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

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

Computational Modelling of Tissue-Engineered Cartilage Constructs

Cartilage is a fundamental tissue to ensure proper motion between bones and damping of mechanical loads. This tissue often suffers damage and has limited healing capacity due to its avascularity. In order to replace surgery and replacement of joints by metal implants, tissue engineered cartilage is seen as an attractive alternative. These tissues are obtained by seeding chondrocytes or mesenchymal stem cells in scaffolds and are given certain stimuli to improve establishment of mechanical properties similar to the native cartilage. However, tissues with ideal mechanical properties were not obtained yet. Computational models of tissue engineered cartilage growth and remodelling are invaluable to interpret and predict the effects of experimental designs. The current model contribution in the field will be presented in this chapter, with a focus on the response to mechanical stimulation, and the development of fully coupled modelling approaches incorporating simultaneously solute transport and uptake, cell growth, production of extracellular matrix and remodelling of mechanical properties.publishe

In Silico-Based Experiments on Mechanistic Interactions between Several Intestinal Permeation Enhancers with a Lipid Bilayer Model

Oral administration of drugs is generally considered convenient and patient-friendly. However, oral administration of biological drugs exhibits low oral bioavailability (BA) due to enzymatic degradation and low intestinal absorption. A possible approach to circumvent the low BA of oral peptide drugs is to coformulate the drugs with permeation enhancers (PEs). PEs have been studied since the 1960s and are molecules that enhance the absorption of hydrophilic molecules with low permeability over the gastrointestinal epithelium. In this study, we investigated the impact of six PEs on the structural properties of a model membrane using molecular dynamics (MD) simulations. The PEs included were the sodium salts of the medium chain fatty acids laurate, caprate, and caprylate and the caprylate derivative SNAC─all with a negative charge─and neutral caprate and neutral sucrose monolaurate. Our results indicated that the PEs, once incorporated into the membrane, could induce membrane leakiness in a concentration-dependent manner. Our simulations suggest that a PE concentration of at least 70–100 mM is needed to strongly affect transcellular permeability. The increased aggregation propensity seen for neutral PEs might provide a molecular-level mechanism for the membrane disruptions seen at higher concentrations in vivo. The ability for neutral PEs to flip-flop across the lipid bilayer is also suggestive of possible intracellular modes of action other than increasing membrane fluidity. Taken together, our results indicate that MD simulations are useful for gaining insights relevant to the design of oral dosage forms based around permeability enhancer molecules

Aggregation Behavior of Medium Chain Fatty Acids Studied by Coarse-Grained Molecular Dynamics Simulation

Medium chain fatty acids (MCFA) are digestion products of lipid-rich food and lipid-based formulations, and they are used as transient permeability enhancers in formulation of poorly permeable compounds. These molecules may promote drug absorption by several different processes, including solubilization, increased membrane fluidity, and increased paracellular transport through opening of the tight junctions. Therefore, understanding the aggregation behavior of MCFAs is important. A number of studies have measured the critical micelle concentration (CMC) of MCFAs experimentally. However, CMC is highly dependent on system conditions like pH, temperature, and the ionic strength of the buffer used in different experimental techniques. In this study, we investigated the aggregation behavior of four different MCFAs using the coarse-grained molecular dynamics (CG-MD) simulations with the purpose to explore if CG-MD can be used to study MCFA interactions occurring in water. The ratio of deprotonated and non-charged MCFA molecules were manipulated to assess aggregation behavior under different pH conditions and within the box sizes of 22x22x44nm(3) and 44nm(3) for 1s. CMCs were calculated by performing CG-MD simulations with an increasing number of MCFAs. The resulting aggregate size distribution and number of free MCFA molecules were used to determine the CMC. The CMCs from simulations for C-8, C-10, and C-12 were 1.8-3.5-fold lower than the respective CMCs determined experimentally by the Wilhelmy method. However, the variation of MCFA aggregate sizes and morphologies at different pH conditions is consistent with previous experimental observation. Overall, this study suggests that CG-MD is suitable for studying colloidal systems including various MCFAs

Molecular simulation as a computational pharmaceutics tool to predict drug solubility, solubilization processes and partitioning

