Multi-agent Modeling Simulation of In-vitro T-cells for Immunologic

Alternatives to Cancer Treatment

David F. Nettleton

1 a

, Vladimir Estivill-Castro

1,2 b

and Enrique Hern

andez Jim

enez

3 c

Department of Information and Communications Technology (DTIC), Universitat Pompeu Fabra, Spain

School of ICT, Grifﬁth University, Brisbane, Australia

Institut d’Investigaci

o Biom

edica de Bellvitge, Barcelona, Spain

Keywords:

Simulation, Multi-agent Systems, Immunology, Cancer Cells.

Abstract:

There is exciting news in recent developments suggesting the potential to treat some human cancers by stim-

ulating the patients own immune system. However, there is still much to understand; therefore, modelling

the battle between those cells that are constituents of the human immune system against tumorous cells can

signiﬁcantly provide insights as mathematical modelling has done regarding the immune system behaviour

against virus infections. In this paper we innovate in two directions. First, we move the modelling of immune

struggles from the sphere of ordinary-differential equation models to the modelling by multi-agent simula-

tions. We highlight the advantages of the multi-agent simulation, for example the consideration of elaborate

spatial proximity interactions. Secondly, we move away from the realm of infectious diseases to the complex

modelling of the stimulation of T-cells and their participation in ﬁghting cancerous cell tumours.

1 INTRODUCTION

Recent developments in immunotherapy (ElSayed,

2018; Sun, 2017) indicate remarkable progress for

the treatment of some human cancers by stimulat-

ing the patient’s immune system (Chen and Mell-

man, 2013; Fern

andez et al., 2013; Pardoll, 2012;

Farag et al., 2002). Nevertheless, the high complex-

ity of the human immune system remains a challenge.

We require progressively more advanced and high

ﬁdelity models for understanding the immune sys-

tem dynamics and mechanisms. In particular, mod-

elling the battle between those cells that are con-

stituents of the human immune system against tu-

morous cells can signiﬁcantly provide insights as

mathematical modelling has already done regarding

the immune system behaviour against virus infec-

tions (Wodarz, 2006). We open the ﬁeld in two direc-

tions. First, we move the modelling of immune strug-

gles from the realm of ordinary-differential equation

models (

Alvarez et al., 2017) to the modelling by

multi-agent simulations (B

adic

a et al., 2018; Karsai

et al., 2016; Zhao and Jin, 2005). We highlight that

https://orcid.org/0000-0002-5852-7716

https://orcid.org/0000-0001-7775-0780

https://orcid.org/0000-0002-8232-8151

the multi-agent simulation enables consideration of

elaborate spatial proximity interactions. Such inter-

actions are extremely important in the modelling of

competition and predator-prey scenarios in ecologi-

cal systems (Karsai et al., 2016). Secondly, we move

from the realm of infectious diseases to the complex

modelling of the stimulation of T-cells and their par-

ticipation in ﬁghting cancerous cell tumours. Most

cancers are not caused by transmissible pathogens;

but, cancer immunotherapy suggests treatment anal-

ogous to infections (Chen and Mellman, 2013).

Adopting a system approach and modelling the

dynamics analogously to ecological systems (Wodarz,

2006) has enabled tremendous progress in the under-

standing of the interactions between pathogens and

the immune system. Such dynamics is modelled by

increasingly more complicated systems of ordinary

differential equations that abstract elements of what is

known by experimental means (

Alvarez et al., 2017;

Eftimie et al., 2016; Linderman et al., 2010).

The mathematical models of infections capture

population dynamic interactions of two types (Ada,

1997; Wodarz, 2006). One is predator-prey interac-

tions, where predators kill prey, and the predator pop-

ulation grows until much fewer prey results also in

a decrease of predator numbers. This is usually the

scenario of killer cells responding to a viral infec-

Nettleton, D., Estivill-Castro, V. and Jiménez, E.

Multi-agent Modeling Simulation of In-vitro T-cells for Immunologic Alternatives to Cancer Treatment.

DOI: 10.5220/0008915601690178

In Proceedings of the 12th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2020) - Volume 1, pages 169-178

ISBN: 978-989-758-395-7; ISSN: 2184-433X

169

tion. Secondly, competition models abstract scenar-

ios where two species dispute a common resource (a

source of food). In the case of the immune system,

one immune cell type may expand more rapidly upon

exposure to infection, preventing another type of im-

mune cell from growing its numbers.

