Exploiting in silico modelling to enhance translation of liver cell therapies from bench to bedside.

Cell therapies are emerging as promising treatments for a range of liver diseases but translational bottlenecks still remain including: securing and assessing the safe and effective delivery of cells to the disease site; ensuring successful cell engraftment and function; and preventing immunogenic responses. Here we highlight three therapies, each utilising a different cell type, at different stages in their clinical translation journey: transplantation of multipotent mesenchymal stromal/signalling cells, hepatocytes and macrophages. To overcome bottlenecks impeding clinical progression, we advocate for wider use of mechanistic in silico modelling approaches. We discuss how in silico approaches, alongside complementary experimental approaches, can enhance our understanding of the mechanisms underlying successful cell delivery and engraftment. Furthermore, such combined theoretical-experimental approaches can be exploited to develop novel therapies, address safety and efficacy challenges, bridge the gap between in vitro and in vivo model systems, and compensate for the inherent differences between animal model systems and humans. We also highlight how in silico model development can result in fewer and more targeted in vivo experiments, thereby reducing preclinical costs and experimental animal numbers and potentially accelerating translation to the clinic. The development of biologically-accurate in silico models that capture the mechanisms underpinning the behaviour of these complex systems must be reinforced by quantitative methods to assess cell survival post-transplant, and we argue that non-invasive in vivo imaging strategies should be routinely integrated into transplant studies.

Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales.

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

A model-informed approach to assess the risk of immune checkpoint inhibitor-induced autoimmune myocarditis.

Immune checkpoint inhibitors (ICIs), as a novel immunotherapy, are designed to modulate the immune system to attack malignancies. Despite their promising benefits, immune-related adverse events (IRAEs) may occur, and incidences are bound to increase with surging demand of this class of drugs in treating cancer. Myocarditis, although rare compared to other IRAEs, has a significantly higher fatal frequency. Due to the overwhelming complexity of the immune system, this condition is not well understood, despite the significant research efforts devoted to it. To better understand the development and progression of autoimmune myocarditis and the roles of ICIs therein, we suggest a new approach: mathematical modelling. Mathematical modelling of myocarditis has enormous potential to determine which parts of the immune system are critical to the development and progression of the disease, and therefore warrant further investigation. We provide the immunological background needed to develop a mathematical model of this disease and review relevant existing models of immunology that serve as the mathematical inspiration needed to develop this field.

Mathematical modelling of autoimmune myocarditis and the effects of immune checkpoint inhibitors.

Autoimmune myocarditis is a rare, but frequently fatal, side effect of immune checkpoint inhibitors (ICIs), a class of cancer therapies. Despite extensive experimental work on the causes, development and progression of this disease, much still remains unknown about the importance of the different immunological pathways involved. We present a mathematical model of autoimmune myocarditis and the effects of ICIs on its development and progression to either resolution or chronic inflammation. From this, we gain a better understanding of the role of immune cells, cytokines and other components of the immune system in driving the cardiotoxicity of ICIs. We parameterise the model using existing data from the literature, and show that qualitative model behaviour is consistent with disease characteristics seen in patients in an ICI-free context. The bifurcation structures of the model show how the presence of ICIs increases the risk of developing autoimmune myocarditis. This predictive modelling approach is a first step towards determining treatment regimens that balance the benefits of treating cancer with the risk of developing autoimmune myocarditis.

A Systematically Reduced Mathematical Model for Organoid Expansion.

