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A simplified 2D mathematical model for tissue growth within a cyclically-loaded tissue engineering scaffold is presented and analyzed. Such cyclic loading has the potential to improve yield and functionality of tissue such as bone and cartilage when grown on a scaffold within a perfusion bioreactor. The cyclic compression affects the flow of the perfused nutrient, leading to flow properties that are inherently unsteady, though periodic, on a timescale short compared with that of tissue proliferation. A two-timescale analysis based on these well-separated timescales is exploited to derive a closed model for the tissue growth on the long timescale of proliferation. Some sample numerical results are given for the final model, and discussed.

We present a combined experimental and theoretical study of the trajectory of a large solid cylindrical disc suspended within a fluid-filled rotating cylindrical vessel. The experimental set-up is relevant to tissue-engineering applications where a disc-shaped porous scaffold is seeded with cells to be cultured, placed within a bioreactor filled with nutrient-rich culture medium, which is then rotated in a vertical plane to keep the growing tissue construct suspended in a state of "free fall." The experimental results are compared with theoretical predictions based on the model of Cummings and Waters (2007), who showed that the suspended disc executes a periodic motion. For anticlockwise vessel rotation three regimes were identified: (i) disc remains suspended at a fixed position on the right-hand side of the bioreactor; (ii) disc executes a periodic oscillatory motion on the right-hand side of the bioreactor; and (iii) disc orbits the bioreactor. All three regimes are captured experimentally, and good agreement between theory and experiment is obtained. For the tissue engineering application, computation of the fluid dynamics allows the nutrient concentration field surrounding a tissue construct (a property that cannot be measured experimentally) to be determined (Cummings and Waters, 2007). The implications for experimental cell-culture protocols are discussed., (2009 Wiley Periodicals, Inc.)

Fluid flow and nutrient transport around a growing tissue construct within a cylindrical bioreactor of circular cross-section are considered. The bioreactor is filled with nutrient-rich culture medium, and the growing tissue construct is modelled as a cylindrical obstacle, also of circular cross-section, at a given (moving) position within the nutrient solution. The bioreactor rotates about its cylindrical axis, and its axial length is small relative to its radius (the high-aspect ratio vessel bioreactor). This small-aspect ratio means that a simple idealized model may be considered, in which (leading order) quantities are averaged across the axial direction. The leading-order fluid flow is then of Hele-Shaw type, and may be solved for explicitly. The trajectory of the tissue construct within the rotating bioreactor is determined by analysis of the various forces acting on it. Several different modes of motion are found to be possible, depending on the experimental conditions, and examples of each type of motion are presented. Additionally, we solve the problem for the nutrient transport around the tissue construct in the special case in which the construct remains fixed in the laboratory frame, and (as the cells proliferate in response to the nutrient available locally) deduce growth rates for the construct. Finally, we discuss our results in the light of possible experimental bioreactor set-ups. We note the present model's limitations, and consider how our work could be extended and improved to inform experimental protocols in future.

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.

Motivated by experimental work (Miller et al. in Biomaterials 27(10):2213-2221, , 32(11):2775-2785, ) we investigate the effect of growth factor driven haptotaxis and proliferation in a perfusion tissue engineering bioreactor, in which nutrient-rich culture medium is perfused through a 2D porous scaffold impregnated with growth factor and seeded with cells. We model these processes on the timescale of cell proliferation, which typically is of the order of days. While a quantitative representation of these phenomena requires more experimental data than is yet available, qualitative agreement with preliminary experimental studies (Miller et al. in Biomaterials 27(10):2213-2221, ) is obtained, and appears promising. The ultimate goal of such modeling is to ascertain initial conditions (growth factor distribution, initial cell seeding, etc.) that will lead to a final desired outcome. [ABSTRACT FROM AUTHOR]