Such mathematical modelling stimulates the ex-

perimental agenda. In the realm of viral infections,

different models of how CTL (cytotoxic T lympho-

cytes or killer T cells) are assisted by CD4 T cell (T

cells that bear the CD4 marker of helper cells) in the

primary response and the resolution of an infection

as well as the memory phase prompted many experi-

ments (Wodarz, 2006, Chapter 4). In particular, im-

munological memory is the preservation of a much

larger number of speciﬁc CTL cells after a virus in-

fection than before the infection. This memory capac-

ity of the immune systems has delicate interactions

with the eradication of the infection. The mathemati-

cal models suggest that there is a trade-off. The virus

population is reduced by a high responsiveness and a

long life span of the memory CTL (Wodarz, 2006).

However, while there has been an extensive liter-

ature of the application of dynamic systems models

ﬁrst to ecological systems (Chase et al., 2002; Kings-

land, 2015) and then to the immune systems (Wodarz,

2006), there is a recent opportunity in two directions.

First, to use the technology of multi-agent simula-

tion and second to apply it to the emerging promise

of the immune systems potential to ﬁght cancer tu-

mours (Chen and Mellman, 2013). Therefore, in this

paper, we describe and test a modelling technique

based on multi-agent systems for simulating systemic

and inter-cellular behaviour for NK (natural killer)

and cancer cells. The clinical approach is to potentiate

the body’s own immune system, using reprogrammed

natural killers (NK is a type of lymphocyte; that is

a white-blood cell) to attack the cancer (or tumour)

cells. Therefore, no harm is caused to normal cells, in

contrast to widely used chemo-therapy approaches.

In order to be effective, NK cells require an opti-

mum programming against the particular cancer cell

adversary. This requires an individualized study of

the patient followed with a directed trial and error pro-

cess which typically is tested on mice with a 14-day

evolution period. Computer simulations could run

in just a few minutes, with a much lower economic

cost and could approach a realistic simulation perfor-

mance relative to the mouse and in-vitro experimen-

tation. Thus, multi-agent simulation could provide

an important step forward in accelerating the ﬁght

against cancer-cell growth.

We incorporate medical know-how to build a

multi-agent simulation model with some degree of

realism. Every model is an abstraction, but we will

highlight the aspects that a multi-agent simulation of-

fers over the dynamic systems approach of using sets

of differential equations. We benchmark our simula-

tions against state of the art empirical in-vitro clinical

experiments, as described by Fern

andez et al. (2013).

Our results demonstrate that an agent system can ac-

curately model the in-vitro experiments in terms of

cytotoxicity, but without the need for deﬁning a set

of differential equations as in dynamic system mod-

els nor a priori assumptions relative to the system, and

giving greater ﬂexibility for trying many different sce-

narios. Our implementation uses random interaction

and cellular random movement in space.

2 THE CASE FOR MULTI-AGENT

SIMULATIONS

Purely clinical approaches to immunological treat-

ment of cancer rely heavily on the use of in vitro

trials with live mice requiring highly specialized pa-

rameterisations. Such parameterisations require deep

medical knowledge. A signiﬁcant part of the chal-

lenge is to anticipate behaviour, and as we explained

before, so far in this ﬁeld, the research has focused

on mathematical modelling in the realm of dynamic

systems abstracted as systems of differential equa-

tions (

Alvarez et al., 2017).

But, the techniques to formulate models of bi-

ological systems, and to solve them includes also

agent-based models, stochastic modelling techniques,

differential equations, spatial simulations, and direct

application of Gillespie’s stochastic simulation algo-

rithm (Barnes and Chu, 2015). Differential equa-

tions are suitable abstractions at the macro-level, but

multi-agent systems are suitable models at the micro-

level behaviour that can determine the macro-level

behaviour. Sets of ordinary differential equations

(ODEs) have limitations pertaining problems involv-

ing spatial interactions or emerging properties (Bor-

shchev and Filippov, 2004). Borshchev and Filippov

(2004) and others (Figueredo et al., 2014) argue ODE

methods exclude emergent and stochastic behaviour.

Louzoun (2007) consider ODE methods too nar-

row, using few reactive types focused on simple dy-

namics. Louzoun (2007) argues that immunological

modelling should incorporate genomic data and ex-

ploit computing power. His review (Louzoun, 2007)

suggests that applications of mathematical models in

immunology are shifting to immunomics: the con-

cepts of high–throughput measurements and system

immunology. Models of ODE systems for immunol-

ogy are categorised as deterministic compartmental

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

170

models (Figueredo et al., 2014) because continuous

values are used for all aspects of the modelling of

individuals in the environment; while multi-agent

systems explicitly represent the individuals. Strac-

quadanio et al. (2011) argue that agent-based mod-

els “seem to be the best suited abstraction to han-

dle the great complexity of the immune system”.