Organoids are three-dimensional multicellular tissue constructs. When cultured in vitro, they recapitulate the structure, heterogeneity, and function of their in vivo counterparts. As awareness of the multiple uses of organoids has grown, e.g. in drug discovery and personalised medicine, demand has increased for low-cost and efficient methods of producing them in a reproducible manner and at scale. Here we focus on a bioreactor technology for organoid production, which exploits fluid flow to enhance mass transport to and from the organoids. To ensure large numbers of organoids can be grown within the bioreactor in a reproducible manner, nutrient delivery to, and waste product removal from, the organoids must be carefully controlled. We develop a continuum mathematical model to investigate how mass transport within the bioreactor depends on the inlet flow rate and cell seeding density, focusing on the transport of two key metabolites: glucose and lactate. We exploit the thin geometry of the bioreactor to systematically simplify our model. This significantly reduces the computational cost of generating model solutions, and provides insight into the dominant mass transport mechanisms. We test the validity of the reduced models by comparison with simulations of the full model. We then exploit our reduced mathematical model to determine, for a given inlet flow rate and cell seeding density, the evolution of the spatial metabolite distributions throughout the bioreactor. To assess the bioreactor transport characteristics, we introduce metrics quantifying glucose conversion (the ratio between the total amounts of consumed and supplied glucose), the maximum lactate concentration, the proportion of the bioreactor with intolerable lactate concentrations, and the time when intolerable lactate concentrations are first experienced within the bioreactor. We determine the dependence of these metrics on organoid-line characteristics such as proliferation rate and rate of glucose consumption per cell. Finally, for a given organoid line, we determine how the distribution of metabolites and the associated metrics depend on the inlet flow rate. Insights from this study can be used to inform bioreactor operating conditions, ultimately improving the quality and number of bioreactor-expanded organoids.

Combining multiple spatial statistics enhances the description of immune cell localisation within tumours.

Digital pathology enables computational analysis algorithms to be applied at scale to histological images. An example is the identification of immune cells within solid tumours. Image analysis algorithms can extract precise cell locations from immunohistochemistry slides, but the resulting spatial coordinates, or point patterns, can be difficult to interpret. Since localisation of immune cells within tumours may reflect their functional status and correlates with patient prognosis, novel descriptors of their spatial distributions are of biological and clinical interest. A range of spatial statistics have been used to analyse such point patterns but, individually, these approaches only partially describe complex immune cell distributions. In this study, we apply three spatial statistics to locations of CD68+ macrophages within human head and neck tumours, and show that images grouped semi-quantitatively by a pathologist share similar statistics. We generate a synthetic dataset which emulates human samples and use it to demonstrate that combining multiple spatial statistics with a maximum likelihood approach better predicts human classifications than any single statistic. We can also estimate the error associated with our classifications. Importantly, this methodology is adaptable and can be extended to other histological investigations or applied to point patterns outside of histology.

Mathematical modelling reveals cellular dynamics within tumour spheroids.

Tumour spheroids are widely used as an in vitro assay for characterising the dynamics and response to treatment of different cancer cell lines. Their popularity is largely due to the reproducible manner in which spheroids grow: the diffusion of nutrients and oxygen from the surrounding culture medium, and their consumption by tumour cells, causes proliferation to be localised at the spheroid boundary. As the spheroid grows, cells at the spheroid centre may become hypoxic and die, forming a necrotic core. The pressure created by the localisation of tumour cell proliferation and death generates an cellular flow of tumour cells from the spheroid rim towards its core. Experiments by Dorie et al. showed that this flow causes inert microspheres to infiltrate into tumour spheroids via advection from the spheroid surface, by adding microbeads to the surface of tumour spheroids and observing the distribution over time. We use an off-lattice hybrid agent-based model to re-assess these experiments and establish the extent to which the spatio-temporal data generated by microspheres can be used to infer kinetic parameters associated with the tumour spheroids that they infiltrate. Variation in these parameters, such as the rate of tumour cell proliferation or sensitivity to hypoxia, can produce spheroids with similar bulk growth dynamics but differing internal compositions (the proportion of the tumour which is proliferating, hypoxic/quiescent and necrotic/nutrient-deficient). We use this model to show that the types of experiment conducted by Dorie et al. could be used to infer spheroid composition and parameters associated with tumour cell lines such as their sensitivity to hypoxia or average rate of proliferation, and note that these observations cannot be conducted within previous continuum models of microbead infiltration into tumour spheroids as they rely on resolving the trajectories of individual microbeads.

