Bi-Modular Flow Characterization in Tissue Engineering Scaffolds Using Computational Fluid Dynamics and Particle Imaging Velocimetry

Generation and evaluation of input values for computational analysis of transport processes within tissue cultures

Techniques for tissue culture have seen significant advances during the last decades and novel 3D cell culture systems have become available. To control their high complexity, experimental techniques and their Digital Twins (modelling and computational tools) are combined to link different variables to process conditions and critical process parameters. This allows a rapid evaluation of the expected product quality. However, the use of mathematical simulation and Digital Twins is critically dependent on the precise description of the problem and correct input parameters. Errors here can lead to dramatically wrong conclusions. The intention of this review is to provide an overview of the state‐of‐the‐art and remaining challenges with respect to generating input values for computational analysis of mass and momentum transport processes within tissue cultures. It gives an overview on relevant aspects of transport processes in tissue cultures as well as modelling and computational tools to tackle these problems. Further focus is on techniques used for the determination of cell‐specific parameters and characterization of culture systems, including sensors for on‐line determination of relevant parameters. In conclusion, tissue culture techniques are well‐established, and modelling tools are technically mature. New sensor technologies are on the way, especially for organ chips. The greatest remaining challenge seems to be the proper addressing and handling of input parameters required for mathematical models. Following Good Modelling Practice approaches when setting up and validating computational models is, therefore, essential to get to better estimations of the interesting complex processes inside organotypic tissue cultures in the future.

2D µ-Particle Image Velocimetry and Computational Fluid Dynamics Study Within a 3D Porous Scaffold

Transport properties of 3D scaffolds under fluid flow are critical for tissue development. Computational fluid dynamics (CFD) models can resolve 3D flows and nutrient concentrations in bioreactors at the scaffold-pore scale with high resolution. However, CFD models can be formulated based on assumptions and simplifications. μ-Particle image velocimetry (PIV) measurements should be performed to improve the reliability and predictive power of such models. Nevertheless, measuring fluid flow velocities within 3D scaffolds is challenging. The aim of this study was to develop a μPIV approach to allow the extraction of velocity fields from a 3D additive manufacturing scaffold using a conventional 2D μPIV system. The μ-computed tomography scaffold geometry was included in a CFD model where perfusion conditions were simulated. Good agreement was found between velocity profiles from measurements and computational results. Maximum velocities were found at the centre of the pore using both techniques with a difference of 12% which was expected according to the accuracy of the μPIV system. However, significant differences in terms of velocity magnitude were found near scaffold substrate due to scaffold brightness which affected the μPIV measurements. As a result, the limitations of the μPIV system only permits a partial validation of the CFD model. Nevertheless, the combination of both techniques allowed a detailed description of velocity maps within a 3D scaffold which is crucial to determine the optimal cell and nutrient transport properties.

In silico regenerative medicine: how computational tools allow regulatory and financial challenges to be addressed in a volatile market

The cell therapy market is a highly volatile one, due to the use of disruptive technologies, the current economic situation and the small size of the market. In such a market, companies as well as academic research institutes are in need of tools to advance their understanding and, at the same time, reduce their R&D costs, increase product quality and productivity, and reduce the time to market. An additional difficulty is the regulatory path that needs to be followed, which is challenging in the case of cell-based therapeutic products and should rely on the implementation of quality by design (QbD) principles. In silico modelling is a tool that allows the above-mentioned challenges to be addressed in the field of regenerative medicine. This review discusses such in silico models and focuses more specifically on the bioprocess. Three (clusters of) examples related to this subject are discussed. The first example comes from the pharmaceutical engineering field where QbD principles and their implementation through the use of in silico models are both a regulatory and economic necessity. The second example is related to the production of red blood cells. The described in silico model is mainly used to investigate the manufacturing process of the cell-therapeutic product, and pays special attention to the economic viability of the process. Finally, we describe the set-up of a model capturing essential events in the development of a tissue-engineered combination product in the context of bone tissue engineering. For each of the examples, a short introduction to some economic aspects is given, followed by a description of the in silico tool or tools that have been developed to allow the implementation of QbD principles and optimal design.

