Cellular Automata Simulation of Osteoblast Growth on Microfibrous-Carbon-Based Scaffolds

A mathematical model for nutrient-limited uniaxial growth of a compressible tissue

We consider the uniaxial growth of a tissue or colony of cells, where a nutrient (or some other chemical) required for cell proliferation is supplied at one end, and is consumed by the cells. An example would be the growth of a cylindrical yeast colony in the experiments described by Vulin et al. (2014). We develop a reaction-diffusion model of this scenario which couples nutrient concentration and cell density on a growing domain. A novel element of our model is that the tissue is assumed to be compressible. We define replicative regions, where cells have sufficient nutrient to proliferate, and quiescent regions, where the nutrient level is insufficient for this to occur. We also define pathlines, which allow us to track individual cell paths within the tissue. We begin our investigation of the model by considering an incompressible tissue where cell density is constant before exploring the solution space of the full compressible model. In a large part of the parameter space, the incompressible and compressible models give qualitatively similar results for both the nutrient concentration and cell pathlines, with the key distinction being the variation in density in the compressible case. In particular, the replicative region is located at the base of the tissue, where nutrient is supplied, and nutrient concentration decreases monotonically with distance from the nutrient source. However, for a highly-compressible tissue with small nutrient consumption rate, we observe a counter-intuitive scenario where the nutrient concentration is not necessarily monotonically decreasing, and there can be two replicative regions. For parameter values given in the paper by Vulin et al. (2014), the incompressible model slightly overestimates the colony length compared to experimental observations; this suggests the colony may be somewhat compressible. Both incompressible and compressible models predict that, for these parameter values, cell proliferation is ultimately confined to a small region close to the colony base.

Coating Methods of Carbon Nonwovens with Cross-Linked Hyaluronic Acid and Its Conjugates with BMP Fragments

The cross-linking of polysaccharides is a universal approach to affect their structure and physical properties. Both physical and chemical methods are used for this purpose. Although chemical cross-linking provides good thermal and mechanical stability for the final products, the compounds used as stabilizers can affect the integrity of the cross-linked substances or have toxic properties that limit the applicability of the final products. These risks might be mitigated by using physically cross-linked gels. In the present study, we attempted to obtain hybrid materials based on carbon nonwovens with a layer of cross-linked hyaluronan and peptides that are fragments of bone morphogenetic proteins (BMPs). A variety of cross-linking procedures and cross-linking agents (1,4-butanediamine, citric acid, and BDDE) were tested to find the most optimal method to coat the hydrophobic carbon nonwovens with a hydrophilic hyaluronic acid (HA) layer. Both the use of hyaluronic acid chemically modified with BMP fragments and a physical modification approach (layer-by-layer method) were proposed. The obtained hybrid materials were tested with the spectrometric (MALDI-TOF MS) and spectroscopic methods (IR and 1H-NMR). It was found that the chemical cross-linking of polysaccharides is an effective method for the deposition of a polar active substance on the surface of a hydrophobic carbon nonwoven fabric and that the final material is highly biocompatible.

A Model for Cell Proliferation in a Developing Organism

In mathematical biology, there is a great deal of interest in producing continuum models by scaling discrete agent-based models governed by local stochastic rules. We discuss a particular example of this approach: a model for the proliferation of neural crest cells that can help us understand the development of Hirschprung's disease, a potentially-fatal condition in which the enteric nervous system of a new-born child does not extend all the way through the intestine and colon. Our starting point is a discrete-state, continuous-time Markov chain model proposed by Hywood et al. (2013a) for the location of the neural crest cells that make up the enteric nervous system. Hywood et al. (2013a) scaled their model to derive an approximate second order partial differential equation describing how the limiting expected number of neural crest cells evolve in space and time. In contrast, we exploit the relationship between the above-mentioned Markov chain model and the well-known Yule-Furry process to derive the exact form of the scaled version of the process. Furthermore, we provide expressions for other features of the domain agent occupancy process, such as the variance of the marginal occupancy at a particular site, the distribution of the number of agents that are yet to reach a given site and a stochastic description of the process itself.

Simulated confluence on micropatterned substrates correlates responses regulating cellular differentiation

While cells are known to behave differently based on the size of micropatterned islands and is thought to be related to cell size and cell-cell contacts, the exact threshold for this difference between small and large islands is unknown. Furthermore, while cell size and cell-cell contacts can be easily manipulated on small islands, they are harder to measure and continually monitor on larger islands. To investigate this size threshold, and to explore cell size, cell-cell contacts, and differentiation, we use a previously established simulation to plan experiments and explain results that we could not explain from experiments alone. We use five seeding densities covering three orders of magnitude over 25-500 µm diameter islands to examine markers of proliferation and differentiation in bone marrow derived mesenchymal cells (cell line). We show that osteogenic markers are most accurately described as a function of confluence for larger islands, but a function of time for smaller islands. We further show, using results of the simulation, that cell size and cell-cell contacts are also related to confluence on larger islands, but only cell-cell contacts are related to confluence on small islands. This work uses simulations to explain experimental results that could not be explained from experiments alone. Together, the simulations and experiments in this work show different differentiation patterns on large and small islands, and this simulation may be useful in planning future studies related to this work. This article is protected by copyright. All rights reserved.

