Designing Biomimetic 3D-Printed Osteochondral Scaffolds for Enhanced Load-Bearing Capacity

Abstract

Osteoarthritis is a debilitating chronic joint disorder that affects millions of people worldwide. Since palliative and surgical treatments cannot completely regenerate hyaline cartilage within the articulating joint, osteochondral (OC) tissue engineering has been explored to heal OC defects. Utilizing computational simulations and three-dimensional (3D) printing, we aimed to build rationale around fabricating OC scaffolds with enhanced biomechanics. First, computational simulations revealed that interfacial fibrils within a bilayer alter OC scaffold deformation patterns by redirecting load-induced stresses toward the top of the cartilage layer. Principal component analysis revealed that scaffolds with 800 μm long fibrils (scaffolds 8A–8H) possessed optimal biomechanical properties to withstand compression and shear forces. While compression testing indicated that OC scaffolds with 800 μm fibrils did not have greater compressive moduli than other scaffolds, interfacial shear tests indicated that scaffold 8H possessed the greatest shear strength. Lastly, failure analysis demonstrated that yielding or buckling models describe interfacial fibril failure depending on fibril slenderness S. Specifically for scaffolds with packing density n = 6 and n = 8, the yielding failure model fits experimental loads with S < 10, while the buckling model fitted scaffolds with S < 10 slenderness. The research presented provides critical insights into designing 3D printed interfacial scaffolds with refined biomechanics toward improving OC tissue engineering outcomes.

Impact statement

The research presented in this manuscript highlights various 3D-printed biomimetic osteochondral interface scaffold designs and fabrication strategies involving computational simulations. The long-term goal of this work is to aid in developing a biomimetic 3D-printed osteochondral scaffold with enhanced load-bearing and regenerative properties that recapitulate the unique osteochondral structure/composition within the knee joint.

Introduction

Osteoarthritis induces pain and reduced movement in over 300 million people worldwide.¹ The resulting osteochondral defect (OCD) from osteoarthritis significantly diminishes patient quality of life.² Diagnosing and treating OCDs early improve a patient's prognosis while preventing OCD injury.³ While palliative and surgical treatments exist to repair OCDs, these options have not demonstrated the capacity to fully regenerate osteochondral (OC) hyaline cartilage.⁴

Tissue engineering is a promising avenue that may provide clinical strategies to repair OC defects. By combining cells, scaffolds, and biomolecules, tissue engineering introduces prospects to regenerate damaged OC tissues without autografting.⁵ Various strategies have been investigated to engineer OC scaffolds.^5,6 However, progress in fabricating OC scaffolds that capture its physiological load-bearing properties remains limited.⁷ As the orthopedic community aims to loosen postoperative rehabilitation guidelines, it is critical to design scaffolds that integrate mechanically stable OC bilayers.⁸ Poor integration of artificial cartilage and bone within engineered OC scaffolds will lead to delamination and failed tissue regeneration.^9,10

To design an OC scaffold, layer-specific structural and biomechanics must be recapitulated. The OC unit has a hierarchical structure consisting of articular cartilage, calcified cartilage, and subchondral bone.¹¹ This composite system has distinct biomechanical properties facilitating load transfer during joint articulation.¹² Of particular interest is that the calcified cartilage functions as an interface connecting articular cartilage to subchondral bone.¹³ This region is distinguished by a thin basophilic border called the tidemark.¹¹ The primary function of calcified cartilage is to transfer load into the subchondral bone.⁴ Structurally, vertically laden collagen fibers originate from the calcified zone that runs through the tidemark and extends into noncalcified cartilage. The undulating pattern provided by the tidemark is suggested to aid in shear resistance.¹⁴ Ultimately, the calcified cartilage is a requisite structure to help transfer and distribute mechanical loadings between the uncalcified cartilage region and the subchondral bone during joint articulation.^15,16

The research presented here focuses on designing a biomimetic OC scaffold with superior load-bearing properties. Our laboratory recently investigated three-dimensional (3D) bioprinting an interface using extrusion 3D-printing and found that few bioinks mimic OC tissue.¹⁷ This study aimed to fabricate a biphasic OC scaffold with enhanced load-bearing properties at the interface by incorporating 3D-printed fibrils. We hypothesized that incorporating fibrils to integrate the cartilage and bone layers will improve compressive and shear strengths within a 3D printed biphasic scaffold. To this end, we first simulated how compressive and shear forces affect an OC scaffold interface through computational modeling. We then reduced the dimensionality of our simulation data using principal component analysis (PCA) to elucidate how OC scaffold design alters mechanical properties. Biphasic OC scaffolds were printed with various interface patterns and subjected to compressive and interfacial shear tests to determine their agreement with simulation data.