Predicting Bone Formation in Mesenchymal Stromal Cell-Seeded Hydrogels Using Experiment-Based Mathematical Modeling.

In vitro bone formation by mesenchymal stromal cells encapsulated in type-1 collagen hydrogels is demonstrated after a 28-day in vitro culture period. Analysis of the hydrogels is carried out by X-ray microcomputed tomography, histology, and immunohistochemistry, which collectively demonstrates that bone formation in the hydrogels was quantifiably proportional to the initial collagen concentration, and subsequently the population density of seeded cells. This was established by varying the initial collagen concentration at a constant cell seeding density (3 × 105 cells/0.3 mL hydrogel), and separately varying cell seeding density at a constant collagen concentration (1 mg/mL). Using these data, a mathematical model is presented for the total hydrogel volume and mineralization volume based on the observed linear contraction dynamics of cell-seeded collagen gels. The model parameters are fitted by comparing the predictions of the mathematical model for the hydrogel and mineralized volumes on day 28 with the experimental data. The model is then used to predict the hydrogel and mineralization volumes for a range of hydrogel collagen concentrations and cell seeding densities, providing comprehensive input/output descriptors for generating mineralized hydrogels for bone tissue engineering. It is proposed that this quantitative approach will be a useful tool for generating in vitro manufactured bone tissue, defining input parameters that yield predictable output measures of tissue maturation. Impact statement This article describes a simple yet powerful quantitative description of in vitro tissue-engineered bone by combining experimental data with mathematical modeling. The overall aim of the article is to examine what is currently known about cell-mediated collagen contraction, and demonstrate that this phenomenon can be exploited to tailor bone formation by choosing a specific set of input parameters in the form of cell seeding density and collagen hydrogel concentration. Our study utilizes a clinically relevant cell source (human mesenchymal stem cells) with a biomaterial that has received regulatory approval for use in humans (collagen type 1), and hence could be useful for clinical applications, as well as furthering our understanding of cell/extracellular matrix interactions in determining in vitro bone tissue formation.

Identifying chondrogenesis strategies for tissue engineering of articular cartilage.

A key step in the tissue engineering of articular cartilage is the chondrogenic differentiation of mesenchymal stem cells (MSCs) into chondrocytes (native cartilage cells). Chondrogenesis is regulated by transforming growth factor-ß (TGF-ß), a short-lived cytokine whose effect is prolonged by storage in the extracellular matrix. Tissue engineering applications aim to maximise the yield of differentiated MSCs. Recent experiments involve seeding a hydrogel construct with a layer of MSCs lying below a layer of chondrocytes, stimulating the seeded cells in the construct from above with exogenous TGF-ß and then culturing it in vitro. To investigate the efficacy of this strategy, we develop a mathematical model to describe the interactions between MSCs, chondrocytes and TGF-ß. Using this model, we investigate the effect of varying the initial concentration of TGF-ß, the initial densities of the MSCs and chondrocytes, and the relative depths of the two layers on the long-time composition of the tissue construct.

Lattice and continuum modelling of a bioactive porous tissue scaffold.

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.

The Fluid Mechanics of Ureteroscope Irrigation.

PURPOSE: To develop a physical understanding of ureterorenoscopy irrigation, we derive mathematical models from basic physical principles and compare these predictions with the results of benchtop experiments. Mathematical modeling can be used to understand the role of inlet pressure, tip deflection, the presence of working tools, geometric properties of the instruments used, and material properties of the irrigation fluid on resulting flow rate. MATERIALS AND METHODS: We develop theoretical models to describe irrigation flow in an idealized setup and compare with benchtop experiments for flow through a straight scope, a scope with a deflected tip, and a scope with a working tool inserted. The benchtop experiments were performed using Boston Scientific LithoVue ureteroscope and a variety of Boston Scientific working tools. Standard ureteroscope working channels have circular cross sections, but using theoretical models we investigate whether modifications to the cross-sectional geometry can enhance flow rates. RESULTS: The theoretical flow predictions are confirmed by experimental results. Tip deflection is shown to have a negligible effect on flow rate, but the presence of working tools decreases flow significantly (for a fixed driving pressure). Flow rate is predicted to improve when tools are placed at the edge of the channel, rather than the center, and modifying the cross-sectional shape from a circle to an ellipse can further increase flow rate. CONCLUSIONS: A mathematical framework is formulated and shown to accurately predict the properties of ureteroscope irrigation flow. The theoretical approach has significant potential in quantifying irrigation flow and improving ureteroscope design.

