Research of Thierry Colin

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 field.
I work mainly with physicians:

Radiologists:
J. Palussière (Institut Bergonié) and F. Cornelis (CHU Bordeaux)
Radiotherapist:
G. Kantor (Institut Bergonié)
Neurosurgeon:
H. Loiseau (CHU Bordeaux)
Neuro-oncologist:
H. Fathallah (University of Alabama at Birmingham)

I have focused on three directions:

1) Theoretical models of tumor growth.
2) Image-based simulation of tumor growth.
3) Cellular and biological aspects of cancer.


1) Theoretical models of tumor growth.
In a series of work together with B. Ribba, O. Saut and E. 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 proliferation and
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, september 2009.

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. 2321–2344, 2010.


 2) 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 framework.
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 parameters.

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 CT-scans.
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 tumor that
is given by the simulation for September and December. Other examples for metastasis to the lung are given in the publications.




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 Bergonié.

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.



Th. Colin, A. Iollo, J.-B. Lagaert and O. Saut, An inverse problem for the the recovery of the vascularization of a tumor.
 
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.


 3) Cellular 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 mice.

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 tissues.

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.