In this review we will discuss how computational methods, and in particular classical molecular dynamics simulations, can be used to calculate solubility of pharmaceutically relevant molecules and systems. To the extent possible, we focus on the non-technical details of these calculations, and try to show also the added value of a more thorough and detailed understanding of the solubilization process obtained by using computational simulations. Although the main focus is on classical molecular dynamics simulations, we also provide the reader with some insights into other computational techniques, such as the COSMO-method, and also discuss Flory-Huggins theory and solubility parameters. We hope that this review will serve as a valuable starting point for any pharmaceutical researcher, who has not yet fully explored the possibilities offered by computational approaches to solubility calculations

Numerical simulation of peristalsis to study co-localization and intestinal distribution of a macromolecular drug and permeation enhancer

In this work, simulations of intestinal peristalsis are performed to investigate the intraluminal transport of macromolecules (MMs) and permeation enhancers (PEs). Properties of insulin and sodium caprate (C10) are used to represent the general class of MM and PE molecules. Nuclear magnetic resonance spectroscopy was used to obtain the diffusivity of C10, and coarse-grain molecular dynamics simulations were carried out to estimate the concentration-dependent diffusivity of C10. A segment of the small intestine with the length of 29.75 cm was modeled. Peristaltic speed, pocket size, release location, and occlusion ratio of the peristaltic wave were varied to study the effect on drug transport. It was observed that the maximum concentration at the epithelial surface for the PE and the MM increased by 397 % and 380 %, respectively, when the peristaltic wave speed was decreased from 1.5 to 0.5 cm sâ\u88\u921. At this wave speed, physiologically relevant concentrations of PE were found at the epithelial surface. However, when the occlusion ratio is increased from 0.3 to 0.7, the concentration approaches zero. These results suggest that a slower-moving and more contracted peristaltic wave leads to higher efficiency in transporting mass to the epithelial wall during the peristalsis phases of the migrating motor complex

Explicit-pH Coarse-Grained Molecular Dynamics Simulations Enable Insights into Restructuring of Intestinal Colloidal Aggregates with Permeation Enhancers

Permeation enhancers (PEs) can increase the bioavailability of drugs. The mechanisms of action of these PEs are complex, but, typically, when used for oral administration, they can transiently induce the alteration of trans- and paracellular pathways, including increased solubilization and membrane fluidity, or the opening of the tight junctions. To elucidate these mechanistic details, it is important to understand the aggregation behavior of not only the PEs themselves but also other molecules already present in the intestine. Aggregation processes depend critically on, among other factors, the charge state of ionizable chemical groups, which is affected by the pH of the system. In this study, we used explicit-pH coarse-grained molecular dynamics simulations to investigate the aggregation behavior and pH dependence of two commonly used PEs—caprate and SNAC—together with other components of fasted- and fed-state simulated intestinal fluids. We also present and validate a coarse-grained molecular topology for the bile salt taurocholate suitable for the Martini3 force-field. Our results indicate an increase in the number of free molecules as a function of the system pH and for each combination of FaSSIF/FeSSIF and PEs. In addition, there are differences between caprate and SNAC, which are rationalized based on their different molecular structures and critical micelle concentrations

Aggregation Behavior of Structurally Similar Therapeutic Peptides Investigated by H-1 NMR and All-Atom Molecular Dynamics Simulations

Understanding of peptide aggregation propensity is an important aspect in pharmaceutical development of peptide drugs. In this work, methodologies based on all-atom molecular dynamics (AA-MD) simulations and H-1 NMR (in neat H2O) were evaluated as tools for identification and investigation of peptide aggregation. A series of structurally similar, pharmaceutically relevant peptides with known differences in aggregation behavior (D-Phe(6)-GnRH, ozarelix, cetrorelix, and degarelix) were investigated. The H-1 NMR methodology was used to systematically investigate variations in aggregation with peptide concentration and time. Results show that H-1 NMR can be used to detect the presence of coexisting classes of aggregates and the inclusion or exclusion of counterions in peptide aggregates. Interestingly, results suggest that the acetate counterions are included in aggregates of ozarelix and cetrorelix but not in aggregates of degarelix. The peptides investigated in AA-MD simulations (D-Phe(6)-GnRH, ozarelix, and cetrorelix) showed the same rank order of aggregation propensity as in the NMR experiments. The AA-MD simulations also provided molecular-level insights into aggregation dynamics, aggregation pathways, and the influence of different structural elements on peptide aggregation propensity and intermolecular interactions within the aggregates. Taken together, the findings from this study illustrate that H-1 NMR and AA-MD simulations can be useful, complementary tools in early evaluation of aggregation propensity and formulation development for peptide drugs