consumption to be described based on the experimental setup investigated. In
contrast to the Monod-type models, Bartolini et al. [112], Mancuso et al. [113],
Bailon-Plaza et al. [114], and Geris et al. [115] used population balance models. For
example, Bailon-Plaza et al. [114] included different cell populations in their model
in order to describe not only hMSC proliferation but also chondrogenic and osteogenic differentiation. However, all models included parameters strongly influenced
by various biological aspects. A discrete formulation of the cells was given by
Schellenberg et al. [116] and Cholewa et al. [117], who both used cellular automaton
models to describe the hMSC cell growth. However, these models did not include a
metabolic description of substrate consumption and metabolite production, which
can have an inhibitory effect on the cell growth. Hoffmann et al. [118] developed an
individual cell-based model with podia, which is able to quantitatively describe the
spatio-temporal organization of MSC culture. They modelled discrete cells and
considered their orientation on a planar surface. Hence, the model considers the
effects of contact inhibition and the organization and orientation of the cell monolayer. However, the model does also not reflect the metabolization of different
substrates or the production of inhibitory metabolites.
4.2 Kinetic Growth Model for the MC-Based hMSC
Expansion: A Case Study
Based on theoretical considerations, an unstructured, segregated, simplistic growth
model was developed for the MC-based hMSC expansion in the SP100 and SP300.
Theoretically, the entire expansion process can be divided into four steps: (I) cell
sedimentation and initial attachment, (II) cell spreading and migration, (III) mitotic
cell division, and (IV) cell growth arrest due to contact or substrate inhibition, which
partially ran in parallel. The general concept of the growth model and the factors that
influence the MC-based culture are shown in Fig. 13. During the cultivation period,
the formation of MC-cell aggregates is promoted due to the increasing number of
cells per bead and periodic particle interactions. The rate of the MC-cell aggregate
formation is influenced by the frequency and strength of the hydrodynamic stresses.
However, the rate of MC-cell aggregate formation was not considered in the current
version of the MC-based growth model because the aggregation process is very
complex and depends on many physical and biological parameters. Due to the fact
that hMSC growth is anchorage-dependent, possible formation of spheroids in the
suspension was not considered in the model. This simplification was justified since
no spheroid formation was observed in the MC-based expansions. Thus, it can be
assumed that cells in suspension do not contribute to an increase in the overall cell
number, with cell growth restricted to the MC surface. To define the starting
conditions, it was assumed that initial cell attachment took place during the cell
attachment phase, which can be described by the attachment constant k at . After the
cells had attached themselves to the MC surface, a short cell adaption phase was
Numerical Methods for the Design and Description of In Vitro Expansion. . .
217
contrast to the Monod-type models, Bartolini et al. [112], Mancuso et al. [113],
Bailon-Plaza et al. [114], and Geris et al. [115] used population balance models. For
example, Bailon-Plaza et al. [114] included different cell populations in their model
in order to describe not only hMSC proliferation but also chondrogenic and osteogenic differentiation. However, all models included parameters strongly influenced
by various biological aspects. A discrete formulation of the cells was given by
Schellenberg et al. [116] and Cholewa et al. [117], who both used cellular automaton
models to describe the hMSC cell growth. However, these models did not include a
metabolic description of substrate consumption and metabolite production, which
can have an inhibitory effect on the cell growth. Hoffmann et al. [118] developed an
individual cell-based model with podia, which is able to quantitatively describe the
spatio-temporal organization of MSC culture. They modelled discrete cells and
considered their orientation on a planar surface. Hence, the model considers the
effects of contact inhibition and the organization and orientation of the cell monolayer. However, the model does also not reflect the metabolization of different
substrates or the production of inhibitory metabolites.
4.2 Kinetic Growth Model for the MC-Based hMSC
Expansion: A Case Study
Based on theoretical considerations, an unstructured, segregated, simplistic growth
model was developed for the MC-based hMSC expansion in the SP100 and SP300.
Theoretically, the entire expansion process can be divided into four steps: (I) cell
sedimentation and initial attachment, (II) cell spreading and migration, (III) mitotic
cell division, and (IV) cell growth arrest due to contact or substrate inhibition, which
partially ran in parallel. The general concept of the growth model and the factors that
influence the MC-based culture are shown in Fig. 13. During the cultivation period,
the formation of MC-cell aggregates is promoted due to the increasing number of
cells per bead and periodic particle interactions. The rate of the MC-cell aggregate
formation is influenced by the frequency and strength of the hydrodynamic stresses.
However, the rate of MC-cell aggregate formation was not considered in the current
version of the MC-based growth model because the aggregation process is very
complex and depends on many physical and biological parameters. Due to the fact
that hMSC growth is anchorage-dependent, possible formation of spheroids in the
suspension was not considered in the model. This simplification was justified since
no spheroid formation was observed in the MC-based expansions. Thus, it can be
assumed that cells in suspension do not contribute to an increase in the overall cell
number, with cell growth restricted to the MC surface. To define the starting
conditions, it was assumed that initial cell attachment took place during the cell
attachment phase, which can be described by the attachment constant k at . After the
cells had attached themselves to the MC surface, a short cell adaption phase was
Numerical Methods for the Design and Description of In Vitro Expansion. . .
217