Until 2006, I have worked on laser-plasma interaction, fluid
mechanics, WKB expansions, water-waves, complex fluids.
I started to work on applications of mathematics to
tumor growth in 2006 and now all my works are devoted to this
I work mainly with physicians:
J. Palussière (Institut
Bergonié) and F. Cornelis (CHU Bordeaux)
G. Kantor (Institut
H. Loiseau (CHU Bordeaux)
of Alabama at Birmingham)
I have focused on three directions:
models of tumor growth.
simulation of tumor growth.
3) Cellular and
biological aspects of cancer.
Theoretical models of tumor growth.
In a series of work together with
Ribba, O. Saut
Grenier we have introduced a generic PDE (partial
differential equations) model for
tumor growth. The models were designed in both vascular
and avascular stage. The model is based on the description
of the evolution of populations of cells. We consider
proliferative cells, quiescent cells and healthy tissues.
The proliferative cells undergo a cell cycle that is
regulated by hypoxia, overpopulation,...
The distribution of oxygen depends on a vascular network
that is obtain through a angiogenesis model that describes
migration of endothelial cells according to
chemotaxis phenomena regulated by several pathway
including secretion of VEGF, PEGF, angiostatin,
angiopoietin... Interaction with the extracellular matrix
and influence of MMP are also considered. Several
mechanical aspects have been
investigated (visco-elasticity, elasticity of membranes,
Darcy's law, ...) Finally, we have also tested the
influence of several
treatments (radiotherapy, chemotherapy, anti-angiogenic
drugs, inhibitors of MMP...). The model has been
implemented in a 3D framework in C++ in the platform
developed by O. Saut.
More details can be found in the following publications:
B. Ribba, Th. Colin, S. Schnell, A multi-scale
mathematical model of cancer growth and radiotherapy
efficacy: The role of cell cycle regulation in response to
irradiation, Theoretical Biology and Medical Modeling
2006, 3:7 (10 Feb 2006).
B. Ribba, O. Saut, T. Colin, D. Bresch, E. Grenier, J.P.
Boissel, A multi-scale mathematical model of
avascular tumor growth to investigate the therapeutic
benefit of anti-invasive agents, Journal of Theoretical
Biology 243 (2006) 532–541.
D. Bresch, Th. Colin, E. Grenier, B. Ribba, O. Saut, O.
Singh and C. Verdier, Quelques méthodes
de paramètre d'ordre avec applications à la
modélisation de processus cancéreux,
ESAIM:proc, vol. 18, 2007.
D. Bresch, T. Colin, E. Grenier, B. Ribba, O. Saut A
viscoelastic model for avascular tumor growth, DCDS
Supplements, 101-108, Volume 2009, Issue : Special,
F. Billy, B. Ribba, O. Saut, H. Morre-Trouilhet, Th.
Colin, D. Bresch, J.-P. Boissel, E. Grenier, J.-P.
Flandrois, A pharmacologically-based multiscale
mathematical model of angiogenesis, and its use in
analysing the efficacy of a new anti-cancer treatment
strategy. Journal of Theoretical Biology, vol. 260, Issue
4, 21 October 2009, Pages 545-562.
Billy F., Saut O., Morre-Trouilhet H., Colin T., Bresch
D., Ribba B., Grenier E. Modèle mathématique
multi-échelle de l'angiogenèse tumorale et
application à l'analyse de l'efficacité de
traitements anti-angiogéniques. Bull Cancer, mars
2008 ; vol.95, numéro spécial : 65.
D. Bresch, T. Colin, E. Grenier, B. Ribba, O. Saut,
Computational modeling of solid tumor growth: the
avascular stage, SIAM J. SCI. COMPUT. Vol. 32, No. 4, pp.
Image-based simulation of tumor growth.
The work described
above are useful in the sense that they give some
integration of the biological knowledge in a numerical
However, these models are far away from a clinical
application. Indeed, even if they are very precise,
they contain a lot
of parameters. The values of the parameters that one
has to use for a particular patient for a given tumor
is unknown and there is no way to determine it.
With J. Palussière, F. Cornelis, G. Kantor, H.
Loiseau and H. Fathallah
(that are all clinicians) we started a research
program on image based-modeling. The idea is to
predict the evolution of a tumor or the response
to a treatment using a nonlinear PDE model and a
series of CT-Scan or MRI of a patient. We start
by extracting of our big model a "simple" PDE model
involving few parameters (let's say around 5
independent parameters). Then we try to find the
"best" values of the parameters that allow to match
with the series of image by solving an optimization
problem; then me make a prediction using this set of
We have tested this strategy on metastasis to the lung
of distant tumor (kidney, bladder, thyroid). We have
time series of CT-scans of patients that are only
under monitoring (i.e. without treatment). We use only
two CT-scans to parametrize our problem and try to
recover the following ones.
