Model-based optimization of radial flow packed-bed bioreactors for tissue engineering

Abstract

Tissue loss or organ failure represents one of the major problems in human health care, and is responsible of impressive social and economic costs worldwide. Current approaches to restore tissues or organs functions consist in tissue replacement with allogeneic or xenogeneic grafts, taken from donors or animals, respectively, or autologous grafts, taken from the patient himself. The use of allogenic and xenogenic grafts is severely limited by the donor shortage and by the difficult integration of the donor tissue within the patient body. Tissue replacement with autografts, although avoiding the risk of immune rejection by the patient, is limited by donor-site morbidity, so that it may be adopted only for small-scale tissue losses. In recent years, tissue engineering has been proposed as a promising alternative to tissue replacement with artificial grafts. According to this approach, biological engineered substitutes for tissue replacement are realized by seeding isolated autologous cells onto three-dimensional (3D) porous supports, termed scaffolds, and by guiding cell proliferation and differentiation in bioreactors, that provide the physiological pericellular environment for tissue development. The major issue for the realization of clinical-scale bioengineered substitutes for tissue replacement is the difficult supply of physiological amounts of dissolved oxygen and nutrients to, as well as metabolic wastes removal from, the cells located in the innermost regions of the 3D constructs (i.e. cell-seeded scaffolds). In particular, it is generally acknowledged that the severe consumption of dissolved oxygen by the cells represents the major limitation for cell survival in the development of bioengineered tissues. Static cultures in which dissolved oxygen and nutrients are supplied to the cells by pure diffusive transport have been shown to enable cell survival only to small-scale constructs. In order to overcome transport limitations of static cultures, dynamic bioreactors have been proposed in which a certain degree of convection is superimposed to pure diffusion to enable solutes transport towards, or away from, the innermost region of large-scale constructs. However, although some improvements over static cultures have been evidenced, dynamic bioreactors proposed so far, such as spinner flasks, rotating wall vessels and direct axial perfusion bioreactors, are still sub-optimal for the realization of clinical-scale bioengineered tissues. Recently, radial perfusion of hollow cylindrical 3D constructs in radial flow packed-bed bioreactors (rPBBs) has been proposed to overcome the limitations of both static and direct axial perfusion bioreactors, in particular for the development of bioengineered liver and bone tissues. In fact, since culture medium is perfused radially to the cells, shorter path lengths and larger cross-sectional areas for solutes transport are featured than those in axial flow bioreactors, that enable cell culture at small pressure drops and superficial velocities, and smoother solutes concentration gradients in the direction of the medium perfusion. Despite these promising features, design of rPBBs is more difficult than that of axial flow packed bed bioreactors. In fact, rPBBs require two void chambers (i.e. the inner hollow cavity and the peripheral annular space) to distribute and collect culture medium flowing across the construct thickness, the fluid dynamics of which may significantly influence radial flux distribution of culture medium along the construct length. Furthermore, the annular construct geometry and the direction of medium perfusion may strongly affect the transport of solutes towards, or from, the cells. The extent of the perfusion flow rates have also to be chosen in order to ensure adequate mass delivery to cells while preventing cell damage and washout. Mathematical models of transport in rPBBs may help optimize bioreactor design for a given application to enable dissolved oxygen and nutrients delivery towards, and metabolic wastes removal from, 3D clinical-scale constructs. However, a systematic analysis of the influence of all the geometrical, transport and operational dimensionless groups on bioreactor behavior aimed to design rPBBs so that solutes transport towards, or from, the cells is maximized and controlled has not been reported yet. This limits the exploitation of the peculiar features of the rPBBs in the development of bioengineered substitutes for tissue replacement. In this thesis, a model-based reference framework is proposed to optimize rPBB design to ensure adequate environmental conditions to cells for the realization of clinical-scale 3D bioengineered substitutes for tissue replacement. In particular, the attention is paid on transport of dissolved oxygen, since its limiting role for the realization of large-scale 3D biological constructs is generally acknowledged. In order to reach the proposed objective, the workflow was divided in three different steps, as follows: 1. A reference framework was first developed based on a one-dimensional stationary transport model, combining convective and dispersive transport of dissolved oxygen with Michaelis-Menten cellular consumption kinetics, to optimize annular construct geometry and direction and extent of the radial superficial velocity of the culture medium across the cell mass for the culture of largescale 3D porous constructs, assuming that radial flux distribution of the culture medium was uniform along the construct length. Dimensional analysis was used to find the dimensionless groups determining bioreactor behavior, under typical conditions for tissue