Inducing chondrogenesis in MSC/chondrocyte co-cultures using exogenous TGF-ß: a mathematical model.

The differentiation of mesenchymal stem cells (MSCs) into chondrocytes (native cartilage cells), or chondrogenesis, is a key step in the tissue engineering of articular cartilage, where the motility and high proliferation rate of MSCs used as seed cells are exploited. Chondrogenesis is regulated by transforming growth factor-beta (TGF-ß), a short-lived cytokine whose effect is prolonged by storage in the extracellular matrix. Tissue engineering applications require the complete differentiation of an initial population of MSCs, and two common strategies used to achieve this in vitro are (1) co-culture the MSCs with chondrocytes, which constitutively produce TGF-ß; or (2) add exogenous TGF-ß. To investigate these strategies we develop an ordinary differential equation model of the interactions between TGF-ß, MSCs and chondrocyte. Here the dynamics of TGF-ß are much faster than those of the cell processes; this difference in time-scales is exploited to simplify subsequent model analysis. Using our model we demonstrate that under strategy 1 complete chondrogenesis will be induced if the initial proportion of chondrocytes exceeds a critical value. Similarly, under strategy 2 we find that there is a critical concentration of exogenous TGF-ß above which all MSCs will ultimately differentiate. Finally, we use the model to demonstrate the potential advantages of adopting a hybrid strategy where exogenous TGF-ß is added to a co-culture of MSCs and chondrocytes, as compared to using either strategy 1 or 2 in isolation.

Mathematical modelling of cell layer growth in a hollow fibre bioreactor.

Generating autologous tissue grafts of a clinically useful volume requires efficient and controlled expansion of cell populations harvested from patients. Hollow fibre bioreactors show promise as cell expansion devices, owing to their potential for scale-up. However, further research is required to establish how to specify appropriate hollow fibre bioreactor operating conditions for expanding different cell types. In this study we develop a simple model for the growth of a cell layer seeded on the outer surface of a single fibre in a perfused hollow fibre bioreactor. Nutrient-rich culture medium is pumped through the fibre lumen and leaves the bioreactor via the lumen outlet or passes through the porous fibre walls and cell layer, and out via ports on the outer wall of the extra-capillary space. Stokes and Darcy equations for fluid flow in the fibre lumen, fibre wall, cell layer and extra-capillary space are coupled to reaction-advection-diffusion equations for oxygen and lactate transport through the bioreactor, and to a simple growth law for the evolution of the free boundary of the cell layer. Cells at the free boundary are assumed to proliferate at a rate that increases with the local oxygen concentration, and to die and detach from the layer if the local fluid shear stress or lactate concentration exceed critical thresholds. We use the model to predict operating conditions that maximise the cell layer growth for different cell types. In particular, we predict the optimal flow rate of culture medium into the fibre lumen and fluid pressure imposed at the lumen outlet for cell types with different oxygen demands and fluid shear stress tolerances, and compare the growth of the cell layer when the exit ports on the outside of the bioreactor are open with that when they are closed. Model simulations reveal that increasing the inlet flow rate and outlet fluid pressure increases oxygen delivery to the cell layer and, therefore, the growth rate of cells that are tolerant to high shear stresses, but may be detrimental for shear-sensitive cells. The cell layer growth rate is predicted to increase, and be less sensitive to the lactate tolerance of the cells, when the exit ports are opened, as the radial flow through the bioreactor is enhanced and the lactate produced by the cells cleared more rapidly from the cell layer.

