Search

The isolated perfused placental cotyledon technique has led to numerous advances in placental biology. Combining placental perfusion with mathematical modelling provides an additional level of insight into placental function. Mathematical modelling of perfusion data provides a quantitative framework to test the understanding of the underlying biology and to explore how different processes work together within the placenta as part of an integrated system. The perfusion technique provides a high degree of control over the experimental conditions as well as regular measurements of functional parameters such as pressure, solute concentrations and pH over time. This level of control is ideal for modelling as it allows placental function to be studied across a wide range of different conditions which permits robust testing of mathematical models. By placing quantitative values on different processes (e.g. transport, metabolism, blood flow), their relative contribution to the system can be estimated and those most likely to become rate-limiting identified. Using a combined placental perfusion and modelling approach, placental metabolism was shown to be a more important determinant of amino acid and fatty acid transfer. In contrast, metabolism was a less important determinant of placental cortisol transfer than initially thought. Identifying the rate-limiting factors in the system allows future work to be focused on the factors that are most likely to underlie placental dysfunction. A combined experimental and modelling approach using placental perfusions promotes an integrated view of placental physiology that can more effectively identify the processes leading to placental pathologies.

Key points: Placental structure and function can be modified as a result of maternal obesity affecting materno-fetal fatty acids (FA) transport. We report for the first time, in humans and in vivo, the kinetics of placental FA transfer in normo-weight and in normolipemic obese pregnant women using stable isotopes. The administration of different tracer FA with similar behaviour to the mother at different time points allows the collection of kinetic information on materno-fetal transfer of FA despite only one sample of placenta and cord can be collected per subject. Computational modelling showed a good fit to the data when considering all maternal plasma lipid classes but not when based only on non-esterified FA. The novel approach using multiple tracer FA administration combined with computational modelling shows a consistent time course of placental tracer FA and predicted total FA accumulation. Abstract: We analyse for the first time the in vivo materno-fetal kinetic transfer of fatty acids (FA) labelled with stable isotopes in control and obese (OB) pregnant women. Labelled FA with a similar metabolism (stearic acid: 13C-SA; palmitic acid: 13C-PA; oleic acid: 13C-OA) were orally administered at −4 h, −8 h and −12 h, respectively prior to elective caesarean section to 10 pregnant women with a body mass index >30 (OB) and 10 with a body mass index in the range 20–25 (NW). Placenta, venous and arterial cord blood were collected obtaining a wide range of FA enrichments. A combined experimental and computational modelling analysis was applied. FA fractional synthesis rate (FSR) in placenta was 11–12% h–1. No differences were observed between NW and normo-lipidemic OB. It was not possible to estimate FA FSR in cord blood with this oral bolus dose approach. Computational modelling demonstrated a good fit to the data when all maternal plasma lipid classes were included but not with modelling based only on the non-esterified FA fraction. The estimated materno-fetal 13C-FA transfer was ∼1%. In conclusion, our approach using multiple 13C-FA tracers allowed us to estimated FSR in placental/maternal plasma but not in fetal/maternal compartments. Computational modelling showed a consistent time course of placental 13C-FA transfer and predicted total fetal FA accumulation during the experiment. We conclude that, in addition to non-esterified FA fraction in the maternal circulation, maternal plasma very low-density lipoprotein and other lipoproteins are important contributors to placental FA transfer to the fetus.

Membrane transporters are considered essential for placental amino acid transfer, but the contribution of other factors, such as blood flow and metabolism, is poorly defined. In this study we combine experimental and modeling approaches to understand the determinants of [14C]phenylalanine transfer across the isolated perfused human placenta. Transfer of [14C]phenylalanine across the isolated perfused human placenta was determined at different maternal and fetal flow rates. Maternal flow rate was set at 10, 14, and 18 ml/min for 1 h each. At each maternal flow rate, fetal flow rates were set at 3, 6, and 9 ml/min for 20 min each. Appearance of [14C]phenylalanine was measured in the maternal and fetal venous exudates. Computational modeling of phenylalanine transfer was undertaken to allow comparison of the experimental data with predicted phenylalanine uptake and transfer under different initial assumptions. Placental uptake (mol/min) of [14C]phenylalanine increased with maternal, but not fetal, flow. Delivery (mol/min) of [14C]phenylalanine to the fetal circulation was not associated with fetal or maternal flow. The absence of a relationship between placental phenylalanine uptake and net flux of phenylalanine to the fetal circulation suggests that factors other than flow or transporter-mediated uptake are important determinants of phenylalanine transfer. These observations could be explained by tight regulation of free amino acid levels within the placenta or properties of the facilitated transporters mediating phenylalanine transport. We suggest that amino acid metabolism, primarily incorporation into protein, is controlling free amino acid levels and, thus, placental transfer.

