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Ubiquitous in embryonic development, tissue fusion is of interest to tissue engineers who use tissue spheroids or organoids as building blocks of three-dimensional (3D) multicellular constructs. This review presents mathematical models and computer simulations of the fusion of tissue spheroids. The motivation of this study stems from the need to predict the post-printing evolution of 3D bioprinted constructs. First, we provide a brief overview of differential adhesion, the main morphogenetic mechanism involved in post-printing structure formation. It will be shown that clusters of cohesive cells behave as an incompressible viscous fluid on the time scale of hours. The discussion turns then to mathematical models based on the continuum hydrodynamics of highly viscous liquids and on statistical mechanics. Next, we analyze the validity and practical use of computational models of multicellular self-assembly in live constructs created by tissue spheroid bioprinting. Finally, we discuss the perspectives of the field as machine learning starts to reshape experimental design, and modular robotic workstations tend to alleviate the burden of repetitive tasks in biofabrication. STATEMENT OF SIGNIFICANCE: Bioprinted constructs are living systems, which evolve via morphogenetic mechanisms known from developmental biology. This review presents mathematical and computational tools devised for modeling post-printing structure formation. They help achieving a desirable outcome without expensive optimization experiments. While previous reviews mainly focused on assumptions, technical details, strengths, and limitations of computational models of multicellular self-assembly, this article discusses their validity and practical use in biofabrication. It also presents an overview of mathematical models that proved to be useful in the evaluation of experimental data on tissue spheroid fusion, and in the calibration of computational models. Finally, the perspectives of the field are discussed in the advent of robotic biofabrication platforms and bioprinting process optimization by machine learning.

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The tumor microenvironment (TME) influences cancer progression. Therefore, engineered TME models are being developed for fundamental research and anti-cancer drug screening. This paper reports the biofabrication of 3D-printed avascular structures that recapitulate several features of the TME. The tumor is represented by a hydrogel droplet uniformly loaded with breast cancer cells (106 cells/mL); it is embedded in the same type of hydrogel containing primary cells-tumor-associated fibroblasts isolated from the peritumoral environment and peripheral blood mononuclear cells. Hoechst staining of cryosectioned tissue constructs demonstrated that cells remodeled the hydrogel and remained viable for weeks. Histological sections revealed heterotypic aggregates of malignant and peritumoral cells; moreover, the constituent cells proliferated in vitro. To investigate the interactions responsible for the experimentally observed cellular rearrangements, we built lattice models of the bioprinted constructs and simulated their evolution using Metropolis Monte Carlo methods. Although unable to replicate the complexity of the TME, the approach presented here enables the self-assembly and co-culture of several cell types of the TME. Further studies will evaluate whether the bioprinted constructs can evolve in vivo in animal models. If they become connected to the host vasculature, they may turn into a fully organized TME.

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A long-standing problem in tissue engineering is the biofabrication of perfusable tissue constructs that can be readily connected to the patient's vasculature. It was partially solved by three-dimensional (3D) printing of sacrificial material (e.g., hydrogel) strands: upon incorporation in another cell-laden hydrogel, the strands were removed, leaving behind perfusable channels. Their complexity, however, did not match that of the native vasculature. Here, we propose to use multicellular spheroids as a sacrificial material and investigate their potential benefits in the context of 3D bioprinting of cell aggregates and/or cell-laden hydrogels. Our study is based on computer simulations of postprinting cellular rearrangements. The computational model of the biological system is built on a cubic lattice, whereas its evolution is simulated using the Metropolis Monte Carlo algorithm. The simulations describe structural changes in three types of tissue constructs: a tube made of a single cell type, a tube made of two cell types, and a cell-laden hydrogel slab that incorporates a branching tube. In all three constructs, the lumen is obtained after the elimination of the sacrificial cell population. Our study suggests that sacrificial cell spheroids (sacrospheres) enable one to print tissue constructs outfitted with a finer and more complex network of channels than the ones obtained so far. Moreover, cellular interactions might give rise to a tissue microarchitecture that lies beyond the bioprinter's resolution. Although more expensive than inert materials, sacrificial cells have the potential to bring further progress towards the biofabrication of fully vascularized tissue substitutes.

