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Validation of Scaffold Design Optimization in Bone Tissue Engineering: Finite Element Modeling versus Designed Experiments Nicholas Uth1, Jens Mueller2, Byran Smucker3, Azizeh-Mitra Yousefi1* 1

Department of Chemical, Paper and Biomedical Engineering, Miami University, Oxford, OH 45056, USA 2 3

Research Computing Support, Miami University, Oxford, OH 45056, USA

Department of Statistics, Miami University, Oxford, OH 45056, USA

*Corresponding author: Azizeh-Mitra (Amy) Yousefi; [email protected]; (513) 529-0766

Abstract This study reports the development of biological/synthetic scaffolds for bone tissue engineering via 3D bioplotting. These scaffolds were composed of poly(L-lactic-co-glycolic acid) (PLGA), type I collagen, and nano-hydroxyapatite (nHA) in an attempt to mimic the extracellular matrix of bone. The solvent used for processing the scaffolds was 1,1,1,3,3,3-Hexafluoro-2-propanol (HFP). The produced scaffolds were characterized by scanning electron microscopy, microcomputed tomography, thermogravimetric analysis, and unconfined compression test. This study also sought to validate the use of finite-element optimization in COMSOL Multiphysics for scaffold design. Scaffold topology was simplified to three factors: nHA content, strand diameter, and strand spacing. These factors affect the ability of the scaffold to bear mechanical loads and how porous the structure can be. Twenty four scaffolds were constructed according to an I-optimal, split-plot designed experiment (DE) in order to generate experimental models of the factor-response relationships. Within the design region, the DE and COMSOL models agreed in their recommended optimal nHA (30%) and strand diameter (460 µm). However, the two methods disagreed by more than 20% in strand spacing (923 µm for DE; 601 µm for COMSOL). Seven scaffolds were 3D-bioplotted to validate the predictions of DE and COMSOL models (4.5 - 9.9 MPa measured moduli). The predictions for these scaffolds showed relative agreement for scaffold porosity (mean absolute percentage error of 4% for DE and 13% for COMSOL), but were substantially poorer for scaffold modulus (52% for DE; 21% for COMSOL), partly due to some simplifying assumptions made by the models. Expanding the design region in future experiments (e.g., higher nHA content and strand diameter), developing an efficient solvent evaporation method, and exerting a greater control over layer overlap could allow developing PLGAnHA-collagen scaffolds to meet the mechanical requirements for bone tissue engineering. Keywords: bone tissue engineering, optimization, simulation, additive manufacturing, 3D bioplotting, designed experiment, scaffold topology, COMSOL

1 Introduction Bone tissue has a limited capacity for regeneration depending on the extent of the damage and the bone involved [1]. In order to repair critical-size defects and nonunions, either bone grafts or synthetic bone-graft substitutes are used to replace the tissue [2]. Grafts and substitutes are in such common use that, every year, at least four million operations worldwide make use of them [3], and this number will only increase as global populations grow. However, there are risks and limitations to these treatments. Bone-graft substitutes are subject to wear over time, immune response, or bone thinning due to stress shielding [2,3]. Grafts taken from donors (allografts) risk immune response or disease transmission [2,3], and grafts from the patient (autografts), while considered ideal, are limited in size/quantity and risk donor site complications and infection [2,3]. Bone tissue

engineering (TE) aims to enable the patient’s body to regenerate the damaged tissue without the need for a donor or risk of spurring immunological action [4–6]. In order to regenerate damaged tissues, TE makes use of porous scaffolds made of biomaterials to act as a cellular matrix and support structure [6–8]. In designing scaffolds, the general consensus is that they should behave as similarly to the tissues they are meant to replace as possible [9,10]. In the case of bone tissue, it is hypothesized that scaffolds need to have a high modulus and adequate porosity based on the bone to be replaced (Table 1), as mechanoregulatory effects are believed to be the key factor in bone tissue regrowth and cellular differentiation [8,9,11,12]. If the scaffold environment (mechanical forces transferred to the cells and vascularization) is unlike physiological conditions, there is a risk that mesenchymal stem cells (MSCs) will differentiate into chondrocytes or fibroblasts, which grow cartilage and fibrous tissues respectively [13,14]. However, stiffness and porosity directly conflict as design factors, which makes the design process critical [15]. Table 1. Mechanical properties of mature bone tissues, as described by literature.

Young’s Modulus

Porosity

50 - 100

MPa

(Trabecular bone)

[16]

2.23 - 25.9

GPa

(Trabecular bone)

[17]

20

GPa

[18]

6

GPa

[19]

1.3 - 20

GPa

(Trabecular bone)

[20]

< 15 > 70 50 - 90

% % %

(Cortical bone) (Trabecular bone) (Trabecular bone)

[21] [21] [22]

There are two key aspects to scaffold design: material choice and topology, both of which can be adjusted to produce scaffolds with properties akin to native tissue [21]. The material choices affect how readily the scaffold will biodegrade, and whether the scaffold will be bioactive [22]. While each class of biomaterial (polymers, metals, and ceramics) have their own individual disadvantages that can restrict their applications in TE, composites can mitigate these limitations and it has been suggested that they can exhibit tissue-mimicking properties [4]. This study made use of a polymer-ceramic-protein composite, which combined the ease of use and controlled biodegradation rate of poly(L-lactic-co-glycolic acid) (PLGA), the mechanical strength and bioactivity of nano-hydroxyapatite (nHA), and the cellular adhesiveness of collagen. PLGA is a synthetic random copolymer of poly(L-lactic acid) (PLLA) and polyglycolic acid (PGA), and has U.S. Food and Drug Administration (FDA) approval for some use in humans

[4]. Its degradation rate has been shown to be customizable in the range of weeks to months based on the ratio of PLLA to PGA. However, PLGA has a low modulus even compared to its component polymers (PLGA 85:15 E = 2.0 GPa, PLLA E = 2.7 GPa, PGA E = 7.0 GPa [23]) due to its amorphous structure. Therefore, on its own, PLGA is not reliable for trabecular bone regeneration [24]. On the other hand, nHA is a ceramic with a high modulus (E = 35-120 GPa for dense ceramics [25,26]) that has been suggested to encourage osteogenesis [4]. In composite materials, nHA improves mechanical properties of scaffolds at low concentrations (tensile: ≤ 0.5 wt% [27], compressive: ≤ 20 wt% [28]), but has adverse effects at higher concentrations [27,28] partly due to nonuniform dispersion. Previous research has also shown that nHA helps cells and proteins attach to scaffold surfaces when integrated into composite scaffold materials [22]. To its detriment, nHA is difficult to process [24], brittle, and degrades slowly (adjustable via ratio of Ca/P [26]). Finally, collagen is another primary component of mammalian tissue matrices, and has been shown to support osteogenesis [4] and cellular attachment [5,27,29]. In addition, crosslinking has been shown to give some control over mechanical properties and degradation of collagen [30]. The solvent 1,1,1,3,3,3-Hexafluoro-2-propanol (HFP) is often used to process the scaffolds composed of collagen. HFP has previously been used in electrospinning studies that made use of PLGAnHA-collagen composites [10,27], and has been suggested to help electrospun collagen behave similarly to collagen in the natural bone matrix [31]. The scaffold topology also plays a role in scaffold modulus and is the primary determinant of porosity. The traditional approach to scaffold topology design and optimization is iterative; the experimental performance of a scaffold informs researchers how they can modify the topology in order to improve the performance of the next scaffold produced [14,32]. Even in cases where finite element (FE) modeling has been used for analysis, it has typically been post hoc in order to modify scaffolds that have already been fabricated and tested [33], or to examine how accurately an FE model represents various designs [34–36]. However, there have been growing numbers of studies, such as by Rainer et al. [37], which made use of computer-aided design (CAD) and finite element analysis (FEA) as a priori scaffold design tools. Through this approach it may be possible to reduce the number of physical scaffolds that must be constructed and tested in order to determine optimal topologies. The resultant 3D models would be simple to produce and test via additive manufacturing (AM), which grant fine control over the topology of generated scaffolds [7,21,36,37]. One such device, the 3D bioplotter (3DBP), constructs scaffolds by layering extruded

