Curvature- and fluid-stress-driven tissue growth in a tissue-engineering scaffold pore

Effects of Elasticity on Cell Proliferation in a Tissue-Engineering Scaffold Pore

Scaffolds engineered for in vitro tissue engineering consist of multiple pores where cells can migrate along with nutrient-rich culture medium. The presence of the nutrient medium throughout the scaffold pores promotes cell proliferation, and this process depends on several factors such as scaffold geometry, nutrient medium flow rate, shear stress, cell-scaffold focal adhesions and elastic properties of the scaffold material. While numerous studies have addressed the first four factors, the mathematical approach described herein focuses on cell proliferation rate in elastic scaffolds, under constant flux of nutrients. As cells proliferate, the scaffold pores radius shrinks and thus, in order to sustain the nutrient flux, the inlet applied pressure on the upstream side of the scaffold pore must be increased. This results in expansion of the elastic scaffold pore, which in turn further increases the rate of cell proliferation. Considering the elasticity of the scaffold, the pore deformation allows further cellular growth beyond that of inelastic conditions. In this paper, our objectives are as follows: (i) Develop a mathematical model for describing fluid dynamics, scaffold elasticity and cell proliferation for scaffolds consist of identical nearly cylindrical pores; (ii) Solve the models and then simulate cellular proliferation within an elastic pore. The simulation can emulate real life tissue growth in a scaffold and offer a solution which reduces the numerical burdens. Lastly, our results demonstrated are in qualitative agreement with experimental observations reported in the literature.

Review on Bioinspired Design of ECM-Mimicking Scaffolds by Computer-Aided Assembly of Cell-Free and Cell Laden Micro-Modules

Tissue engineering needs bioactive drug delivery scaffolds capable of guiding cell biosynthesis and tissue morphogenesis in three dimensions. Several strategies have been developed to design and fabricate ECM-mimicking scaffolds suitable for directing in vitro cell/scaffold interaction, and controlling tissue morphogenesis in vivo. Among these strategies, emerging computer aided design and manufacturing processes, such as modular tissue unit patterning, promise to provide unprecedented control over the generation of biologically and biomechanically competent tissue analogues. This review discusses recent studies and highlights the role of scaffold microstructural properties and their drug release capability in cell fate control and tissue morphogenesis. Furthermore, the work highlights recent advances in the bottom-up fabrication of porous scaffolds and hybrid constructs through the computer-aided assembly of cell-free and/or cell-laden micro-modules. The advantages, current limitations, and future challenges of these strategies are described and discussed.

Review on Porous Scaffolds Generation Process: A Tissue Engineering Approach

Porous scaffolds have been widely explored for tissue regeneration and engineering in vitro three-dimensional models. In this review, a comprehensive literature analysis is conducted to identify the steps involved in their generation. The advantages and disadvantages of the available techniques are discussed, highlighting the importance of considering pore geometrical parameters such as curvature and size, and summarizing the requirements to generate the porous scaffold according to the desired application. This paper considers the available design tools, mathematical models, materials, fabrication techniques, cell seeding methodologies, assessment methods, and the status of pore scaffolds in clinical applications. This review compiles the relevant research in the field in the past years. The trends, challenges, and future research directions are discussed in the search for the generation of a porous scaffold with improved mechanical and biological properties that can be reproducible, viable for long-term studies, and closer to being used in the clinical field.

Regenerative medicine meets mathematical modelling: developing symbiotic relationships

Successful progression from bench to bedside for regenerative medicine products is challenging and requires a multidisciplinary approach. What has not yet been fully recognised is the potential for quantitative data analysis and mathematical modelling approaches to support this process. In this review, we highlight the wealth of opportunities for embedding mathematical and computational approaches within all stages of the regenerative medicine pipeline. We explore how exploiting quantitative mathematical and computational approaches, alongside state-of-the-art regenerative medicine research, can lead to therapies that potentially can be more rapidly translated into the clinic.

Cell proliferation and migration explain pore bridging dynamics in 3D printed scaffolds of different pore size

Tissue growth in bioscaffolds is influenced significantly by pore geometry, but how this geometric dependence emerges from dynamic cellular processes such as cell proliferation and cell migration remains poorly understood. Here we investigate the influence of pore size on the time required to bridge pores in thin 3D-printed scaffolds. Experimentally, new tissue infills the pores continually from their perimeter under strong curvature control, which leads the tissue front to round off with time. Despite the varied shapes assumed by the tissue during this evolution, we find that time to bridge a pore simply increases linearly with the overall pore size. To disentangle the biological influence of cell behaviour and the mechanistic influence of geometry in this experimental observation, we propose a simple reaction-diffusion model of tissue growth based on Porous-Fisher invasion of cells into the pores. First, this model provides a good qualitative representation of the evolution of the tissue; new tissue in the model grows at an effective rate that depends on the local curvature of the tissue substrate. Second, the model suggests that a linear dependence of bridging time with pore size arises due to geometric reasons alone, not to differences in cell behaviours across pores of different sizes. Our analysis suggests that tissue growth dynamics in these experimental constructs is dominated by mechanistic crowding effects that influence collective cell proliferation and migration processes, and that can be predicted by simple reaction-diffusion models of cells that have robust, consistent behaviours.

