Directional Cellular Dynamics for Tissue Morphogenesis and Tumour

Characterization by Aggressive Cancer Cells Identiﬁcation

Abdoulaye Sarr

, Petra Miglierini

, Alexandra Fronville

and Vincent Rodin

Computer Science Department, Universit

e de Brest, UMR CNRS 6285, Lab-STICC, CID, IHSEV,

20 avenue Le Gorgeu, Brest, France

Department of Radiotherapy, University Hospital Morvan, Institute of Oncology and Haematology,

2 avenue Foch, Brest, France

Keywords:

Morphogenesis, Tissue Prediction, Tumour Classiﬁcation, Viability Algorithms.

Abstract:

Due to the availability of large amount of medical data and the improvements of computers’ capacities, an

increase of tools for medical applications has been noted. In the case of cancer, this results in some application

and treatment successes in radiotherapy. However, on the one hand, high therapeutic results are yet to be seen,

and on the other hand, unpleasant side effects are still widely observed. In the ﬁrst case, it may arise from the

avoidance of any damage to healthy structures implying ineffective treatment, and in the second case it may

be, due to lethal doses deposited in the tumour, leading to an unacceptable damage to one or more healthy

structures. Thus, it would be useful to simulate the effects of any treatment prior to its application. Thereby,

we are focusing on the proposition of computational methods serving to give insights for decisions aid tools in

radiotherapy. In this paper, we provide algorithms for tissue growth prediction where cells are elements of a 2D

cellular automaton oriented multi-agent system. Then, we propose a novel method to predict and characterize

the evolution of a pathological tissue under cells irradiation. We show that the more cells destroyed during the

radiotherapy are linked to aggressive cancer cells, the more the treatment lead to an impaired result in terms

of growth. By contrast, we highlight that there exists cells less linked to these aggressive cancer cells that are

more suitable to target for an effective and efﬁcient radiotherapy. Based on the dominant cells (linked or not

linked to aggressive cancer cells), we introduce a novel method to classify tumours.

1 INTRODUCTION

Cancer is one of the most serious worldwide health

issues with respect to its incidence and mortality. The

main treatment besides surgery and chemotherapy is

radiotherapy. Tumour growth and response to radio-

therapy have become subject to many studies by com-

puter scientists. This results in techniques which are

able, for instance, to give a prediction of the tumour

growth, from which it can be possible to decide if it is

required or not to invoke immediately a therapy.

Indeed, given the pace of technological advances,

software solutions for medical supports are more and

more developed despite the considerable challenges.

In cancer ﬁeld, several planning strategies have been

developed. For example, early radiotherapy treatment

used forward treatment planning which consists of

specifying values for all parameters, then the dose cal-

culation software computes the dose distribution. If

this latter is judged not acceptable by the oncologist,

the initial values of the parameters are then adapted

by trial-and-error until the dose distribution is sat-

isfactory. This is used in (Henzen et al., 2014) for

modulated electron radiotherapy. An electron beam

model is used to calculate dose distributions of elec-

tron beams shaped by a photon multi leaf collimator.

Conversely, inverse planning is to specify the desired

outcome (such as dose distribution) and to compute

beam intensities that produce this outcome without

any trial-and-error process (Ehrgott and Winz, 2008).

In any case, planning strategies are expected to be

enough efﬁcient and reliable to help achieving highly

accurate therapies.

In section 2, we present our morphogenesis model

that underlies the growth of tumours and allows to

predict their evolution for a desired number of cells

to reach. It is in terms of instructions for cells (divi-

sion by choosing a speciﬁc geometric direction, qui-

escence, differentiation) that have governed the evolu-

tion of the tissue from a previous state (which can be

290

Sarr, A., Miglierini, P., Fronville, A. and Rodin, V.

Directional Cellular Dynamics for Tissue Morphogenesis and Tumour Characterization by Aggressive Cancer Cells Identiﬁcation.

