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Scaffolds with a High Surface Area-to-Volume Ratio and Cultured Under Fast Flow Perfusion Result in Optimal O_{2} Delivery to the Cells in Artificial Bone Tissues

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## Abstract

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## Featured Application

**Optimization of Scaffold Design and Flow Perfusion Culturing Conditions for Maximal Delivery of Oxygen to the Cells Embedded Deep Inside of Engineered Tissues.**

## Abstract

_{2}delivery to the cells residing in the interior of tissue engineering scaffolds make it challenging to grow artificial tissues of clinically-relevant sizes. This study uses image-based simulation in order to provide insight into how to better optimize the scaffold manufacturing parameters, and the culturing conditions, in order to resolve the O

_{2}bottleneck. To do this, high resolution 3D X-ray images of two common scaffold types (salt leached foam and non-woven fiber mesh) are fed into Lattice Boltzmann Method fluid dynamics and reactive Lagrangian Scalar Tracking mass transfer solvers. The obtained findings indicate that the scaffolds should have maximal surface area-to-solid volume ratios for higher chances of the molecular collisions with the cells. Furthermore, the cell culture media should be flown through the scaffold pores as fast as practically possible (without detaching or killing the cells). Finally, we have provided a parametric sweep that maps how the molecular transport within the scaffolds is affected by variations in rates of O

_{2}consumption by the cells. Ultimately, the results of this study are expected to benefit the computer-assisted design of tissue engineering scaffolds and culturing experiments.

## 1. Introduction

_{2}, nutrients, etc.) to the inner pore spaces of scaffolds, given that the cells consume them in large quantities as they build tissue. Among these, O

_{2}plays a critical role in the cell growth and proliferation, and thus its high concentrations have been correlated with both increased cellularity [3] and cell viability [4]. Conversely, a deficiency in O

_{2}can result in a hypoxic cell state, which is commonly associated with decreased metabolic activity and potentially undesirable differentiation behavior [5,6,7]. Hence, optimal oxygen transport is important in maintaining tissue function and overall survival within the artificial tissues. For that reason, bone tissue engineering scaffolds are typically cultured in perfusion bioreactors, the idea behind which is to facilitate the mass transfer using flow.

_{2}delivery to the cells is made difficult by the complexity of the pore network architectures in which they reside. This is because most large scaffolds are not transparent enough for microscopy, and it is also difficult to measure the O

_{2}concentrations at different locations within the scaffolds. Furthermore, the O

_{2}uptake rate by the cells changes over time [3]. All these complications make the problem even more difficult to solve manually. For these reasons, computer simulation of the O

_{2}transport and consumption offers itself as a viable alternative for obtaining insight into the microenvironment, which is experienced by the cells seeded on the surfaces of the scaffold pores.

_{2}) within scaffolds is uncommon when compared to flow parameters, such as stimulatory fluid shear stress, permeability, and pressure (see Table II in Ref. [8]). Furthermore, Table 1 below summarizes our overview of the few O

_{2}models that we did find in literature. From it, it can be seen that the studies commonly use idealized geometries for the scaffolds (e.g., a homogeneous porous medium) instead of realistic image-based. In reality, however, the scaffold architectures may be inhomogeneous. Moreover, many of the models either do not take into account specificities of bone tissue engineering, such as the need for flow perfusion, which generates a stimulatory shear environment natural to the bone canaliculi [9,10]. Instead, many models either target tissue engineering in general, or they may be specific to other tissue engineering disciplines; for example, Ferroni et al. [11] modeled a cardiac scaffold, which is cultured under pulsatile flow (not the case for bone). Finally, few of the models take into account O

_{2}consumption by the cells. And among those that do, the rate is typically assumed to be constant. Thus, we were not able to find a single bone tissue engineering model that accounted for all of the following: the realistic scaffold structure, O

_{2}diffusion, convection, and variable consumption rates.