We acknowledge that the discrete-event scheduling of

Gillespie methods has been incorporated with multi-

agent simulation into mixed platforms (Montagna

et al., 2016). In particular, some variants of Gille-

spie’s discrete-event scheduling have been applied

to the simulation of the spatial interaction between

cells (Shimoni et al., 2011; Engblom, 2019).

The model accuracy is believed to be negatively

impacted by the exclusion of information on proxim-

ity (Stracquadanio et al., 2011) because most immune

interactions take place within local spatial regions of

the environment.

This advantage of multi-agent systems has been

illustrated in the ﬁeld of ecology (B

adic

a et al., 2018)

and other speciﬁc disciplines (Montagna and Viroli,

2010; Montagna et al., 2010, 2016). Multi-agent sys-

tems have been used to explore what-if scenarios of

environments that combine cell proliferation and ran-

dom walks of cells on regular lattices, reactions for

nutrients and growth factors (Figueredo et al., 2013a).

Researchers use different modelling environ-

ments, but for multi-agent system modelling, the

Repast Simphony (North et al., 2013) is common.

In particular, Repast Simphony was used to illustrate

multi-agent systems simulations as an alternative to

dynamic systems of differential equations for the clas-

sical predator-prey scenario (Tatara et al., 2006).

3 RELATED WORK

The nearest work to our approach here is the appli-

cation of agent simulations of immune cell (effec-

tors) and tumour cell interactions (Figueredo et al.,

2013b, 2014). The focus of Figueredo et al. (2013b)

and Figueredo et al. (2014) is to compare a differen-

tial equation model (Gillespie) with an agent based

model. Figueredo et al. (2013b) and Figueredo et al.

(2014) ﬁnd that the agent-based model effectively

simulates the system and also ﬁnd patterns which

were unseen by the former. However, they do not

use distance based parameters, and as mentioned ear-

lier, spatial information (proximity) is considered cru-

cial (Stracquadanio et al., 2011). We do incorporate

proximity in our model. Figueredo et al. (2013b)

and Figueredo et al. (2014) do not relate the effector

and tumour cells to real biological equivalents; their

analysis is in-silico (Figueredo et al., 2014); that is,

pure simulation. Thus, Figueredo et al. (2013b) and

Figueredo et al. (2014) simulations were not matched

against any real experimental values. However, they

did include parameters for cell life and damage in-

curred to the effector cells by the tumour cells. In

terms of physical characteristics, IL2 is stimulatory

for the effector cells and TGF-beta suppresses the ef-

fectors and stimulates tumour growth.

An advantages of multi-agent systems is the dis-

crete event integration of the engagement within the

agents in a spatial sphere of inﬂuence. Other related

work incorporating spatial considerations into an eco-

logical model is in the area of computational epidemi-

ology (Jindal and Rao, 2017).

4 SIMULATION CASE STUDY

Firstly, we will deﬁne the following acronyms: IL15

(Interleukin-15), NKG2D (Natural Killer-gene 2D),

MICA (MHC class I polypeptide-related sequence

A), ULBP2 (UL16 binding protein 2) and HLA class

1 (Human Leukocyte Antigen).

Figure 1: Features on NK and Tumour cells (HTB-186).

We chose as our case study study the interac-

tion between tumour cells (HTB-186) and NK cells

under different conditions (Fern

andez et al., 2013).

Fern

andez et al. (2013) cultivated NK and HTB-186

tumour cells in vitro from 54 medulloblastoma pa-

tients. For the simulation we focus on the results

shown in (Fern

andez et al., 2013, Fig. 3), which

record the resulting cytotoxicity of NKs for differ-

ent blocking and stimulation conditions. Five con-

ditions are recorded: (i) Resting NK; (ii) IL15 stimu-

lated NK; (iii) Blocking of NKG2D (on NK), MICA

and ULBP2 (on HTB-186); (iv) HLA class 1 blocking

on HTB-186; (v) IL15 stimulated NK and HLA class

1 blocking on HTB-186. Note that (ii), (iv) and (v)

favour greater cytotoxicity of NK, whereas (iii) re-

duces cytotoxicity of NK. In the case of (iii), this is

Multi-agent Modeling Simulation of In-vitro T-cells for Immunologic Alternatives to Cancer Treatment

171

because NKG2D is the NK cell receptor and MICA

and ULBP2 are tumour (HTB-186) ligands for NK.

