IEEE Computational Intelligence Magazine - November 2021 - 94

570 cancer cell agents) undergoes
growth of a simulated period
of 7 days. At that point, the
treatment is injected into the
simulated area, comprising of
450 cargo agents and 50 worker
agents, emulating the therapeutic
compound and NPs, respectively.
A simulated period of
3 days is then executed, where
the worker agents transport the
cargo agents (therapeutic compound)
and deposit them near
the cancer cell agents that decay
and die because of the increased
concentration of drug agents.
The fitness function of the
given point in the parameter
space is the number of cancer
cell agents remaining after the
simulated period of 10 days.
Every simulation of these
TABLE 1 Unaltered parameters of PhysiCell simulator.
PARAMETER
Damage rate
Repair rate
VALUE
Drug death rate
Elastic coefficient
Cargo O2 relative uptake
Cargo apoptosis rate
Cargo relative adhesion
Cargo relative repulsion
Cargo release O2 threshold
Maximum relative cell adhesion distance
Maximum elastic displacement
Maximum attachment distance
Minimum attachment distance
10 days runs on an Intel®
Xeon® CPU E5-2650 at
2.20 GHz with 64GB RAM
(using 8 of the 48 cores) and is completed
at approximately 5 minutes of wallclock
time. Because of the stochastic
nature of the simulator, a static sampling
approach is employed, considering
the mean of 5 runs with the same
parameters. In order to further minimize
the noise caused by the stochasticity of
the simulator and, also, to speed up the
optimization process, alternations in the
original source code are made in order
to load a single tumor at the initializaMotility
shutdown detection threshold
Attachment receptor threshold
Worker migration speed
Worker apoptosis rate
Worker O2 relative uptake
0.03333 min-1
0.004167 min-1
0.004167 min-1
0.05 min-1
0.1 min-1
4.065e-5 min-1
5
10 mmHg
1.25
50 μm
18 μm
14 μm
0.001
0.1
2 nm/min
0 min-1
0.1 min-1
randomly produced population
of solutions and evolution is
applied for 200 evaluations of
each individual/solution. Thus,
the results are provided for each
test after approximately a day
wall-clock time of repeatedly
running the simulator.
To accommodate the functionality
of injecting the region
around the cancer tumor with
more than one types of NPs
with different parameters, we
made appropriate alternations
in the source code of the simulator.
Without loss of generality
a maximum of 10 different
types of NPs is defined. The
amount of NPs (worker agents)
is set to 50, despite the number
of types of NPs. These 50 NPs
are equally divided among
different NP types. For in -
stance, in testing 2 NP types,
50 worker agents are divided
tion of the simulator and apply the therapy
for 3 days (as described in [28]).
One specific tumor, which was
derived after a simulated growth of
7 days of an initial tumor, is used as the
new initial state and the treatment is
injected to the simulated area at t = 0.
Then, 3 days are simulated and the evaluation
of a single solution needs 1.5
minutes of wall-clock time (7.5 minutes
for the 5 runs for static sampling). Each
test in the following starts with the same
into two groups of 25; with 5 types of
NPs, the size of each group is ten, etc.
Further technical details of the additions/alternations
of the initial source
code can be found in the Supplementary
Material.
V Genome Growth in the
Simulator
The optimization of the design of NPs
for drug delivery initially uses a standard
steady-state EA and mutation operators
Average Fitness of Population.
Best Individual Fitness of a Population.
1,000
800
850
900
950
020406080 100 120 140 160 180 200
Generations
(a)
1,000
800
850
900
950
1
1
1
1
1
1 11 1
1 1
020406080 100 120 140 160180 200
Generations
(b)
FIGURE 11 Results from example run of the EA. (a) Evolution of average fitness of the population and (b) evolution of the best individual in the
population (where numbers indicate the number of types NPs).
94 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2021
Average Fitness of Population
Best Fitness of Population

IEEE Computational Intelligence Magazine - November 2021

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