Lastly, we performed a failure analysis of the interface fibrils undergoing compression and determined the best-fit failure model. The results from this study provide valuable insights into the biomechanics within biphasic OC scaffolds and the design of interface regions to enhance the regenerative outcomes of OC scaffolds.

Materials and Methods

Computational modeling

A 3D stationary solid mechanics model was developed using COMSOL Multiphysics Version 5.6 (COMSOL, Burlington, MA). We assessed how compression and shear affect OC scaffolds with a biomimetic interface. Three distinct structures were generated: (1) a bone layer with a 400 μm pore size; (2) cylindrical fibrils along the scaffold interface; and (3) casted cartilage. Interface fibrils integrate the cartilage and bone layers while recapitulating the OC calcified cartilage region (Fig. 1A). Twenty-eight different interface patterns were devised by varying the interface layer height, interface fibril diameter, and fibril packing density (Table 1). Two custom materials (with Poisson's ratio ν, density ρ, and Young's modulus E) were applied to their respective domains. COMSOL simulated either vertical compressive or lateral shear forces during articulation (Fig. 1B).^18,19 The materials were assumed to be homogeneous and isotropic, and linear elastic material behavior was assumed across the entire domain.

FIG. 1.

(A) The OC unit possesses a hierarchical structure comprising articular cartilage, calcified cartilage, and subchondral bone. The calcified cartilage region serves as the interface connecting the articular cartilage and subchondral bone through vertically laden collagen fibrils. Therefore, the geometry of the OC scaffold was designed to recapitulate collagen fibrils in the calcified cartilage region. (B) The boundary loads applied to the OC scaffolds were representative of the maximum physiological loads experienced by human knee joints, while a fixed constraint was applied to the bottom surface of the scaffold. A factorial study was designed to examine the effect of the interface layer height, interface fibril diameter, and interface fibril packing density on the biomechanics of the OC scaffolds. Twenty-eight different interface patterns were examined with the 3D stationary solid mechanic's model. The simulations assessed the stress and deformations experienced by the interface fibrils and the cartilage layer when subjected to the boundary load. The parameters and values selected for the 3D solid mechanics simulations of the OC scaffolds. 3D, three-dimensional; OC, osteochondral.

Table 1.

All Experimental Groups of the 3 × 3 × 3 Factorial Study on Osteochondral Interface Designs

Experimental groups	Layer height	Fibril diameter	Fibril packing density
C0	0 μm	0 μm	0 × 0
4A-C	400 μm	400 μm	6 × 6, 8 × 8, 10 × 10
4D-F	400 μm	600 μm	6 × 6, 8 × 8, 10 × 10
4G-I	400 μm	800 μm	6 × 6, 8 × 8, 10 × 10
8A-C	800 μm	400 μm	6 × 6, 8 × 8, 10 × 10
8D-F	800 μm	600 μm	6 × 6, 8 × 8, 10 × 10
8G-I	800 μm	800 μm	6 × 6, 8 × 8, 10 × 10
16A-C	1600 μm	400 μm	6 × 6, 8 × 8, 10 × 10
16D-F	1600 μm	600 μm	6 × 6, 8 × 8, 10 × 10
16G	1600 μm	800 μm	6 × 6, 8 × 8, 10 × 10

The bottom surfaces of the geometry were set as fixed constraints, while a horizontal boundary load of 3.0 MPa and/or vertical boundary load of 50.0 MPa, respectively, was applied to the top surface boundaries of the model (Fig. 1A).^20–22 The element size for the physics-controlled mesh was set to normal, which resulted in 188681 tetrahedral elements of the solid mesh. The results were used to map the first and third principal stresses (P1 and P3), von Mises stress, and displacement of the scaffolds. The convergence of all finite element analysis (FEA) simulations was defined by establishing a minimum relative tolerance value (0.001) that must be larger than the estimated error in each iteration. Error was estimated by solution-based or residual methods (residual factor: 1000), taking the minimum error value between the two techniques and comparing it to the set relative tolerance value. If either error is smaller than the relative tolerance, iterations are terminated.

Principal component analysis

PCA biplots were produced from the simulation data using R programming language (R 4.2.2). Data generated by the cartilage layer undergoing compression or shear formed into matrices consisting of values for each interfacial displacement, Von Mises stress, first principal stress, and third principal stress. The corresponding matrices were decomposed into two principal components to generate a biplot. The PCA biplots consist of loading vectors to convey trends in the predominant stresses applied on OC scaffold interfaces based on altering interfacial layer height, fibril diameter, and packing density.

