title: Tissue growth in a rotating bioreactor. Part I: mechanical stability.
abstract: We develop mathematical models to provide insights into the morphology of a tissue construct formed from a single-cell suspension in culture media, within a rotating bioreactor. The bioreactor consists of a cylindrical vessel of circular cross-section rotating about its longitudinal axis with constant angular speed. Experimental studies show that at rotation rates below a critical value, the cells 'self-assemble' to form smooth 'nodules' that are approximately cylindrical with elliptical cross-section; however, at rotation rates above a critical value, an amorphous construct forms with a highly irregular boundary. The construct is denser than the surrounding culture media and histological studies indicate that the interior of the construct, which is a mix of apoptotic cells and culture media, is surrounded by an outer rim of proliferating cells and collagen. The construct is modelled as a viscous fluid drop surrounded by an extensible membrane in a (less dense) immiscible viscous fluid within a rotating bioreactor. We consider both thin-disk and slender-pipe bioreactors for which the aspect ratio, L(*)/a(*) (where L(*) and a(*) are the bioreactor length and radius, respectively), is small and large, respectively, and obtain a series of spatially 2D problems (independent of the axial coordinate). We then examine the hypothesis that the construct morphology is a result of the mechanical forces that it experiences by considering the interfacial stability of an initially circular fluid-fluid interface to small-amplitude, oscillatory perturbations. The instability is driven by the density difference between the two fluids, and we investigate the effect of the rotation rate, the (time-dependent) gravitational field, and the material and geometrical properties of the system on the stability properties.
authors.affiliation: Division of Applied Mathematics, University of Nottingham, Nottingham, NG7 2RD, UK. sarah.waters@nottingham.ac.uk
authors.forename: S L
authors.initials: SL
authors.lastname: Waters
authors.forename: L J
authors.initials: LJ
authors.lastname: Cummings
authors.forename: K M
authors.initials: KM
authors.lastname: Shakesheff
authors.forename: F R A J
authors.initials: FR
authors.lastname: Rose
mesh_terms: D000465:Algorithms; D000818:Animals; D019149:Bioreactors; D018929:Cell Culture Techniques / Q000295:instrumentation / Q000379:methods; D006112:Gravitation; D006801:Humans; D019563:Mechanics; D008954:Models, Biological; D012212:Rheology; D012399:Rotation; D023822:Tissue Engineering / Q000295:instrumentation* / Q000379:methods