_{2}transport and uptake by the cells in realistic bone tissue engineering scaffolds. To do this, we use two types of commonly-implemented types: the salt leached foam and the non-woven fiber mesh poly-L-lactic acid (PLLA) scaffolds. Their geometries are scanned in 3D using high resolution micro-computed tomography (µCT), and are imported into our image-based Lattice Boltzmann Method (LBM) flow [16,17,18,19] and reactive Lagrangian Scalar Tracking (rLST) mass transport [20] solvers. A big advantage of the latter is it can model particles with a range of reactivity, which is informative about how cells that are not necessarily starved for O

_{2}consume it. In this way, a more complete picture of O

_{2}transport within the different types of BTE scaffolds can be constructed. The overall computational scheme is depicted in Figure 1.

## 2. Materials and Methods

#### 2.1. Scaffold Fabrication

^{2}. The collected non-woven fiber stack then had a 7 cm center cut sheet obtained from it. Finally, using an 8 mm diameter die, discs were punched from the layered fiber sheets. The resulting scaffolds used in culturing were 8 mm diameter and ~2.3 mm thickness. Average fiber diameter was measured optically, using a Nikon HFX-II microscope.

_{2}O) under agitation for 2 days to leach out NaCl. Entire DIH

_{2}O volumes were replaced twice per day. Leached discs were then removed from DIH

_{2}O and placed under vacuum to remove moisture from the scaffolds. The resulting products were 8 mm diameter, 2.3 mm thick discs. Porosity of scaffolds was determined by measuring the solid volume (mass of the scaffold divided by the density of PLLA) and by comparing it to the total scaffold volume (assuming a cylindrical scaffold shape).

#### 2.2. 3D Imaging and Virtual Reconstruction

#### 2.3. Fluid Flow Modeling: Lattice Boltzmann Method (LBM)

#### 2.4. Oxygen Transport Modeling: Reactive Lagrangian Scalar Tracking (rLST)

_{0}is the nominal molecular diffusivity (i.e., the diffusivity that the particles would have if their motion was purely Brownian). It can also be expressed in terms of the dimensionless Schmidt number Sc, which depends on the carrier fluid’s viscosity. The molecular diffusivity of O

_{2}in the cell culture medium (assumed to be an aqueous solution at the physiological temperature of T = 37 °C) was 2.62 × 10

^{−5}cm

^{2}/s, which corresponded to a Schmidt number of 328.14.

_{2}consumption by the cells, each of the rLST particles had a probability ‘q’ to react upon colliding with the scaffold walls: ranging from q = 0 (non-reactive) to q = 1 (fully reactive).

_{2}. Since second order reactions (reactions between solute particles) were not considered for this model, any interactions between the rLST markers were neglected (i.e., they did not affect each other’s path). This approximation is good for a dilute solution. The simulation was allowed to evolve for a total of 10,000-time steps, which were needed to achieve equilibration. The ’Mersenne Twister’ random number generator with a cycle of length (2

^{19937}−1) was used for all random number generation in the rLST code [35].

## 3. Results

_{2}is vital to the cell survival in the 3D bone tissue engineering scaffolds. Yet, choosing the optimal scaffold manufacturing parameters and the culturing flow conditions is non-trivial, due to the complex transport phenomena occurring in the pore networks of the engineered tissue constructs. For this reason, we have performed image-based simulation of the fluid flow and of the O

_{2}transport that occur within two common types of bone tissue engineering PLLA scaffolds: the salt-leached foam and the non-woven fiber mesh.

_{2}is affected by the rate at which it is consumed by the cells, we considered different probabilities with which its molecules can react upon colliding with the scaffold walls. Specifically, we examined the condition of a uniform coverage of the scaffold surfaces with O

_{2}-starved cells in Figure 3, Figure 4, Figure 5 and Figure 6, while Figure 7 considers the case of the cells not starved for O

_{2}. Namely, the former corresponds to an infinite surface reaction rate (i.e., instantaneous consumption of every O

_{2}molecule that collides with a scaffold wall). It should be treated as a limiting case scenario, which allows for a comparison of different scaffold structures on an equivalent basis.

