curing environment can affect adhesive strength of PMCs when the amount of amino acid is excessive (>50%), or when the formulation cures too slowly, or incompletely (washout).

Effect of Surface Roughness on PMC Adhesive Strength
A separate set of shear samples (PMMA, 27%, or 90% PMC) were prepared on aluminum cubes ( Figure 3D) with differing levels of surface roughness (Table 3). Palacos PMMA, a biomaterial approved by the food and drug administration (FDA) for augmentation of orthopaedic devices, was used as a material control. Since the mechanism underlying PMMA adhesion to metal surfaces is expected to be similar for PMCs (physical bonding and Van der Waals forces [37]), we hypothesized that similar (e.g., a decrease in shear strength with increased surface roughness) trends would be observed for both materials. Palacos was noticeably tacky during mixing, similar to PMCs. The bond strength of PMMA to metal was expected to range from 4-10 MPa [38,39], roughly 1 to 2 times as strong as PMCs. Palacos produced an average shear strength of 7.04 MPa on the roughest (2.17 µm), and 4.44 MPa on the smoothest (1.27 µm) surfaces, respectively. The average shear strength decreased with decreasing roughness only for PMMA samples ( Figure 3D, group #24 vs. 25  Adhesive failure is often attributed to the presence of defects, and lower bond strength adhesives are expected to be more sensitive to defects. Therefore, we hypothesized that a low strength formulation (90% PMC) might be more sensitive to surface roughness. When comparing between different formulations of PMC, with significantly different adhesive strength, the failure mode is expected to shift from adhesive to cohesive failure as the adhesive strength decreases. Indeed, this was the case in the present study ( Figure 4). However, regardless of failure mode, the adhesive strength was not affected by surface roughness (Figure 3D, group #27 vs. 28 and 29, 30 vs. 31 and 32; p > 0.167, p > 0.999; Games-Howell). Collectively, these results suggest that PMCs are relatively insensitive to surface roughness.

Failure Mode Analysis
The observed failure modes (Figure 4, Figure 5(A1-A4)) included: (a) purely cohesive failure (100% of both surfaces covered with adhesive), (b) pure adhesive failure (0% of one surface covered with adhesive), (c) mixed mode failure (no overlapping regions of cohesive failure, but adhesive remained on both surfaces), and (d) combined mode failure, a unique form of mixed mode failure where adhesive and cohesive failure occurred distinctly, in separate regions within the adhesive layer [17]. An increase in amino acid content changed the failure mode from adhesive failure towards predominantly cohesive failure ( Figure 4A). When comparing between different strength formulations of PMC ( Figure 4B-D), the failure mode correlated with the adhesive strength, and cure conditions; higher strength formulations (27%-50% PMC) failed by adhesive and mixed mode failure, while weaker formulations (>50% PMC) failed via cohesive and combined failure modes. H 3 PO 4 accelerated the setting time and altered the failure mode towards adhesive failure in the 70% PMC formulation ( Figure 4C), suggesting that the low shear strength of formulations with excess amino acid may reflect incomplete curing or washout-related effects.  Figure 5C cohesive failure, Figure 5E combined mode failure), revealed that these failure modes reflected washout (organic phase was missing, leaving behind granular particles), and aberrant curing. An organic surface layer ( Figure 5E, inset image, organic layer "OL"), which wetted and adhered to surfaces, was often found attached to the adherend surface at points of failure ( Figure 5D), though small areas, where the organic layer remained bound to the adhesive bulk, were visible at the adhesive failure interface ( Figure 5E, red arrows). In cases of adhesive failure, and mixed mode failure, the interface between the surface layer and the bulk often failed at leaving behind fragments attached to both the metal surface and adhesive layer ( Figure 5D, high magnification image of organic layer shown in inset). The surface of the fractured adhesive layer, in cases of adhesive and mixed mode failure, appeared amorphous ( Figure 5E inset image of fracture cross section), while cohesive and combined mode failure samples (low strength PMC) displayed granular, unreacted calcium phosphate particles.