strands of material. By adjusting the diameter and distance between extruded strands, it is possible to design various topologies with porosity and modulus in mind. CAD has shown promise in scaffold design, but in certain cases simulations tend to overpredict scaffold performance to varying degrees. Some studies have suggested that this is due to limitations in simulating micro-topologies (cracks, pores, material inconsistencies) [36] and the way material mechanical properties are applied to the model [38]. In order to validate CAD scaffold design, COMSOL Multiphysics software has been used in this study to optimize the topology of 3DBP scaffolds made of PLGA-nHA-collagen. HFP has been used as a solvent to uniformly disperse nHA (up to 30%) within the scaffold, while serving as a safer alternative for collagen than most organic solvents. The COMSOL design aimed to find the optimal set of strand diameter, strand spacing (pore size) and nHA% (3 factors) that maximized the compressive modulus of the scaffolds, subject to a constraint on scaffold porosity. The results of numerical optimization have been compared to an optimized statistical model generated via a designed experiment (DE). It was hypothesized that both the experimental (DE) and COMSOL (FE) models should suggest similar optimal topologies (±20% design factor value agreement). Both models were expected to yield an optimal topology within the design space while satisfying the recommended porosity for use in (trabecular) bone regeneration (porosity ≥ 50% [39]). A compressive modulus ≥ 10 MPa [2] was targeted in this study, although there is no consensus on the optimal range of scaffold modulus for bone tissue engineering. Despite offering a design-driven approach to scaffold fabrication, AM techniques often have limited spatial resolutions. Therefore, some level of uncertainty is associated with the produced scaffold architectures. Hence, this study also examines the sensitivity of FE simulations to the topological parameters of 3DBP scaffolds (e.g., strand overlap and pore size). Moreover, the sensitivity analysis looks into the role of solid matrix properties (such as compressive modulus and Poisson’s ratio) on the predicted compressive modulus of porous scaffolds.

2. Materials & Methods 2.1 Materials PLGA (Resomer LG 824 S) was purchased from Evonik Industries (Germany). DSM Biomedical (Exton, PA) graciously provided type 1 collagen powder (PN 20003-04). nHA (nanopowder,
25 MPa). Table 3. Compressive modulus predictions and porosity estimation with respect to applied Poisson’s ratio () and layer thickness-to-strand height ratio (L/H) (top rows), and with respect to applied strand spacing (EtE) and solid-block modulus (E) (bottom rows). D = 460 m.  0.40 0.49 0.40 0.49

L/H

EtE (m)

Solid-block Modulus E (MPa)

0.70

600

11.9

0.85

600

11.9

0.49

0.70

0.49

0.70

600 900 600 900

11.9 237

Scaffold Compressive Modulus (MPa) 5.71 5.79 3.81 3.88 5.64 4.38 113 87.6

Scaffold Porosity (%) 53.8 53.8 59.9 60.1 54.2 63.6 54.2 63.6

Optimization: A boundary integral objective for optimization was defined and examined at the top surface boundaries where the displacement took place. The objective expression examined compressive modulus as a ratio between third principal stress and the prescribed compressive strain. Third principal stress was used as the stress term, as it assumes the maximum possible compressive stress experienced at the boundary region. The Nelder-Mead optimization method was then used to maximize the objective function. Radius and EtE spacing were used as control variables. The radius was initially 190 µm, but was allowed to range between 150-230 µm. The

spacing began at 800 m, and could range between 600-1000 m. Porosity was then constrained within 50-99% void space.

3 Results 3.1 Rheological Characterization Variations in the formula component ratios, especially in the case of the HFP, can induce variations in the plotting behavior. In addition to homogeneity, the viscoelastic properties affect how material is dispensed from the bioplotting needle. Rheological analysis was performed to determine the crossover frequencies between the storage and loss modulus (see Fig. 2 a-c) of the three formula variations. The inverse of this frequency value generated relaxation times of 0.117 s, 0.113 s, and 0.143 s for the 0%, 15%, and 30% formulae, respectively. Hence, it appeared that the effect of nHA on the rheological behavior of the formula was more pronounced at 30% nHA, which is also evident from the superimposed rheological data for each formula in Fig. 2d-f. 3.2 Scaffold Characterization TGA analysis of a 30% nHA mixture sample (m = 16.7 mg) compared to its solid components on day 0 (Fig. 3a) indicated that, by 190ºC, 25.4% of the formula mass was lost. Based on the collagen curve, the protein can account for less than 1% of that mass (88.3% remaining, as shown in Table 4). PLGA and nHA were unaffected at that temperature (99.6% and 99.3% remaining, respectively). Therefore, the remaining mass loss can be attributed to HFP evaporation (67.2% remaining). Knowing this and the initial mass ratios of the solid components (9.33 PLGA : 4 nHA : 1 collagen), mass balance equations (Eqs. 3-6) were derived and solved to approximate the mass of HFP within a 30% nHA scaffold (Eqn. 7). Assuming that the non-solvent components of a scaffold do not change over the air-drying period (Fig. 3a-3b), a dry-basis analysis (Table 4) was used to modify Eqn. 7. The dry-basis equation (Eqn. 8) allowed tracking the concentration of HFP within a drying scaffold across 42 days. 𝑚20 = 𝑚𝑃𝐿𝐺𝐴20 + 𝑚𝑛𝐻𝐴20 + 𝑚𝐶𝑜𝑙𝑙𝑎𝑔𝑒𝑛20 + 𝑚𝐻𝐹𝑃20

(3)

𝑚190 = 0.996 𝑚𝑃𝐿𝐺𝐴20 + 0.993 𝑚𝑛𝐻𝐴20 + 0.883 𝑚𝐶𝑜𝑙𝑙𝑎𝑔𝑒𝑛20 + 0.672 𝑚𝐻𝐹𝑃20

(4)

𝑚𝑃𝐿𝐺𝐴20 = 9.33 𝑚𝐶𝑜𝑙𝑙𝑎𝑔𝑒𝑛20 ,

𝑚𝑛𝐻𝐴20 = 4 𝑚𝐶𝑜𝑙𝑙𝑎𝑔𝑒𝑛20

𝑚𝐻𝐹𝑃20 = 3.13𝑚20 − 3.17𝑚190 𝑚𝐻𝐹𝑃20 (𝑑𝑟𝑦 𝑏𝑎𝑠𝑖𝑠) = 𝑚𝐻𝐹𝑃20 (

(5-6) (7)

𝑚𝑑𝑟𝑦,0 𝑚𝑑𝑟𝑦,𝑡

)

(8)

In these equations, 𝑚20 and 𝑚190 are the TGA masses at 20ºC and 190ºC, respectively, 𝑚𝑑𝑟𝑦,0 is the total dry mass % (non-solvent components) on day 0 within a TGA sample, and 𝑚𝑑𝑟𝑦,𝑡 is the corresponding dry mass % at different drying times (7-42 days).

Figure 2. Rheological properties of the three formulae used: (a) 0% nHA, (b) 15% nHA, and 30% nHA, (d-f) comparisons of the properties for each formula. Figure 3c compares the TGA mass % data (solid lines) and the constructed mass % curves (symbols) based on the approximated HFP loss over time. There is a good agreement between the

experimental TGA mass % and the calculated values, except at temperatures exceeding 300ºC (day 7-42). Above this temperature, the mass loss for PLGA and collagen is significant (Fig. 3a). Hence, the use of TGA data for each dry component to approximate the overall mass loss leads to some discrepancy. In addition, the mechanism of mass loss could be different for the original wet formula and that of dried/dense scaffolds. The estimated mass % of HFP across 42 days has been plotted in Fig. 3d. The inset image schematically shows the relationship between the TGA mass % and the dry-basis mass % of HFP. At the time of mixing, HFP concentration in a 30% nHA scaffold was 76.6% (day 0). The first seven days was when the most evaporation took place, the concentration reduced by 50% (dry basis). By day 42, concentration reduced by another 11%. Based on this curve, a 28-day drying time was selected for the scaffolds produced. This allowed as much solvent extraction as possible before mechanical testing, while keeping the time expense required reasonable.