_{2}“survival distance” in the stream-wise direction (the X-direction), as a function of the scaffold structure and the cell-culture media perfusion flow rate. The survival distance is defined as the distance that the rLST markers (representing the O

_{2}molecules) travel on average, until they are “consumed” via a collision with a scaffold wall. From this figure, it is apparent that the survival distance in the stream-wise direction increases as the flow rate goes up. This is consistent with the Taylor–Aris dispersion theory, which states that the effective diffusivity in the stream-wise direction should increase with the square of the Peclet number [20,34]:

_{2}molecule in an aqueous cell culture media at T = 37 °C, as was discussed in the methods section. Hence, according to Equation (2), the Peclet number will increase proportionally with the value of Re, which depends on the velocity of the fluid. This leads to a higher effective diffusivity of the solute in the stream-wise direction, and thus, the O

_{2}can make it further into the scaffold before it is fully consumed by the cells.

_{2}is also inversely proportional to the specific surface area of the scaffold. This makes sense, because the O

_{2}molecules have a smaller chance to collide with the scaffold’s surface when it has less area exposed. Furthermore, Figure 3 shows that the foam scaffolds have a lower specific surface area than the fiber ones. This leads to noticeably longer survival distances of O

_{2}in the foam scaffolds.

_{2}transport within its structure. To that end, Equation (3) shows how the surface area-to-total volume ratio ‘S’ of a fiber mesh scaffold is related to its porosity and fiber diameter (see Supplementary Materials for derivation):

_{Fiber}is the fiber diameter and ε is the scaffold porosity. Similarly, Equation (4) shows how the surface area-to-total volume ratio ‘S’ of a foam scaffold is related to its porosity and salt grain diameter (see Supplementary Materials for derivation):

_{SaltGrain}is the diameter of the salt grains used for leaching, and ε is the scaffold porosity. Therefore, for a known scaffold porosity and diameter combination, one can relate these geometric parameters to the surface area-to-total volume ratio of the scaffold (and thus, to the results of this manuscript). It is also important to note that while S

_{Fiber}goes down with an increasing porosity ε, S

_{Foam}displays the opposite behavior, as can be seen from the Equations (3) and (4).

_{2}molecules in the scaffolds. Figure 5 plots this quantity as a function of the flow rate and the specific surface area of the scaffolds for the limiting case of fully reactive rLST particles. Conversely to the survival distance in Figure 3, the survival time in Figure 5 decreases with the flow rate, though the effect of the specific surface area remains the same, and the survival time varies inversely-proportionally to it. Combining the results from both of the figures, it becomes apparent that fully reactive molecules get carried to a farther distance by a higher flow rate. However, they take a shorter time to get consumed by the cells on the surface of the scaffolds. This is especially true for the scaffold geometries with a higher exposed surface area.

_{eff}, with which the O

_{2}molecules get consumed in the scaffolds, after accounting for the mass transfer limitations. To that end, Figure 6 is a plot of k

_{eff}as a function of the flow rate and specific surface area of the scaffold for the limiting case of an infinitely fast surface consumption of O

_{2}. It reaffirms the previously observed trends, which show that the O

_{2}is consumed faster in the scaffold structures with the higher surface area-to-solid volume ratios. Furthermore, it also supports the finding that increasing the cell culture media flow rate through the scaffold leads to a faster O

_{2}consumption in its pores.

_{2}, however, the rLST particles can be made to have a finite (as opposed to infinite) probability of becoming consumed upon collision with the scaffold walls. Thus, Figure 7 explores the role that the different cell affinities for consuming the O

_{2}have on its transport in the pores. In this case, the rLST particles with the different reactivities are all released simultaneously, and their survival times are compared as a function of the cell culture media flow rate and the scaffold type.

_{2}in the fiber scaffolds (solid lines) has a shorter survival time than in the foam ones (dotted lines), regardless of the cells’ affinity for its uptake. This is consistent with the trends in the previous section, which showed that the fiber scaffolds have a higher specific surface area than the foams. This makes them more efficient at delivering the O

_{2}molecules to the cells; and 2) the second trend essentially says that for a given surface reaction rate, the consumption of O

_{2}will take longer at the slower flows. This is again consistent with a similar trend that was shown in Figure 5, where the survival time increased with the slower flow rate.