DOI: 10.5220/0005830702900295

In Proceedings of the 9th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2016) - Volume 3: BIOINFORMATICS, pages 290-295

ISBN: 978-989-758-170-0

its ﬁrst cell) until its current state (made by a few pair

of cells). Thus, assuming that the tissue is only sub-

ject to these instructions in a well-guided morphogen-

esis process, we deduce its evolution for latter times

(section 3). Thereby, according to the predicted evo-

lution, one can conclude if a therapy is required and

which one is more convenient. In the case where this

is radiotherapy, we propose to simulate the effects of

cells irradiation on the tumour’s growth so as to de-

termine if the destroyed cells are linked or not to the

aggressive cancer cells (section 4). In this paper, we

consider that beams’ modality, geometry and inten-

sity are given, while we are focusing on the target of

the beams, i.e cells. We are interested in knowing the

cells which are relevant to irradiate and those which

are not. Besides, since we have an individual-based

model whose morphological dynamic relies mainly

on spatial constraints of cells, we have been much

more concerned to know which cells have to be ap-

propriately chosen for irradiation rather than how the

radiation parameters have to be set. Hence, we focus

on the impacts of the destruction of certain cells on

tumour’s growth. In other words, the death of which

cells of the tumour will make it grow:

• slower ?

• faster ?

• or normally ?

Each cell of the tumour can be classiﬁed according

to the effect it involves among these three. The largest

cell type determines the category of the tumour. The

categorization we propose in section 5 allows us to

know in advance the expected results of potential ra-

diotherapy of tumours. We present in section 6 some

future works that aim to acknowledge some limiting

factors of studying cancer in vivo and even more so

through in silico experiments.

2 VIABILITY CONCEPTS FOR

MORPHOGENESIS

Rely on the viability theory to tackle issues in mor-

phogenesis requires ﬁrst to properly deﬁne some con-

cepts of this theory in the case of multicellular sys-

tem. In previous work, we described mathematically

the state, controls and both local and global morpho-

logical dynamics of tissues. Some points of that for-

malization are highlighted in this section.

K ⊂ P (X) denotes the morphological environ-

ment (X = R

denotes the set of containment cells,

contained in the complement of vitellus

In biology, the vitellus is the energy reserve used by the

Cells x ∈ X ∪

0 are either characterized by their

position (living cells) or by their death made of tis-

sues L which are subsets of cells (L ∈ P (X)).

The subset of eight genetic actions d of cells is:

A := {(1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1),

(0, 0, −1), (0, 0, 0),

A is made of the six geometric directions, the ori-

gin and the empty set. Here, we restrict morphogene-

sis in the plan:

A := {(0, 1), (0, −1), (1, 0), (−1, 0), (0, 0),

For convenience, we replace

(0, 1), (0, −1), (1, 0), (−1, 0), (0, 0) and

0 re-

spectively by 1, 2, 3, 4, 5 and 6.

A := {1, 2, 3, 4, 5, 6}

These genetic actions allow to describe cells’ be-

haviours:

1. Transitions x 7→ x + d, where d ∈ {1, 2, 3, 4} (ac-

tion)

2. Quiescence x 7→ x + 5 = x (no action)

3. Apoptosis x 7→ x + 6 = 6 (programmed cell death)

A genetic process g is a possible combination of

genetic actions g := {d

, ..., d

} ∈ A

. Operating a ge-

netic process under a given criterion, either for mi-

gration or for division, means that the process scans

successively x + d

, ..., x + d

until the ﬁrst time when

the criterion is satisﬁed. For every tissue (phenotype),

there is a set of speciﬁc genetic processes (genotype)

that allows to achieve it starting from a single cell.

We had generated the all phenotypes that can be ob-

tained after any number of division (1, 2, 3 or 4) of a

single cell (Sarr et al., 2014). Indeed, starting with a

single cell, at each step, we compute from the previ-

ous tissues all the possible conﬁgurations of tissue we

can reach by cell division. This issue is a particular

case of polyominoes computing while we have added

some biological constraints. The conﬁgurations are

saved in the edges of a graph. Besides, we save in

vertices all the events that have been involved : divi-

sion, quiescence, differentiation. Thereby, from any

edge in the graph, we can reconstruct the way back

to the single cell. This characterization results in the

determination of the lineage of any phenotype and us-

ing that lineage we construct the underlying genotype

with respect to our model (see example in ﬁgure 1).