Refer to Figure 1 for an illustration of features on the

NK and tumour cells. Also note that, as the in-vitro

experiments have a duration of approximately three

hours, we do not consider proliferation or cell death.

4.1 Representation as a Dynamic

System Model

We now illustrate how the in-vitro experiment of our

case study ( Fern

andez et al. (2013)) would be mod-

elled as a “dynamic system model”.

Figure 2: Stock and ﬂow diagram for NK and HTB-186

tumour.

A dynamic system model typically consists of a

stock and ﬂow diagram (Figure 2), a set of differen-

tial equations to represent the behaviour of the stocks

(Figure 3), a set of algebraic equations to deﬁne the

ﬂows (Figure 4), and a set of control parameters used

by the system (Figure 5). In Figure 2, the three stocks

are NKs, IL15 and Tumour cells. The ﬂow on the top

right indicates the number of NK cells which are ef-

fective against the Tumour cells, and this is affected

positively by IL15 and the NKG2D activating recep-

tor (hence they are preceded by a +). The ﬂow on

the bottom right indicates the number of Tumour cells

being killed by NKs, and this is positively affected

by MICA and ULDP2 ligands (+) and negatively by

HLA class I expression (-).

IL-15 is used as potential therapy to enhance NK

anti-tumoral activity. Additionally, IL-15 has been

shown to enhance the anti-tumor immunity of CD8+

T cells in pre-clinical models. In the current model

IL-15 is considered as a stimulator, but without local-

ization in the physical space, assuming it is homoge-

neously distributed and affects all NK’s equally. In

this sense, it’s considered in the same way as MICA,

NKG2D and ULBP. They are either present (or ac-

tive) or absent (or blocked). This also agrees with

the predator-prey model: NK are predators, HLA are

the prey, and IL-15 acts as a stimulator for NK. How-

ever, in future work the deﬁnition of IL-15 as an agent

could be considered.

Figure 3: Differential equations for stocks in Figure 2.

Figure 4: Differential equations for ﬂows of Figure 2.

Figure 5: Control parameters for the dynamic system of

Figure 2.

5 AGENT MODEL

With reference to the simulation case study described

in Section 4, we will simulate two agent classes (us-

ing Repast Simphony (North et al., 2013)): agent-type

NK and agent-type Tumour. In our spatial environ-

ment, both classes are reactive agents (acting inde-

pendently, exhibiting control over their internal state).

Such individual agent behaviour is deﬁned by global

rules as well as local rules.

NK-cells have short-term goal directed behaviour

for probabilistically aiming for a Tumour cell. We

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

172

Table 1: Agent control parameters.

Tumour cells NK-cells

speed of reproduction speed of reproduction range of range of distance kill dormant/activate

movement rate movement rate kill distance detection probability period

0.003 0.0 0.01 0.0 0.5 1.0 0.6 2

name Agent control parameters those values regulat-

ing the agents’ actions; these control parameters spec-

ify behaviour for the agents. A second set of param-

eters incorporates the experimental cellular informa-

tion.

The metric used to evaluate the ﬁt of the simu-

lation to the in-vitro experiments is the number of

surviving Tumour cells when equilibrium is reached.

That is, the difference between the Tumour cell count

from Fernandez’s in-vitro experiments (Table 4) and

the Tumour cell count resulting from the agent model

(Table 5), which are shown in Figure 10.

The Repast source code of the system is available

at:github.com/dnettlet/AgentSim1.

In the ﬁrst control parameter set (refer to Table 1),

for each agent type (NK or Tumour) we incorporate

the following control parameters (and their values)

based on experimental information ( Fern

andez et al.

(2013)): speed of movement of the agent instances in

the deﬁned space; reproduction rate of the agents; dis-

tance at which a given agent type NK is able to detect

another agent type Tumour, and the distance at which

NK can kill (remove from participation in the simula-

tion) an agent of the class Tumour; and the probabil-

ity that, when NK is within distance to kill a Tumour

agent, it effectively eliminates the Tumour agent. The

dormant period is the number of cycles an NK-cell re-

quires to become dormant in the absence (within de-

tect distance) of Tumour cells. Likewise, the active

period is the number of cycles an NK-cell requires to

become active in the presence (within detect distance)

of Tumour cells.

Table 1 shows the initial value settings for the

control parameter set. Also, we use the values

by Fern

andez et al. (2013) to assign set-up values:

• Number of cycles without detecting tumour cells

for NK cells to become dormant (assigned as 2)

• Number of cycles having detected tumour cells

for NK cells to become active (assigned as 2)

• Initial number of tumour cells (assigned as 400)

• Initial number of NK cells (assigned as 400 for

ratio 1:1)

Each of the agent control parameters of Table 1 can

be related with a real biochemical process (e.g. kill

distance approximates the docking distance).

