Flow, suspension and mixing dynamics in DASGIP bioreactors, Part 2

Funding information Centre for Doctoral Training (CDT), Engineering and Physical Sciences Research Council, Grant/Award Number: EP/ L015218/1; Future Vaccine Research Manufacturing Hub (Vax-Hub), Grant/Award Number: EP/N509577/1 Abstract This work aims to characterize the mixing and suspension dynamics occurring within two commercially available DASGIP bioreactor configurations, equipped with a twoblade paddle impeller with large impeller to tank diameter ratio, D/T = 0.97. Both continuous and intermittent agitation modes were employed to determine the impact that agitation strategy has upon mass transfer and microcarrier settling/suspension. This paper builds upon the flow dynamics data presented in Part 1 for a flat bottom DASGIP bioreactor and shows how intermittent agitation can break-up regions of slow mixing observed during continuous agitation, therefore substantially increasing the mixing efficiency of the system. Similarly, it was found that microcarrier characteristics might significantly affect the level of suspension when the impeller is in dwell status when intermittent agitation modes are used.


| INTRODUCTION
Reproducible and scalable cell culture protocols are necessary to further develop and commercialize cell-based therapeutics. In contrast to traditional monolayer-based cultures, three-dimensional (3D) cell culture techniques offer an attractive platform to increase productivity and improve monitoring and control. In this case however, mixing and suspension dynamics play a crucial role, and bioreactor operating conditions must be carefully selected to provide an optimal environment for cell growth. Cells cultured within a heterogeneous system, due to either poor suspension and/or mixing, are exposed to spatial gradients in oxygen, pH, nutrients and temperature. This is especially true for large scale operation, resulting in compromised cell viability, proliferation, differentiation pathways, metabolism and achievable overall yields. 1 The first section of this introduction focuses on suspension dynamics, with direct implications on 3D culture techniques (i.e., embryoid bodies [EB] or microcarrier [MC]-based), while the second section addresses mixing characteristics in commercial bioreactors.
Suspension performances within a reactor are commonly determined using the Zwietering criterion, which consists in finding the minimum rotational speed corresponding to particles at rest for less than 2 s on the base of a reactor. 2 The "just suspended speed," N js , can be calculated from Equation (1): where S is a dimensionless parameter, depending on the impeller clearance, C, and impeller diameter, D, particle diameter, D p , fluidsolid density difference, Δρ, liquid density, ρ L , fluid kinematic viscosity, υ, and solids percentage, X. This correlation was originally developed for chemical engineering applications, such as suspension of catalysts and reaction products and batch-wise dissolution of solids, with solid particle densities nearly three-times greater than those of MCs or EB in typical bioprocesses. As a consequence, Equation (1) was found to over predict N js of MCs by nearly 50%. 4 MCs are in fact highly porous and their effective solid density should be estimated from Equation (2) before using the N js correlation in Equation (1).
When adherent-dependent cells, such as stem cells, are cultured within a 3D bioreactor, they are typically grown in the form of EB, that is, adhered to one another, or on the surface of MC. Both the degree of suspension and settling will depend upon the bioreactor and impeller configuration, the operating conditions employed, as well as EB/MC size, morphology and density. In fact, these three properties are likely to change over the course of a cell culture. For example, EB aggregates of iPSCs were found to increase in size 25% over the course of differentiation to cardiomyocytes, 6,7 while cell elongation of iPSC EBs was achieved during differentiation to neuronal cells with further morphological changes noted as the cells matured. 8 Similarly, commercially available MCs, such as Cytodex, Cytopore (both GE Healthcare), Hillex, (SoloHill) and Cultispher (Percell Biolytica) vary significantly in shape, size, density, material, surface charge or coating and may be microporous or macroporous in structure. 9 Seldom studies have been undertaken investigating how different MC types affect cell culture. Rafiq et al 10  In this work cells were successfully cultured at N js , for cell culture densities of 1-5 × 10 5 cells/ml, however it was indicated that the just suspended speed may not provide sufficient oxygen mass transfer for higher cell densities.  Three commercially available MCs were used for suspension characterization: Cytopore 1, Cytodex 3 and Cultispher-G (see Table 1).
They were selected to mimic EB properties at different time points during cell culture, as described in References 6 and 7 These works report a 25% increase in EB size over the course of cardiogenic differentiation, in addition to a 45% increase in EB settling. This was taken into account using MCs with similar density (ρ ≈ 1.04 g/cm 3 ), but with varying combination of size and porosity, which results in different effective density (Table 1). Microscope images of each MC type are also provided for illustration at ×120 and ×600 magnification using an inverted brightfield microscope.
Similar to the work of Olmos et al, MCs were stained using 0.4% Trypan Blue (Sigma-Aldrich, United States), 22 and all experiments were conducted at a fixed concentration of 1 g/L. Images for each condition were then recorded at a frequency of 2 Hz for 5 min for all agitation modes. The MCs were then allowed to fully settle inbetween experiments and images were processed using a purposelywritten MATLAB code.
As images were recorded from the side of the vessel, a direct measurement of MC homogeneity across the reactor volume was obtained. In the following, a fully homogeneous distribution of MCs corresponds to a fully suspended environment. The suspension/ homogeneity index, H(N), was determined from Equation (3): where I N is the cumulative brightness of the image at speed N, I 0 represents the image brightness when the system is stationary and fully settled and I max denotes when the system is completely suspended and homogeneous. The data were fitted with the sigmoidal function of Equation (4): where parameters a and x 0 are found from a nonlinear regression analysis (R 2 -squared fitting of >.95). This curve was then used to determine the minimum speed to reach full homogenization, N H , when H = 95%.

