# Modeling of the Mechanical Behavior of 3D Bioplotted Scaffolds Considering the Penetration in Interlocked Strands

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Material Preparation for Fabrication

_{2}was added to the print bath to induce immediate crosslinking as the material was extruded in the scaffold fabrication process, as described below.

#### 2.2. Design and Fabrication of Scaffolds

^{TM}system (EnvisionTEC GmbH, Gladbeck, Germany) was used to fabricate scaffolds by printing alginate solution into the 50 mM CaCl

_{2}solution to induce crosslinking layer-by-layer. Specifically, the 3% alginate solution was maintained at 10 °C for 10 min in a low-temperature dispensing head. Alginate was dispensed at 18–20 °C using a conical needle with the inner diameter of 200 µm. The scaffolds were printed in a 12-well tissue culture plate coated with PEI, with each well containing 1 mL of 50 mM CaCl

_{2}to crosslink alginate immediately after dispensing. The pressure was set at 0.2 bar and head speed of 8 mm/s selected during printing. Printing conditions are presented in Table 1. After fabrication, scaffolds were maintained in the crosslinking solution for a time period sufficient to allow the Ca

^{2+}ions to penetrate and crosslink the whole structure.

^{TM}system by employing the procedure and printing conditions similar to the above scaffold fabrication except the zero distance set between two adjacent strands.

#### 2.3. Image Analyzing

^{®}1.48v Software (National Institute of Health, Gaithersburg, MD USA). The strand diameter, height, and pore size of the fabricated scaffold were obtained using the aforementioned software (n = 10). Moreover, the projected area on the plane of loading, which is needed for the calculation of stress was obtained using the dimensions obtained from these images prior to performing mechanical testing.

#### 2.4. Mechanical Testing

^{−1}) with a defined preload of 1 N. Before doing any experiment, specimens were placed between the loading plates of the machine and the load cell was set to zero. ASTM D-695 standard was used to assess the elastic modulus of both bulk gels and porous scaffolds of alginate [25], as reported in the standard guide for characterization and testing of biomaterial scaffolds used in tissue-engineered medical products (ASTM: F2150-13) [26]. Porous scaffolds were kept in a CaCl

_{2}crosslinking solution and extracted from the solution immediately prior to mechanical testing. It should be noted that keeping fabricated samples of alginate in the incubator at 37 °C temperature (humidified environment containing 5% CO

_{2}) did not have any significant effect on the elastic modulus. Hence, to simplify the experiment, samples were kept in a refrigerator (4 °C) before the experiment. It is noted that there was a nonlinear region at the beginning of the stress-strain curves, termed as the toe-region. This region makes the calculation of the elastic modulus (the slope of the first linear part of the curve) difficult. Based on the method provided in ASTM D-695 standard, a line was used to fit the first linear section of the curves and the intersection of this line and the strain axis is terms as the corrected zero-strain point.

#### 2.5. Finite Element Modeling

_{x}and P

_{z}, respectively, and the length of material exceeding the main borders of the scaffold by E

_{x}and E

_{z}(Figure 3a). It should be mentioned that for applying the compressive load, the upper and lower sides of the modeled scaffolds were trimmed with the value of Δ

_{L}. Using these parameters, the dimensions of the scaffold can be calculated using the following relationships:

_{x}, L

_{y}, and L

_{z}are the length of the scaffold in each direction.

#### 2.6. Statistical Analysis

^{®}17.1 software (State College, PA, USA) and confidence level for all intervals was considered as two-sided intervals with 95% value and, thus, p-value less than 0.05 was considered significant.

## 3. Results and Discussion

#### 3.1. Model Verification

^{®}Software, the elastic modulus of bulk gel and porous scaffolds are then examined and reported, and finally the results of the developed finite element model are presented and compared with the experimental measurements.

^{®}Software. The average pore size was 0.39 ± 0.03 mm and 0.47 ± 0.06 mm in Z and X directions, respectively. The strand diameter and height of the scaffold were also measured as 0.58 ± 0.06 mm and 2.63 ± 0.12 mm in Z and X directions, respectively. To measure the penetration, the original CAD design and the printed scaffolds were compared in terms of the layer height. The penetration was calculated based on the difference in heights, giving a value of 510 µm. Table 2 shows the parameters obtained from geometrical features of the fabricated scaffold and they were used in the simulation of the model, as input data.

_{x}= 551 µm and P

_{z}= 487 µm, while the model predicted 21.35 KPa (Figure 6). As it was mentioned, the elastic modulus of scaffolds fabricated based on parameters reported in Table 2 (P

_{x}= 470 µm and P

_{z}= 390 µm) was 32.1 ± 0.6 KPa, while the model predicted 28.76 KPa. In addition, for bulk gel, the elastic modulus of 42.3 ± 1.58 KPa was calculated experimentally, while the simulation predicted 37.94 KPa, as the elastic modulus. In the case of a bulk gel, P

_{x}= P

_{z}= 0 was considered for the modeling purpose.