The second control parameter set (Table 2) consti-

tutes the experimental parameters of the real in-vitro

Table 2: Experiments, and their settings.

Experiment Resting IL15 ULBP2 MICA NKG2D HLAI

1 1 0 0 0 0 0

2 0 1 0 0 0 0

3 0 0 1 1 1 0

4 0 0 0 0 0 1

5 0 1 0 0 0 1

Table 3: Factors to incorporate stimulus or inhibition into

NK-cells behaviour.

Experiment Resting IL15 ULBP2 MICA NKG2D HLAI

1 1.1 0 0 0 0 0

2 0 1.1 0 0 0 0

3 0 0 0.9 0.9 0.9 0

4 0 0 0 0 0 1.1

5 0 1.1 0 0 0 1.1

experiments by Fern

andez et al. (2013). The original

labels for these experiments are 1 to 5 Fern

andez et al.

(2013). Each in-vitro experiment is deﬁned by six test

conditions.

Table 2 indicates for each experiment, whether an

experimental feature is present or not. For example, in

Experiment 5, IL15 and HLAI are present, indicated

by a 1. When a feature is present, it acts as a stimulant

or inhibitor on the cytotoxicity (refer to Fern

andez

et al. (2013)).

We incorporate the experimental features into the

multi-agent simulation, as having either a stimulant

role or inhibitor role in the agents parameters (the val-

ues in Table 1). We apply them as multipliers that

either magnify or reduce the effect of the agents be-

havioural parameters. A magnifying multiplier will

be larger than 1 and a reducing multiplier will be less

than 1. Therefore, the conditions in Table 2 were cor-

rected to the multipliers in Table 3.

We apply this effect (which inﬂuences NK-cell be-

haviour) by affecting the behavioural parameters of

NK-cells of Table 1. For example, the IL15 and HLAI

features potentiate the cytotoxicity, (NKs kill a higher

percentage of Tumour cells) and they are both present

in Experiment 5, so the weights from Table 3 adjust

the NK-cell agent control parameters as follows:

kill distance =

number of features

∏

i=1

kill distance × w

i j

where j is ﬁxed as the experiment number (5 in this

case). As an example, consider for Experiment 5 (Ta-

ble 3, Row 5) that the non-zero weights w are 1.1

(for IL15) and 1.1 (for HLAI), and the kill distance

is initially set to 0.5. Thus, the new kill distance in

the ﬁrst iteration will be 0.5 × 1.1 = 0.55, and in the

Multi-agent Modeling Simulation of In-vitro T-cells for Immunologic Alternatives to Cancer Treatment

173

second iteration, 0.55 × 1.1 = 0.605. Similarly,

detect distance =

number of features

∏

i=1

detect distance × w

i j

On the other hand, in Experiment 3 (Table 3, Row 3)

the NKG2D feature dampens the cytotoxicity (re-

duces the NK kill rate on Tumour cells). This is a re-

duction weight of 0.9 that is multiplied with the agent

control parameters, so experiments with the presence

of NKG2D will see both “kill distance” and “detec-

tion distance” affected by the value 0.9.

We incorporated the effect of experimental fea-

tures to spatial behavioural features of the agents only

to three agent control parameters of only the NK-

cells. That is, we only affect the kill distance, de-

tection distance and kill probability of NK-cells. Be-

sides biological realism, initial simulations with our

agents showed only these behavioural components

had meaningful effects (number of Tumour cells re-

maining when system reaches equilibrium). Never-

Figure 6: State space deﬁnition for agent interactions.

theless, despite the incorporation of inhibitors and

stimulants to NK-cells, the interactions between NK-

cells and tumour cells is not magniﬁed or reduced uni-

formly across all experiments. Thus, the interaction

of agent control parameter values (in Table 1) feature

weighting (in Table 3) requires further regulation. To

achieve such regulation, we used a third weight w

adjust all the NK-agents behavioural components uni-

formly but for each experiment and ratio. That is, the

weight w

adjusts the effect of the weights of Table 3

when applied to Table 1. Table 5 shows the optimised

weights w

resulting in high ﬁdelity with simulations

achieving consistently the equilibrium point to the re-

quired cytotoxicity.

