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

Abstract

Cell proliferation within a fluid-filled porous tissue-engineering scaffold depends on a sensitive choice of pore geometry and flow rates: regions of high curvature encourage cell proliferation, while a critical flow rate is required to promote growth for certain cell types. When the flow rate is too slow, the nutrient supply is limited; when it is too fast, cells may be damaged by the high fluid shear stress. As a result, determining appropriate tissue-engineering-construct geometries and operating regimes poses a significant challenge that cannot be addressed by experimentation alone. In this paper, we present a mathematical theory for the fluid flow within a pore of a tissue-engineering scaffold, which is coupled to the growth of cells on the pore walls. We exploit the slenderness of a pore that is typical in such a scenario, to derive a reduced model that enables a comprehensive analysis of the system to be performed. We derive analytical solutions in a particular case of a nearly piecewise constant growth law and compare these with numerical solutions of the reduced model. Qualitative comparisons of tissue morphologies predicted by our model, with those observed experimentally, are also made. We demonstrate how the simplified system may be used to make predictions on the design of a tissue-engineering scaffold and the appropriate operating regime that ensures a desired level of tissue growth.

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

“…Depletion of active cells is important to explain tissue‐deposition slowdown observed experimentally in vitro and in vivo . This depletion, and more generally, the inclusion of cell behaviours, is not captured by mean curvature flow models of tissue growth …”

“…Some of these controls are mechanistically induced by the tissue's evolving geometry such as the crowding and spreading of tissue constituents due to spatial constraints, while other geometric controls relate to influences on cell behaviours such as level of activity, proliferation, and death . Mathematical models of tissue growth and morphogenesis commonly model the overall geometric control by mean curvature flows, whereby the normal velocity of the tissue interface is simply proportional to the local curvature . These phenomenological models do not consider the cellular component of tissue synthesis, and as such, are unable to disentangle the mechanistic and cell behavioural origins of curvature dependence in tissue growth.…”

Regenerative medicine meets mathematical modelling: developing symbiotic relationships

“… I want to model… My data are… Consider this kind of maths Example refs Basic regenerative biology Gene regulation & transcriptional control Transcriptomics, time-course of gene/protein expression, live imaging of gene/protein expression Differential equations for e.g. concentration of mRNA, stochastic models for control of gene expression by proteins 69 – 71 Cell migration Cell tracking, population snapshot, time-course of population Cell-based, differential equations, statistical 17 , 18 , 26 , 27 Cell-cell signalling Cell counts, time-course of cell number, signalling molecule concentration Differential equations, hybrid models 37 – 40 , 62 , 64 Relevant to bioreactors Lineage choice, differentiation, cell reprogramming Clonal tracking, live imaging of cell phenotype, transcriptomics, epigenomics, metabolic activity Stochastic and deterministic differential equation models of cell division & differentiation Relevant models from different applications: 19 , 28 – 30 , 72 Pattern formation, growth High-content microscopy images/movies Cell-based, differential equations 9 , 11 , 14 , 31 , 32 , 41 , 46 – 48 , 50 , 51 , 53 – 58 , 73 Bioreactor optimisation Flow rates, inlet and outlet solute concentrations, cell distributions Differential equations …”

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

“…Given the complex culture environment in perfusion bioreactors, where the fluid flow stimulates cell proliferation and tissue growth alters in turn the fluid flow, recent investigations have turned to modeling approaches to optimize their tissue production [11].…”

“…Recently, the experimental evidence that the geometry strongly influences the tissue morphology and growth kinetics in static conditions [29,36] motivated the development of new models. Indeed, tissue growth kinetics under perfusion is determined as a function of both the curvature of the tissue growth front and the fluid shear stress [11,37], although these predictions are still to be validated against experimental data at the pore scale. Overall, given the complexity of the biophysical phenomena at stakes in perfusion bioreactors, modeling and numerical simulations in simplified controlled settings, appear as valuable investigative tools.…”