Extracellular matrix stiffness has a profound effect on the behavior of many cell types. Adherent cells apply contractile forces to the material on which they adhere and sense the resistance of the material to deformation-its stiffness. This is dependent on both the elastic modulus and the thickness of the material, with the corollary that single cells are able to sense underlying stiff materials through soft hydrogel materials at low (

Uptake of system L amino acid substrates into isolated placental plasma membrane vesicles in the absence of opposing side amino acid (zero-trans uptake) is incompatible with the concept of obligatory exchange, where influx of amino acid is coupled to efflux. We therefore hypothesized that system L amino acid exchange transporters are not fully obligatory and/or that amino acids are initially present inside the vesicles. To address this, we combined computational modeling with vesicle transport assays and transporter localization studies to investigate the mechanism(s) mediating [14C]L-serine (a system L substrate) transport into human placental microvillous plasma membrane (MVM) vesicles. The carrier model provided a quantitative framework to test the 2 hypotheses that L-serine transport occurs by either obligate exchange or nonobligate exchange coupled with facilitated transport (mixed transport model). The computational model could only account for experimental [14C]L-serine uptake data when the transporter was not exclusively in exchange mode, best described by the mixed transport model. MVM vesicle isolates contained endogenous amino acids allowing for potential contribution to zero-trans uptake. Both L-type amino acid transporter (LAT)1 and LAT2 subtypes of system L were distributed to MVM, with L-serine transport attributed to LAT2. These findings suggest that exchange transporters do not function exclusively as obligate exchangers.—Widdows, K. L., Panitchob, N., Crocker, I. P., Please, C. P., Hanson, M. A., Sibley, C. P., Johnstone, E. D., Sengers, B. G., Lewis, R. M., Glazier, J. D. Integration of computational modeling with membrane transport studies reveals new insights into amino acid exchange transport mechanisms.

Placental amino acid transport is required for fetal development and impaired transport has been associated with poor fetal growth. It is well known that placental amino acid transport is mediated by a broad array of specific membrane transporters with overlapping substrate specificity. However, it is not fully understood how these transporters function, both individually and as an integrated system. We propose that mathematical modelling could help in further elucidating the underlying mechanisms of how these transporters mediate placental amino acid transport. The aim of this work is to model the sodium independent transport of serine, which has been assumed to follow an obligatory exchange mechanism. However, previous amino acid uptake experiments in human placental microvillous plasma membrane vesicles have persistently produced results that are seemingly incompatible with such a mechanism; i.e. transport has been observed under zero-trans conditions, in the absence of internal substrates inside the vesicles to drive exchange. This observation raises two alternative hypotheses; (i) either exchange is not fully obligatory, or (ii) exchange is indeed obligatory, but an unforeseen initial concentration of amino acid substrate is present within the vesicle which could drive exchange. To investigate these possibilities, a mathematical model for tracer uptake was developed based on carrier mediated transport, which can represent either facilitated diffusion or obligatory exchange (also referred to as uniport and antiport mechanisms, respectively). In vitro measurements of serine uptake by placental microvillous membrane vesicles were carried out and the model applied to interpret the results based on the measured apparent Michaelis–Menten parameters Km and Vmax. In addition, based on model predictions, a new time series experiment was implemented to distinguish the hypothesised transporter mechanisms. Analysis of the results indicated the presence of a facilitated transport component, while based on the model no evidence for substantial levels of endogenous amino acids within the vesicle was found., Highlights • Initial rate and time course data for serine uptake in placental membrane vesicles. • Integrated model analysisof facilitative diffusion vs obligatory exchange. • Dependency apparent Michaelis–Menten constants on internal concentrations. • Uptake in placental vesicles was consistent with a facilitative transport component. • No effects of any internal endogenous substrate in vesicles were apparent.

Introduction A healthy pregnancy depends on placental transfer from mother to fetus. Placental transfer takes place at the micro scale across the placental villi. Solutes from the maternal blood are taken up by placental villi and enter the fetal capillaries. This study investigated the effect of maternal blood flow on solute uptake at the micro scale. Methods A 3D image based modelling approach of the placental microstructures was undertaken. Solute transport in the intervillous space was modelled explicitly and solute uptake with respect to different maternal blood flow rates was estimated. Fetal capillary flow was not modelled and treated as a perfect sink. Results For a freely diffusing small solute, the flow of maternal blood through the intervillous space was found to be limiting the transfer. Ignoring the effects of maternal flow resulted in a 2.4 ± 0.4 fold over-prediction of transfer by simple diffusion, in absence of binding. Villous morphology affected the efficiency of solute transfer due to concentration depleted zones. Interestingly, less dense microvilli had lower surface area available for uptake which was compensated by increased flow due to their higher permeability. At super-physiological pressures, maternal flow was not limiting, however the efficiency of uptake decreased. Conclusions This study suggests that the interplay between maternal flow and villous structure affects the efficiency of placental transfer but predicted that flow rate will be the major determinant of transfer.