Effects of Particles Diffusion on Membrane Filters Performance

Membrane filtration fouling is a very complex process and is determined by many properties such as the membrane internal morphology, membrane pore structure, flow rate and contaminant properties. In a very slow filtration process or during the late stage of filtration, when the flow rate is naturally low and Péclet number is small, particle diffusion is essential and cannot be neglected, while in typical filtration models, especially in moderate and fast filtration process, the main contribution stems from the particle advection. The objectives of this study is to formulate mathematical models that can (i) investigate how filtration process varies under possible effects of particles diffusion; and (ii) describe how membrane morphology evolves and investigate the filtration performance during the filtration process. We also compare the results with the case that diffusion is less important and make a prediction about what kind of membrane filter pore structure should be employed to achieve a particular optimum filtration performance. According to our results, the filtrate and efficiency of particle separation are found to be under the trade-off relationship, and the selection of the membrane properties depends on the requirement of the filtration.

Channeling Effect and Tissue Morphology in a Perfusion Bioreactor Imaged by X-Ray Microtomography

BACKGROUND

Perfusion bioreactors for tissue engineering hold great promises. Indeed, the perfusion of culture medium enhances species transport and mechanically stimulates the cells, thereby increasing cell proliferation and tissue formation. Nonetheless, their development is still hampered by a lack of understanding of the relationship between mechanical cues and tissue growth.

METHODS

Combining tissue engineering, three-dimensional visualization and numerical simulations, we analyze the morphological evolution of neo-tissue in a model bioreactor with respect to the local flow pattern. NIH-3T3 cells were grown under perfusion for one, two and three weeks on a stack of 2 mm polyacetal beads. The model bioreactor was then imaged by X-ray micro-tomography and local tissue morphology was analyzed. To relate experimental observations and mechanical stimulii, a computational fluid dynamics model of flow around spheres in a canal was developed and solved using the finite element method.

RESULTS

We observe a preferential tissue formation at the bioreactor periphery, and relate it to a channeling effect leading to regions of higher flow intensity. Additionally, we find that circular crater-like tissue patterns form in narrow channel regions at early culture times. Using computational fluid dynamic simulations, we show that the location and morphology of these patterns match those of shear stress maxima. Finally, the morphology of the tissue is qualitatively described as the tissue grows and reorganizes itself.

CONCLUSION

Altogether, our study points out the key role of local flow conditions on the tissue morphology developed on a stack of beads in perfusion bioreactors and provides new insights for effective design of hydrodynamic bioreactors for tissue engineering using bead packings.

A Hybrid Model of Cartilage Regeneration Capturing the Interactions Between Cellular Dynamics and Porosity

To accelerate the development of strategies for cartilage tissue engineering, models are necessary to investigate the interactions between cellular dynamics and the local microenvironment. We use a discrete framework to capture the individual behavior of cells, modeling experiments where cells are seeded in a porous scaffold or hydrogel and over the time course of a month, the scaffold slowly degrades while cells divide and synthesize extracellular matrix constituents. The movement of cells and the ability to proliferate is a function of the local porosity, defined as the volume fraction of fluid in the surrounding region. A phenomenological approach is used to capture a continuous profile for the degrading scaffold and accumulating matrix, which will then change the local porosity throughout the construct. We parameterize the model by first matching total cell counts in the construct to chondrocytes seeded in a polyglycolic acid scaffold (Freed et al. in Biotechnol Bioeng 43:597-604, 1994). We investigate the influence of initial scaffold porosity on the total cell count and spatial profiles of cell and ECM in the construct. Cell counts were higher at day 30 in scaffolds of lower initial porosity, and similar cell counts were obtained using different models of scaffold degradation and matrix accumulation (either uniform or cell-specific). Using this modeling framework, we study the interplay between a phenomenological representation of scaffold architecture and porosity as well as the potential continuous application of growth factors. We determine parameter regimes where large cellular aggregates occur, which can hinder matrix accumulation and cellular proliferation. The developed modeling framework can easily be extended and can be used to identify optimal scaffolds and culture conditions that lead to a desired distribution of extracellular matrix and cell counts throughout the construct.

A level-set method for the evolution of cells and tissue during curvature-controlled growth

Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic or cell behavioural in nature. The control of geometry on tissue growth has been evidenced in many in vivo and in vitro experiments, including bone remodelling, wound healing, and tissue engineering scaffolds. In this paper, we propose a generalisation of a mathematical model that captures the mechanistic influence of curvature on the joint evolution of cell density and tissue shape during tissue growth. This generalisation allows us to simulate abrupt topological changes such as tissue fragmentation and tissue fusion, as well as three dimensional cases, through a level-set-based method. The level-set method developed introduces another Eulerian field than the level-set function. This additional field represents the surface density of tissue-synthesising cells, anticipated at future locations of the interface. Numerical tests performed with this level-set-based method show that numerical conservation of cells is a good indicator of simulation accuracy, particularly when cusps develop in the tissue's interface. We apply this new model to several situations of curvature-controlled tissue evolutions that include fragmentation and fusion.