Table 4. Summary of non-solvent components and HFP mass % over time at 190ºC based on TGA data. Mass (%)

Mass % (T°C) / Mass % (20°C)

T (°C)

Day

PLGA

nHA

Collagen

HFP

20

0

15.2

6.53

1.63

76.6

1.0

1.0

1.0

1.0

1.0

1.0

0

15.2

6.49

1.44

51.5

0.996

0.993

0.883

0.672

0.746

0.987

7

15.1

6.48

1.40

51.2

0.989

0.993

0.857

0.669

0.742

0.981

14

5.88

6.47

0.83

4.27

0.386

0.990

0.506

0.056

0.175

0.563

21

0.23

6.46

0.42

5.90

0.015

0.988

0.254

0.077

0.130

0.303

28

0.21

6.44

0.35

5.40

0.014

0.986

0.216

0.070

0.124

0.299

42

0.18

6.42

0.28

4.52

0.012

0.983

0.174

0.059

0.114

0.294

190

PLGA

nHA

Collagen

HFP

Total (wet)

Total (dry)

Figure 3. (a) Comparison of mass % up to 800C for a 30% nHA formula and the non-solvent components; (b) TGA mass loss curves for 30% nHA scaffold as it dried for 42 days. The inset image shows the temperature zone of interest for the calculation of evaporated HFP. (c) Comparison of the TGA mass % data and the constructed mass % curves (symbols) based on the approximated HFP loss over time, (d) HFP mass concentration within a 30% nHA scaffold as it dried for 42 days. HFP concentration was approximated via Eqn. 7 (original basis: TGA%) and Eqn. 8 (dry basis, with respect to non-solvent components on day 0). The SEM evaluated the strand width (D) and strand spacing (EtE) for the scaffolds using the top-down perspective, while the cross-sectional view was used to determine the strand height (H) in order to estimate the average diameter and porosity of the scaffold. Figure 4a and 4b show the top-down and cross-sectional SEM views of the scaffolds for run 6 and run 3, respectively. The estimated porosities of all scaffolds appeared to be over 50% (Table 5). At the lowest spacing and highest diameter for the 24 runs, the porosities were approximately 56-58% void space.

Figure 4. (a) SEM image of scaffold (run 6) in top-down view, and (b) scaffold (run 3) in crosssection view. Table 5. Experimentally determined characteristics of the DE scaffolds. Run Avg Strand SD Number Diameter (µm) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

428 519 318 426 394 358 408 466 376 472 317 363 331 445 363 336 402 355 288 445 292 454 473 445

12.6 26.9 8.6 32.1 3.2 6.8 6.3 18.0 10.4 18.5 4.9 14.5 12.8 13.6 24.1 3.1 5.7 17.4 6.0 7.6 5.2 35.7 8.8 13.4

Avg EtE Spacing (µm)

SD

Avg H (µm)

SD

Avg Porosity (%)

SD

Avg Comp. Modulus (MPa)

SD

869 638 552 664 701 860 687 498 717 904 501 886 884 478 1012 703 683 969 565 744 679 869 478 428

16.3 16.2 47.4 35.3 29.3 36.1 40.6 20.1 9.9 17.4 18.1 104.2 30.7 8.0 22.1 27.5 20.1 13.9 77.0 31.6 100.3 67.2 5.3 27.7

278 320 273 322 319 267 286 326 318 335 285 285 313 321 350 269 284 303 258 322 282 325 335 324

10 7 4 7 21 6 15 10 5 10 8 13 13 4 8 26 4 7 2 25 16 9 8 9

76.3 62.1 73.7 67.1 70.0 79.4 72.1 58.8 71.5 70.2 71.1 77.7 77.7 59.5 75.8 77.2 72.5 78.7 77.0 68.4 78.2 70.7 56.3 56.3

0.4 1.9 2.1 1.2 1.7 0.8 0.6 1.1 0.8 2.1 1.1 2.0 1.1 0.7 1.0 2.7 0.6 1.2 1.9 2.7 1.6 4.2 1.5 3.5

5.44 4.36 2.77 4.85 3.27 1.48 3.22 5.16 2.08 2.40 1.64 0.894 5.69 9.07 8.48 6.05 2.48 2.06 1.31 3.59 1.80 2.63 3.53 3.10

0.268 0.156 0.206 0.244 0.390 0.184 0.284 0.370 0.123 0.199 0.039 0.015 0.119 0.396 0.679 0.354 0.113 0.072 0.085 0.197 0.129 0.095 0.188 0.154

The CT image of a 3D scaffold containing 30% nHA is shown in Fig. 5a. Figure 5b depicts the cross-sectional 2D view of the same scaffold, where the color scale bar represents the density in g-HA/cm3. Overall, these two images indicate that nHA particles were evenly distributed

throughout the scaffold. The total volume % of the solid matrix was 54% according to the CT analysis, which translates to a porosity of 46% (void space). Figure 5c gives the 2D view of a scaffold with 0% nHA, for which the estimated CT porosity was 58%. Finally, Fig. 5d and 5e demonstrate that over 50% of the density distribution for the 30% nHA scaffold lies between 0.302-0.422 g-HA/cm3, whereas for the 0% nHA scaffold the corresponding density range is 0.109-0.123 g-HA/cm3 (in the absence of nHA particles). These values approximate the density of the 3DBP strands for these two scaffold compositions. It should be noted that the porosities estimated for these scaffold topologies using Eqn. 2 were 52% and 66%, respectively. These estimates were based on their topological dimensions (for 30% nHA: D540 m, EtE570 m, H380 m, and for 0% nHA: D400 m, EtE610 m, H330 m). Therefore, the porosity calculated using Eqn. 2 overestimated the actual (CT) porosities by 15%. This is partly due to a layer thickness (L) smaller than 300 m for the bottom layers of the scaffolds (see Fig. 4b).

Figure 5. (a) The CT image of a 3D scaffold with 30% nHA, and (b and c) the 2D crosssectional view of the scaffolds with 30% nHA and 0% nHA, respectively. (d and e) Distribution % of the density (in g-HA/cm3) throughout the scaffolds. The CT porosities were 46% and 58% for the two scaffolds, respectively (52% and 66% calculated using Eqn. 2).

Figure 6a demonstrates three examples of the stress-strain behavior for scaffolds between 0% and 40% strain. Although the system is nonlinear at larger strain values, the stress-strain relationship around the 10% strain region behaved reasonably linearly. Compressive modulus was thus determined by taking the slope of the trend comprised of the point closest to 10% strain and the 4 adjacent points above and below it (Table 5). Figure 6b compares the two highest and lowest compressive modulus values found among the 24 run trial. The minimum modulus was observed for run 12 due to a low average strand diameter (D  363 m, 0% nHA) and a high pore size (EtE  886 m), whereas the 30% nHA scaffolds had the highest compressive moduli, ranging from 5.69 MPa to 9.07 MPa (run 14) for the different scaffold architectures. The results of scaffold characterization for all 24 runs have been summarized in Table 5 and Fig. 7.

Figure 6. (a) Stress-strain behavior of DE scaffolds 9, 10, and 11. Material behavior is reasonably linear at low compressive strains (~10% region). (b) The two highest and lowest compressive modulus values found among the 24 run trial.

Optimal scaffold design often aims to maximize either the porosity or the compressive modulus, subject to certain constraints. Based on the porosity-factor scatter plot (Fig. 7, bottom 3

plots), the average strand diameter and strand spacing appear to have visible effects on porosity. Plotting the compressive modulus versus the factor values (Fig. 7, top 3 plots) shows that %nHA appears to have the largest consistent effect on modulus, whereas diameter seems to have a smaller positive impact. The best scaffold designs for porosity, high spacing and low diameter, were able to reach over 75%. Based on this, even if the optimal scaffold design for compressive modulus were to fall in the denser area of the design region, the topology would still satisfy the minimum porosity of 50%.

