# Time-Dependent Shear Stress Distributions during Extended Flow Perfusion Culture of Bone Tissue Engineered Constructs

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## Abstract

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## 1. Introduction

## 2. Results

#### 2.1. Construct Cellularity

#### 2.2. Calcium Deposition

#### 2.3. Shear Stress Distributions over Time

#### 2.4. Effects of Calcium Deposition on Localized Shear Fields

#### 2.5. Average Wall Shear Stress

## 3. Discussion

## 4. Materials and Methods

#### 4.1. Scaffold Manufacturing

#### 4.2. Cell Expansion, Seeding and Culture

#### 4.3. Construct Cellularity

^{®}dsDNA assay (Invitrogen). At each sacrificial time point, the construct was removed from the cassette and rinsed in PBS to remove any cells not adhered to the scaffold. Subsequently, the scaffolds were cut into eight pieces, placed in 1 mL of deionized (DI) H${}_{2}$O and stored at −20 ${}^{\circ}$C. Each construct underwent three freeze/thaw cycles to lyse the cells. Fluorescent analysis was conducted on a Synergy HT Multi-Mode Microplate Reader (BioTek Instruments, Inc., Winooski, VT, USA) at an excitation wavelength of 480 nm and an emission wavelength of 520 nm. All samples and standards were run in triplicate. Resulting values were then divided by the previously-determined dsDNA content per cell.

#### 4.4. Construct Calcium Deposition

#### 4.5. Imaging and Reconstruction

#### 4.6. CFD Simulations

#### Lattice Boltzmann Simulations

#### 4.7. Statistical Analysis

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Construct cellularity for each construct over the culture period. The horizontal dashed line indicates the initial amount of cells seeded. The vertical dotted line indicates the switch in flow rates, from 0.15 mL/min during seeding to 0.5 mL/min for culture. Values are given as the mean ± the standard error of the mean (n = 4).

**Figure 2.**Calcium levels present within each construct over the culture period. The horizontal dotted line represents the background signal for an empty construct. Values are given as the mean ± the standard error of the mean (n = 4). The # signifies the significantly lowest value ($p<$ 0.01).

**Figure 3.**Summary of mineralized tissue (hard extracellular matrix (ECM)) deposited in cultured constructs rendered during microcomputed tomography ($\mu $CT) with Simple Viewer for samples taken on Days 8, 11 and 16, respectively.

**Figure 4.**(Left) 2D grayscale view of the scaffold after $\mu $CT imaging. The top row is a view of the entire scaffold, while the bottom row is a magnified view of the indicated area of interest. (Right) 2D view of the scaffold after $\mu $CT imaging with ECM indicated in red.

**Figure 5.**Wall shear stress distributions based on the day a construct was removed from culture and imaged.

**Figure 6.**Summary of wall shear stress heat maps for constructs cultured under osteoconductive conditions. (

**a**) Wall shear heat maps for Day 1 (far left) to Day 11 (far right) obtained using the custom lattice Boltzmann method code. (

**b**) Scale bar: values given in $\frac{\mathrm{g}}{{\mathrm{cm}\xb7\mathrm{s}}^{2}}$.

**Figure 7.**Summary of average shear stress per layer for a 0.5 mL/min flow rate. Values are given as the mean ± the standard error of the mean (n = 3). Significance calculated via analysis of variance (ANOVA) with the Tukey honest significant difference (HSD) post-hoc analysis.

**Figure 8.**Common synthetic polymeric scaffolds used for tissue engineering. Scaffolds manufactured using spunbonding and imaged using scanning electron microscopy (SEM).

**Figure 9.**Schematic of the custom in-house perfusion bioreactor system. The right image shows the combination of the bioreactor body, scaffold cassettes and stand.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Williams, C.; Kadri, O.E.; Voronov, R.S.; Sikavitsas, V.I.
Time-Dependent Shear Stress Distributions during Extended Flow Perfusion Culture of Bone Tissue Engineered Constructs. *Fluids* **2018**, *3*, 25.
https://doi.org/10.3390/fluids3020025

**AMA Style**

Williams C, Kadri OE, Voronov RS, Sikavitsas VI.
Time-Dependent Shear Stress Distributions during Extended Flow Perfusion Culture of Bone Tissue Engineered Constructs. *Fluids*. 2018; 3(2):25.
https://doi.org/10.3390/fluids3020025

**Chicago/Turabian Style**

Williams, Cortes, Olufemi E. Kadri, Roman S. Voronov, and Vassilios I. Sikavitsas.
2018. "Time-Dependent Shear Stress Distributions during Extended Flow Perfusion Culture of Bone Tissue Engineered Constructs" *Fluids* 3, no. 2: 25.
https://doi.org/10.3390/fluids3020025