ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

3.2 Model parameters
The model parameters used for the simulations are listed in tabel 1. This set represents the standard
conditions for cell expansion on spherical microbeads and the values are derived or estimated
from data in the literature ([8, 11, 10]). Simulations can be used to estimate how the mechanical
microenvironment will be influenced when specific parameters are changes from their base values.
4 RESULTS AND DISCUSSION
Table 1: Base parameter set for the individual-based model
4.1 Effect of proliferation on mechanical stress
Parameter Symbol Units Value
timestep ∆t s 0.001
simulation time Tend s 0.45e-6
conjugate gradient precision emax m/s 5e-12
division controll stiffness Kd N/m 6e-5
division size R0 m 4.5e-6
division size sdev δdiv m 0.1e-6
division force threshold Fd,max N 0.5e-9
division time Td s 10e3
growth time Tg s 140e3
attr constant cell-cell Ka,cc J/m 2 10e-6
attr constant cell-bead Ka,cb J/m 2 20e-6
youngs modulus cell Ec Pa 500
poisson ratio cell νc 0.4
perp fric coef cells γ ⊥ kg/s 20e-6
par fric coef cells γ kg/s 20e-6
youngs modulus bead Eb Pa 1000
poisson ratio bead νb 0.4
perp fric coef cells γ ⊥,s kg/s 1e-5
par fric coef cells γ ,s kg/s 1e-5
cell-cell migration force Fm N 0
cell-bead migration force Fm,s N 0
viscosity µ Pa·s 3e-3
temperature T K 310
In Figure 2, the evolution of the number of cells and the mechanical stress between cells in a microcarrier
is shown. Due to the normal distribution superimposed on the growth time, the increase
in cell number during the cytokinesis cycles has a sigmoidal shape instead of a step shape. As
the cell number progresses, the discrete doubling cycles will change in a continuous exponential
growth curve. When the cells proliferate and become more confluent on the bead, the compressive
stresses build up until full confluency is reached at around 115h. The standard deviation of
the stresses (indicated by the light red area) increases during the proliferation. The simulations
indicate that the mechanical microenvironment might be very heterogenous, even at very small
aggregate sizes. When the cell number increases, the compressive mechanical stress builds up in
the aggregate. In the intermediate phase the stresses relax only by a small amount.