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. © 2009 Elsevier Ltd. All rights reserved.

In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.

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.

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.

Based on previously published experimental work, computational models were developed to simulate the effect of different dynamic compression regimens on the activity of chondrocytes seeded in agarose constructs. In particular, the balance between proliferation and matrix synthesis can be adjusted by applying different intervals of continuous or intermittent mechanical compression. A phenomenological compartment based-modeling approach was used as first model. A more mechanistic cell cycle model was used as the second model. The compartment-based modeling approach was found to be useful in representing a balance between proliferation and proteoglycan synthesis, when the effect of a certain stimulation protocol is known. In order to predict the response to different intervals of mechanical stimulation, however, a more mechanistic cell cycle-based approach is required. The cell cycle model supports an important role of the onset of loading. In addition, an inhibitory effect of further loading is required, which is more likely to be related to cell cycle progression velocity than to a decreased probability of commitment to the cell cycle. The mechanisms behind this inhibitory effect and the computational implementation, however, require further investigation.

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 48h, 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.

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.

Amino acid transfer to the fetus is dependent on several different factors. While these factors can be understood in isolation, it is still not possible to predict the function of the system as a whole. In order to do this an integrated approach is required which incorporates the interactions between the different determinants of amino acid transfer. Computational modelling of amino acid transfer in the term human placenta provides a mechanism by which this integrated approach can be delivered. Such a model would be invaluable for understanding amino acid transfer in both normal and pathological pregnancies.In order to develop a computational model it is necessary to determine all the biological factors which are important contributors to net amino acid transfer and the ways in which they interact. For instance, how different classes of amino acid transporter must interact to transfer amino acids across the placenta. Mathematically, the kinetics of each type of transporter can be represented by separate equations that describe their transfer rate as a non-linear function of amino acid concentrations. These equations can then be combined in the model to predict the overall system behaviour. Testing these predictions experimentally will demonstrate the strengths and weaknesses of the model, which can then be refined with increasing complexity and retested in an iterative fashion.In this way we hope to develop a functional computational model which will allow exploration of the factors that determine amino acid transfer across the placenta. This model may also allow the development of strategies to optimise placental transfer in pathologies associated with impaired amino acid transfer such as fetal growth restriction

The clinical application of macro-porous scaffolds for bone regeneration is significantly affected by the problem of insufficient cell colonization. Given the wide variety of different scaffold structures used for tissue engineering it is essential to derive relationships for cell colonization independent of scaffold architecture. To study cell population spreading on 3D structures decoupled from nutrient limitations, an in vitro culture system was developed consisting of thin slices of human trabecular bone seeded with Human Bone Marrow Stromal Cells, combined with dedicated microCT imaging and computational modeling of cell population spreading. Only the first phase of in vitro scaffold colonization was addressed, in which cells migrate and proliferate up to the stage when the surface of the bone is covered as a monolayer, a critical prerequisite for further tissue formation. The results confirm the model's ability to represent experimentally observed cell population spreading. The key advantage of the computational model was that by incorporating complex 3D structure, cell behavior can be characterized quantitatively in terms of intrinsic migration parameters, which could potentially be used for predictions on different macro-porous scaffolds subject to additional experimental validation. This type of modeling will prove useful in predicting cell colonization and improving strategies for skeletal tissue engineering.

Improved biological and mechanical functionality of musculoskeletal tissue-engineered constructs is required for clinical application, which can only be achieved by comprehensive multidisciplinary research. This review focuses on the contribution of computational modelling as a framework for obtaining an integrated understanding of key processes, which include: nutrient transport and utilization, matrix formation, cell population dynamics, cell attachment and migration, and local cell-cell interactions. Such an integrated perspective of these key aspects will be critical to open up new directions in tissue engineering research, as significant progress can be made by combining existing computational and experimental methods. Furthermore, theoretical modelling has enormous potential in applications ranging from the interpretation of experimental results and the identification of the main governing processes, to the optimization of practical tissue engineering protocols with implications therein for an increasing ageing population.

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.

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.

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.