Figure 7. Scatter plots of the factor-response relationships: compressive modulus plots (top), porosity plots (bottom) 3.3 DE Optimization The fitted split-plot regression models, based on the experimental data in Fig. 7, can be viewed as second-order approximations of the relationship between the responses and the factors. They are given as follows:

𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝐶𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒 𝑀𝑜𝑑𝑢𝑙𝑢𝑠 = 2.94 + 2.76(𝑛) + 1.86(𝑛2 ) + 1.39(𝑑) + 0.71(𝑛)(𝑑) 𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦 = 75.64 − 5.95(𝑑) + 3.07(𝑠) − 2.31(𝑠 2 )

𝑛=

[(%𝑛𝐻𝐴)−0.15] 0.15

,

𝑑=

(𝐷−380) 80

,

𝑠=

(𝐸𝑡𝐸−800)

(9) (10)

(11-13)

200

Equations 9 and 10 have been plotted in Fig. 8, where the solid lines represent the effects of each factor on a given response (porosity or modulus). The compressive modulus fitted equation is comprised of a quadratic effect due to %nHA, a linear effect caused by strand diameter, and an interaction term where the two have a multiplicative effect on the response. The interaction term, although not as influential as the quadratic effect of %nHA, indicates that the positive effect of either factor is diminished if the other factor is at a small value. Conceptually, if a 30% nHA formula were utilized, the use of thin strands would reduce the amount of material present, mitigating the effect of the material choice. Similarly, high diameter strands are less effective if they are composed of material with low mechanical strength. Strand spacing was determined to have a negligible effect on compressive modulus, so it was not included in the model. In comparison, the porosity fitted model is solely composed of the architectural factors: strand diameter and strand spacing. Unlike the compressive modulus model, the strand spacing factor has a quadratic effect on porosity, and strand diameter has a linear effect. Levels of the factors that predict a maximum modulus with a porosity constrained above 50% are demonstrated in Fig. 8. Based on the DE model and within the design region, our estimate of the optimal scaffold design is 30% nHA, 460 µm strand diameter, and 923 µm strand spacing. For nHA composition, selecting the highest level is ideal, as it has the largest effect on compressive modulus of all factors with no detrimental effect on porosity. Selecting strand spacing is the inverse scenario: choosing a high spacing has a positive effect on porosity without any detrimental effect on compressive modulus. (Note that there could be a detrimental effect, but our experimental data suggested this effect would be negligible.) Strand diameter is the only factor that affects both responses, according to our empirical model. It is possible to choose the maximum diameter for its positive effect on compressive modulus since the porosity response is still within acceptable bounds. The experimental models predict that, for this optimized design, the resultant scaffold would have a compressive modulus of 9.66 MPa, and a porosity of 70.7%. This porosity is highly

desirable, but the modulus is slightly less than the 10 MPa targeted for bone regeneration. Note that for a strand spacing of 600 µm, recommended by COMSOL, a DE porosity of 65% would be predicted (Fig. 8, bottom row). As there are physical reasons to believe that less spacing will increase modulus, this design strategy will favor a higher modulus while keeping the porosity at a desirable level.

Figure 8. Optimization profile for the system. Solid lines indicate the effects of each factor on a given response; dotted lines indicate the values selected for each factor and the total result on the responses. The quality of fit was observed by comparing the experimental responses to the predicted responses (Fig. 9). If the correlation between the actual and predicted values is high, it means that model is accounting for a large degree of the variation in the data. The compressive modulus model and experimental results show general agreement (R2=0.87), but the porosity model shows even more (R2=0.96). Note that these measures would be even higher if all linear, interaction, and quadratic terms were included in the models. However, only the largest effects were retained in order to increase the predictive quality of the models for new scaffolds.

Figure 9. Plots of experimental response versus predicted response for (a) compressive modulus and (b) porosity. 3.4 COMSOL Optimization Optimizations were run at three levels of compressive modulus (E) corresponding to the three %nHA levels. All three optimizations iterated through the same topologies, and finished at a topology of 460 µm strand diameter and 601 µm strand spacing (Table 6). As the architectural factors were identical, the three simulations agreed upon a resultant porosity of 54.3%. The predicted compressive moduli, however, varied according to the assumed ceramic composition, improving as %nHA did. At the highest nHA level, the predicted compressive modulus was 5.67 MPa. Figure 10 shows the surface plot of the stress experienced at the top surface of the scaffold model. As the color bar indicates, the peaks of stress are in alignment with the strands of the previous layer. Table 6. Abridged results of COMSOL optimization. The module began at the same diameter and strand spacing, and searched in the same order for 30 iterations. Iteration 1 5 10 15 20 25 30

Strand Diameter Strand Spacing (µm) (µm) 380 416 431 454 457 459 460

800 710 659 605 600 601 601

Porosity (%) 65.2 60.8 58.9 54.7 54.3 54.3 54.3

Compressive Modulus (MPa) 0% nHA

15% nHA

30% nHA

0.32 0.36 0.39 0.44 0.45 0.45 0.45

1.63 1.85 2.00 2.25 2.27 2.28 2.29

4.03 4.59 4.95 5.58 5.63 5.65 5.67

Figure 10. Surface plot of the stress experienced at the top surface of the scaffold model. Peaks of stress are in alignment with the strands of the previous layer. 3.5 Validation Results Seven 30% nHA scaffolds were plotted in order to validate the predictions of DE and COMSOL models (Table 7). Figure 11a and 11b compare the two models with respect to their modulus predictions and porosity estimations, while Figure 11c and 11d depict their absolute percentage errors, respectively. The mean absolute percentage error (MAPE) was calculated for the DE predictions and COMSOL simulations. With regards to porosity estimation for the seven validation scaffolds, the DE model had a MAPE of about 4%. COMSOL, on the other hand, had a MAPE of 13% and consistently underestimated the scaffold porosity. This may be due to how the simulation utilizes a constant layer overlap parameter (L/H=0.7). However, this ratio tends to vary, particularly in bottom layers close to the plotting platform. Another factor that could contribute to underestimated porosity was that each strand in COMSOL was defined as a cylinder of circular cross-section (average D) to accommodate the iterative optimization process. It should be noted that, as CT results indicated, Eqn. 2 tends to overestimate the experimental (SEM) porosity by ∼15%. Therefore, the COMSOL porosities could still offer good estimates for the actual porosities of these scaffolds (L/H=0.7). Nevertheless, when experimental L/H (0.56 - 1.0 from SEM) were used in the simulations, COMSOL substantially underestimated the measured porosities for L/H < 0.7 (Table 7). This is because at a high layer overlap, the shape of strands tends to deviate even further from a circular cross-section.

Table 7. Comparison between the experimentally determined validation scaffold physical characteristics and the predicted results based on Eqs. 9 and 10 (DE) and the COMSOL model. nHA (%)

Avg. Diam. (µm)

Avg. ETE (µm)

SEM L/H

Experimental Modulus (MPa)

DE Predicted Modulus (MPa)

COMSOL Predicted Modulus (L/H = 0.70) (MPa)

COMSOL Predicted Modulus (SEM L/H) (MPa)

Experimental Porosity (%)

DE Predicted Porosity (%)

COMSOL Porosity (L/H = 0.70) (%)

COMSOL Porosity (SEM L/H) (%)

30%

416 ± 8

555 ± 16

0.66

5.07 ± 0.17

8.51

5.36

6.09

71.4 ± 1.8

65.7

55.3

53.0

30%

425 ± 16

555 ± 12

0.70

5.10 ± 0.10

8.74

5.46

5.46

65.4 ± 0.3

65.1

54.7

54.7

30%

333 ± 4

932 ± 9

1.00

5.48 ± 0.13

6.33

3.5

0.14

81.9 ± 0.9

80.1

71.0

78.9

30%

309 ± 20

981 ± 11

1.00

5.89 ± 0.19

5.69

3.16

0.14

83.6 ± 1.4

81.8

74.3

81.1

30%

469 ± 8

851 ± 53

--

5.23 ± 0.34

9.91

4.67

--

68.5 ± 2.2

69.6

62.3

--

30%

482 ± 18

525 ± 17

0.56

9.92 ± 1.16

10.3

6.07

7.77

54.1 ± 1.2

59.4

50.1

41.9

30%

460 ± 28

864 ± 48

--

4.52 ± 1.52

9.66

4.58

--

69.5 ± 1.6

70.5

63.0

--

Figure 11. (a & b) Comparison between the COMSOL and DE porosities and moduli for the validation scaffolds, (c & d) comparison of their absolute error (%) for porosity estimations and modulus predictions, respectively. These COMSOL simulations were for a constant layer overlap (L/H = 0.7).