Fabrication of OC interface scaffolds

A 3D rectangular prism 10.0 mm (length) × 10.0 mm (width) × 4.0 mm (height) with 400 μm strut diameter and pore size was generated in SolidWorks (Waltham, MA). Biomimetic interface fibrils recapitulating fibers in the calcified cartilage layer were added to the top of the 3D printed bone layer. LOCTITE^® 3D MED 413™ (Henkel Corporation), a commercially available resin with appropriate flexural, compressive, and tensile properties, was utilized to fabricate the bone layer with the interface fibrils using an Envision ONE cDLP printer (ETEC). Total 3D print time was ∼30 min. LOCTITE was printed using ultraviolet (UV) light at 5 mW/cm² intensity, with an exposure time of 28 s per 100 μm layer. The printed samples were rinsed with isopropanol to remove excess uncured resin, and the samples were subjected to final curing in a UV flash box (PCA 4000, ETEC) such that structures were exposed for 2000 flashes at 10 flashes per second using 150 W light power.

To prepare the bilayer OC scaffolds, medical grade silicone elastomer (Factor II, Incorporated) was mixed with its associated crosslinker at a 10:1 ratio by weight before being cast on top of the 3D printed bone layer and cured overnight at 37°C. Mechanical tests were subsequently performed on the fully fabricated OC scaffolds to determine the shear and compressive strength at the interface layer.

Mechanical studies

The compressive strength of the OC scaffolds was determined immediately after preparation at room temperature on an Instron 5942 mechanical tester (Instron, Norwood, MA) at a constant compressive displacement rate of 10 mm/min, with a preload of 0.001 N (strain = 0). The modulus was calculated from the linear region of the stress–strain curve between 0% and 30% strain.

The interface integration of the OC scaffolds was tested utilizing a special adaptor attached to an Instron universal testing machine, like the design used by Zhang et al.¹⁰ The adaptor helped position the 3D printed subchondral bone layer into a space geometrically analogous to an OCD. All tests (n = 5 samples/group) were performed at a rate of 1 mm min⁻¹. The peak load at failure was defined as the highest point of the first perceived peak of the force–displacement curve. The interfacial shear strength was calculated using the peak shear load at failure divided by the total area of the square substrate.

Lastly, the failure load of the interface fibrils was extracted from the load–displacement curve of each printed scaffold type and compared with the theoretical failure loads from yielding or buckling behavior. Failure load from yielding (F_y) is computed as:

Where S_y is the yield strength of LOCTITE 3D MED 413, A is the total fibril area under compression, n is the packing density of the interface fibrils read as n × n, and d is the diameter of each fibril. Buckling failure is assessed by:

$$F_b=E{n}^2\frac{{\pi }^{2}I}{{\left(kh\right)}^2}$$ (2)

Where E is the elastic modulus, I is the moment of area of the fibrils normal to the compressive load, h is the height of each fibril, and k is the effective length factor. We take k = 2, indicating the fibrils are under fixed-free conditions. We also take each fibril to have a circular cross-section, giving . This results in an expanded expression for F_b:

$$F_b=E\frac{n^2{\pi }^3}{16}\frac{{\left(\frac{d}{2}\right)}^4}{h^2}$$ (3)

To assess the error associated with 3D printing each structure, we incorporated a value $\delta$ such that the nominal diameter d is adjusted to $d\to d+2\delta$. This results in:

and

$$F_b=E\frac{n^2{\pi }^3}{16}\frac{{\left(\frac{d}{2}+{\delta }_b\right)}^4}{L^2}$$ (5)

With ${\delta }_y$ and ${\delta }_b$ corresponding to the defect values associated with the yield and buckling model, respectively. A value of $\delta >0$ indicates that overprinting of the fibrils has occurred while $\delta <0$ indicates that underprinting has occurred.

Statistics

All experiments were conducted with n = 5, and GraphPad Prism was used for all statistical analyses. The resulting datasets were assessed for normality using the Shapiro–Wilk Test. All quantitative assessments were statistically compared using a one-way analysis of variance (ANOVA) test, followed by a post hoc Tukey's test. All tests assumed equal variance and were conducted with 95% confidence intervals (p < 0.05).

Results

Compression simulation with PCA

While computational simulation tools have previously predicted various properties of 3D printed OC scaffolds, more work is required to broaden their use and application in tissue engineering.