For example, consider that the optimizer weight

has been settled as the value 0.73 (see Table 5)

for Experiment 5 and NK to tumor cell ratio equal

to 1, then for all features i and Experiment j = 5, the

weights w in Table 3 are updated thus:

∀i, j ∈ I=1:6,J=1:5, w

i j

= w

i j

Figure 7: Agent simulation for Experiment 5, ratio 1:1.

Figure 8: Agent simulation for Experiment 5, ratio 4:1.

To illustrate the process, consider for Experiment 5

(Table 3, Row 5) that the non-zero weights w are 1.1

(for IL15) and 1.1 (for HLAI), and the kill distance is

initially set to 0.5. Thus, the new kill distance in the

ﬁrst iteration will be 0.5 × 1.1 × 0.73 = 0.4015, and

in the second iteration, 0.55 × 1.1 × 0.4015 = 0.3224.

We repeat the experimental conditions (Table 2)

for the in-vitro experiments with real NK-cells and tu-

mour cells for four different initial ratios of NK-cells

and tumour cells, following exactly the ratio of NK-

cells to tumour cells suggested by Fern

andez et al.

(2013) and appearing in Table 4. Table 4 also shows

survival ratios in our experiments.

Each experiment was repeated several times to

verify that the same equilibrium point was reached

with the same weight. In some cases the result was

unstable (some runs did not stop at target) and this is

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

174

Table 4: Resulting cytotoxicity percentage for each ratio of

agent classes in in-vitro experiments.

Experiment Ratio

1 2 4 8

1 14 16 19 26

2 19 27 40 45

3 10 10 11 13

4 42 55 66 73

5 41 57 74 87

due to the stochastic nature of the agent system. In

this case, the weight value was varied slightly in up-

per and lower bound until a stable equilibrium was

found on repeats. In future work an automatic opti-

mization such as hill climbing with a ﬁtness function

could be used.

In summary, in our simulation, NK-cell agents and

tumour-cell agents interact (refer to Figure 1) as per

the effects of inhibitors and stimulants (refer to Ta-

ble 3) that are tuned (by w

) to impact the behavioural

parameters (Table 1) in a two dimensional state space

(as illustrated by Figure 6). The kill distance and de-

tect distance represent the physical distance in the bi-

ological system for locking on (via ligands and recep-

tors) and detection of chemical substances by the NK

cell which signal the presence of a tumour cell. Note

that the predator (NK) agents perform a random walk

until a tumour cell falls within detect distance, then

the NK moves directly towards the tumour.

Figure 7 and Figure 8 show two scenes from

our multi-agent simulations using the Repast Sim-

phony (North et al., 2013). Both correspond to the

settings of Experiment 5, where Figure 7 has a ratio

of 1:1 NK-cell agents to tumour cell agents, with ini-

tial cell populations of 400 for each agent type. On

the other hand, Figure 8 is the case where the ratio

is 4:1, with initial cell populations of 1600 NK-cell

agents and 400 tumour cells. The tumour cells are

coloured red and the NKs are coloured blue. For Fig-

ure 7, the system has reached an equilibrium at 237

tumour cells, which matches the cytoxicity of 41%

obtained in the in-vitro experiment.

Figure 8 shows the situation where the system has

reached an equilibrium at 106 tumour cells, which

matches to the cytoxicity of 74% as obtained in the

in-vitro experiment.

6 EXPERIMENTS

We now detail the results of the experiments to

simulate the in-vitro clinical experiments presented

by Fern

andez et al. (2013). Table 5 shows a total

of 20 experiments given that we ran 4 ratios in 5 ex-

periments. Our results show that for all the ratios and

all of the experiments, we can successfully reproduce

the cytotoxicity percentage combinations. That is, in

each case, we achieve convergence to the target %

of tumour cells killed with error margin (%target vs

%real) of between -1.5% and +2.25% (last column

in Table 5). It can be seen that a lower weight (col-

umn 3) was found to be optimum for experiments 1,

2 and 4, whereas higher values were required for ex-

periments 3 and 5. This is due to the fact that the

experimental settings involve only one inhibitor (or

stimulant) in one set of experiments while the latter

experiments involve more factors.

Figures 9 to Figure 11 provide graphical illustra-

tions of the results of Table 5. In particular, Figure 9

shows the weight values w

we found for each exper-

iment and ratio. It can be seen that for each experi-

ment, the weights decrease inversely with respect to

the ratios. Also it can be seen that higher cytotox-

icity requires a higher weight but more overriding is

the combination of multiple factors (especially Exper-

iment 3). Figure 10 shows the simulated cytotoxic-

ity for each experiment and ratio. We obtain remark-

able similarity to the in-vitro results, our Figure 10

matches Fern

andez et al. (2013, Figure 3). Note that

Figure 11 shows the error margin (real in-vitro val-

ues (Fern

andez et al., 2013, Figure 3) vs our multi-

agent simulated cytotoxicity) for each experiment and

ratio. The relative errors are never more than 2.25%.