The DE model fared worse in predicting the moduli for the seven validation scaffolds. However, the moduli predicted by the DE model agreed well with the experimental values when the strand diameter (D) was the dominant factor affecting the scaffold modulus (at very low or very high D values: sample 3, 4, and 6). The experimental modulus values were within 16% of the DE prediction values in these three cases, whereas the mean absolute prediction error for all seven validation scaffolds was 52%. This is not surprising as L/H ratio was not accounted for in the DE model, while EtE spacing had no effect on the DE model response (see Fig. 8 and Table 3). In practice, it is a tremendous challenge to use L/H as an independent DE factor, as it is highly affected by the rheological properties of the formula, plotting speed, plotting pressure, and the dispensing needle diameter. COMSOL was better at predicting the modulus than the designed experiment. Overall, COMSOL better predicted the modulus when the scaffold had an intermediate experimental porosity range (65 - 71%, sample 1, 2, 5 and 7). The experimental modulus values were within 11% of the COMSOL prediction values in these four cases (for L/D=0.7), whereas the mean absolute prediction error for all seven samples was 21%. COMSOL simulations using variable L/H (from SEM) highly under-predicted the modulus of sample 3 and 4 (> 30% absolute error). The lack of overlap between the successive layers (L/H=1) led to a significant drop in the predicted COMSOL modulus. It should be noted that sample 3 and 4 had higher compressive moduli than scaffolds in the low end of the porosity range (e.g., sample 1 and 2). As noted previously, solvent is still present within the scaffolds even after 28 days of drying. It may be possible that due to the increased EtE spacing (> 900 m) and low strand diameter (D < 350 m), sample 3 and 4 had improved solvent evaporation rates, which would contribute to the overall mechanical performance of the scaffold. In case of sample 6, the porosity and L/H values were the lowest of all the validation scaffolds, so it had the highest compressive modulus (in agreement with the DE model). An L/H value close to 0.5 represents a very dense scaffold with highly overlapping layers. Thus, sample 6 showed an experimental modulus similar to a solid block for this formula. This scaffold was much denser at its bottom layers, which cannot be realistically replicated in a COMSOL model. The SEM L/H values used in the simulations were only reflective of the middle-to-top layers of the actual scaffolds. 3.6 Methodology Comparison The two models suggested using the highest values for strand diameter and nHA content. However, the experimental model found the effect of strand spacing on modulus to be insignificant, while

the simulation predicted an improvement to modulus by reducing the spacing and increasing the number of strands per layer as a result. That said, the spacing only has an effect on porosity in the experimental model, so it would be feasible to use the topology suggested by COMSOL because the reduction in porosity would still fall within the acceptable bounds according to the experimental model.

4 Discussion Composites made of collagen and hydroxyapatite (HA) are attractive biocompatible materials as they possess the organic and mineral constituents of bone [46–48]. Scaffolds made of collagen and HA with/without synthetic polymers have been widely produced by electrospinning (ES) [49–52] and conventional scaffold fabrication techniques [53–57]. The flexibility of generating broad pore size ranges and mechanical properties by additive manufacturing (AM) makes it a superior alternative to ES and conventional techniques [58–61]. Hence, this work investigated the mechanical properties of PLGA-nHA-collagen composite scaffolds produced by 3D bioplotting (3DBP) using HFP as a solvent. The amount of solvent retention was quantified over scaffold drying time (0-42 days) based on mass balance principles and thermogravimetric analysis (TGA). The methodology presented herein required a small sample size and could assist researchers in analyzing solvent retention in tissue-engineering scaffolds and other biomaterials. A fundamental requirement for tissue-engineered bone grafts is the ability to integrate with the host tissues while providing the capacity for remodeling and load-bearing [62,63]. The rapid restoration of biomechanical function is crucial in functional TE, emphasizing the need for optimal scaffold designs [64–66]. In recent years, finite element (FE) modeling has been extensively used to design 3D scaffolds by a variety of AM techniques [8,32,33,37,38,63,67]. Designed experiment (DE) have also been used for scaffold design, by accounting for a multitude of factors affecting the physical performance and biological outcomes of 3D scaffolds [21,68–70]. The aim of this study was to compare the FE and DE methods for the design of bone TE scaffolds. Computational over-prediction of scaffold performance has been partly attributed to the presence of a micro-topology on the surface of scaffolds that has not been accounted for in simulation models, and it has been suggested that the architecture of the scaffold affects the degree of the impact [36,38]. The COMSOL model presented here under-predicted compressive modulus of the scaffolds in 5 validation cases (out of 7). In comparison to other AM methods, such as

sintering, scaffolds produced by 3D bioplotting have distinctly smooth surfaces [6]. Thus, it is possible that the lack of a micro-topology reduced the risk of over-prediction by the COMSOL model. The prediction capability of FE models also depends on the range of applied compressive strains. For an idealized simple cubic strand layout (L/H = 1, no overlap between layers), it has been reported that FE simulations tend to under-predict the absolute values of compressive stress at low strains ( 25 MPa) for a stiffer solid matrix (E > 100 MPa). In light of this, the DE model should be able to readily capture the effect of strand spacing for scaffolds made of stiffer materials. The negative impact of porosity on compressive modulus is well established [7,20,83]. Any factor that affects porosity, such as strand spacing, should affect the modulus as well. Giannitelli et al. (2014) examined the effect of strand spacing on their simulation model and found that (even when porosity was held constant) larger strand spacing values reduced scaffold stiffness [7]. The cause of this disagreement between our two models may be further indicated by Fig. 12, which outlines the compressive modulus predicted by COMSOL as it iterated across the design region. At iteration 10, COMSOL increased porosity by increasing strand spacing and decreasing diameter. This resulted in a decrease in compressive modulus; however, the degree of impact was dependent on the material assumed. The 30% material (with the largest compressive modulus) suffered the largest loss in compressive modulus, whereas the 0% nHA simulation was less affected.

Figure 12. Compressive modulus of COMSOL scaffold model across iterations of the optimization process. It has been recommended that bone tissue scaffolds have a minimum pore size of 300 µm [20,66,84]. Although, it has been suggested by Fisher et al. (2002) that pore sizes up to 800 µm perform similarly to 300 µm pores in vivo [85]. This supports the use of the strand spacing suggested by COMSOL, but not the spacing recommended by the experimental model. In addition, the use of such a large spacing may cause a significant lack of surface area available for cellular attachment. Thus, it may be more beneficial to consider a smaller strand spacing than the experimental model suggests. Such a decision still produces scaffolds with acceptable porosities, because the experimental model indicated that all the strand spacing values within the design region resulted in porosities greater than 50%. The impact of large pore sizes on the accuracy of FE simulations should be further investigated in future studies. Size effects matter, particularly when the microstructural length scale of the porous material approaches the macroscale dimensions of the sample [86].

5 Conclusions A 3D bioplotter was used to produce 24 bone tissue scaffolds according to a split-plot designed experiment (DE). These scaffolds were made of PLGA, nHA and type I collagen using HFP as a

solvent. Mathematical models were generated relating nHA content and strand diameter to compressive modulus, and strand diameter and spacing to porosity. An optimized scaffold design generated from the experimental data was compared to an optimal design given by the COMSOL optimization module. Seven validation scaffolds were produced to cover COMSOL and DE optimal design ranges. These scaffolds had measured moduli between 4.5-9.9 MPa, depending on strand diameter, spacing and layer overlap. The main hypothesis of this study was that both the experimental (DE) and COMSOL (FE) models should suggest similar optimal topologies (±20% design factor value agreement). Within the design region, the DE and COMSOL models agreed in their recommended optimal nHA (30%) and strand diameter (460 µm). However, the two methods disagreed by more than 20% in strand spacing (923 µm for DE; 601 µm for COMSOL), for reasons discussed previously in this paper. The predicted results for the seven validation scaffolds showed relative agreement for scaffold porosity (mean absolute percentage error of 4% for DE and 13% for COMSOL), but the predictions were substantially poorer for scaffold modulus (52% for DE; 21% for COMSOL). Topology optimization has a great potential in improving the efficiency of scaffold design, even in cases where the property values are over/under-predicted. Expanding the design region in future experiments (e.g., higher nHA content and strand diameter), developing a more efficient solvent evaporation method, and exerting a greater control over layer overlap could allow developing PLGA-nHA-collagen scaffolds to meet the mechanical requirements for bone TE.