During our first simulation, the average displacement and stress values were obtained for all 28 OC interface scaffolds undergoing 50 MPa compressive strain (Supplementary Tables S1 and S2). Figure 2A and B displays representative contour plots used to assess our four measured mechanical properties of interest, namely, average horizontal (y-axis) displacement and stress (von Mises, first principal and third principal). To start, we examined how the cartilage layer of the OC scaffold responded to compression (Fig. 2A). Scaffold C0, our control scaffold with no interface fibrils, experienced the greatest displacement (56.07 mm) and von Mises stress (34.02 MPa) at the cartilage layer with respect to all other OC scaffolds. Moreover, the third principal stress (−54.02 MPa) was most elevated within scaffold C0. When interface fibrils were incorporated into the scaffold design, the scaffolds experienced decreased displacement (1.77 to 41.81 mm) and von Mises stress (3.99 to 28.26 MPa) overall. Additionally, the third principal stress (−2.68 to −0.71 MPa) did not reach the magnitudes exhibited within scaffold C0.

FIG. 2.

Simulation results on OC interface scaffolds experiencing compression. (A) Representative displacement and stress contour plots of the OC scaffold cartilage layer subjected to compressive strain. When interface fibrils extend into the cartilage layer, the stresses and displacement are predominantly focused on the region of the cartilage layer unsupported by the interface fibrils. (B) Representative displacement and stress contour plots of the interface fibrils subjected to compressive strain. Within OC scaffolds with interface fibrils, the fibrils themselves bear most of the impact of the compressive strain. Without the interface fibrils, the stresses and deformation act directly on the bone layer of the OC scaffold. (C) Two principal components were identified to describe most of the biomechanical changes experienced by the cartilage layer upon the compressive strain. (D) Two principal components were identified to explain the biomechanics within the interface fibrils subjected to compressive strain. No statistics were performed for (C) and (D) since the datasets were computationally generated.

We also examined how each interface fibril design responded to compression (Fig. 2B). When interface fibril diameter and packing density were constant, 400 μm height fibril scaffolds (scaffolds 4A–4I) experienced less displacement (0.31–0.64 mm) than scaffolds with 800 or 1600 μm fibril heights (scaffolds 8A–8I and 16A–16I). However, 400 μm fibrils experienced more stresses (von Mises stress: 387.10 to 1630.90 MPa; first principal stress: 194.00 to 843.37 MPa; third principal stress: −986.63 to −241.06 MPa) than their 800 or 1600 μm counterparts.

PCA was carried out, and the results were depicted in biplots. The biplot allows for better visualization of the biomechanical changes occurring within the cartilage layer and interfacial fibrils based on differences in the four measured mechanical properties. The diagrammed principal component space represents a four-dimension mechanical property dataset reduced into a two-dimension principal component space. The principal components, Comp. 1 and Comp. 2, cumulatively capture the greatest data variance, thereby, information arising from the original four-dimension dataset.

Biplots also show loading vectors, which project their magnitude and relationship with other mechanical properties based on their length and angle with other vectors, respectively.

Biomechanical differences within the cartilage layers are described with a biplot (Fig. 2C). The biplot shows that the cartilage layers most affected by displacement and von Mises stress are assembled toward the right half of the biplot (scaffolds C0, 4A, and 4D). Then, the cartilage layer most affected by first principal stress is located toward the bottom right quadrant of the biplot (scaffolds 8I). Lastly, the cartilage layers most affected by the third principal stress congregate toward the biplot's bottom left quadrant (scaffolds 16C, 16F, and 16I).

PCA was also carried out to examine the biomechanical differences of the interface fibril designs (Fig. 2D). In this study, the biplot reveals that the interface fibril designs most affected by displacement are congregated toward the upper third portion of the biplot (scaffolds 16A, 16B, and 16C). The designs most influenced by von Mises stress and first principal stress are localized toward the bottom right half of the biplot (scaffolds 4A, 4B, 8A, and 8B). Lastly, the designs most affected by third principal stress are located toward the left third portion of the biplot (scaffolds 8I, 16H, and 16I).

Shear simulation with PCA

The average displacement, von Mises stress, first principal stress, and third principal stress values were acquired from all simulations involving the 28 OC interface scaffolds undergoing shear strain of 3 MPa (Supplementary Tables S3 and S4). When the OC scaffold possessed no interface fibrils (scaffold C0), the cartilage layer experienced the greatest horizontal displacement (12.20 mm) and von Mises stress (5.41 MPa) at the cartilage layer when compared with all other OC scaffolds (Fig. 3A). Furthermore, the first and third principal stresses (3.12 and −3.11 MPa, respectively) were most elevated within scaffold C0. In comparison, all 27 OC scaffolds with interface fibrils experienced a decrease in displacement (0.69–8.85 mm) and von Mises stress (1.48–4.64 MPa). However, the first and third principal stresses within these scaffolds did not reach the stress magnitudes exhibited by scaffold C0.