| Mixing time characterization experiments
Mixing time measurements were conducted using the same experi- T A B L E 1 Diameter (D 50 , D 5 , D 95 ), density (ρ, ρ s,eff ), porosity (Φ) and inverted microscope images at 120 and ×600 magnification for three commercial microcarriers close to the working fluid (ρ = 1.00 g/cm 3   suggesting that once suspended Cultispher-G is more efficiently lifted. This may be attributed to the increase in MC porosity, which according to Equation (2), results in a reduction of the effective density of a particle. Applying Equation (2), the effective density for Cultispher-G is ≈ 1.02 g/cm 3 while for Cytodex 3 is 1.04 g/cm 3 .
This may suggest that the decrease in MC size, as previously highlighted, is more significant to suspend at lower speeds, how- where A and V are the particle external surface and volume respectively, while C D is the drag coefficient for a smooth sphere in turbu- Finally, it must be noted that when the agitation is resumed full resuspension occurs rapidly, t r = 2-4 s, for all dwell times investigated.
Similar to the suspension measurements, Cytopore 1 was the quickest to resuspend, while Cytodex 3 took the longest.    To assess the impact of continuous and intermittent agitation strategies on power, the space-averaged maximum local shear rate, γ**, and velocity magnitude, U rz **, calculated from Part 1 of this work, were averaged over one cycle, including both a motion and a dwell phase (T inv + T dwell ). These two quantities can be used as a basic power indicator to assess the system efficiency for the two agitation strategies adopted. This data is summarized in Table 5. Taking the continuous agitation mode as a reference, it is worth to point out that dwell times in the range T dwell = 500-1,500 ms (italic values), showed higher values of both averaged shear rate and velocity magnitude, implying that a greater amount of power was used. This is also reflected in faster mixing times (see Table 5). The differences in physical properties of the MCs, that is, size, porosity and effective density, were shown to vary the suspension/settling profile during intermittent agitation. This highlights the need for consideration of suspension dynamics, for example, over the course of a cell differentiation process, when morphological characteristics of MCs or EB evolve over time. T A B L E 5 Average shear rate (γ**) and velocity magnitude (U rz **) across the bioreactor volume over one cycle, considered as T inv + T dwell , and mixing time (t m ) for continuous agitation, N = 90 rpm, and intermittent agitation, N = 90 rpm, T inv = 30 s and T dwell = 500-30,000 ms