In moderate-strength ( Figure 4. While the surface layer appeared amorphous and organic, prior studies have identified that the surface of PMC is actually mineralized with nanoscale, disordered calcium phosphate [10]. In most cases of adhesive and mixed mode failures, failure occurred at the interface between the organic surface layer and the bulk of PMC (adhesive zone). A close visual inspection revealed that: (a) predominantly, the organic surface layer remained bound to the surface of the opposing metal cube, rather than bound to the adhesive layer ( Figure 5E, red arrows); and (b) both the surface and underlying bulk layer of PMC display topography matching the surface features of the opposing cube ( Figure 5E, red arrows). It is likely that both the surface layer and limited portions of the PMC bulk engage in physical bonding (mechanical inter-digitation) with the opposing adherend surface.
Collectively, the mechanical test and failure mode analysis suggest that: (a) PMCs with a low shear strength (>1 MPa) typically fail cohesively, suggesting the limited cohesive strength prevents an evaluation of the true adhesive strength in these samples; (b) PMCs with strengths between 1-2 MPa failed via a mixture of adhesive and cohesive failure modes, suggesting that failure did not arise exclusively from the adhesive zone layer, and that the observed shear strength did not reflect the true adhesive strength; (c) PMCs with strengths above 2 MPa failed via purely adhesive, and mixed mode failure, suggesting that failure is occurring in the adhesive zone layer and internally (cohesive), and that the true adhesive strength of PMC is within this range (2-4 MPa); (d) some PMC formulations (e.g., high amino acid containing formulations) produce different adhesive strengths depending upon handling and curing conditions, therefore multiple conditions should be evaluated to confirm the true strength is measured, with 100% humidity recommended; (e) considering that washout and curing properties are critical, and may not be obvious until after adhesive testing is completed (e.g., failure mode analysis), laboratory testing in 100% humidity rather than liquids is recommended; and most importantly, (f) though there appeared to be a relationship between failure mode and the adhesive strength, high strength PMC formulations (27-50%) were equally insensitive to surface roughness as lower strength PMC (70%-90%), suggesting that the true (theoretical) adhesive strength of PMC may reflect the wetting and bonding properties of the organic surface layer, while the observed (laboratory) adhesive strength reflects the likelihood of failure outside the adhesion zone layer (e.g., at the interface between the surface and bulk of PMC, or within the bulk in cases of cohesive failure).

Scatter Plot Analysis
The following factors were controlled in this study: surface roughness, curing conditions, grip force, grip duration, PMC formulation, and mixing method. The following covariates (uncontrolled factors) were recorded for each sample: application time, average bond thickness, the thickest bond, or thinnest bond thickness, bond unevenness (difference between the thickest and thinnest bond, normalized to the average bond thickness for the sample), and the failure mode ( Table 1). The correlation strength between each individual factor and the outcome measure (adhesive strength), was explored in scatter plots, with replications of a single formulation of PMC ( Figure 6A-D, n = 242 total, n = 12 or 36 per group, 27% PMC, groups #1-13), or a series of PMC formulations with differing amounts of phosphoserine ( Figure 6E-H, n = 12 or 36 per group, 27-90% PMC, groups #3, [14][15][16][17][18][19][20][21]. The coefficient of determination (R 2 ) was less than 0.25 for all continuous variable scatter plots ( Figure 6A-D, 27% PMC, groups #1-13), comparing shear strength to: application time ( Figure 6A), average bond thickness ( Figure 6B), the thinnest (red) and thickest (black) bond ( Figure 6C), and bond unevenness ( Figure 6D). No trend was obvious in the sample mean distribution using categorical scatter plots for: cure type, grip force, grip time, or mixing method (data not shown). A second set of scatter plots (aggregated) evaluated the relationship between different strength PMC formulations ( Figure 6E-H, n = 12 or 36 per group, 27%-90% PMC, groups #3, [13][14][15][16][17][18][19][20][21], and: application time ( Figure 6E), average bond thickness ( Figure 6F), the thinnest (red) and thickest bond ( Figure 6G), and bond unevenness ( Figure 6H). A number of studies have investigated the relationship between bond thickness and adhesive strength, with some reporting similar results (poor correlation) [33,34,40], a positive correlation [23,41], or a negative correlation [21,42]. The downward trend between bond thickness and adhesive strength suggests that the average shear strength of PMC decreased with increasing bond thickness (Y = −2.7772x + 3.2501) at a rate of approximately −8.54% per an increase in bond thickness of 100 um (R 2 = 0.218) assuming a linear relationship. It is likely there are other factors not explored in this study that may account for the remaining, unexplained variability.

