Modelling of extrusion-based bioprinting via quasi-analytical and FSI computational approaches

Bioprinting is an emerging technology belonging to the class of additive manufacturing (AM) techniques applied to the biofabrication of living tissues. Through the computer-aided design (CAD), cell-laden biocompatible materials are deposited layer-by-layer in 3D sca olds, miming the complex 3D micro-environment of the extra-cellular matrix (ECM), and allowing cells to proliferate, maturate, differentiate and secrete its own ECM in order to achieve the tissue growth. The main aims of bioprinting are declined in several research fields such as tissues and organs transplantation, study of pathological conditions in human diseases, drug discovery and personalized-medicines development, and more recently printing of cultured meat and support to the human space exploration. The main component of this technology is the bio-ink composed by the uid phase, made up of polymers cytocompatibles and additive chemicals to improve the printing process, and by the solid phase represented by the cells of the specific tissue to reproduce. Among all available bioprinting processes, they can be principally grouped in three categories based on the printing physical principle: the droplet-based bioprinting, which uses thermal, piezoelectric or acoustic sources to generate and deposit droplets onto a substrate; the light-assisted bioprinting, employing a laser source to irradiate a specific coated metal ribbon to produce droplets falling onto a substrate; the extrusion-based bioprinting (EB), which uses mechanical screw-driven motors or a pneumatic systems to extrudes continuous laments through a nozzle, usually a syringe equipped with a piston. In particular, this thesis addresses the extrusion-based process which compared to the other technologies presents the advantage to have an a ordable and simple setup, and a wide arrays of bio-inks in terms of viscosity and chemical properties. It is a multi-disciplinary application across biology, chemistry, medicine and engineering disciplines and it presents a multi-scale nature ranging between the cell and the nozzle dimensions. Due to the high number of variables intervening during the process and specific for each bio-ink, the experimental trial and error optimization is very expensive. Therefore, computational models would allow to reduce the optimization costs accelerating the scale-up process, and to better understand the phenomena occurring during extrusion. Byfocusing on the phase upstream the nozzle outlet, several works are present in literature describing the extrusion process by assuming different rheological models for the bio-ink and using different numerical techniques. They consider the bio-ink as a homogeneous uid and characterize its rheological behaviour through non-Newtonian inelastic models. Among the models used, the Bird-Cross-CarreauYasuda (BCCY) model provides a more accurate relationship and better fitting capabilities of experimental data. On the other hand, it necessitates an ad hoc optimization procedure for the calibration of model parameters. This requirement is due to its intrinsic problem of parameters identifiability as analysed by Gallagher et al.[16], which could in addition determine unreliable ow solutions. Regarding the uid-structure interaction (FSI) analyses between the uid and cells, so far only few examples has been found in literature. In particular, Abedini et al. analysed the cell viability of only a single cell aggregate owing in a cylindrical nozzle within a power law uid, and Muller et al.[18] evaluated the stress and strain only of a single cell owing out the nozzle exit. The main aims of this thesis are: - the presentation of an alternative rheological model developed to solve the parameters identifiability problem of the BCCY model, to have a more physical rheological relationship, and to derive reliable and approximated analytical solutions for bio-ink ows. - the proposal of a quasi-analytical framework developed to provide a simple and ready-to-use solution for bio-inks owing in cylindrical and slightly tapered nozzles. - the presentation of a numerical FSI approach based on the immersed boundary method (IB) developed to have a more detailed description of stresses experienced by a population of cells during the extrusion through a convergent shaped nozzle and owing in a BCCY uid, at the expense of a higher computational cost. Specifically, the alternative model presents a more reliable physical interpretation of rheological parameters and very good fitting capabilities with a coefficient of determination R2 LMAPE of 931%. The quasi-analytical solution applied to cylindrical nozzles has been validated through parametric comparisons with numerical results, showing in the worst case a maximum error on the extrusion velocity about 35%. It has been also applied and validated to reproduce an experimental bioprinting setup through a conical nozzle, giving a pressure drop 64% greater than the experimental value. Regarding the FSI model, the comparison between the numerical results and the classic approach about the cell shear stresses shows a very different behaviour. In the convergent region of the nozzle, the FSI analyses report unsteady results with peak values of shear stresses. Next, in the following needle part of the nozzle, the classic solution overestimates and underestimates the mean and maximum shear stresses acting on cells respectively. In particular, the maximum to mean shear stress ratio can reach a value of 328%, highlighting the need of a FSI approach to have a more accurate and detailed analysis of the cell dynamics during the extrusion.