6 Acknowledgements This work was partially funded by the Ohio Board of Regents, the Ohio Third Frontier Program grant entitled: “Ohio Research Scholars in Layered Sensing”, IDCAST, Miami University’s Office for the Advancement of Research (OARS), and the College of Engineering and Computing (CEC). The authors wish to thank DSM Biomedical (Exton, PA) for generously supplying type 1 collagen used in this study. The authors also wish to thank Kathleen LaSance from the University of Cincinnati for CT analysis, Dr. Justin Saul for rheological measurements, Dr. Catherine Almquist, Dr. Jessica Sparks, Doug Hart, Matt Duley, Judy Bohnert, Rosa Akbarzadeh, Cara Janney and Carlie Focke for their technical assistance, and Laurie Edwards for her administrative assistance.

References 1.

2. 3.

4. 5.

6.

7.

8.

9.

10.

11.

12. 13.

14.

15.

16.

Razi H, Checa S, Schaser K-D, Duda GN. Shaping scaffold structures in rapid manufacturing implants: a modeling approach toward mechano-biologically optimized configurations for large bone defect. J Biomed Mater Res B Appl Biomater. 2012 Oct;100(7):1736–45. http://www.ncbi.nlm.nih.gov/pubmed/22807248 Hollister SJ. Porous scaffold design for tissue engineering. Nat Mater. 2005 Jul;4(7):518–24. http://www.ncbi.nlm.nih.gov/pubmed/16003400 Brydone AS, Meek D, Maclaine S. Bone grafting, orthopaedic biomaterials, and the clinical need for bone engineering. Proc Inst Mech Eng Part H J Eng Med . 2010 Dec 1;224 (12):1329–43. http://pih.sagepub.com/content/224/12/1329.abstract Liu X, Ma PX. Polymeric scaffolds for bone tissue engineering. Ann Biomed Eng. 2004 Mar;32(3):477–86. Sachlos E, Czernuszka JT. Making tissue engineering scaffolds work. Review: the application of solid freeform fabrication technology to the production of tissue engineering scaffolds. Eur Cell Mater. 2003 Jun;5:29–40. Yeong W-Y, Chua C-K, Leong K-F, Chandrasekaran M. Rapid prototyping in tissue engineering: challenges and potential. Trends Biotechnol. 2004 Dec;22(12):643–52. http://www.ncbi.nlm.nih.gov/pubmed/15542155 Giannitelli SM, Rainer A, Accoto D, De Porcellinis S, De-Juan-Pardo EM, Guglielmelli E, et al. Optimization Approaches for the Design of Additively Manufactured Scaffolds. In: Fernandes RP, Bartolo JP, editors. Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior. Dordrecht: Springer Netherlands; 2014. p. 113–28. http://dx.doi.org/10.1007/978-94-007-7073-7_6 Boccaccio A, Ballini A, Pappalettere C, Tullo D, Cantore S, Desiate A. Finite element method (FEM), mechanobiology and biomimetic scaffolds in bone tissue engineering. Int J Biol Sci. 2011 Jan;7(1):112–32. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3030147&tool=pmcentrez&rendertype =abstract Kelly DJ, Prendergast PJ. Prediction of the optimal mechanical properties for a scaffold used in osteochondral defect repair. Tissue Eng. 2006 Sep;12(9):2509–19. http://www.ncbi.nlm.nih.gov/pubmed/16995784 Ngiam M, Liao S, Patil AJ, Cheng Z, Chan CK, Ramakrishna S. The fabrication of nanohydroxyapatite on PLGA and PLGA/collagen nanofibrous composite scaffolds and their effects in osteoblastic behavior for bone tissue engineering. Bone. 2009 Jul;45(1):4–16. http://www.ncbi.nlm.nih.gov/pubmed/19358900 Sandino C, Lacroix D. A dynamical study of the mechanical stimuli and tissue differentiation within a CaP scaffold based on micro-CT finite element models. Biomech Model Mechanobiol. 2011 Jul;10(4):565–76. http://www.ncbi.nlm.nih.gov/pubmed/20865437 Hsieh W-T, Liu Y-S, Lee Y, Rimando MG, Lin K, Lee OK. Matrix dimensionality and stiffness cooperatively regulate osteogenesis of mesenchymal stromal cells. Acta Biomater. 2016;32:210–22. Checa S, Prendergast PJ. A mechanobiological model for tissue differentiation that includes angiogenesis: a lattice-based modeling approach. Ann Biomed Eng. 2009 Jan;37(1):129–45. http://www.ncbi.nlm.nih.gov/pubmed/19011968 Khayyeri H, Checa S, Tägil M, O’Brien FJ, Prendergast PJ. Tissue differentiation in an in vivo bioreactor: in silico investigations of scaffold stiffness. J Mater Sci Mater Med. 2010 Aug;21(8):2331–6. http://www.ncbi.nlm.nih.gov/pubmed/20037774 Hollister SJ, Maddox RD, Taboas JM. Optimal design and fabrication of scaffolds to mimic tissue properties and satisfy biological constraints. Biomaterials. 2002 Oct;23(20):4095–103. http://www.ncbi.nlm.nih.gov/pubmed/12182311 Sanz-Herrera JA, García-Aznar JM, Doblaré M. On scaffold designing for bone regeneration: A computational multiscale approach. Acta Biomater. 2009 Jan;5(1):219–29.

17.

18. 19. 20. 21.

22. 23.

24.

25. 26. 27.

28.

29. 30.

31. 32.

33.

34.

35.

36.

http://www.ncbi.nlm.nih.gov/pubmed/18725187 Milan J-L, Planell J a, Lacroix D. Simulation of bone tissue formation within a porous scaffold under dynamic compression. Biomech Model Mechanobiol. 2010 Oct;9(5):583–96. http://www.ncbi.nlm.nih.gov/pubmed/20204446 Rho JY, Ashman RB, Turner CH. Young’s modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements. J Biomech. 1993 Feb;26(2):111–9. Schaffler MB, Burr DB. Stiffness of compact bone: effects of porosity and density. J Biomech. 1988;21(1):13–6. Karageorgiou V, Kaplan D. Porosity of 3D biomaterial scaffolds and osteogenesis. Biomaterials. 2005;26(27):5474–91. http://linkinghub.elsevier.com/retrieve/pii/S0142961205001511 Kim JY, Cho D-W. The optimization of hybrid scaffold fabrication process in precision deposition system using design of experiments. Microsyst Technol. 2008 Nov 4;15(6):843–51. http://link.springer.com/10.1007/s00542-008-0727-8 Kim S-S, Sun Park M, Jeon O, Yong Choi C, Kim B-S. Poly(lactide-co-glycolide)/hydroxyapatite composite scaffolds for bone tissue engineering. Biomaterials. 2006;27(8):1399–409. Gentile P, Chiono V, Carmagnola I, Hatton P V. An Overview of Poly(lactic-co-glycolic) Acid (PLGA)-Based Biomaterials for Bone Tissue Engineering. Int J Mol Sci. 2014;15(3):3640. http://www.mdpi.com/1422-0067/15/3/3640 Marra KG, Szem JW, Kumta PN, DiMilla PA, Weiss LE. In vitro analysis of biodegradable polymer blend/hydroxyapatite composites for bone tissue engineering. J Biomed Mater Res. 1999 Dec;47(3):324–35. Orlovskii VP, Komlev VS, Barinov SM. Hydroxyapatite and Hydroxyapatite-Based Ceramics. Inorg Mater. 2002;38(10):973–84. http://dx.doi.org/10.1023/A:1020585800572 Wang H. Hydroxyapatite degradation and biocompatibility. Ohio State University; 2004. Jose M V, Thomas V, Xu Y, Bellis S, Nyairo E, Dean D. Aligned bioactive multi-component nanofibrous nanocomposite scaffolds for bone tissue engineering. Macromol Biosci. 2010 Apr;10(4):433–44. Shuai C, Yang B, Peng S, Li Z. Development of composite porous scaffolds based on poly(lactideco-glycolide)/nano-hydroxyapatite via selective laser sintering. Int J Adv Manuf Technol. 2013;69(1):51–7. http://dx.doi.org/10.1007/s00170-013-5001-2 Lai ES, Anderson CM, Fuller GG. Designing a tubular matrix of oriented collagen fibrils for tissue engineering. Acta Biomater. 2011 Jun;7(6):2448–56. Barnes CP, Pemble CW, Brand DD, Simpson DG, Bowlin GL. Cross-linking electrospun type II collagen tissue engineering scaffolds with carbodiimide in ethanol. Tissue Eng. 2007 Jul;13(7):1593–605. http://www.ncbi.nlm.nih.gov/pubmed/17523878 Matthews JA, Wnek GE, Simpson DG, Bowlin GL. Electrospinning of collagen nanofibers. Biomacromolecules. 2002;3(2):232–8. Lacroix D, Planell JA, Prendergast PJ. Computer-aided design and finite-element modelling of biomaterial scaffolds for bone tissue engineering. Philos Trans A Math Phys Eng Sci. 2009 May 28;367(1895):1993–2009. http://www.ncbi.nlm.nih.gov/pubmed/19380322 Giannitelli SM, Accoto D, Trombetta M, Rainer A. Current trends in the design of scaffolds for computer-aided tissue engineering. Acta Biomater. 2014 Feb;10(2):580–94. http://www.ncbi.nlm.nih.gov/pubmed/24184176 McIntosh L, Cordell JM, Wagoner Johnson a J. Impact of bone geometry on effective properties of bone scaffolds. Acta Biomater. 2009 Feb;5(2):680–92. http://www.ncbi.nlm.nih.gov/pubmed/18955024 Melchels FP, Bertoldi K, Gabbrielli R, Velders AH, Feijen J, Grijpma DW. Mathematically defined tissue engineering scaffold architectures prepared by stereolithography. Biomaterials. 2010 Sep;31(27):6909–16. http://www.ncbi.nlm.nih.gov/pubmed/20579724 Cahill S, Lohfeld S, McHugh PE. Finite element predictions compared to experimental results for the effective modulus of bone tissue engineering scaffolds fabricated by selective laser sintering. J