FIG. 3.

Simulation results on OC interface scaffolds experiencing shear. (A) Representative displacement and stress contour plots of the cartilage layer subjected to shear. Similar to compression simulations, the stresses and displacement are focused on the region of the cartilage layer unsupported by the interface fibrils. (B) Representative displacement and stress contour plots of the OC scaffold interface fibrils subjected to shear. The interface fibrils within OC scaffolds help distribute some of the stresses away from the cartilage layer of the scaffold. Without the interface fibrils, the shear directly acts on the entire cartilage layer of the OC scaffold. (C) Two principal components were identified to explain most of the biomechanics experienced within the cartilage layer, 89.4% and 10.6%, respectively. PCA results for compression, Scaffolds 8C, 8D, and 8E lie closest to the origin and possess the biomechanics to withstand maximal physiological shear. (D) Two principal components were identified to explain the biomechanics experienced within the interface fibrils, 98.5% and 1.5%, respectively. PCA also indicates that scaffolds 8A–8I possess the targeted biomechanics to withstand shear. No statistics were performed for (C) and (D) since the datasets were computationally generated. PCA, principal component analysis.

We also examined how the interface fibrils responded to shear (Fig. 3B). We found that the scaffold designs with the 1600 μm interface fibrils (scaffolds 16A–16I) experienced more displacement (0.16–1.34 mm) and stresses (von Mises stress: 31.91 to 346.87 MPa; first principal stress: 17.31 to 182.00 MPa; third principal stress: −181.69 to −17.28 MPa) than scaffolds with short interface fibril heights (scaffolds 4A–4I and 8A–8I).

When PCA was performed to understand shear biomechanics within the cartilage layer, two principal components explained the biomechanical events (Fig. 3C). This biplot indicates that the cartilage layers most affected by displacement and von Mises stress are assembled toward the top portion of the biplot. Scaffold C0 was predicted to be most influenced by displacement. For scaffolds with interface fibril designs, scaffolds with 800 μm height interface fibrils (scaffolds 8A–8I) were generally influenced less by displacement than those scaffolds with 400 or 1600 μm height interface fibrils. Then, the cartilage layers most affected by von Mises and first principal stress are located toward the bottom right quadrant of the biplot (scaffold 8I). Lastly, the cartilage layers most affected by third principal stress are congregated toward the top left quadrant of the biplot (scaffolds 16C).

A biplot was generated for the interface fibril simulations, and two principal components were identified to explain the biomechanics experienced within the interface fibrils. The biplot (Fig. 3D) shows that the biomechanical activity within the interface fibril patterns under shear was comparable to how they behaved under compression. The interface fibril patterns most influenced by displacement are congregated toward the upper third portion of the biplot (scaffolds 16A, 16B, and 16C). The designs most influenced by von Mises stress and first principal stress are also toward the bottom right half of the biplot (scaffolds 4A, 4B, 8A, and 8B). Finally, the designs most affected by third principal stress are located toward the left third portion of the biplot (scaffolds 8I, 16H, and 16I).

Compressive modulus and interfacial shear strength of OC interface scaffolds

Based on PCA interpretations, we selected scaffolds 8A–8H for further investigation due to their ability to minimize displacement and maximize von Mises stress, as they are subjected to a relatively balanced amount of tensile and compressive stresses. We fabricated the OC scaffold with a mechanical interlocking interface through digital light processing (DLP) 3D printing and casting (Fig. 4A). All printed scaffolds possessed the 3D printed bone layer, and the cartilage layer was cast on top of the interface fibrils extending from the bone layer, which recapitulates the histological arrangement and dimensions of the OC unit.¹¹ There were significant differences in compressive moduli among the tested OC interface scaffolds between (*p < 0.05; **p < 0.01; ***p < 0.001; *p < 0.0001; Tukey's multiple comparison; n = 5) (Fig. 4B). Specifically, scaffold 16I exhibited the greatest compressive moduli with respect to the 400 and 800 μm high scaffolds (scaffolds 4A, 8A–8I). No statistical difference was found in compressive moduli between scaffolds 16I and C0.

FIG. 4.

