Bram G. Sengers

Predicting local cell deformations in engineered tissue constructs: a multilevel finite element approach

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.

An integrated finite-element approach to mechanics, transport and biosynthesis in tissue engineering

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.

Computational study of culture conditions and nutrient supply in cartilage tissue engineering.

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 constructapos;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.

Experimental characterization and computational modelling of two-dimensional cell spreading for skeletal regeneration

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.

Nutrient utilization by bovine articular chondrocytes: a combined experimental and theoretical approach

A combined experimental-numerical approach was adopted to characterize glucose and oxygen uptake and lactate production by bovine articular chondrocytes in a model system. For a wide range of cell concentrations, cells in agarose were supplemented with either low or high glucose medium. During an initial culture phase of 48 h, oxygen was monitored noninvasively using a biosensor system. Glucose and lactate were determined by medium sampling. In order to quantify glucose and oxygen uptake, a finite element approach was adopted to describe diffusion and uptake in the experimental model. Numerical predictions of lactate, based on simple relations for cell metabolism, were found to agree well for low glucose, but not for high glucose medium. Oxygen did not play a role in either case. Given the close association between chondrocyte energy metabolism and matrix synthesis, a quantifiable prediction of utilization can present a valuable contribution in the optimization of tissue engineering conditions.

The local matrix distribution and the functional development of tissue engineered cartilage, a finite element study

Assessment of the functionality of tissue engineered cartilage constructs is hampered by the lack of correlation between global measurements of extra cellular matrix constituents and the global mechanical properties. Based on patterns of matrix deposition around individual cells, it has been hypothesized previously, that mechanical functionality arises when contact occurs between zones of matrix associated with individual cells. The objective of this study is to determine whether the local distribution of newly synthesized extracellular matrix components contributes to the evolution of the mechanical properties of tissue engineered cartilage constructs. A computational homogenization approach was adopted, based on the concept of a periodic representative volume element. Local transport and immobilization of newly synthesized matrix components were described. Mechanical properties were taken dependent on the local matrix concentration and subsequently the global aggregate modulus and hydraulic permeability were derived. The transport parameters were varied to assess the effect of the evolving matrix distribution during culture. The results indicate that the overall stiffness and permeability are to a large extent insensitive to differences in local matrix distribution. This emphasizes the need for caution in the visual interpretation of tissue functionality from histology and underlines the importance of complementary measurements of the matrix’s intrinsic molecular organization.

Pore Geometry Regulates Early Stage Human Bone Marrow Cell Tissue Formation and Organisation

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.

Design criteria for a printed tissue engineering construct: a mathematical homogenization approach

Cartilage tissue repair procedures currently under development aim to create a construct in which patient-derived cells are seeded and expanded ex vivo before implantation back into the body. The key challenge is producing physiologically realistic constructs that mimic real tissue structure and function. One option with vast potential is to print strands of material in a 3D structure called a scaffold that imitates the real tissue structure; the strands are composed of gel seeded with cells and so provide a template for cartilaginous tissue growth. The scaffold is placed in the construct and pumped with nutrient-rich culture medium to supply nutrients to the cells and remove waste products, thus promoting tissue growth. In this paper we use asymptotic homogenization to determine the effective flow and transport properties of such a printed scaffold system. These properties are used to predict the distribution of nutrient/waste products through the construct, and to specify design criteria for the scaffold that will optimize the growth of functional tissue.

Characterisation of human bone marrow stromal cell heterogeneity for skeletal regeneration strategies using a two-stage colony assay and computational modelling

Skeletal regeneration and tissue engineering strategies rely critically on the efficient expansion of progenitor cell populations whilst simultaneously preserving multipotentiality and the ability to induce differentiation towards bone and cartilage. Cell population heterogeneity has a significant impact on this process, but is currently poorly quantified, hampering the interpretation of experimental results and the design of optimised expansion protocols. The objective of this study was to characterise individual human bone marrow stromal cell heterogeneity in terms of colony expansion potential. For this purpose, a novel two-stage CFU-F assay was developed in which cells from primary single cell-derived colonies were detached and reseeded again at clonal density as single cells to form new secondary colonies. This clearly demonstrated how secondary colony growth potential varies markedly both between and within primary colonies. Depending on the primary colony, cells either generated small secondary colonies only, or else a wide range of colony sizes. Using computational modelling it was shown how such colony heterogeneity could arise from hierarchical progenitor cell populations and what the limits of such a population structure were in explaining the experimental data. In addition the model demonstrated the significant potential impact of cell mobility on expansion potential and its implications for inducing population heterogeneity. This combined experimental-computational approach will ascertain the impact of cell culture protocols on the expansion potential and functional composition of heterogeneous progenitor populations. Such insights are likely to be of crucial importance for the success of skeletal regeneration strategies.

Computational modelling of amino acid transfer interactions in the placenta.

Amino acid transfer from mother to fetus via the placenta plays a critical role in normal development, and restricted transfer is associated with fetal growth restriction. Placental amino acid transfer involves the interaction of 15 or more transporters and 20 amino acids. This complexity means that knowing which transporters are present is not sufficient to predict how they operate together as a system. Therefore, in order to investigate how placental amino acid transfer occurs as a system, an integrated mathematical/computational modelling framework was developed to represent the simultaneous transport of multiple amino acids. The approach was based on a compartmental model, in which separate maternal, syncytiotrophoblast and fetal volumes were distinguished, and transporters were modelled on the maternal‐ and fetal‐facing membranes of the syncytiotrophoblast using Michaelis–Menten‐type kinetics. The model was tested in comparison with placental perfusion experiments studying serine–alanine exchange and found to correspond well. The results demonstrated how the different transporters can work together as an integrated system and allowed their relative importance to be assessed. Placental–fetal serine exchange was found to be most sensitive to basal membrane transporter characteristics, but a range of secondary, less intuitive effects were also revealed. While this work only addressed a relatively simple three amino acid system, it demonstrates the feasibility of the approach and could be extended to incorporate additional experimental parameters. Ultimately, this approach will allow physiological simulations of amino acid transfer. This will enhance our understanding of these complex systems and placental function in health and disease.