A genetic process is identiﬁed by its colour. All cells

whose last division is achieved with that genetic pro-

cess carry its colour and thus deﬁne a pattern. For

prediction, these genetic processes will be the con-

trols that allow cells to behave in their environment

according to some rules that will be described in the

following section.

embryo during its development.

Directional Cellular Dynamics for Tissue Morphogenesis and Tumour Characterization by Aggressive Cancer Cells Identiﬁcation

291

Figure 1: One of the 1029 possible phenotypes and its geno-

type obtained after 4 division of a single cell. The tissue

shows three colours representing three genetic processes :

turquoise, purple and brown. Each is an ordered se-

quence of the four genetic actions (1:north, 2:south, 3:east

and 4:west). These genetic processes are the minimum re-

quired ones to design this tissue. The colour level distin-

guishes cell status during the division cycle. Light coloured

cells are the ones already divided and the dark ones are

those newly created in the cycle, they are both quiescent.

The third category does not appear in this ﬁgure, they are the

proliferating cells which are awaiting to division (medium

coloured). Besides, the three colours show that two differ-

entiations occur while generating this tissue. Indeed, if a

cell has to change a genetic process to be able to divide, its

colour and that of its daughter are set to the colour of the

new genetic process. A tissue appearing with one colour

would mean that it is made of just one genetic process and

no differentiation occurs, i.e all cells were able to divide

using the same ordered sequence of genetic actions. The

arrows distinguish cell lineage as the creation of the tissue

goes on.

3 TISSUE’S SHAPE PREDICTION

The prediction determines the state of a tissue in any

latter times, given a number of cells or a number of

division cycles. The genetic processes are applied to

make the tissue grow for latter times through the cel-

lular mechanisms of mitosis, quiescence and differ-

entiation. The action of one cell x involves a local

morphological dynamic which locally transforms the

tissue L at a local process time. The global morpho-

logical dynamic transforms the morphological envi-

ronment K at the end of every cell division cycle af-

ter the processing of all cells. The only constraints

this growth can face are spatial ones, arising from the

morphological environment and cells themselves.

Our 2D model consists of a grid of automaton ele-

ments which represent our biological cells. The state

of each element is deﬁned by a state vector including

three components that correspond to the features of

interest in this case study: (i) occupation, i.e. an ele-

ment is either occupied by a cell or is an empty space,

(ii) cell status, i.e. the cell is either in a proliferative

state (allowed to divide), quiescent (to prevent cells

newly created or already processed in the current di-

vision cycle to divide) or locked due to a lack of space

for division in the four possible directions (by setting

to “on” the evolution lock factor of the cell : ELF) and

(iii) cell colour that identiﬁes the genetic process it is

associated with (dark level meaning that ELF is “on”

and light level meaning that ELF is “off”).

An example is presented below. Figure 2 repre-

sents the current state of the tissue and ﬁgure 3 the

results of the prediction.

Figure 2: This is one of the 61 phenotypes reached after 3

division cycles of a single cell. We can notice also the three

genetic processes that are put into play.

After having predicted the evolution of the tu-

mour, it may appear that a radiotherapy is required

to give some survival beneﬁts to the patient. In the

following section, we propose a decision support to

assess the impacts of cells irradiation on a tumour’s

growth. By the way, this simulation allows us to make

a classiﬁcation of the tumour’s cells with respect to

the impact of their removal from the tumour. We

assume that the cells whose removal causes a high

growth of the tumour are strongly linked to the ag-

gressive cancer cells.

4 TUMOUR’S CELLS

IRRADIATION

To the point that surgeons cannot remove the tumour,

radiotherapy can be an interesting alternative since it

can shrink or at least slow down the growth of the

tumour over time. This would signiﬁcantly improve

patients’ quality of life.

Radiotherapy is one of the many therapies to

treat cancer. It consists of using high energy doses

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292

Figure 3: We show two prediction cases: after some given

number of division cycles (top) and with a certain number

of cells (down).

of radiation to destroy cancer cells while sparing

the surrounding healthy tissues. Radiotherapy is di-

rected towards a particular location of the body unlike

chemotherapy, for instance, which is a systemic treat-

ment that spreads throughout the whole body.