37.

38.

39.

40.

41. 42. 43. 44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

Mater Sci Mater Med. 2009 Jun;20(6):1255–62. http://www.ncbi.nlm.nih.gov/pubmed/19199109 Rainer A, Giannitelli SM, Accoto D, De Porcellinis S, Guglielmelli E, Trombetta M. Load-adaptive scaffold architecturing: a bioinspired approach to the design of porous additively manufactured scaffolds with optimized mechanical properties. Ann Biomed Eng. 2012 Apr;40(4):966–75. http://www.ncbi.nlm.nih.gov/pubmed/22109804 Doyle H, Lohfeld S, McHugh P. Predicting the Elastic Properties of Selective Laser Sintered PCL/βTCP Bone Scaffold Materials Using Computational Modelling. Ann Biomed Eng. 2013 Sep 21;42(3):661–77. http://www.ncbi.nlm.nih.gov/pubmed/24057867 Blecha LD, Rakotomanana L, Razafimahery F, Terrier A, Pioletti DP. Targeted mechanical properties for optimal fluid motion inside artificial bone substitutes. J Orthop Res. 2009 Aug;27(8):1082–7. Raymond H. Myers, Douglas C. Montgomery CMA-C. Response Surface Methodology: Process and Product Optimization Using Designed Experiments. Edition 4th, editor. New York: Wiley; 2016. Wu CFJ, Hamada MS. Experiments: Planning, Analysis, and Optimization. 2nd Editio. New York: Wiley; 2009. Goos P, Jones B. Optimal Design of Experiments: A Case Study Approach. Hoboken, NJ; 2011. Jones B, Nachtsheim CJ. Split-Plot Designs : What, Why, and How. J Qual Technol. 2009;41(4):340–61. Akkouch A, Zhang Z, Rouabhia M. A novel collagen/hydroxyapatite/poly(lactide-co-εcaprolactone) biodegradable and bioactive 3D porous scaffold for bone regeneration. J Biomed Mater Res Part A. 2011;96A(4):693–704. http://dx.doi.org/10.1002/jbm.a.33033 Landers R, Pfister A, Hübner U, John H, Schmelzeisen R, Mülhaupt R. Fabrication of soft tissue engineering scaffolds by means of rapid prototyping techniques. J Mater Sci. 2002;37(15):3107–16. http://dx.doi.org/10.1023/A:1016189724389 Banglmaier RF, Sander EA, Vandevord PJ. Induction and quantification of collagen fiber alignment in a three-dimensional hydroxyapatite-collagen composite scaffold. Acta Biomater. 2015;17:26–35. http://dx.doi.org/10.1016/j.actbio.2015.01.033 David F, Levingstone TJ, Schneeweiss W, de Swarte M, Jahns H, Gleeson JP, et al. Enhanced bone healing using collagen–hydroxyapatite scaffold implantation in the treatment of a large multiloculated mandibular aneurysmal bone cyst in a thoroughbred filly. J Tissue Eng Regen Med. 2015;9(10):1193–9. http://dx.doi.org/10.1002/term.2006 Quinlan E, Thompson EM, Matsiko A, O’Brien FJ, López-Noriega A. Functionalization of a Collagen–Hydroxyapatite Scaffold with Osteostatin to Facilitate Enhanced Bone Regeneration. Adv Healthc Mater. 2015;4(17):2649–56. http://dx.doi.org/10.1002/adhm.201500439 Tang Y, Chen L, Zhao K, Wu Z, Wang Y, Tan Q. Fabrication of PLGA/HA (core)collagen/amoxicillin (shell) nanofiber membranes through coaxial electrospinning for guided tissue regeneration. Compos Sci Technol. 2016;125:100–7. Kwak S, Haider A, Gupta KC, Kim S, Kang I-K. Micro/Nano Multilayered Scaffolds of PLGA and Collagen by Alternately Electrospinning for Bone Tissue Engineering. Nanoscale Res Lett. 2016;11(1):1–16. http://dx.doi.org/10.1186/s11671-016-1532-4 Zhou Y, Yao H, Wang J, Wang D, Liu Q, Li Z. Greener synthesis of electrospun collagen/ hydroxyapatite composite fibers with an excellent microstructure for bone tissue engineering. Int J Nanomedicine. 2015;10:3203–15. Ribeiro N, Sousa SR, van Blitterswijk CA, Moroni L, Monteiro FJ. A biocomposite of collagen nanofibers and nanohydroxyapatite for bone regeneration. Biofabrication. 2014;6(3):35015. http://stacks.iop.org/1758-5090/6/i=3/a=035015 Murphy CM, Schindeler A, Gleeson JP, Yu NYC, Cantrill LC. A collagen–hydroxyapatite scaffold allows for binding and co-delivery of recombinant bone morphogenetic proteins and bisphosphonates. Acta Biomater. 2014;10(5):2250–8. Villa MM, Wang L, Huang J, Rowe DW, Wei M. Bone tissue engineering with a collagen–

55.

56.

57.

58.

59.

60.

61. 62.

63.

64. 65.

66.

67.

68.

69.

70.