GLM, Linear Regression
A stepwise linear regression model revealed that: (a) the correlation between shear strength and the fixed factors "cure condition", "grip force", "grip duration", and "mixing method" was poor (R 2 = 0.069), in agreement with the scatter plot analysis; (b) the inclusion of the following covariates, stepwise in separate "blocks", improved the correlation model: average bond thickness (R 2 = 0.273), unevenness (R 2 = 0.282), and failure mode (R 2 = 0.308). The selected factors were used in a general linear model and the following factors were significant contributors (p < 0.05) to the model accuracy: average bond thickness and failure mode (Table 4, model significance p < 0.001, Whites test p = 0.590). This model was built using replications of a single formulation of PMC (Table 4, n = 242 total, n = 12 or 36 per group, 27% PMC, groups #1-13). Three covariates were excluded from the linear regression model, "application time", "thickest bond thickness" and "thinnest bond thickness", because they were collinear with other factors. The second regression model was built using different formulations (phosphoserine mole %) of PMC (Table 4, n = 142 total, n = 12 or 36 per group, 27%-90% PMC, groups #3, [13][14][15][16][17][18][19][20][21]. A stepwise linear regression model revealed that: (a) the correlation between shear strength and the fixed factors "cure condition", "grip duration", and "formulation" was weak (R 2 = 0.216); (b) inclusion of the following covariates, stepwise in separate "blocks", improved the correlation model: average bond thickness (R 2 = 0.237), unevenness (R 2 = 0.243), and the failure mode (R 2 = 0.377). The selected factors were used in a general linear model and the following factors were significant contributors to the model accuracy: average bond thickness, formulation, and the failure mode (Table 4, model significance p < 0.001, Whites test p = 0.106). Three covariates were excluded from the linear regression model, "application time", "thickest bond thickness", and "thinnest bond thickness", because they were collinear with other factors.
The results of linear regression analysis suggest that: (a) the various curing conditions, grip force and grip duration, and the mixing method were not significant predictors of adhesive shear strength; (b) variations in the adhesive strength of PMC are correlated with the bond thickness; and (c) adhesive strength was strongly correlated with the failure mode.

Discussion
The purpose of this study was (a) to identify which factors contribute to adhesive strength in PMCs, and (b) to bridge disparate test conditions, thereby allowing for comparisons/predictions on how PMC formulations behave in both the laboratory and the clinic. In the present study, we have shown that PMC is relatively insensitive to the adherend surface properties (consistent average strength of 2-3 MPa, and minimal strength of 1.5-2 MPa, on metals and bone over a range of 1.27-2.17 µm). Surgeons are more concerned with the minimal strength of an adhesive since premature failure or poor bonding can impair healing or lead to secondary injury. In the clinic, an adhesive must perform consistently in challenging physiological environments, on uneven surfaces, and when the surgeon cannot ensure a thin adhesive layer. Uneven bond lines can lead to stress concentration, and multi-mode loading (bending, tension and shear), which is known to produce shear strengths that do not correlate with bond thickness [42]. We have shown that PMCs are not affected by uneven bond lines and adhere with comparable strength to steel, aluminum, and cortical bone surfaces.