Mathematical modelling of blood-brain barrier failure and oedema.

Injuries such as traumatic brain injury and stroke can result in increased blood-brain barrier (BBB) permeability. This increase may lead to water accumulation in the brain tissue resulting in vasogenic oedema. Although the initial injury may be localized, the resulting oedema causes mechanical damage and compression of the vasculature beyond the original injury site. We employ a biphasic mixture model to investigate the consequences of BBB permeability changes within a region of brain tissue and the onset of vasogenic oedema. We find that such localized changes can indeed result in brain tissue swelling and suggest that the type of damage that results (stress damage or strain damage) depends on the ability of the brain to clear oedema fluid.

A multiphase model for chemically- and mechanically- induced cell differentiation in a hollow fibre membrane bioreactor: minimising growth factor consumption.

We present a simplified two-dimensional model of fluid flow, solute transport, and cell distribution in a hollow fibre membrane bioreactor. We consider two cell populations, one undifferentiated and one differentiated, with differentiation stimulated either by growth factor alone, or by both growth factor and fluid shear stress. Two experimental configurations are considered, a 3-layer model in which the cells are seeded in a scaffold throughout the extracapillary space (ECS), and a 4-layer model in which the cell-scaffold construct occupies a layer surrounding the outside of the hollow fibre, only partially filling the ECS. Above this is a region of free-flowing fluid, referred to as the upper fluid layer. Following previous models by the authors (Pearson et al. in Math Med Biol, 2013, Biomech Model Mechanbiol 1-16, 2014a, we employ porous mixture theory to model the dynamics of, and interactions between, the cells, scaffold, and fluid in the cell-scaffold construct. We use this model to determine operating conditions (experiment end time, growth factor inlet concentration, and inlet fluid fluxes) which result in a required percentage of differentiated cells, as well as maximising the differentiated cell yield and minimising the consumption of expensive growth factor.

Global contraction or local growth, bleb shape depends on more than just cell structure.

When the plasma membrane of a cell locally delaminates from its actin cortex the membrane is pushed outwards due to the cell׳s internal fluid pressure. The resulting spherical protrusion is known as a bleb. A cell׳s ability to function correctly is highly dependent on the production of such protrusions with the correct size and shape. Here, we investigate the nucleation of large blebs from small, local neck regions. A mathematical model of a cell׳s membrane, cortex and interconnecting adhesions demonstrates that these three components are unable to capture experimentally observed bleb shapes without the addition of further assumptions. We have identified that combinations of global cortex contraction and localised membrane growth are the most promising methods for generating prototypical blebs. Currently, neither proposed mechanism has been fully tested experimentally and, thus, we propose experiments that will distinguish between the two methods of bleb production.

Propagation of damage in brain tissue: coupling the mechanics of oedema and oxygen delivery.

Brain tissue swelling, or oedema, is a dangerous consequence of traumatic brain injury and stroke. In particular, a locally swollen region can cause the injury to propagate further through the brain: swelling causes mechanical compression of the vasculature in the surrounding tissue and so can cut off that tissue's oxygen supply. We use a triphasic mathematical model to investigate this propagation, and couple tissue mechanics with oxygen delivery. Starting from a fully coupled, finite elasticity, model, we show that simplifications can be made that allow us to express the volume of the propagating region of damage analytically in terms of key parameters. Our results show that performing a craniectomy, to alleviate pressure in the brain and allow the tissue to swell outwards, reduces the propagation of damage; this finding agrees with experimental observations.

Multiphase modelling of the effect of fluid shear stress on cell yield and distribution in a hollow fibre membrane bioreactor.