## 4. Discussion

_{2}mass transfer is affected by the scaffold manufacturing and the flow perfusion culturing parameters in bone tissue engineering scaffolds. The knowledge obtained from the reported results is needed in order to overcome the product-size limitations, which are commonly experienced due to hypoxia and necrosis in the center of large scaffolds. To solve the problem, we used an image-based approach of scanning the true scaffold structures in 3D using a high resolution µCT, and then fed the obtained geometries to our in-house parallelized fluid flow (LBM) and mass transport (rLST) solvers. Two scaffolds commonly used in bone tissue engineering, the salt leached foam and the nonwoven fiber mesh, were used for this study. The O

_{2}transport results were parametrized as a function of the specific surface area of the scaffold, the flow rate in the bioreactor, and the affinity to consume the molecule by the cells.

_{2}uptake by them, which results in a higher consumption (i.e., shorter survival times and distances) of the molecules in the scaffold. Furthermore, by increasing the flow rate in the bioreactor, the O

_{2}transport can be both facilitated (as seen from the shorter survival time in Figure 4) and delivered deeper into the scaffold (as seen from the longer survival distance in Figure 3). Thus, the overall effective O

_{2}reaction coefficient k

_{eff}can be increased by maximizing both the specific surface area of the scaffold and the flowrate through its pores. This is evident from Figure 6.

_{2}delivery to the cells has also been reported by Bergemann et al. [4]. However, increasing it indefinitely is not an option because there is a trade-off with the shear forces exerted on the cells by the flow. Specifically, values in the range of 0.1–25 dynes/cm

^{2}[36,37,38] are generally considered to be beneficial because they mimic the natural microenvironment in bone canaliculi [9,10] and have been shown to promote tissue regeneration [39,40,41,42]. On the other hand, an excessive shear in the range of 26–54 dynes/cm

^{2}and higher can cause cell lysing and/or detachment from the scaffold [43,44]. Therefore, there is some optimal flow rate, which was found to be 45 μL/min by the Bergemann et al. study [4]. However, this value is specific to their scaffold-and-cell combination, and it could vary for other alternatives. Therefore, both image-based numerical simulations and cell viability assays are necessary for tuning the optimal conditions for other types of cultures. Whereas, at least the physical understanding provided in our study should be applicable across all scaffold types because they are expressed in terms of the specific surface area.

_{2}transport depends on its consumption by the cells. In this case, we are not assuming that the cells are O

_{2}-starved (and as a result take up every oxygen molecule that collides with them). Instead, we vary consumption rate of the O

_{2}at the scaffold surface in order to measure how this affects its transport in the scaffold. The results reported in this figure allow other researchers to understand the changes in the scaffold’s transport microenvironment over time. They also show how the flowrate and specific surface area trends are affected by the cell-specific O

_{2}consumption rates.

_{2}. Additionally, the scaffold’s structure in the real experiment could change due to wetting forces, fiber flexibility, and the natural degradation of PLLA. The latter produces acidic byproducts, whose removal is facilitated by the fluid flow [45], yet in our study, the scaffold’s structure remains static throughout the virtual experiment.

## 5. Conclusions

_{2}in scaffolds cultured in perfusion bioreactors is of interest to the fields of bone and other types of tissue engineering. Specifically, understanding how to control it can be instrumental to resolving product size limitations when it comes to culturing organ-sized scaffolds. Therefore, we performed an image-based simulation study, in which we showed that the scaffolds with the higher surface area-to-solid volume ratio result in a more efficient transfer of O

_{2}. Additionally, we showed that the effect can be increased further by flowing the cell culture media through the scaffold faster. Serendipitously, this also delivers the O

_{2}deeper into the scaffold pores, which is key to overcoming the product-size limitations mentioned earlier. Furthermore, we provided a parametric sweep over the rates of O

_{2}consumption by the cells situated on the scaffold surfaces. This visual aid yields insight into how the different cell affinities for consuming the O

_{2}can affect the molecule’s transport through the biological porous media. Finally, the computational framework presented in this study can serve as a viable tool for optimizing the scaffold design and experimental culturing protocols for other types of tissue engineering as well.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The image-based modeling methodology used in this work; scaffolds are scanned in 3D via high resolution μCT, reconstructed in silico, and the resulting geometries are used by the LBM and rLST solvers.