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A better monitoring of pregnant women, mainly during the third trimester of pregnancy and an easy communication between physician and patients are very important for the prevention and good health of baby and mother. The paper presents an integrated system as support for the Obstetrics - Gynaecology domain consisting in two modules: a mobile application, ObGynCare, dedicated to the pregnant women and a new component of the Obstetrics-Gynaecology Department Information System dedicated to the physicians for a better monitoring of the pregnant women. The mobile application informs the pregnant women about their status, permits them to introduce glycaemia and weight values and has as option pulse and blood pressure acquisition from a smart sensor and provides results in a graphic format. It also provides support for easy patient-doctor communication related to any health problems. ObGyn Care offers nutrition recommendations and gives the pregnant women the possibility to enter a social space of common interests using social networks (Facebook) to exchange useful and practical information. Data collected from patients and from sensor are stored on the cloud and the physician may access the information and analyse it. The extended module of the Obstetrics-Gynaecology Department Information System already developed supports the physicians to visualize weekly, monthly, or on a trimester, the patient data and to discuss with her through the chat module. The mobile application is in test by pregnant women and medical personnel.

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The organisation of a heterotypic multicellular system is intensely studied in developmental biology, tissue engineering and regenerative medicine.To address this problem, we have created a computational model of a biological system made of two cell populations of various cohesivities, and simulated its evolution on the surface of biomaterials of different adhesivities. To this end, it was necessary to extend our SIMMMC application with algorithms that treat two cell types. We have observed, in accordance with experiments that, depending on the strength of cell-substrate adhesion, different structures emerge by the self-assembly of the two cell populations. The agreement with experimental results validates the extended version of the SIMMMC application, suggesting that this tool might offer useful insights for tissue engineers.

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Chemotaxis is a morphogenetic mechanism that consists of cell movement along a concentration gradient. Since cell adhesion is essential for cell migration and tissue integrity, and morphogenesis also involves chemotactic cell movement, we conducted a study of the influence of adhesion and chemotaxis on cell seeding of scaffolds. We built three-dimensional models of a cell aggregate, respectively of a cell suspension, in the vicinity of a porous scaffold that contained a chemoattractant substance. We assumed that the chemoattractant is released at a steady rate, creating a constant concentration gradient. To study the interplay of adhesion and chemotaxis, we simulated cell seeding using an algorithm based on the Metropolis Monte Carlo method. We varied the chemotactic strength, which describes the extent to which cells tend to move along the chemoattractant gradient. We found that, for the same energetic and geometric conditions, the distribution of cells within the scaffold hinges on the chemotactic strength. Our study suggests that cell seeding of tissue engineering scaffolds may be enhanced by incorporating chemoattractants of controlled release rate into the scaffold.

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Cell migration is important in embryogenesis, metastasis and wound healing. Often, morphogenesis involves chemotactic cell movement up or down chemical gradients. We have developed a computational model of a cell suspension in the vicinity of a porous scaffold that incorporates a chemoattractant substance. In order to study the interplay of adhesion and chemotaxis on cell seeding , we developed a computational model of the system and simulated its evolution using a Metropolis Monte Carlo algorithm. We varied the chemotactic strengths of the cells in order to identify the optimal conditions for a rapid and uniform seeding.

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One of the most important challenges of contemporary biology is understanding how cells assemble into tissues. The complexity of morphogenesis calls for computational tools able to identify the dominant mechanisms involved in shaping tissues. This narrative review presents individual-based computational models that proved useful in simulating phenomena of interest in tissue engineering (TE), a research field that aims to create tissue replacements in the laboratory. First, we briefly describe morphogenetic mechanisms. Then, we present several computational models of cellular and subcellular resolution, along with applications that illustrate their potential to address problems of TE. Finally, we analyze experiments that may be used to validate computational models of tissue constructs made of cohesive cells. Our analysis shows that the models available in the literature are not exploited to their full potential. We argue that, upon validation, a computational model can be used to optimize cell culture conditions and to design new experiments.

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Tissue engineering (TE) aims at building multicellular structures in the laboratory in order to regenerate, to repair or replace damaged tissues. In a well-established approach to TE, cells are cultured on a biocompatible porous structure, called scaffold. Cell seeding of scaffolds is an important first step. Here we study conditions that assure a uniform and rapid distribution of cells within the scaffold. The movement of cells has been simulated using the Metropolis Monte Carlo method, based on the principle that cellular system tends to achieve the minimum energy state. For different values of the model parameters, evolution of the cells' centre of mass is followed, which reflects the distribution of cells in the system. For comparison with experimental data, the concentration of the cells in the suspension adjacent to the scaffold is also monitored. Simulations of cell seeding are useful for testing different experimental conditions, which in practice would be very expensive and hard to perform. The computational methods presented here may be extended to model cell proliferation, cell death and scaffold degradation.

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The paper presents an overview of human tissue engineering and modelling-simulating methods currently in use. Tissue engineering is a promising alternative for the reconstruction of altered or totally damaged biological tissue, applied to eliminate the complications associated to traditional transplants.

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