Figure 12 shows a benchmark of performance of

our simulations. We ran Repast Simphony 2.6 in

“batch mode” for environment with different num-

ber of cells. For this benchmark, we used Exper-

iment 5 with ratio 1:1 NK to tumour cells. We

used a Lenovo laptop with Intel Core i7-7500U, CPU

@2.7Ghz (64bit processor), 12GB RAM, Windows

10 64bit operating system. It can be seen that the pro-

cessing time ﬁts to a third degree polynomial, where

9600 cells marks the saturation point of the com-

puter. The performance would of course be improved

using a GPU and/or multi core parallel processing,

which would allow for a much greater number of

cells, though for the current set of experiments this

was not considered necessary as the stochastic nature

and distance based interactions depend on density of

cells per square unit of space rather than pure quan-

tity. However, testing with greater quantities will be a

potential aspect for future work.

6.1 Discussion

From the results it can be seen that by manipulating

the control parameters we can accurately simulate the

real in-vitro experiments by Fern

andez et al. (2013).

The ﬂexibility of the multi-agent simulation pays-off!

This promises to reduce the time needed for clinical

Multi-agent Modeling Simulation of In-vitro T-cells for Immunologic Alternatives to Cancer Treatment

175

Table 5: Results of Experiments 1 to 5 for different ratios

of NK to Tumour cells.

Experiment Ratio Weight w’ #Target #Real %Target %Real %Deviation

1 1 0.36 344 345 14 13.75 - 0.25

1 2 0.3 336 329 16 17.75 + 1.75

1 4 0.245 324 316 19 21 + 2.0

1 8 0.228 296 294 26 26.5 + 0.5

2 1 0.38 324 325 19 18.75 - 0.25

2 2 0.33 293 298 27 25.5 - 1.5

2 4 0.297 240 234 40 41.5 + 1.5

2 8 0.24 220 211 45 47.25 + 2.25

3 1 0.72 360 361 10 9.75 - 0.25

3 2 0.70 360 364 10 9 - 1.00

3 4 0.66 356 349 11 12.75 + 1.75

3 8 0.61 348 348 13 13 0.0

4 1 0.56 232 230 42 42.5 + 0.5

4 2 0.5 180 183 55 54.25 - 0.75

4 4 0.439 136 131 66 67.25 + 1.25

4 8 0.347 108 105 73 73.75 + 0.75

5 1 0.73 236 237 41 40.75 - 0.25

5 2 0.693 172 166 57 58.5 + 1.5

5 4 0.645 104 106 74 73.5 - 0.5

5 8 0.62 52 53 87 86.75 - 0.25

Figure 9: Weight values for each experiment and ratio.

testing for customized patient treatment where every

day counts. The multi-agent system which allows

the creation of thousands of ‘virtual’ cells permits a

much closer stochastic type interaction, in contrast

to the typical differential equation approach. Also,

the agent simulation allows the deﬁnition of a virtual

space (a grid with N × M dimensions) in which the

agents move and interact. This, combined with the

kill distance and detection distance parameters allow

to approximate the real chemical detection between

cells, and the lock-on distance between receptors and

ligands. The approximation is due to the mapping

onto the two dimensional grid where the agents are

deﬁned. The kill probability also reﬂects the stochas-

tic/probabilistic nature of the process: the probability

that an NK will realistically kill a Tumour cell when

within the kill distance. Whether the NK kills a Tu-

mour cell or not can depend on semi-random aspects

such as locking orientation, particularities of the indi-

Figure 10: Simulated cytotoxicity per experiment and ratio.

Figure 11: Error margin for each experiment and ratio.

vidual NK-cell and the Tumour cell in the encounter,

and probabilistic events such as movement of adjacent

cells. Finally, the steps with no tumour cells controls

the predator-prey interaction, which does happen in

the in-vitro environment. Here, we incorporate it as a

deactivation of the NK-cell; that is, if in N cycles no

tumour cell has entered into the detect distance of a

given NK-cell, then it becomes dormant. This param-

eter together with the detect distance are major pa-

rameters in steering the simulation: as more tumour

cells are killed and become less prevalent, more NK-

cells will become inactive. However, the NK-cells

reactivate again if the inverse happens: tumour cells

come within detect distance during at least N cycles.

