Fluid flow in a Porous Scaffold for Microtia by Lattice Boltzmann Method

The birth deformity of ear, known as microtia, varies from a minimal deformed ear to the absence of auricular tissue or anotia. This malformation has been treated by reconstructing the external ear, mainly by autogenous rib cartilage in auricular repair. The fabrication of the ear framework is a prolonged reconstructive procedure and depends of the surgeon’s skill. In order to avoid these inconveniences and reduce surgery time, it was proposed in a previous work to use implants made with biocompatible materials. One of these is a scaffold made by fused deposition modeling using PLA based in the three-dimensional geometry of the ear cartilage. The aim of this work is to evaluate the feasibility of this scaffold to perform cell culture in a perfusion biorreactor by estimating the flow transport characteristics in porous media using a scaffold with the porous geometry of the human auricular cartilage for microtia. Flow and heat transfer through the scaffold were simulated by the lattice Boltzmann method, and permeability and shear stress distribution were obtained at different Reynolds numbers. The permeability values of the scaffold achieved are in the order of magnitude of scaffolds used for cell culture. Linear dependencies between maximum shear stress and Reynolds number, and between maximum shear stress and permeability were obtained. The values of shear stress achieved correspond to high percentage of cell viability. The scaffolds for microtia treatment with the proposed filling pattern select is appropriate for cell culture in a perfusion bioreactor with characteristics similar to those described herein

Numerical Solution of a Complete Formulation of Flow in a Perfusion Bone-Tissue Bioreactor Using Lattice Boltzmann Equation Method

We report the key findings from numerical solutions of a model of transport within an established perfusion bioreactor design. The model includes a complete formulation of transport with fully coupled convection-diffusion and scaffold cell attachment. It also includes the experimentally determined internal (Poly-L-Lactic Acid (PLLA)) scaffold boundary, together with the external vessel and flow-port boundaries. Our findings, obtained using parallel lattice Boltzmann equation method, relate to (i) whole-device, steady-state flow and species distribution and (ii) the properties of the scaffold. In particular the results identify which elements of the problem may be addressed by coarse grained methods such as the Darcy approximation and those which require a more complete description. The work demonstrates that appropriate numerical modelling will make a key contribution to the design and development of large scale bioreactors.Comment: 9 pages, 3 figure

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

AbstractMathematical 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

Mathematical Modelling and Computational Simulation of in vitro Tissue Culture Processes

To develop or engineer artificial tissues in tissue engineering, a detailed knowledge of the in vitro culture process including cell and tissue growth inside porous scaffolds, nutrient transport, and the shear stress acting on the cells is of great advantage. It has been shown that obtaining such information by means of experimental techniques is exceedingly difficult and in some ways impossible. Mathematical modelling and computational simulation based on computational fluid dynamics (CFD) has emerged recently to be a promising tool to characterize the culture process. However, due to the complicated structure of porous scaffolds, modelling and simulation of the in vitro cell culture process has been shown to be a challenging task. Furthermore, due to the cell growth during the culture process, the geometry of the scaffold structure is not constant, but changes with time, which makes the task even more challenging. To overcome these challenges, the research presented in this thesis is aimed at developing a CFD-based mathematical model and multi-time scale computational framework for culturing cell-scaffold constructs placed in perfusion bioreactors. To predict the three-dimensional (3D) cell growth in a porous tissue scaffold placed inside a perfusion bioreactor, a model is developed based on the continuity and momentum equations, a convection-diffusion equation and a suitable cell growth equation, which characterize the fluid flow, nutrient transport and cell growth, respectively. To solve these equations in a coupled fashion, an in-house FORTRAN code is developed based on the multiple relaxation time lattice Boltzmann method (MRT LBM), where the D3Q19 MRT LBM and D3Q7 MRT LBM models have been used for the fluid flow and mass transfer simulation, respectively. In the model cell growth equation, the transport of nutrients, i.e. oxygen and glucose, as well as the shear stress induced on the cells are considered for predicting the cell growth rate. In the developed model and computational framework, the influence of the dynamic strand surface on the local flow and nutrient concentration has been addressed by using a two-way coupling between the cell growth and local flow field and nutrient concentration, where a control-volume method within the LBM framework is applied. The simulation results provide quantification of the biomechanical environment, i.e. fluid velocity, shear stress and nutrient concentration inside the bioreactor. The final simulation applied the cell growth model to the culture of a three-zone tissue scaffold where the scaffold strands were initially seeded with cells. The prediction for the 3D cell growth rate indicates that the increase in the cell volume fraction is much higher in the front region of the scaffold due to the higher nutrient supply. The higher cell growth in the front zone reduces the permeability of the porous scaffold and significantly reduces the nutrient supply to the middle and rear regions of the scaffold, which in turn limit the cell growth in those regions. However, implementation of a bi-directional perfusion approach, which reverses the flow direction for second half of the culture period, is shown to significantly improve the nutrient transport inside the scaffold and increase the cell growth in the rear zone of the scaffold. The results in this study also demonstrate that the developed mathematical model and computational framework are capable of realistically simulating the 3D cell growth over extended culture periods. As such, they represent a promising tool for enhancing the growth of tissues in perfusion bioreactors