Numerical investigation of dynamic microorgan devices as drug screening platforms. Part II: Microscale modeling approach and validation

The authors have previously reported a rigorous macroscale modeling approach for an in vitro 3D dynamic microorgan device (DMD). This paper represents the second of a two-part model-based investigation where the effect of microscale (single liver cell-level) shear-mediated mechanotransduction on drug biotransformation is deconstructed. Herein, each cell is explicitly incorporated into the geometric model as single compartmentalized metabolic structures. Each cell's metabolic activity is coupled with the microscale hydrodynamic Wall Shear Stress (WSS) simulated around the cell boundary through a semi-empirical polynomial function as an additional reaction term in the mass transfer equations. Guided by the macroscale model-based hydrodynamics, only 9 cells in 3 representative DMD domains are explicitly modeled. Dynamic and reaction similarity rules based on non-dimensionalization are invoked to correlate the numerical and empirical models, accounting for the substrate time scales. The proposed modeling approach addresses the key challenge of computational cost towards modeling complex large-scale DMD-type system with prohibitively high cell densities. Transient simulations are implemented to extract the drug metabolite profile with the microscale modeling approach validated with an experimental drug flow study. The results from the author's study demonstrate the preferred implementation of the microscale modeling approach over that of its macroscale counterpart.

A tracer liquid image velocimetry for multi-layer radial flow in bioreactors

Background

This paper presents a Tracer Liquid Image Velocimetry (TLIV) for multi-layer radial flow in bioreactors used for cells cultivation of tissue engineering. The goal of this approach is to use simple devices to get good measuring precision, specialized for the case in which the uniform level of fluid shear stress was required while fluid velocity varied smoothly.

Methods

Compared to the widely used Particles Image Velocimetry (PIV), this method adopted a bit of liquid as tracer, without the need of laser source. Sub-pixel positioning algorithm was used to overcome the adverse effects of the tracer liquid deformation. In addition, a neighborhood smoothing algorithm was used to restrict the measurement perturbation caused by diffusion. Experiments were carried out in a parallel plates flow chamber. And mathematical models of the flow chamber and Computational Fluid Dynamics (CFD) simulation were separately employed to validate the measurement precision of TLIV.

Results

The mean relative error between the simulated and measured data can be less than 2%, while in similar validations using PIV, the error was around 8.8%.

Conclusions

TLIV avoided the contradiction between the particles’ visibility and following performance with tested fluid, which is difficult to overcome in PIV. And TLIV is easier to popularize for its simple experimental condition and low cost.

Modeling mechanical signals on the surface of µCT and CAD based rapid prototype scaffold models to predict (early stage) tissue development

In the field of tissue engineering, mechano-regulation theories have been applied to help predict tissue development in tissue engineering scaffolds in the past. For this, finite element models (FEMs) were used to predict the distribution of strains within a scaffold. However, the strains reported in these studies are volumetric strains of the material or strains developed in the extracellular matrix occupying the pore space. The initial phase of cell attachment and growth on the biomaterial surface has thus far been neglected. In this study, we present a model that determines the magnitude of biomechanical signals on the biomaterial surface, enabling us to predict cell differentiation stimulus values at this initial stage. Results showed that magnitudes of the 2D strain--termed surface strain--were lower when compared to the 3D volumetric strain or the conventional octahedral shear strain as used in current mechano-regulation theories. Results of both µCT and CAD derived FEMs from the same scaffold were compared. Strain and fluid shear stress distributions, and subsequently the cell differentiation stimulus, were highly dependent on the pore shape. CAD models were not able to capture the distributions seen in the µCT FEM. The calculated mechanical stimuli could be combined with current mechanobiological models resulting in a tool to predict cell differentiation in the initial phase of tissue engineering. Although experimental data is still necessary to properly link mechanical signals to cell behavior in this specific setting, this model is an important step towards optimizing scaffold architecture and/or stimulation regimes.

Investigation of the in vitro culture process for skeletal-tissue-engineered constructs using computational fluid dynamics and experimental methods

The in vitro culture process via bioreactors is critical to create tissue-engineered constructs (TECs) to repair or replace the damaged tissues/organs in various engineered applications. In the past, the TEC culture process was typically treated as a black box and performed on the basis of trial and error. Recently, computational fluid dynamics (CFD) has demonstrated its potential to analyze the fluid flow inside and around the TECs, therefore, being able to provide insight into the culture process, such as information on the velocity field and shear stress distribution that can significantly affect such cellular activities as cell viability and proliferation during the culture process. This paper briefly reviews the CFD and experimental methods used to investigate the in vitro culture process of skeletal-type TECs in bioreactors, where mechanical deformation of the TEC can be ignored. Specifically, this paper presents CFD modeling approaches for the analysis of the velocity and shear stress fields, mass transfer, and cell growth during the culture process and also describes various particle image velocimetry (PIV) based experimental methods to measure the velocity and shear stress in the in vitro culture process. Some key issues and challenges are also identified and discussed along with recommendations for future research.