Of the factors investigated, the average bond thickness and amino acid content were the strongest predictors of adhesive strength. The dependence of adhesive strength on bond thickness has been studied extensively, though the optimal bond thickness and benefits of thicker, or thinner bonds, appear to be relative to each individual adhesive material [17][18][19]23]. While bond thickness is a critical determinant of structural adhesive strength, tissue adhesives, such as dental resins show poor correlations [33]. PMCs with a range of adhesive strengths have been created, previously, by varying the amino acid content [8,10]. We now extend those findings to include test conditions that mimic the clinic, and conditions that are conducive to exploratory, mechanistic testing (e.g., 100% humidity) [30]. In ongoing/future studies, a library of alternative amino acids, organic analogues, or synthetic analogues will be used to explore the mechanisms underlying adhesion, and how amino acid chemistry affects the adhesive strength and the interaction between the organic and inorganic phases in PMCs. The present work represents a necessary precursor to these ongoing studies by: (a) establishing how PMC behaves in conditions that minimize confounding effects (e.g., mixing method, washout resistance, etc.), and (b) providing a large dataset of variability in adhesive strength for subsequent power analysis, of the required sample size, to identify differences in adhesive strength due to varied chemistries.
Perhaps most importantly, we have identified a previously unrecognized source of interfacial failure that occurs in PMCs. Prior studies have suggested that the failure mode correlates poorly with adhesive strength for adhesive-and mixed-mode failure because failure can arise from multiple sources [34,40]. Even when the adhesive strength is significantly greater than the cohesive strength, if defects are present, interfacial stress concentrates within the bulk, or normal forces (bending) occur, a strong adhesive can fail cohesively [19]. In the present study, the failure mode strongly correlated with PMC adhesive strength, with high-adhesive-strength PMCs (>2 MPa) failing adhesively (including mixed mode failures), and low adhesive strength PMCs (<1.5 MPa) failing cohesively (including combined mode failures). The change in failure mode appeared to reflect an increase in the cohesive strength (high amino acid %, low adhesive strength PMCs did not cure completely), rather than changes in the adhesive strength. As the bulk strength increased, crack/failure initiation shifted from the bulk, to the next weakest phase: the interface between the surface layer (adhesive zone layer) and the bulk of PMC [21,37,43]. Since failure occurred primarily at the interface between the adhesion zone layer and PMC bulk, and since high-and low-strength PMCs were insensitive to surface roughness, we hypothesize that higher adhesive strengths might be obtained by strengthening interpenetration and bonding between the surface and the bulk layers of PMC. Strengthening the dissipative matrix is a common approach to improve the toughness and adhesive strength [36,37,44]. Additional studies are needed to confirm these results, quantitatively, and to investigate the nanoscale properties of the surface layer of PMC.
There are a number of factors that are likely to impact adhesive strength that were not investigated in the present study (e.g., curing temperature). It should be noted that select tissues have low oxygen content, particularly cartilage. While PMCs have shown good bond strength to such tissues ex vivo [10], additional testing is needed to confirm whether the adhesive effect or setting reactions are affected by hypoxia. The predictive power of the linear regression model (R 2 = 0.358) and single factor correlations (R 2 = 0.218) was quite low. As a result, roughly 70%-80% of the variability in adhesive strength remains unexplained.
While the present study sought to predict the behavior of PMC on tissues, large variability in the surface properties, sample preparation (e.g., cutting with band saw, polishing, etc.), and tissue architecture (variation between regions of the bone, within and between different animal tissue sources, etc.) could easily obscure the correlation results. Therefore, in the present study, metal samples were used to ensure control of the surface properties and the reproducibility of the testing methods and results. In the present study, the use of proteins was also avoided (e.g., fetal bovine serum in the curing liquid). Despite rigorous surface cleaning methods, proteins are difficult to remove completely, and leftover proteins can affect how the surface of the adhesive orients, nucleates, and bonds to the surface of the metal cube. Protein was also avoided, as a possible source of variation, because the correlation model developed in the present study would require duplication of a large number of samples, to account for the effects of protein on the correlation model. It should be noted that protein-rich bone cubes were used in the present study, and comparable bond strengths were obtained, compared to metal cubes. In future studies, the adhesive strength should be tested in actual physiological liquids (e.g., human plasma) and on live tissues (in vivo) to identify the reliability, and variations in adhesive strength following actual clinical use.