Overcoming conventional modeling limitations using image- driven lattice-boltzmann method simulations for biophysical applications

The challenges involved in modeling biological systems are significant and push the boundaries of conventional modeling. This is because biological systems are distinctly complex, and their emergent properties are results of the interplay of numerous components/processes. Unfortunately, conventional modeling approaches are often limited by their inability to capture all these complexities. By using in vivo data derived from biomedical imaging, image-based modeling is able to overcome this limitation. In this work, a combination of imaging data with the Lattice-Boltzmann Method for computational fluid dynamics (CFD) is applied to tissue engineering and thrombogenesis. Using this approach, some of the unanswered questions in both application areas are resolved. In the first application, numerical differences between two types of boundary conditions: “wall boundary condition” (WBC) and “periodic boundary condition” (PBC), which are commonly utilized for approximating shear stresses in tissue engineering scaffold simulations is investigated. Surface stresses in 3D scaffold reconstructions, obtained from high resolution microcomputed tomography images are calculated for both boundary condition types and compared with the actual whole scaffold values via image-based CFD simulations. It is found that, both boundary conditions follow the same spatial surface stress patterns as the whole scaffold simulations. However, they under-predict the absolute stress values approximately by a factor of two. Moreover, it is found that the error grows with higher scaffold porosity. Additionally, it is found that the PBC always resulted in a lower error than the WBC. In a second tissue engineering study, the dependence of culture time on the distribution and magnitude of fluid shear in tissue scaffolds cultured under flow perfusion is investigated. In the study, constructs are destructively evaluated with assays for cellularity and calcium deposition, imaged using µCT and reconstructed for CFD simulations. It is found that both the shear stress distributions within scaffolds consistently increase with culture time and correlate with increasing levels of mineralized tissues within the scaffold constructs as seen in calcium deposition data and µCT reconstructions. In the thrombogenesis application, detailed analysis of time lapse microscopy images showing yielding of thrombi in live mouse microvasculature is performed. Using these images, image-based CFD modeling is performed to calculate the fluid-induced shear stresses imposed on the thrombi’s surfaces by the surrounding blood flow. From the results, estimates of the yield stress (A critical parameter for quantifying the extent to which thrombi material can resist deformation and breakage) are obtained for different blood vessels. Further, it is shown that the yielding observed in thrombi occurs mostly in the outer shell region while the inner core remains intact. This suggests that the core material is different from the shell. To that end, we propose an alternative mechanism of thrombogenesis which could help explain this difference. Overall, the findings from this work reveal that image-based modeling is a versatile approach which can be applied to different biomedical application areas while overcoming the difficulties associated with conventional modeling

Biospecific Affinity Chromatography: Computational Modelling via Lattice Boltzmann Method and Influence of Lattice-Based Dimensionless Parameters

Based on a dynamic (i.e. time-dependent) one-dimensional approach, this work applied lattice Boltzmann method (LBM) to computationally model biospecific affinity chromatography (BAC). With governing equations expressed in lattice-based dimensionless form, LBM was implemented in D1Q2 lattice by assigning particle distribution functions to adsorbate concentration in both fluid and solid phases. The LBM simulator was firstly tested in view of a classic BAC work on lysozyme and the streaming step relating to adsorbate concentration in the solid-phase was suppressed from the LBM code with no loss of functionality. Expected behaviour of breakthrough curves was numerically reproduced and the influence of lattice-based dimensionless parameters was examined. The LBM simulator was next applied so as to assess lattice-based dimensionless parameters regarding an experimental BAC work on lipase

Spatial and Temporal Scaling of Unequal Microbubble Coalescence

We numerically study coalescence of air microbubbles in water, with density ratio 833 and viscosity ratio 50.5, using lattice Boltzmann method. The focus is on the effects of size inequality of parent bubbles on the interfacial dynamics and coalescence time. Twelve cases, varying the size ratio of large to small parent bubble from 5.33 to 1, are systematically investigated. The “coalescence preference,” coalesced bubble closer to the larger parent bubble, is well observed and the captured power-law relation between the preferential relative distance χ and size inequality γ, math formula, is consistent to the recent experimental observations. Meanwhile, the coalescence time also exhibits power-law scaling as math formula, indicating that unequal bubbles coalesce faster than equal bubbles. Such a temporal scaling of coalescence on size inequality is believed to be the first-time observation as the fast coalescence of microbubbles is generally hard to be recorded through laboratory experimentation