Even though the prediction method we present

above can provide a future view of the tumour, for

probable comparison, classiﬁcation and even for pre-

scribing suitable therapeutic scenarios, it gives no

proposal towards the therapy itself. For the sake of

effective and efﬁcient radiotherapy, it would be inter-

esting to know the role of the cells which are intended

to be destroyed in the fate of the tumour. In fact, ac-

cording to the phenotype of a tumour and its morpho-

logical dynamic governed by its genotype, there ex-

ists among all cancer cells, some which are strongly

linked to the aggressive ones. Knowing that destroy

those cells will result in a high growth, we would bet-

ter identify them and avoid them while irradiating the

tumour. Some studies reported that sublethal radi-

ation could promote expansion of cancer stem cells

which are a subpopulation of the tumour resistant to

the conventional cancer therapies including radiother-

apy (Suh and Lee, 2015). The aggressive cancer cells

can be identiﬁed by the most proliferative cells after

the tumour radiation. Indeed, the removal of a cell

can either ﬂow to the degeneration of the tumour or

lead to its regeneration with a higher growth.

In our proposition, to assess if a cell is linked or

not to the aggressive cancer cells, we simulate its re-

moval and then let the tumour grows during a given

number of division cycles. Finally we compare the

growth rate with the one if there is no irradiation. If

we notice that the growth is faster than the normal, we

consider that the irradiation of that cell will be “dan-

gerous”, because linked to the aggressive cancer cells.

If it is similar to that, we consider that the irradiation

will have neither a beneﬁt, nor a harmful effects, it is

just “unproductive”. And if it is slower than that, the

irradiation will be an “effective” one, because the cell

is independent from the aggressive cancer cells.

We have implemented algorithms relying on these

principles to identify each cell in any given tumour

with respect to the aggressive cancer cells. When the

technique is applied to the tissue depicted in ﬁgure 2,

the results are as follows (assessment of the growths

are done after 20 division cycles):

• Removal of cell number 6 is the most effective,

it leads to the slowest growth (4% smaller than the

normal).

• Removal of cell number 3 is the most danger-

ous, it leads to the fastest growth (5% bigger than

the normal)

• Removal of cells number 1, 7, 4 and 2 are

all unproductive. The growth of the tumour will

remain the same as the normal

Thereby, we are able to put light on the role that

the death of each cell would have on the fate of the

tumour. This allows to identify three types of cells

within a tumour. Afterwards, we will rely on these

results to characterize any tumour with respect to the

type of cells that mainly composes it.

5 TUMOUR

CHARACTERIZATION

Main tumours classiﬁcation techniques are based on

shape factors of tumours’ regions and texture mea-

sures. For instance, (Ng and Bischof, 1992) proposed

a method for the mammographic detection and clas-

siﬁcation of two types of breast tumours. The method

identiﬁed them as follows: circular, bright masses

with a fuzzy boundary and stellate lesions surrounded

by a radiating structure of sharp. In (Rangayyan et al.,

1997), it is highlighted the importance of combining

lesion edge deﬁnition with shape information for tu-

mours classiﬁcation. The potential of acutance is used

to quantify the sharpness of tumours’ boundaries. An

application of this technique is proposed to discrim-

inate between benign and malignant mammographic

Directional Cellular Dynamics for Tissue Morphogenesis and Tumour Characterization by Aggressive Cancer Cells Identiﬁcation

293

tumours. Our approach of virtual tumour classiﬁca-

tion places more emphasis to the cells of the tumour

rather than its shape and texture. In the previous sec-

tion, we highlighted the inﬂuence of the removal of

certain cells in the tumour growth. We have shown

that the choice of cells to be irradiated had utmost im-

portance for effective and efﬁcient radiotherapy.

Fair classiﬁcation should give an insight of the na-

ture of any tumour without repeating every time the

same identiﬁcation processes, so well that it may al-

low to determine more quickly therapies to apply. To

classify a tumour, we simulate successively the irradi-

ation of each of its cells and observe its evolution. De-

pending on the results of these simulations, we know

what are the dominant cell types in the tumour, which

allows us to classify it in one of the six categories we

deﬁne in table 1.

