Limited cell ingrowth is a major problem for tissue engineering and the clinical application of porous biomaterials as bone substitutes. As a first step, migration and proliferation of an interacting cell population can be studied in two-dimensional culture. Mathematical modelling is essential to generalize the results of these experiments and to derive the intrinsic parameters that can be used for predictions. However, a more thorough evaluation of theoretical models is hampered by limited experimental observations. In this study, experiments and image analysis methods were developed to provide a detailed spatial and temporal picture of how cell distributions evolve. These methods were used to quantify the migration and proliferation of skeletal cell types including MG63 and human bone marrow stromal cells (HBMSCs). The high level of detail with which the cell distributions were mapped enabled a precise assessment of the correspondence between experimental results and theoretical model predictions. This analysis revealed that the standard Fisher equation is appropriate for describing the migration behaviour of the HBMSC population, while for the MG63 cells a sharp front model is more appropriate. In combination with experiments, this type of mathematical model will prove useful in predicting cell ingrowth and improving strategies and control of skeletal tissue regeneration.

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A multilevel finite element approach is applied to predict local cell deformations in engineered tissue constructs. Cell deformations are predicted from detailed nonlinear FE analysis of the microstructure, consisting of an arrangement of cells embedded in matrix material. Effective macroscopic tissue behavior is derived by a computational homogenization procedure. To illustrate this approach, we simulated the compression of a skeletal muscle tissue construct and studied the influence of microstructural heterogeneity on local cell deformations. Results show that heterogeneity has a profound impact on local cell deformations, which highly exceed macroscopic deformations. Moreover, microstructural heterogeneity and the presence of neighboring cells leads to complex cell shapes and causes non-uniform deformations within a cell.

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Porous architecture has a dramatic effect on tissue formation in porous biomaterials used in regenerative medicine. However, the wide variety of 3D structures used indicates there is a clear need for the optimal design of pore architecture to maximize tissue formation and ingrowth. Thus, the aim of this study was to characterize initial tissue growth solely as a function of pore geometry. We used an in vitro system with well-defined open pore slots of varying width, providing a 3D environment for neo-tissue formation while minimizing nutrient limitations. Results demonstrated that initial tissue formation was strongly influenced by pore geometry. Both velocity of tissue invasion and area of tissue formed increased as pores became narrower. This is associated with distinct patterns of actin organisation and alignment depending on pore width, indicating the role of active cell generated forces. A mathematical model based on curvature driven growth successfully predicted both shape of invasion front and constant rate of growth, which increased for narrower pores as seen in experiments. Our results provide further evidence for a front based, curvature driven growth mechanism depending on pore geometry and tissue organisation, which could provide important clues for 3D scaffold design.

A finite-element approach was formulated, aimed at enabling an integrated study of mechanical and biochemical factors that control the functional development of tissue engineered constructs. A nonlinear biphasic displacement-velocity-pressure description was combined with adjective and diffusive solute transport, uptake and biosynthesis. To illustrate the approach we focused on the synthesis and transport of macromolecules under influence of fluid flow induced by cyclic compression. In order to produce net transport the effect of dispersion was investigated. An abstract representation of biosynthesis was employed, three cases were distinguished: Synthesis dependent on a limited small solute, synthesis dependent on a limited large solute and synthesis independent of solute transport. Results show that a dispersion model can account for augmented solute transport by cyclic compression and indicate the different sensitivity to loading that can be expected depending on the size of the limiting solute.

Placental amino acid transfer is a complex process that is essential for fetal development. Impaired amino acid transfer causes fetal growth restriction, which may have lifelong health consequences. Transepithelial transfer of amino acids across the placental syncytiotrophoblast requires accumulative, exchange and facilitated transporters on the apical and basal membranes to work in concert. However, transporters alone do not determine amino acid transfer and factors that affect substrate availability, such as blood flow and metabolism, may also become rate‐limiting for transfer. In order to determine the rate‐limiting processes, it is necessary to take a systems approach which recognises the interdependence of these processes. New technologies have the potential to deliver targeted interventions to the placenta and help poorly growing fetuses. While many factors are necessary for amino acid transfer, novel therapies need to target the rate‐limiting factors if they are going to be effective. This review will outline the factors which determine amino acid transfer and describe how they become interdependent. It will also highlight the role of computational modelling as a tool to understand this process.

Different culture conditions for cartilage tissue engineering were evaluated with respect to the supply of oxygen and glucose and the accumulation of lactate. A computational approach was adopted in which the culture configurations were modeled as a batch process and transport was considered within constructs seeded at high cell concentrations and of clinically relevant dimensions. To assess the extent to which mass transfer can be influenced theoretically, extreme cases were distinguished in which the culture medium surrounding the construct was assumed either completely static or well mixed and fully oxygenated. It can be concluded that severe oxygen depletion and lactate accumulation can occur within constructs for cartilage tissue engineering. However, the results also indicate that transport restrictions are not insurmountable, providing that the medium is well homogenized and oxygenated and the construct's surfaces are sufficiently exposed to the medium. The large variation in uptake rates of chondrocytes indicates that for any specific application the quantification of cellular utilization rates, depending on the cell source and culture conditions, is an essential starting point for optimizing culture protocols.