Fabrication of OC scaffolds, compression testing, and interfacial shear test on biomimetic OC interface scaffolds. (A) The OC scaffold with a mechanically interlocking interface was fabricated utilizing DLP-based 3D printing and casting. (B) There were significant differences in compressive moduli among the tested OC interface scaffolds between (*p < 0.05; **p < 0.01; ***p < 0.001; *p < 0.0001; Tukey's multiple comparison; n = 5). Scaffold 16I exhibited the greatest compressive moduli with respect to all other OC scaffolds. (C) There were significant differences in interfacial shear strength among the tested OC interface scaffolds between (ns = no significance; ****p < 0.0001; Tukey's multiple comparison; n = 5). Scaffold 8H demonstrated the greatest interfacial shear strength with all other OC scaffolds. DLP, digital light processing.

All OC interface scaffolds were subjected to the shear test, as previously described.¹⁷ There were significant differences in interfacial shear strength among the tested OC interface scaffolds between (ns = no significance; *p < 0.05; **p < 0.01; ***p < 0.001; Tukey's multiple comparison; n = 5) (Fig. 4C). Specifically, Scaffold 8H demonstrated the greatest interfacial shear strength with respect to the other 800 μm high scaffolds (scaffolds 8A–8G, 8I) and the control scaffolds (scaffolds C0, 4A, 16I).

Compressive failure and curve fitting

For scaffolds with packing density n = 6 (scaffolds under A, D, and G) and n = 8 (scaffolds under B, E, and H), the yielding failure model acts as an acceptable fit for the experimental failure load at fibril slenderness values $S<21.33$, whereas the buckling model fits scaffolds with failure loads of $S\ge 21.33$ (Fig. 5A). However, for scaffolds with packing density n = 10 (scaffolds under C, F, and I), the yield model was only appropriate for scaffolds that achieved $S<16$ and $h<1600\mu m$, as the buckling model provided a superior fit for $S\ge 16$ with $h=1600\mu m$. However, scaffolds with $d=800\mu m$ and $h\le 800\mu m$ (4I and 8I) deviated significantly from the yielding model, likely due to overprinting originating from the tight packing density. For all scaffolds, ${\delta }_y∕d$ increased approximately monotonically with diameter (Fig. 5B). The variability of ${\delta }_b$ (maximum: $4.35\mu m$) across fibrils with the same heights was demonstrated to be less compared with ${\delta }_y$ (maximum: $15.35\mu m$) (Fig. 5B, C). Defect values for scaffolds with packing density n = 6 remained mostly below 0% for ${\delta }_b$ and ${\delta }_y$.

FIG. 5.

Failure loads and associated experimental defect values. (A) Failure load versus slenderness ratio (4 h/day) for varying fibril lengths. Solid lines represent the yield model and dashed lines represent the buckling model. (B) Defect associated with yield failure model. (C) Defect associated with buckling failure model. (D) Ratio of yield defect to buckling defect. Points in the red region indicate that buckling behavior dominates. Points in the blue region indicate that yielding behavior dominates. Corresponding standard deviations (A–D) represent error bars.

For scaffolds with packing densities n = 8 or n = 10, ${\delta }_y$ shows more stratification with values above and below 0% across fibrils with the same heights demonstrating varying levels of under or overprinting. The relative error between the theoretical failure models is presented in Supplementary Table S5.

Discussion

Regenerating damaged OC tissue remains a substantial challenge in orthopedics. While numerous therapeutic solutions have been explored to regenerate the OC complex effectively, there has yet to be a singular approach to establish itself as the predominant strategy to treat large OCDs clinically. Monophasic scaffolds are insufficient in repairing the functional and structural properties of the OC unit.²¹ Alternatively, multilayered scaffolds with an interface have been examined more recently since a stable OC interface expediates successful OC repair and graft integration.²² While some groups have tried to attain more stable OC integration through biological bonding or enzymatic pretreatment of articular cartilage, the interfacial shear strength of these scaffolds fails to meet physiological requirements.^23–25 Others have demonstrated that mechanically interlocking the cartilage portion of the scaffold into the porous bone layer could enhance OC scaffolds by improving interfacial strength.^10,26

Our simulations helped assess the deformation and stress experienced by OC interfaces when subjected to maximal physiological load (Supplementary Tables S1–S4). The average horizontal displacement and stress values were extracted from the simulations and analyzed (Figs. 2A, B, 3A, B).¹⁷

Overall, simulations revealed that several of the OC scaffolds exhibit failure resistance values within the range requisite to survive within physiological loads, as the cortical bone and cartilage regions have been noted to experience compressive strengths 197 and 8 MPa, respectively, and shear strengths 8 and 3 MPa, respectively.²⁵ The computational simulations served as a valuable tool to assess the deformation and stress experienced by the 28 OC scaffolds under physiological loading conditions. However, it was difficult to ascertain which OC scaffolds would perform best under physiological compression and shear. Therefore, we sought a statistical data reduction method to better assess the combined effects of displacement and stresses on OC scaffold biomechanics, while considering the varying degree of intercorrelation and interaction among our four measured variables—displacement, von Mises stress, and first and third principal stresses.