#### 3.2. Some More Simulation Results

_{2}, the number of available Ca

^{2+}ions in the crosslinking media decreases gradually with the fabrication of successive layers. Such a variable concentration of Ca

^{2+}ions can affect the structure and thus the mechanical properties of the printed scaffolds [32]. As such, the effect of the crosslinker mechanism can be taken into consideration for improving the accuracy of model prediction. Also, fluid viscosity is temperature-dependent and therefore temperature, changing during the printing process, can affect the fluid flow, which is also responsible for degraded structures in the bioplotted scaffolds. Another important factor influencing the mechanical behavior of porous scaffolds is microstructure degradation from the designed one [33,34,35,36]. Thus, in order to enhance the accuracy of numerical models, one way is to identify these changes and degradations and specify them or their effects in the model. Moreover, it was reported that pore distribution and orientation of strands are not stable throughout the printed scaffold and it can influence the mechanical properties of scaffolds [37]. All of these can result in the degradation of the structure of scaffolds, thus affecting the error between the predicted and real values of scaffolds mechanical properties.

^{2}= 99.61%) to quantitatively specify the effect of each term on the elastic modulus. For this purpose, the degree of penetration, strand diameter, pore size, and extra materials in X and Z directions, and the number of layers in Y direction were considered in the model. The number of layers in X and Z directions were assumed as five. In addition, considering the effect of major factors (Δ

_{0}, D, P

_{z}, P

_{x}, E

_{z}, E

_{x}, and N

_{y}), all the interactions amongst the aforementioned factors were considered in the model. Accordingly, with respect to the p-value, some parameters were not appeared to be significant. However, regarding the interaction between various terms, these factors showed a significant effect Significant interactions were identified amongst many factors including penetration*N

_{y}, D*N

_{y}, D*P

_{z}, D*P

_{x}, N

_{y}*P

_{z}, and N

_{y}*P

_{x}. Figure 8 shows the effect of each factor on the elastic modulus demonstrating the significant effect of different terms on the elastic modulus.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Illustration of printing alginate scaffolds: (

**a**) computer-aided-design (CAD) model; (

**b**) sliced layers; and (

**c**) 3D-Bioplotter used for scaffold printing, with an inserted image showing the alginate scaffold printed in a tissue culture plate.

**Figure 3.**(

**a**) Applied parameters in finite element model including the amount of penetration within layers (Δ

_{0}), pore size in the X and Z directions (P

_{x}and P

_{z}), E

_{x}and E

_{z}as the extra material exceeding the main borders of the scaffold. Δ

_{L}is also the amount of trimmed value of the upper and lower sides of the modeled scaffolds for applying the compressive load and D is the strand diameter and (

**b**) applied boundary conditions and meshed part.

**Figure 5.**Effect of penetration within layers on the elastic modulus of alginate scaffolds with a strand diameter of 0.58 mm and a distance of 1 mm between two adjacent strands.

**Figure 6.**Effect of pore size on the elastic modulus (pattern fill column bars show experimental results for bioplotted scaffolds with (P

_{x}

_{,z}= 0), (P

_{x}= 470 and P

_{z}= 390), and (P

_{x}= 551 and P

_{z}= 487)).

**Figure 7.**Effect of the number of layers on the elastic modulus (pattern fill column bars show experimental results for bioplotted scaffolds with 16 (24.25 ± 0.64 KPa), 24 (26.85 ± 0.92 KPa), and 31 layers (32.1 ± 0.60 KPa)).

**Figure 8.**Effect of (

**a**) Δ

_{0}and N

_{y}; (

**b**) Δ

_{0}and D; (

**c**) E

_{x}and E

_{z}; and (

**d**) P

_{z}and P

_{x}on the elastic modulus (EM).

Concentration | Needle Diameter (µm) | Head Speed (mm/s) | Pressure (bar) | Temperature (°C) | Crosslinker |
---|---|---|---|---|---|

3% (w/v) | 200 | 8 | 0.2 | 18–20 | CaCl_{2} (50 mM) |

Parameters | Values (µm) |
---|---|

N_{x} | 7 |

N_{yx} | 15 |

N_{yz} | 16 |

N_{z} | 7 |

D | 580 |

$\Delta $_{0} | 510 |

$\Delta $_{L} | 10 |

P_{x} | 470 |

P_{z} | 390 |

E_{x} | 10 |

E_{z} | 10 |

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**MDPI and ACS Style**

Naghieh, S.; Sarker, M.D.; Karamooz-Ravari, M.R.; McInnes, A.D.; Chen, X. Modeling of the Mechanical Behavior of 3D Bioplotted Scaffolds Considering the Penetration in Interlocked Strands. *Appl. Sci.* **2018**, *8*, 1422.
https://doi.org/10.3390/app8091422

**AMA Style**

Naghieh S, Sarker MD, Karamooz-Ravari MR, McInnes AD, Chen X. Modeling of the Mechanical Behavior of 3D Bioplotted Scaffolds Considering the Penetration in Interlocked Strands. *Applied Sciences*. 2018; 8(9):1422.
https://doi.org/10.3390/app8091422

**Chicago/Turabian Style**

Naghieh, Saman, M. D. Sarker, Mohammad Reza Karamooz-Ravari, Adam D. McInnes, and Xiongbiao Chen. 2018. "Modeling of the Mechanical Behavior of 3D Bioplotted Scaffolds Considering the Penetration in Interlocked Strands" *Applied Sciences* 8, no. 9: 1422.
https://doi.org/10.3390/app8091422