We present a simplified two-dimensional model of fluid flow, nutrient transport and cell distribution in a hollow fibre membrane bioreactor, with the aim of exploring how fluid flow can be used to control the distribution and yield of a cell population which is sensitive to both fluid shear stress and nutrient concentration. The cells are seeded in a scaffold in a layer on top of the hollow fibre, only partially occupying the extracapillary space. Above this layer is a region of free-flowing fluid which we refer to as the upper fluid layer. The flow in the lumen and upper fluid layer is described by the Stokes equations, whilst the flow in the porous fibre membrane is assumed to follow Darcy's law. Porous mixture theory is used to model the dynamics of and interactions between the cells, scaffold and fluid in the cell-scaffold construct. The concentration of a limiting nutrient (e.g. oxygen) is governed by an advection-reaction-diffusion equation in each region. Through exploitation of the small aspect ratio of each region and asymptotic analysis, we derive a coupled system of partial differential equations for the cell volume fraction and nutrient concentration. We use this model to investigate the effect of mechanotransduction on the distribution and yield of the cell population, by considering cases in which cell proliferation is either enhanced or limited by fluid shear stress and by varying experimentally controllable parameters such as flow rate and cell-scaffold construct thickness.

Evaluation of the growth environment of a hydrostatic force bioreactor for preconditioning of tissue-engineered constructs.

Bioreactors have been widely acknowledged as valuable tools to provide a growth environment for engineering tissues and to investigate the effect of physical forces on cells and cell-scaffold constructs. However, evaluation of the bioreactor environment during culture is critical to defining outcomes. In this study, the performance of a hydrostatic force bioreactor was examined by experimental measurements of changes in dissolved oxygen (O2), carbon dioxide (CO2), and pH after mechanical stimulation and the determination of physical forces (pressure and stress) in the bioreactor through mathematical modeling and numerical simulation. To determine the effect of hydrostatic pressure on bone formation, chick femur skeletal cell-seeded hydrogels were subjected to cyclic hydrostatic pressure at 0-270 kPa and 1 Hz for 1 h daily (5 days per week) over a period of 14 days. At the start of mechanical stimulation, dissolved O2 and CO2 in the medium increased and the pH of the medium decreased, but remained within human physiological ranges. Changes in physiological parameters (O2, CO2, and pH) were reversible when medium samples were placed in a standard cell culture incubator. In addition, computational modeling showed that the distribution and magnitude of physical forces depends on the shape and position of the cell-hydrogel constructs in the tissue culture format. Finally, hydrostatic pressure was seen to enhance mineralization of chick femur skeletal cell-seeded hydrogels.

Optimising cell aggregate expansion in a perfused hollow fibre bioreactor via mathematical modelling.

The need for efficient and controlled expansion of cell populations is paramount in tissue engineering. Hollow fibre bioreactors (HFBs) have the potential to meet this need, but only with improved understanding of how operating conditions and cell seeding strategy affect cell proliferation in the bioreactor. This study is designed to assess the effects of two key operating parameters (the flow rate of culture medium into the fibre lumen and the fluid pressure imposed at the lumen outlet), together with the cell seeding distribution, on cell population growth in a single-fibre HFB. This is achieved using mathematical modelling and numerical methods to simulate the growth of cell aggregates along the outer surface of the fibre in response to the local oxygen concentration and fluid shear stress. The oxygen delivery to the cell aggregates and the fluid shear stress increase as the flow rate and pressure imposed at the lumen outlet are increased. Although the increased oxygen delivery promotes growth, the higher fluid shear stress can lead to cell death. For a given cell type and initial aggregate distribution, the operating parameters that give the most rapid overall growth can be identified from simulations. For example, when aggregates of rat cardiomyocytes that can tolerate shear stresses of up to 0:05 Pa are evenly distributed along the fibre, the inlet flow rate and outlet pressure that maximise the overall growth rate are predicted to be in the ranges 2.75 x 10(-5) m(2) s(-1) to 3 x 10(-5) m(2) s(-1) (equivalent to 2.07 ml min(-1) to 2.26 ml min(-1)) and 1.077 x 10(5) Pa to 1.083 x 10(5) Pa (or 15.6 psi to 15.7 psi) respectively. The combined effects of the seeding distribution and flow on the growth are also investigated and the optimal conditions for growth found to depend on the shear tolerance and oxygen demands of the cells.