PCA is a statistical method that helps extract key information from a multivariate dataset consisting of multiple parameters through functions of principal components.²⁶ With PCA, similarities between observations can be identified on a biplot. Recently, PCA has been utilized to predict the feedability and printability of various polymers for 3D printing with good results.^26,27 Therefore, we decided to perform PCA on our simulation results to predict which OC scaffolds would perform best when exposed to compression and shear. Since the OC unit is subject to compression, tension, and shear, we aimed to locate the scaffolds that minimized displacement and maximized von Mises stress, to balance the amount of tensile and compressive stresses.^4,11 Based on this biomechanical design criteria, the OC scaffolds of interest would be localized around the origin of loading vectors in the biplots.

While there were significant differences in compressive moduli among the tested OC interface scaffolds, the scaffolds that possessed the greatest compressive moduli were not the ones indicated to perform the best by PCA (Fig. 4B). Scaffold 16I demonstrated the greatest compressive moduli with respect to the OC scaffolds with 400 and 800 μm height interface fibrils. We proceeded to perform interfacial shear tests on our OC interface scaffolds. Again, there were significant differences in interfacial shear strength among the tested OC interface scaffolds (Fig. 4C). However, OC scaffolds with 800 μm height interface fibrils generally possessed greater shear strength than the other scaffolds, as indicated by PCA. Ultimately, scaffold 8H demonstrated the greatest interfacial shear strength with respect to the other 800 μm height scaffolds and control scaffolds.

For decades, OC tissue engineering studies involved testing scaffold compositions for a scaffold that involves tuning numerous variables that are not fully captured by traditional data representation.^28,29 PCA is a powerful statistical method to deconvolve interpretations from complex multidimensional datasets. For example, Tabriz et al. utilized PCA to compare the printability of various pharmaceutical grade polymers and identified how each mechanical property affected the printability.²⁷ In this study, we successfully utilized PCA to guide our OC scaffold design and determined the correct cluster of scaffolds that exhibited enhanced shear strengths upon shear testing. Furthermore, PCA displays promise as a tool to interpret the biomechanical outcomes of the OC scaffolds undergoing physiological load.

Our study's limitations may have reduced the predictive capacity of PCA, as the compression testing showed that the OC scaffolds with 800 μm interface fibril heights did not possess greater compressive moduli than the scaffolds with different interface fibril heights. First, the development of our solid mechanics model was guided by the capabilities of our DLP 3D printer. While printed constructs from a DLP-based 3D printer have been noted to achieve a theoretical resolution of 15 μm, we designed the minimum diameter of the interface fibrils to be 400 μm because it was the most consistently printable diameter for this study.

Additionally, there is some discrepancy in how the OC scaffolds would behave in an OCD in silico versus in situ. While we only included Young's modulus, Poisson's ratio, and density of the materials as parameters for the computational simulations, various other parameters can be included in our solid mechanics model, such as porosity, stiffness, permeability, or degradation rate.^30,31 Moreover, we initially assumed that the materials would be linearly elastic to facilitate the computational simulations; future studies should consider that materials such as silicone exhibit nonlinear hyperelastic behavior.³²

Although articular cartilage also displays some hyperelastic properties, the location of hyperelastic behavior in stress–strain curves of silicone can differ from that of cartilage.³³ Furthermore, it is also important to consider that the viscoelasticity and poroelasticity of silicone are different from those observed in articular cartilage.^34,35 Furthermore, silicone also exhibits hysteresis when unloading, which could limit the design of the OC scaffold.³³ Other materials, such as hydrogels and cartilage extracellular matrix components, could better mimic the properties of cartilage in future scaffold designs.^36,37 Lastly, the assumption of isotropy in the model also poses a limitation because articular cartilage is characterized by heterogeneity and anisotropy due to the arrangement of collagen fibrils within its distinct layers.³⁸ However, the porous base structure and the vertically oriented fibrils of our scaffold geometry are an initial foray into introducing a degree of anisotropy that aims to mimic the mechanical behavior seen in cartilage.⁴

Nevertheless, we will need to expand the scaffold design parameter space in future studies and get closer to the architectural complexity of the OC complex to improve our future computational models, PCA interpretations, and, ultimately, our OC scaffold designs.