Three-dimensional microfluidic collagen hydrogels for investigating flow-mediated tumor-endothelial signaling and vascular organization

Hyperpermeable tumor vessels are responsible for elevated interstitial fluid pressure and altered flow patterns within the tumor microenvironment. These aberrant hydrodynamic stresses may enhance tumor development by stimulating the angiogenic activity of endothelial cells lining the tumor vasculature. However, it is currently not known to what extent shear forces affect endothelial organization or paracrine signaling during tumor angiogenesis. The objective of this study was to develop a three-dimensional (3D), in vitro microfluidic tumor vascular model for coculture of tumor and endothelial cells under varying flow shear stress conditions. A central microchannel embedded within a collagen hydrogel functions as a single neovessel through which tumor-relevant hydrodynamic stresses are introduced and quantified using microparticle image velocimetry (μ-PIV). This is the first use of μ-PIV in a tumor representative, 3D collagen matrix comprised of cylindrical microchannels, rather than planar geometries, to experimentally measure flow velocity and shear stress. Results demonstrate that endothelial cells develop a confluent endothelium on the microchannel lumen that maintains integrity under physiological flow shear stresses. Furthermore, this system provides downstream molecular analysis capability, as demonstrated by quantitative RT-PCR, in which, tumor cells significantly increase expression of proangiogenic genes in response to coculture with endothelial cells under low flow conditions. This work demonstrates that the microfluidic in vitro cell culture model can withstand a range of physiological flow rates and permit quantitative measurement of wall shear stress at the fluid-collagen interface using μ-PIV optical flow diagnostics, ultimately serving as a versatile platform for elucidating the role of fluid forces on tumor-endothelial cross talk.

Simulation of cell seeding within a three-dimensional porous scaffold: a fluid-particle analysis

Cell seeding is a critical step in tissue engineering. A high number of cells evenly distributed in scaffolds after seeding are associated with a more functional tissue culture. Furthermore, high cell densities have shown the possibility to reduce culture time or increase the formation of tissue. Experimentally, it is difficult to predict the cell-seeding process. In this study, a new methodology to simulate the cell-seeding process under perfusion conditions is proposed. The cells are treated as spherical particles dragged by the fluid media, where the physical parameters are computed through a Lagrangian formulation. The methodology proposed enables to define the kinetics of cell seeding continuously over time. An exponential relationship was found to optimize the seeding time and the number of cells seeded in the scaffold. The cell distribution and cell efficiency predicted using this methodology were similar to the experimental results of Melchels et al. One of the main advantages of this method is to be able to determine the three-dimensional position of all the seeded cells and to, therefore, better know the initial conditions for further cell proliferation and differentiation studies. This study opens up the field of numerical predictions related to the interactions between biomaterials, cells, and dynamics media.

Prediction of permeability of regular scaffolds for skeletal tissue engineering: a combined computational and experimental study

Scaffold permeability is a key parameter combining geometrical features such as pore shape, size and interconnectivity, porosity and specific surface area. It can influence the success of bone tissue engineering scaffolds, by affecting oxygen and nutrient transport, cell seeding efficiency, in vitro three-dimensional (3D) cell culture and, ultimately, the amount of bone formation. An accurate and efficient prediction of scaffold permeability would be highly useful as part of a scaffold design process. The aim of this study was (i) to determine the accuracy of computational fluid dynamics (CFD) models for prediction of the permeability coefficient of three different regular Ti6Al4V scaffolds (each having a different porosity) by comparison with experimentally measured values and (ii) to verify the validity of the semi-empirical Kozeny equation to calculate the permeability analytically. To do so, five CFD geometrical models per scaffold porosity were built, based on different geometrical inputs: either based on the scaffold's computer-aided design (CAD) or derived from 3D microfocus X-ray computed tomography (micro-CT) data of the additive manufactured (AM) scaffolds. For the latter the influence of the spatial image resolution and the image analysis algorithm used to determine the scaffold's architectural features on the predicted permeability was analysed. CFD models based on high-resolution micro-CT images could predict the permeability coefficients of the studied scaffolds: depending on scaffold porosity and image analysis algorithm, relative differences between measured and predicted permeability values were between 2% and 27%. Finally, the analytical Kozeny equation was found to be valid. A linear correlation between the ratio Φ(3)/S(s)(2) and the permeability coefficient k was found for the predicted (by means of CFD) as well as measured values (relative difference of 16.4% between respective Kozeny coefficients), thus resulting in accurate and efficient calculation of the permeability of regular AM scaffolds.