71.

hydroxyapatite scaffold and culture expanded bone marrow stromal cells. J Biomed Mater Res Part B Appl Biomater. 2015;103(2):243–53. http://dx.doi.org/10.1002/jbm.b.33225 Kon E, Delcogliano M, Filardo G, Busacca M, Di Martino A, Marcacci M. Novel nano-composite multilayered biomaterial for osteochondral regeneration: a pilot clinical trial. Am J Sports Med. 2011 Jun;39(6):1180–90. http://www.ncbi.nlm.nih.gov/pubmed/21310939 Zhou C, Ye X, Fan Y, Ma L, Tan Y, Qing F, et al. Biomimetic fabrication of a three-level hierarchical calcium phosphate/collagen/hydroxyapatite scaffold for bone tissue engineering. Biofabrication. 2014;6(3):035013. http://www.ncbi.nlm.nih.gov/pubmed/24873777 Akkouch A, Zhang Z, Rouabhia M. Engineering bone tissue using human dental pulp stem cells and an osteogenic collagen-hydroxyapatite-poly (L-lactide-co-ε-caprolactone) scaffold. J Biomater Appl. 2014;28(6):922–36. http://www.ncbi.nlm.nih.gov/pubmed/23640860 Liu W, Wang D, Huang J, Wei Y, Xiong J, Zhu W, et al. Low-temperature deposition manufacturing: A novel and promising rapid prototyping technology for the fabrication of tissueengineered scaffold. Mater Sci Eng C. 2016; El-Ayoubi R, Eliopoulos N, Diraddo R, Galipeau J, Yousefi A-M. Design and Fabrication of 3D Porous Scaffolds to Facilitate Cell-Based Gene Therapy. Tissue Eng Part A. 2008 Jun;14(6):1037– 48. http://www.liebertonline.com/doi/abs/10.1089/ten.tea.2006.0418 Coutu DL, Yousefi AM, Galipeau J. Three-dimensional porous scaffolds at the crossroads of tissue engineering and cell-based gene therapy. J Cell Biochem. 2009 Oct 15;108(3):537–46. http://www.ncbi.nlm.nih.gov/pubmed/19681040 Yousefi AM, Gauvin C, Sun L, Diraddo RW, Fernandes J. Design and Fabrication of 3D-Plotted Polymeric Scaffolds in Functional Tissue Engineering. Polym Eng Sci. 2007;47(5):608–18. Bhumiratana S, Vunjak-Novakovic G. Concise Review: Personalized human bone grafts for reconstructing head and face, stem cells translational medicine. Stem Cells Transl Med. 2012;1:64– 9. Yousefi AM, Hoque ME, Prasad RGS V., Uth N. Current strategies in multiphasic scaffold design for osteochondral tissue engineering: A review. J Biomed Mater Res Part A. 2015;103(7):2460–81. http://doi.wiley.com/10.1002/jbm.a.35356 Guilak F, Butler DL, Goldstein SA, Money D (Eds. . Functional Tissue Engineering. New York: Springer; 2003. Ingber DE, Mow VC, Butler D, Niklason L, Huard J, Mao J, et al. Tissue engineering and developmental biology: going biomimetic. Tissue Eng. 2006 Dec;12(12):3265–83. http://www.ncbi.nlm.nih.gov/pubmed/17518669 Akbarzadeh R, Minton JA, Janney CS, Smith TA, James PF, Yousefi AM. Hierarchical polymeric scaffolds support the growth of MC3T3-E1 cells. J Mater Sci Mater Med. 2015;26(2):116–27. http://link.springer.com/10.1007/s10856-015-5453-z Olivares AL, Marsal E, Planell JA, Lacroix D. Finite element study of scaffold architecture design and culture conditions for tissue engineering. Biomaterials. 2009 Oct;30(30):6142–9. http://www.ncbi.nlm.nih.gov/pubmed/19674779 Hoelzle DJ, Alleyne AG, Wagoner Johnson AJ. Micro-robotic deposition guidelines by a design of experiments approach to maximize fabrication reliability for the bone scaffold application. Acta Biomater. 2008;4(4):897–912. Weiss LE, Amon CH, Finger S, Miller ED, Romero D, Verdinelli I, et al. Bayesian computer-aided experimental design of heterogeneous scaffolds for tissue engineering. Comput Des. 2005 Sep;37(11):1127–39. http://linkinghub.elsevier.com/retrieve/pii/S0010448505000345 Chen Y-L, Lee H-P, Chan H-Y, Sung L-Y, Chen H-C, Hu Y-C. Composite chondroitin-6sulfate/dermatan sulfate/chitosan scaffolds for cartilage tissue engineering. Biomaterials. 2007 May;28(14):2294–305. Duoss EB, Weisgraber TH, Hearon K, Zhu C, Small W, Metz TR, et al. Three-Dimensional Printing of Elastomeric, Cellular Architectures with Negative Stiffness. Adv Funct Mater. 2014;24(31):4905–13. http://dx.doi.org/10.1002/adfm.201400451

72.

73.

74.

75.

76.

77.

78.

79. 80.

81.

82.

83.

84. 85.

86.

Minton J, Janney C, Akbarzadeh R, Focke C, Subramanian A, Smith T, et al. Solvent-free polymer/bioceramic scaffolds for bone tissue engineering : fabrication, analysis, and cell growth. J Biomater Sci Polym Ed. 2014;25(16):1856–74. Wagoner Johnson AJ, Herschler BA. A review of the mechanical behavior of CaP and CaP/polymer composites for applications in bone replacement and repair. Acta Biomater. 2011 Jan;7(1):16–30. http://www.ncbi.nlm.nih.gov/pubmed/20655397 Yousefi AM, Oudadesse H, Akbarzadeh R, Wers E, Lucas-Girot A. Physical and Biological Characteristics of Nanohydroxyapatite and Bioactive Glasses used for Bone Tissue Engineering. Nanotechnol Rev. 2014;3(6):527–52. Wei G, Ma PX. Structure and properties of nano-hydroxyapatite/polymer composite scaffolds for bone tissue engineering. Biomaterials. 2004 Aug;25(19):4749–57. http://www.ncbi.nlm.nih.gov/pubmed/15120521 Mathieu LM, Bourban P-E, Månson J-AE. Processing of homogeneous ceramic/polymer blends for bioresorbable composites. Compos Sci Technol. 2006;66(11–12):1606–14. http://www.sciencedirect.com/science/article/pii/S0266353805004355 Zhang CY, Lu H, Zhuang Z, Wang XP, Fang QF. Nano-hydroxyapatite/poly(L-lactic acid) composite synthesized by a modified in situ precipitation: preparation and properties. J Mater Sci Mater Med. 2010 Dec;21(12):3077–83. http://www.ncbi.nlm.nih.gov/pubmed/20890640 Gay S, Arostegui S, Lemaitre J. Preparation and characterization of dense nanohydroxyapatite/PLLA composites. Mater Sci Eng C. 2009 Jan;29(1):172–7. http://linkinghub.elsevier.com/retrieve/pii/S0928493108001239 Ignjatovic N, Delijic K, Vukcevic M, Uskokovic D. Microstructure and mechanical properties of hot-pressed hydroxyapatite/poly-L-lactide biomaterials. Bioceramics. 2000;192:737–40. Shikinami Y, Okuno M. Bioresorbable devices made of forged composites of hydroxyapatite (HA) particles and poly-L-lactide (PLLA): Part I. Basic characteristics. Biomaterials. 1999 May;20(9):859–77. Huebsch N, Lippens E, Lee K, Mehta M, Koshy ST, Darnell MC, et al. Matrix elasticity of voidforming hydrogels controls transplanted-stem-cell-mediated bone formation. Nature Materials 2015 Dec;14(12):1269-77. Guo R, Merkel AR, Sterling JA, Davidson JM, Guelcher SA. Substrate Modulus of 3D-Printed Scaffolds Regulates the Regenerative Response in Subcutaneous Implants through the Macrophage Phenotype and Wnt Signaling. Biomaterials, 2015;73:85-95. Ryan G, McGarry P, Pandit A, Apatsidis D. Analysis of the mechanical behavior of a titanium scaffold with a repeating unit-cell substructure. J Biomed Mater Res B Appl Biomater. 2009 Aug;90(2):894–906. Sun L, Parker ST, Syoji D, Wang X, Lewis JA, Kaplan DL. Direct-write assembly of 3D silk/hydroxyapatite scaffolds for bone co-cultures. Adv Heal Mater. 2012;1:729–35. Fisher JP, Vehof JWM, Dean D, van der Waerden JPCM, Holland TA, Mikos AG, et al. Soft and hard tissue response to photocrosslinked poly(propylene fumarate) scaffolds in a rabbit model. J Biomed Mater Res. 2002 Mar;59(3):547–56. Onck PR, Andrews EW, Gibson LJ. Size effects in ductile cellular solids. Part I: modelling. Int J Mech Sci. 2001;43:681–699.