The category of the tumour depends on the main

response we can expect from its irradiation which :

1. does not inﬂuence, neither in good, nor in bad way

the growth of the tumour

2. accelerates tumour growth

3. stunts the growth of the tumour

4. stunts the growth of the tumour or at least main-

tains it to its normal pace

5. accelerates tumour growth or at best maintains it

to its normal pace

6. can either accelerate or stunt the growth of the tu-

mour

We have in ﬁgure 4 an example of classiﬁcation.

We also implement an algorithm such as for a

given set of tumours, it classiﬁes each tumour in a

category and then gives the resulting statistical dis-

tribution. Assuming that the set to process is the all

possible phenotypes after 3 division cycles of a single

cell, the distribution is depicted in ﬁgure 5.

6 DISCUSSIONS AND

CONCLUSIONS

We formalize in a mathematical model some generic

features of cell division. Then using a cellular au-

tomaton whose rules capture the principles of that

model, we propose a prediction method for tissue evo-

lution. The interesting shapes predicted contribute to

establish the reliability of our approach of morpho-

genesis. We applied this prediction method to deduce

the latter states of a pathological tissue, given one of

its previous states. Then, we highlight the importance

of selecting suitable beams and energy intensities to

Figure 4: Example of 5 tissues classiﬁed each in a different

tumour category. In ﬁgure 5, we show the entire distribution

of the set of 8-cells tumours in the six categories.

Figure 5: Distribution of the 61 8-cells tissues per tumour

category. The cell division cycle for assessing the growth

of the tissue after irradiation is set to 10. We can notice that

there is no [0-] tumour in the studied set.

ﬁt properly the tumour size and shape in radiother-

apy. However, we claim that it would be more inter-

esting to ﬁnd the most cost-effective scheme in terms

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Table 1: The different categories of tumours and their description.

Category Notation

Unproductive

Zero : [0]

Dangerous

Negative [-]

Effective

Positive [+]

At Worst Unproductive

Zero/Positive : [0+]

At Best Unproductive

Zero/Negative : [0-]

Effective at Best and Dangerous at Worst

Positive/Negative : [+-]

of cells to irradiate so as to ensure a slow growth of the

tumour after shrinkage. If such method is taken into

account by decision support tools for cancer therapy,

it would more safeguard the healthy cells because the

whole tumour will not be blindly irradiated. Indeed,

it ensures that radiation is directed on speciﬁc cells

within the tumour, relevant to be destroyed due to the

fact that they are not or weakly linked to the aggres-

sive cancer cells. For this purpose, the algorithm we

implement does not randomly remove multiple cells

in one fell swoop, as it could be simple to do, but it

chooses each cell and determine its role in the growth

of the tumour. Then, we found that it was more rel-

evant to classify tumours according to their potential

response to radiotherapy rather than to their shape and

texture. Thereby, based on the growth we expected

after radiotherapy, we were able to classify a tumour

among six deﬁned categories. We acknowledge that

in silico experiments remain far from clinical applica-

tions but they allow to test and produce new assump-

tions in order to better understand the livings and con-

trol the disturbances they face. Hence, although the

computational experiments we conducted in this pa-

per remain up to now theoretical, they provide new

avenues of research in the ﬁeld of cancer therapy to

be more effective. If such decision making methods

and tools are validated and implemented, we are con-

vinced that inadvertent use of imagery prior to treat-

ment and some therapy drawbacks could be avoided.

In future works, we aim to take into account the cel-

lular neighbouring exchange in addition to the direc-

tions of division instructions. Indeed, due to what is

called the tumour microenvironment, results obtained

in vitro on the isolated cancer cells may dramatically

differ from the observed behaviours of the tumour un-

der in vivo radiation (Thompson and Maity, 2014).

These discrepancies are induced by a complex con-

stellation of extracellular and intracellular factors on

the tumour. They are yet to be understood for fair in

vitro experiments and even more so to be taken into

account in in silico simulations. Besides the role and

clinical implications of tumour microenvironment, it

is also hard to predict in an accurate way, for a same

cancer shape or type, the responsiveness of the radia-

tion from a patient to another one. Depending on the

degree of the individual susceptibility variation, the

predicted results may be more or less far from the ob-

served results, except predictive tests related to some

clinical researches on blood lymphocyte.

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