Morphological switch is associated with increase in cell-cell contacts, ALP, and confluence above a minimum island area to perimeter ratio

During osteogenic differentiation in vitro, stem-like cells seeded at a low-density spread and are isolated. As the cells proliferate and mature, they become more cuboidal in shape with more cell-cell contacts. However, the coordination of this switch in cell morphology from elongated to cuboidal, cell-cell contacts, and differentiation is not known. In this work, we present results from experiments and a simulation of cell proliferation on protein-micropatterned islands that, independent of island size (25-1,000 μm) or shape (circles, squares, and hollow squares), shows a distinct morphological switch that is better described as a function of island confluence than time in culture, the standard measure in cell culture experiments. The simulation and experiments show cell morphology and island cell density versus confluence collapse to a single curve for all islands if the island area to perimeter ratio is ≥25 μm. Cell-cell contacts in the simulation and alkaline phosphatase (ALP) expression in experiments, a common marker for osteogenic differentiation, show exponential growth with confluence, rapidly increasing after the switch at ≈0.5 confluence. Furthermore, cell morphology, density, contacts, and ALP are better predicted by confluence than time in culture. The variability with time in culture leads to challenges in not only interpreting data but also in comparing data across research laboratories. This simulation can be used to predict cell behavior on different size and shape islands and to plan and optimize experiments that explore cell behavior as a function of a wide range of island geometries.

Modelling uniaxial non-uniform yeast colony growth: Comparing an agent-based model and continuum approximations

Biological experiments have shown that yeast can be restricted to grow in a uniaxial direction, vertically upwards from an agar plate to form a colony. The growth occurs as a consequence of cell proliferation driven by a nutrient supply at the base of the colony, and the height of the colony has been observed to increase linearly with time. Within the colony the nutrient concentration is non-constant and yeast cells throughout the colony will therefore not have equal access to nutrient, resulting in non-uniform growth. In this work, an agent based model is developed to predict the microscopic spatial distribution of labelled cells within the colony when the probability of cell proliferation can vary in space and time. We also describe a method for determining the average trajectories or pathlines of labelled cells within a colony growing in a uniaxial direction, enabling us to connect the microscopic and macroscopic behaviours of the system. We present results for six cases, which involve different assumptions for the presence or absence of a quiescent region (where no cell proliferation occurs), the size of the proliferative region, and the spatial variation of proliferation rates within the proliferative region. These six cases are designed to provide qualitative insight into likely growth scenarios whilst remaining amenable to analysis. We compare our macroscopic results to experimental observations of uniaxial colony growth for two cases where only a fixed number of cells at the base of the colony can proliferate. The model predicts that the height of the colony will increase linearly with time in both these cases, which is consistent with experimental observations. However, our model shows how different functional forms for the spatial dependence of the proliferation rate can be distinguished by tracking the pathlines of cells at different positions in the colony. More generally, our methodology can be applied to other biological systems exhibiting uniaxial growth, providing a framework for classifying or determining regions of uniform and non-uniform growth.

Integrated Design Approaches for 3D Printed Tissue Scaffolds: Review and Outlook

Emerging 3D printing technologies are enabling the fabrication of complex scaffold structures for diverse medical applications. 3D printing allows controlled material placement for configuring porous tissue scaffolds with tailored properties for desired mechanical stiffness, nutrient transport, and biological growth. However, tuning tissue scaffold functionality requires navigation of a complex design space with numerous trade-offs that require multidisciplinary assessment. Integrated design approaches that encourage iteration and consideration of diverse processes including design configuration, material selection, and simulation models provide a basis for improving design performance. In this review, recent advances in design, fabrication, and assessment of 3D printed tissue scaffolds are investigated with a focus on bone tissue engineering. Bone healing and fusion are examples that demonstrate the needs of integrated design approaches in leveraging new materials and 3D printing processes for specified clinical applications. Current challenges for integrated design are outlined and emphasize directions where new research may lead to significant improvements in personalized medicine and emerging areas in healthcare.

Polyurethane/polylactide-based biomaterials combined with rat olfactory bulb-derived glial cells and adipose-derived mesenchymal stromal cells for neural regenerative medicine applications

Research concerning the elaboration and application of biomaterial which may support the nerve tissue regeneration is currently one of the most promising directions. Biocompatible polymer devices are noteworthy group among the numerous types of potentially attractive biomaterials for regenerative medicine application. Polylactides and polyurethanes may be utilized for developing devices for supporting the nerve regeneration, like nerve guide conduits or bridges connecting the endings of broken nerve tracts. Moreover, the combination of these biomaterial devices with regenerative cell populations, like stem or precursor cells should significantly improve the final therapeutic effect. Therefore, the composition and structure of final device should support the proper adhesion and growth of cells destined for clinical application. In current research, the three polymer mats elaborated for connecting the broken nerve tracts, made from polylactide, polyurethane and their blend were evaluated both for physical properties and in vitro, using the olfactory-bulb glial cells and mesenchymal stem cells. The evaluation of Young's modulus, wettability and roughness of obtained materials showed the differences between analyzed samples. The analysis of cell adhesion, proliferation and morphology showed that the polyurethane-polylactide blend was the most neutral for cells in culture, while in the pure polymer samples there were significant alterations observed. Our results indicated that polyurethane-polylactide blend is an optimal composition for culturing and delivery of glial and mesenchymal stem cells.