Lung metastasis: The test
case presented below concerns a metastasis to the lung
of a bladder tumor. On the left, on can see 3
No treatment was given to the patient during this
period. We have used only the image of June and
September to perform the simulation.
In the middle, the volume of the metastasis measured
on the scan are the circles while the continuous line
is the volume that is given
by the simulation. On the right, in red on has the
is given by the simulation for September and December.
Other examples for metastasis to the lung are given in
Liver metastasis: We have
also some preliminary results concerning metastasis to
the lung of a GIST (Gastro-Intestinal Stromal Tumor).
When the metastasis is discovered,
the patient receives immatinib until he escapes
the treatment. He then receives sunatinib until the
next escape time. In the example below we show on the
first line the curves of the volume of the metastasis
measured on the successive CT-scans with respect to
time. The CT-scans correspond (from left to right
and from top to bottom) to the control by the
first treatment, then the escape and then the control
bu the second treatment.
The curve below corresponds to a modeling of this
evolution (note that this is not a prediction,
contrary to the case of the lung).
All the data come from Institut
With H. Fathallah (University of Alabama at
Birmingham), we have developed a 3D model of
glioblastomas that shows the three layer
structure of GBM: a necrotic core, a proliferative rim
surrounded by a cloud of invasive cells. These
elements can be seen on different sequences of
MRI (T1, T1 gado and Flair) also it is still an open
problem to characterize precisely these elements on
these images. Below we have given a
simulation of such a simulation together with an MRI
and a biopsy of a glioblastoma.
Data of UAB.
Colin, A. Iollo, J.-B. Lagaert and O. Saut, An inverse
problem for the the recovery of the vascularization of
Th. Colin, H. Fathallah, J.-B. Lagaert, O. Saut, A
Multilayer Model for GBM: Effects of Invasive Cells
and Anti-Angiogenesis on Growth. Submitted.
T. Colin, A. Iollo, D. Lombardi, O. Saut
System Identification in Tumor Growth Modeling Using
Semi-empirical Eigenfunctions. Math. Models Methods
Appl. Sci. 22, 1250003 (2012).
T. Colin, A. Iollo, D. Lombardi and O. Saut,
Prediction of the Evolution of Thyroidal Lung Nodules
Using a Mathematical Model, ERCIM News, No 82,
pp. 37-38, July 2010.
and biological aspects of cancer.
We have some work in progress with the team of A.
Bikfalvi on the formation of the premetastatic niche in the
We have studied the mobility and adhesion properties of endothelial
cells on a scaffold in collaboration with the team of M.-Ch. Durrieu
at the CBMN.
A macroscopic model describing the endothelial cell migration on
bioactive micropatterns is presented. Its major biological
assumption is that the cells produce a chemical substance so as to
gather, but the bioactive chemical substance does not diffuse any
chemoattractants: it just attracts the cells to locate on it.
Mathematically, mass conservation, global existence and uniqueness
results are shown. Numerically, the model behaves in good agreement
with the biological experiments. Despite the lack of direct
attraction of the bioactive patterns, the non-washed out endothelial
cells end up on the patterns since the cells adhered on the
micropatterns produce more chemoattractants than the cells outside
the bioactive materials. We have observed two facts that have been
reported by the experiments:
1. For a given surface of bioactive material, the process of cell
migration is more efficient with a large number of thin strips than
with a small number of large strips.
2. There exists a minimum value of the initial density of
endothelial cells to be imposed in order to have an optimal cell
migration towards bioactive patterns.
We therefore believe that this model is a first step towards better
understanding of cell migration on micropatterns, the long-term goal
being optimal designing of patterns in order to build biological
Results obtained in M.-C. Durrieu's team.
Endothelial cells so cultured form extensive cell-cell interactions.
In some configurations, accumulation of endothelial cell junctions
implies that some cells form tube-like structures.
In the previous work, we have derived a continuous model of cell
migration. That approach makes possible the description of the
evolution of endothelial cell densities. As described above, the
results are qualitatively in good agreements with the
experiments. Nevertheless such a continuous model does not
take the cell orientation into account, which is an experimental
data. Cell orientation on the micropatterns plays a crucial role in
the formation of tube-like structure. Since such experimental
measurements are available, we choose to elaborate a discrete model.
The principle of the discrete models is to compute the behavior of
each cell and their relation with the other cells at each time step.
We derive an agent-based model taking both single cell migration and
orientation into account.
On of the point is to be able to quantify the alignment phenomena.
Alignment of the cells on 100μm strips, comparison between experimental and numerical result.
This work still in progress...
T. Colin, M.-C. Durrieu, J. Joie, Y.
Lei, Y. Mammeri, C. Poignard, O. Saut, Modeling of the
migration of endothelial cells on bioactive
micropatterned polymers, to appear in Mathematical
Biosciences and engineering.