A mathematical model and computational framework for three-dimensional chondrocyte cell growth in a porous tissue scaffold placed inside a bi-directional flow perfusion bioreactor.

The in vitro chondrocyte cell culture for cartilage tissue regeneration in a perfusion bioreactor is a complex process. Mathematical modeling and computational simulation can provide important insights into the culture process, which would be helpful for selecting culture conditions to improve the quality of the developed tissue constructs. However, simulation of the cell culture process is a challenging task due to the complicated interaction between the cells and local fluid flow and nutrient transport inside the complex porous scaffolds. In this study, a mathematical model and computational framework has been developed to simulate the three-dimensional (3D) cell growth in a porous scaffold placed inside a bi-directional flow perfusion bioreactor. The model was developed by taking into account the two-way coupling between the cell growth and local flow field and associated glucose concentration, and then used to perform a resolved-scale simulation based on the lattice Boltzmann method (LBM). The simulation predicts the local shear stress, glucose concentration, and 3D cell growth inside the porous scaffold for a period of 30 days of cell culture. The predicted cell growth rate was in good overall agreement with the experimental results available in the literature. This study demonstrates that the bi-directional flow perfusion culture system can enhance the homogeneity of the cell growth inside the scaffold. The model and computational framework developed is capable of providing significant insight into the culture process, thus providing a powerful tool for the design and optimization of the cell culture process.

Turbulent blood flow in a cerebral artery with an aneurysm.

Unruptured intracranial aneurysms are common in the general population, and many uncertainties remain when predicting rupture risks and treatment outcomes. One of the cutting-edge tools used to investigate this condition is computational fluid dynamics (CFD). However, CFD is not yet mature enough to guide the clinical management of this disease. In addition, recent studies have reported significant flow instabilities when refined numerical methods are used. Questions remain as to how to properly simulate and evaluate this flow, and whether these instabilities are really turbulence. The purpose of the present study is to evaluate the impact of the simulation setup on the results and investigate the occurrence of turbulence in a cerebral artery with an aneurysm. For this purpose, direct numerical simulations were performed with up to 200 cardiac cycles and with data sampling rates of up to 100,000 times per cardiac cycle. Through phase-averaging or triple decomposition, the contributions of turbulence and of laminar pulsatile waves to the velocity, pressure and wall shear stress fluctuations were distinguished. For example, the commonly used oscillatory shear index was found to be closely related to the laminar waves introduced at the inlet, rather than turbulence. The turbulence energy cascade was evaluated through energy spectrum estimates, revealing that, despite the low flow rates and Reynolds number, the flow is turbulent near the aneurysm. Phase-averaging was shown to be an approach that can help researchers better understand this flow, although the results are highly dependent on simulation setup and post-processing choices.

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.

Prediction of cell growth rate over scaffold strands inside a perfusion bioreactor.

Mathematical and computational modeling of the dynamic process where tissue scaffolds are cultured in perfusion bioreactors is able to provide insight into the cell and tissue growth which can facilitate the design of tissue scaffolds and selection of optimal operating conditions. To date, a resolved-scale simulation of cell growth in the culture process, by taking account of the influences of the supply of nutrients and fluid shear stress on the cells, is not yet available in the literature. This paper presents such a simulation study specifically on cartilage tissue regeneration by numerically solving the momentum, scalar transport and cell growth equations, simultaneously, based on the lattice Boltzmann method. The simulation uses a simplified scaffold that consists of two circular strands placed in tandem inside a microchannel, with the object of identifying the effect of one strand on the other. The results indicate that the presence of the front strand can reduce the cell growth rate on the surface of the rear strand, depending on the distance between them. As such, the present study allows for investigation into the influence of the scaffold geometry on the cell growth rate within scaffolds, thus providing a means to improve the scaffold design and the culture process.

Modelling and simulation of the chondrocyte cell growth, glucose consumption and lactate production within a porous tissue scaffold inside a perfusion bioreactor.

Mathematical and numerical modelling of the tissue culture process in a perfusion bioreactor is able to provide insight into the fluid flow, nutrients and wastes transport, dynamics of the pH value, and the cell growth rate. Knowing the complicated interdependence of these processes is essential for optimizing the culture process for cell growth. This paper presents a resolved scale numerical simulation, which allows one not only to characterize the supply of glucose inside a porous tissue scaffold in a perfusion bioreactor, but also to assess the overall culture condition and predict the cell growth rate. The simulation uses a simplified scaffold that consists of a repeatable unit composed of multiple strands. The simulation results explore some problematic regions inside the simplified scaffold where the concentration of glucose becomes lower than the critical value for the chondrocyte cell viability and the cell growth rate becomes significantly reduced.

Computational modelling of the scaffold-free chondrocyte regeneration: a two-way coupling between the cell growth and local fluid flow and nutrient concentration.

The in vitro chondrocyte cell culture process in a perfusion bioreactor provides enhanced nutrient supply as well as the flow-induced shear stress that may have a positive influence on the cell growth. Mathematical and computational modelling of such a culture process, by solving the coupled flow, mass transfer and cell growth equations simultaneously, can provide important insight into the biomechanical environment of a bioreactor and the related cell growth process. To do this, a two-way coupling between the local flow field and cell growth is required. Notably, most of the computational and mathematical models to date have not taken into account the influence of the cell growth on the local flow field and nutrient concentration. The present research aimed at developing a mathematical model and performing a numerical simulation using the lattice Boltzmann method to predict the chondrocyte cell growth without a scaffold on a flat plate placed inside a perfusion bioreactor. The model considers the two-way coupling between the cell growth and local flow field, and the simulation has been performed for 174 culture days. To incorporate the cell growth into the model, a control-volume-based surface growth modelling approach has been adopted. The simulation results show the variation of local fluid velocity, shear stress and concentration distribution during the culture period due to the growth of the cell phase and also illustrate that the shear stress can increase the cell volume fraction to a certain extent.

Modeling of cell cultures in perfusion bioreactors.

Cultivating cells and tissues in bioreactors is a critical step in forming artificial tissues or organs prior to transplantation. Among various bioreactors, the perfusion bioreactor is known for its enhanced convection through the cell-scaffold constructs. Knowledge of mass transfer is essential for controlling the cell culture process; however, obtaining this information remains a challenging task. In this research, a novel mathematical model is developed to represent the nutrient transport and cell growth in a 3-D scaffold cultivated in a perfusion bioreactor. Numerical methods are employed to solve the equations involved, with a focus on identifying the effect of factors such as porosity, culturing time, and flow rate, which are controllable in the scaffold fabrication and culturing process, on cell cultures. To validate the new model, the results from the model simulations were compared to the experimental results extracted from the literature. With the validated model, further simulations were carried out to investigate the glucose and oxygen distribution and the cell growth within the cell-scaffold construct in a perfusion bioreactor, thus providing insight into the cell culture process.