**Figure 2.**Visual comparison of the two scaffold architecture types used in this study. LEFT COLUMN—Salt-Leached Porous Foam Scaffold; RIGHT COLUMN—Non-woven Fiber Mesh Scaffold. TOP ROW—Three dimensional reconstructions of 8-mm-diameter and 2.3-mm-thickness scaffolds, obtained via µCT imaging (described in our previous works [16,17,25]). BOTTOM ROW—SEM close-ups of representative regions on the scaffolds’ surfaces. Images are shown at two different magnifications to illustrate morphological feature scales of the two scaffold types. Both of the scaffolds are made from poly-L-lactic acid.

**Figure 3.**Survival distance in the stream-wise direction as a function of perfusion flow rate and scaffold architecture. Data is plotted for the limiting case of the fully reactive Lagrangian Scalar Tracking (rLST) particles.

**Figure 4.**Survival distances in the Y & Z directions, as a function of the scaffold geometry and perfusion flow rate. Data is plotted for the limiting case of the fully reactive rLST particles. Both scaffolds types are chosen to have a similar specific surface area.

**Figure 5.**Survival time in the stream-wise direction as a function of perfusion flow rate and scaffold architecture. Data is plotted for the limiting case of the fully reactive rLST particles.

**Figure 6.**Effective O

_{2}reaction coefficient k

_{eff}as a function of perfusion flow rate and scaffold architecture. Data is plotted for the limiting case of the fully reactive rLST particles.

**Figure 7.**O

_{2}survival time as a function of the consumption rate by the cells on the scaffold surface. Data is plotted for salt leached foam and non-woven fiber mesh scaffolds at four different flow rates.

**Table 1.**Literature overview of O

_{2}simulations in tissue engineering scaffolds, shows that image-based simulation of convection with diffusion and reaction has not yet been done.

Scaffold Type | Simulated Geometry | O_{2} Diffusion | O_{2} Convection | O_{2} Reaction | Varied Parameter | Citation |
---|---|---|---|---|---|---|

45S5 Bioglass-PCL Robocast, Bioactive Glass 70S30C Sol-Gel Foamed and Titania Foam Replicated | Micro-computed Tomography | Yes | No | No | Void Fraction | Fiedler et al. [12] |

Cardiac Tissue Eng. | Idealized | Yes | Yes | No | Squeeze Pressure | Ferroni et al. [11] |

Microchanneled Hydrogel | Idealized | Yes | No | No | Microchannel Configuration | Arrigoni et al. [13] |

Periodically Self-Repeated Representative Volume Element | Idealized | Yes | No | Yes | Geometry of the Repeating Element | Li et al. [14] |

Bone Tissue Eng. Molded Tantalum | Idealized | Yes | Yes | Yes | Flow rate | Bergemann et al. [4] |

Homogeneous Porous Medium | Idealized | Yes | Yes | Yes | Flow rate, Porosity | Yan et al. [15] |

© 2019 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/).

## Share and Cite

**MDPI and ACS Style**

Nguyen, T.D.; Kadri, O.E.; Sikavitsas, V.I.; Voronov, R.S. Scaffolds with a High Surface Area-to-Volume Ratio and Cultured Under Fast Flow Perfusion Result in Optimal O_{2} Delivery to the Cells in Artificial Bone Tissues. *Appl. Sci.* **2019**, *9*, 2381.
https://doi.org/10.3390/app9112381

**AMA Style**

Nguyen TD, Kadri OE, Sikavitsas VI, Voronov RS. Scaffolds with a High Surface Area-to-Volume Ratio and Cultured Under Fast Flow Perfusion Result in Optimal O_{2} Delivery to the Cells in Artificial Bone Tissues. *Applied Sciences*. 2019; 9(11):2381.
https://doi.org/10.3390/app9112381

**Chicago/Turabian Style**

Nguyen, Thanh Danh, Olufemi E. Kadri, Vassilios I. Sikavitsas, and Roman S. Voronov. 2019. "Scaffolds with a High Surface Area-to-Volume Ratio and Cultured Under Fast Flow Perfusion Result in Optimal O_{2} Delivery to the Cells in Artificial Bone Tissues" *Applied Sciences* 9, no. 11: 2381.
https://doi.org/10.3390/app9112381