For the in-vitro experiments, the activator for the

NK (IL15) and the ligands/receptors (NKG2D on the

NK cell, MICA, ULBP2 and HLAI on the tumour

cell) were pre-selected by clinical trials, as well as

the type of tumour cell (HTB-186 MB). Hence, in or-

der to build an even more accurate decision-support

system (DSS) for clinical trials, the agent simulation

would need to serve as a back-end to the DSS which

would, for a given combination of tumour type, NK-

cell type, activator and set of ligands/receptors, pro-

duce the expected result, that is the resulting kill rate

(cytotoxicity). It may be infeasible to expect to build

a general system for every cancer treatment, and it

would be likely that specialized systems (knowledge

bases) would be loaded for speciﬁc types of cancer.

One form of action could be the following: by

successfully simulating a diversity of in-vitro clini-

cal experiments, the optimum control parameters and

weights would be found for the corresponding cases.

This would build a knowledge-base of cases. Thus,

when a new case is presented, the closest historical

case would be retrieved and used as the basis for a

new simulation. Ideally, it would be possible not only

to ﬁnd the optimum control parameter set of the agent

system, but also the combination of activator, lig-

ands/receptors to block or to potentiate maximal cy-

totoxicity. This would result in a system with just one

parameter as input (the tumour cell type) and a set of

parameters as output (immune system cell type, acti-

vators, ligands/receptors to block/potentiate, resulting

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

176

Figure 12: Number of cells vs processing time - Experi-

ment 5, ratio 1:1.

cytotoxicity). As a further enhancement, a DSS could

also answer questions such as: what would be the re-

sults if we use IL2 instead of IL15? If we block ligand

B instead of A, receptor Y instead of X, and so on. Is

it possible to reach 100% cytotoxicity? In general, we

could ask “what is the set of clinical parameters which

maximizes cytotoxicity?”

Returning to the current simulation, there remain

issues to evaluate: how close is the spatial represen-

tation to the real in-vitro physical environment. We

have used a 40 by 50 unit grid, where the agents them-

selves have no explicit dimension, but where the de-

tect distance value starts at 1.0 units and the kill dis-

tance starts at 0.5 units. How well does this map onto

the real physical space? Also, how many cells are

necessary to represent the in-vitro cell populations.

We have used a minimum of 400 and a maximum

of 3200 in the simulations. Is that enough to repre-

sent the stochastic behaviour? Also, the agent simu-

lation is deﬁned on a two dimensional grid, whereas

the in-vitro is acting in a three dimensional space.

These aspects limit the scope of the simulation. How-

ever, even with these limitations, we would say that

the agent simulation is much more realistic than the

differential equation model, and follows similar lines

to agent simulations in general. As future work, we

could try to implement a 3D graph-data structure in-

stead of the 2D grid, in which graph nodes represent

the cells, which are in turn, linked to neighbourhoods

of adjacent cells.

Also, it could be said that the agent system per

se is somewhat limited to a detect/kill functionality

within a parameter-deﬁned range. As a future step, in-

hibitors/stimulators could be modelled as entities in-

stead of modulators of parameter values, to account

for possible spatial effects, for example.

7 CONCLUSIONS

We have demonstrated the high ﬂexibility of multi-

agent simulations in two aspects. First, modelling as-

pects of the real interaction between tumour cells and

the naturally existing NK-cells, as they are inhibited

or stimulated in real in-vitro environments. Secondly,

we can use the multi-agent system’s additional param-

eters to explore and optimise the best combinations

which inﬂuence the inhibitors and stimulatory com-

pounds on NK-agents to approximate the cytotoxicity.

Our results show that by manipulating the control pa-

rameters we can accurately simulate the real in-vitro

experiments of Fern

andez et al. (2013).

This is a promising step for assisting the need

for clinical testing for customized patient treatment

where every day counts. The multi-agent system

which allows the creation of thousands of “virtual”

cells permits a much closer stochastic type interac-

tion, in contrast to the typical ODE approach.

This research has resulted in new ideas for future

work, such as, how to build a true decision-support

system which can give the clinical trial set-up (im-

mune cell type, activator, which ligands and receptors

to inhibit/potentiate) to maximize cytotoxicity for a

given tumour cell type.

ACKNOWLEDGEMENTS

We are grateful to the anonymous reviewers for their

suggestions. We are also grateful to Sergio Nettle-

ton (Universitat Polit

ecnica de Catalunya, Barcelona,

Spain) for the Repast programming support.

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