engineering. In particular, according to this model, bioreactor behavior was shown to depend on the perfusion flow direction parameter, g; the dimensionless construct Darcy permeability, kL/R3; the inner hollow cavity radius-to-construct thickness ratio, R/dC; the maximal radial Peclet number, Perad,max; the Thiele modulus, fC; the saturation parameter, b. The effectiveness of oxygen supply to the cells was expressed in terms of the non-hypoxic fractional construct volume. Model predictions suggest that outward perfusion (i.e. form the construct inner surface towards the outer peripheral surface) of 3D annular porous constructs having small curvature (i.e., high inner hollow cavity radius-to-annular thickness ratio) at high perfusion flow rates, (i.e high maximal radial Peclet numbers) may enhance dissolved oxygen supply to the cells as compared to cell culture in static and axial flow bioreactors. 2. A design criterion to optimize rPBB design in order to achieve uniform radial flux distribution of the culture medium along the construct length was obtained, based on a two-dimensional stationary transport model of momentum in all the rPBB compartments (i.e. inner hollow cavity, porous construct, peripheral annulus), assuming that medium is perfused outwards according to the results obtained with the 1D model. In particular, momentum transport in the void spaces of the rPBB was described according to the Navier-Stokes equation, whereas Darcy-Brinkman equation was used to describe momentum transport in the porous construct. Dimensional analysis showed that the uniformity of radial flux distribution of the culture medium along the construct length depends on: a reduced Reynolds number, Rein; the construct aspect ratio, L/R; the inner hollow cavity radius-toconstruct thickness ratio, R/dC; the inner hollow cavity radius-to-peripheral annulus thickness ratio, R/dE; the construct-to-hollow cavity permeability ratio, k/R2. The influence of R/dC and R/dE was lumped in one dimensionless group (i.e. the hollow cavity-to-peripheral annulus cross-sectional area ratio, x), as suggested by literature results. The design criterion, termed CORFU (Criterion Of Radial Flux Uniformity), was shown to depend on all the dimensionless groups found by dimensional analysis. In particular, according to the CORFU criterion, uniform radial flux distribution of the culture medium along the construct length may be achieved by adjusting the values of the dimensionless groups determining rPBB behavior in order to ensure that the ratio between the total axial pressure drop in the void spaces is maintained within ±10% of the radial pressure drop across the construct. 3. The momentum transport model was integrated with a mass transport model to assess the actual effect of the radial flux distribution of the culture medium along the construct length on dissolved oxygen transport and to design rPBBs for a given therapeutic objective. Transport of dissolved oxygen in the construct was described in terms of the convection-diffusion-reaction equation, and dissolved oxygen consumption was described according to the Michaelis-Menten kinetics. Oxygen mass transfer coefficients accounting for the external mass transport at cell/medium interface were estimated for a bed of Raschig rings transport-equivalent to porous scaffolds adopted for tissue engineering. Dimensional analysis showed that, in addition to the dimensionless groups obtained for the momentum transport model previously listed, bioreactor behavior, which was expressed in terms of the Non-Hypoxic Fractional Construct Volume, depends on the following dimensionless groups: the maximal radial Peclet number, Perad,max; the construct-to-hollow cavity diffusivity ratio, DC/DH (and, analogously, the construct-to-peripheral annulus diffusivity ratio, DC/DE); the Sherwood number, Sh; the saturation parameter, b; the Thiele modulus, fC; the squared surface Thiele modulus-to-Sherwood number ratio, fs 2/Shp. The effect of the dimensionless number on bioreactor behavior was investigated under working conditions typical of tissue engineering. Model predictions suggested how to optimize bioreactor design in order to ensure controlled oxygen supply to cells for different tissue engineering applications. Medium radial flux distribution was shown to significantly influence oxygen spatial distribution inside the construct under conditions in which oxygen depletion is not properly compensated by oxygen supply to cells. The effect of medium radial flux distribution on oxygen supply becomes less important if oxygen consumption is compensated by oxygen supply. Model predictions also suggest that higher Rein influences oxygen spatial distribution from the top towards the bottom of the bioreactor for non-uniform medium radial flux distribution, giving higher uniformity of oxygen distribution along bioreactor length. The radial perfusion rates have to be optimized not only to control radial flux distribution, but also to enable adequate supply of dissolved oxygen to the cells while preventing cell wash out, at any given stage of tissue development. In particular, model predictions suggest that at the beginning of the culture medium flow rates may be kept low to avoid cell damage or wash out, whereas, as cells proliferate and differentiate, the medium flow rates should be gradually increased to balance out the increasing metabolic requirements of cells. In particular, higher perfusion flow rates enable more adequate oxygen supply to cells for a given value of fC. Finally, choosing perfusion rates that cause minimal Damköhler number, Darad,min = fC 2/Perad,max, to be small were shown to ensure adequate pericellular oxygenation (i.e. NHy-FCV around 1) for tissue development