To guide future solid mechanics model configurations for OC tissue engineering, we investigated the physics involved in the failure of all interface fibril designs. Analyzing failure conditions is a crucial consideration for functional tissue engineering.³⁹ Structures under compression can fail in various ways, changing both the maximum failure loads and the appropriate design constraints. Therefore, we aimed to develop models that predict interfacial fibrils' failure modes under compression. To better elucidate the structural changes experienced by the OC scaffolds during compression, we performed failure analysis on all interface fibril designs.

The failure analysis demonstrated that both the yielding and buckling models fit the failure behavior of printed scaffolds at different fibril heights, diameters, and packing densities. The yielding model fits most sampled scaffold behavior, while the buckling model is restricted to scaffolds with larger fibril slenderness. This is consistent with classical Euler beam buckling, in which beams with large slenderness ratios are likely to undergo buckling failure before yielding.⁴⁰ With the addition of the defect parameter $\delta$, structural errors arising from the printing process can be analyzed and used to adjust classical models for yielding and buckling to fit the experimental data better. The defects ${\delta }_y$ and ${\delta }_b$ produced reasonable values for all scaffolds, not exceeding 30% for their corresponding $\delta ∕d$ percentages. The variability of ${\delta }_b$ across fibrils with the same heights was less compared with ${\delta }_y$. This is most likely due to the sensitivity of their corresponding equations to its defect value; F_y has a second-order $\delta$ term, while F_b has a fourth-order $\delta$ term. Therefore F_b can take on larger values with a smaller perturbation to its defect relative to F_y.

For most scaffolds, $\delta ∕d$ remained below 0%, indicating that the printer is underprinting the diameters of fibrils, which decreases the failure load from the theoretical buckling and yielding models. Scaffolds with $\delta ∕d$ greater than 0% show evidence of overprinting, which increases the effective failure load. This behavior is most exaggerated for packing density 10 × 10, where there is a marked increase in $\delta ∕d$ for $d>600$. This may be due to the overlapping of fibrils during printing. We can compute a “critical defect” ${\delta }_{cr}$ for which fibrils in the scaffold are likely to begin melding by examining the point at which fibrils begin overlapping. This results in the expression:

$$t-\left(d+2{\delta }_{cr}\right)>0$$ (6)

Where t is the spacing between the centers of fibers. We compute the nominal spacing for a scaffold as $t=\frac{L-\left(2s+dn\right)}{n-1}$, where L is the length of one side of the scaffold and s is the smallest distance from the edge of a fiber to the edge of the scaffold. By substituting in (6), we obtain the condition:

$$\frac{L-\left(2s+d\left(2n-1\right)\right)}{2\left(n-1\right)}>{\delta }_{cr}$$ (7)

For a given scaffold with defect $\delta$, if $\delta >{\delta }_{cr}$ fibril overlapping will likely occur. From (7), we can see those scaffolds with n = 10 and increasing diameters are most susceptible to fibril overlap, consistent with the heightened $\delta ∕d$ values and apparent overprinting observed in Figure 5D.

Conclusion

We utilized computational simulations, PCA, and DLP 3D printing to better design biomimetic OC scaffolds with superior load-bearing properties. The displacement and stress simulations of OC scaffolds indicated that interface fibril patterns redirect the area of deformation and load-induced stresses toward the top cartilage layer. From PCA, we identified that scaffolds 8A–8H possessed the ideal combination of biomechanical properties—minimal displacement, maximum von Mises stress, and a balanced amount of tensile and compressive forces—to withstand the load-bearing forces within the OC unit. While compression testing revealed that the PCA-predicted OC scaffolds did not have greater compressive moduli than other OC scaffolds, interfacial shear tests indicated that scaffolds 8A–8H possessed greater shear strength than other OC scaffolds with 400 and 1600 μm interface fibrils. Finally, the failure analysis revealed that yielding and buckling models describe the failure behavior of interfacial fibrils subjected to compression. The results from this study provide a feasible assessment strategy to evaluate the biomechanics of 3D printed OC scaffolds.

Authors' Contributions

R.H.C. designed, executed, and analyzed studies and was the primary writer; B.C.K. supported the design and execution of the computational simulations and mechanical testing studies; G.J.K. helped execute the computational studies and mechanical testing experiments; E.M. supported the design and analysis involving PCAs; E.D. supported the design of the computational simulations; T.L. and J.D.P. aided in the interpretations of the results and writing of the article; and J.P.F. oversaw the design, execution, analysis, and writing of the article.

Data Availability

Raw data were generated at the Fischell Department of Bioengineering, University of Maryland, College Park, Maryland. Derived data supporting the findings of this study are available from the corresponding author on request.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was supported by the National Institutes of Health (P41 EB023833), the Osteo Science Foundation (23052316), and the MPower Professorship.