Section: New Results

Cancer modelling

We have improved our generic mathematical models describing tumor growth. These models were then specialized for several types of cancer (thyroidal lung nodules, brain tumors). The algorithm used to recover the parameters of these models from medical images has also been greatly improved and is now adapted to run on HPC architectures.

• Secondary tumors in the lung:

  The mathematical models describing the growth of secondary in the lungs have now settled and are well understood. The main focus of the year was to keep on using these models on patient data. New clinical case were selected by clinicians from the Institut Bergonié, there are currently under study. The model is currently able to reproduce the growth observed on 5 clinical cases. Huge improvements to the calibration algorithms were made. The initial seeding of the algorithms was a weak point of the procedure and the robustness regarding the time-derivative of the observations is now much more accurate. A complete rewrite of the routines was done to improve their versatility and efficiency. Previously, the numerical simulations and calibration were performed in 2D (clinicians selected the most relevant slice showing the evolution of the tumor). Work is now ongoing to switch to full 3D computations and calibration. A newly hired engineer is testing our calibration technique on a dozen of clinical cases.

• Metastasis to the liver of a GIST

  We have derived a continuous model describing the growth of a GIST metastasis to the liver treated with Glivec and Sutent. This model is able to qualitatively reproduce the evolution observed on two different patients. Work has also started on developing new markers computed from the texture of the tumor seen on images to be able to detect any change in the response to treatment. This was the subject of an internship in the General Electric Healthcare research center. The results are promising so far.

• Modeling glioblastomas:

  In 2011, a hierarchy of models describing the growth of brain tumors was developed (and described in a submitted paper) in collaboration with University of Alabama at Birmingham. As we wished to obtain models that could be calibrated from patient data and yet be reasonably accurate, we believe that these models are suitable trade-offs between the simplicity of the Swanson's model (the only one used on patient data of brain tumors so far) and the accuracy of more complex models (that cannot really produce quantitative results). We have derived a new model that allows us to study the efficency of anti-angiogenic therapies. It seems to predict that the efficacy of these treatments is limited, this could be confirmed by a world-wide ongoing clinical study. Work is ongoing with this model to develop new marker to quantify patient anti-angiogenic drugs as soon as possible. This collaboration will be made stronger by a new Phd in UAB co-advised by T. Colin.

• Modelling of electrochemotherapy :

  Two articles related to the electrical cell modelling have been done ( [59] , [56] ) . The first one deals with the influence of the ionic fluxes on the transmembrane voltage potential and on the cell volume. The main insight of the results consists in linking the transmembrane potential with the cell volume: it has been observed experimentally that cells with a low voltage potential do divide, whereas cells with high voltage potential do not, and the obtained relationship between voltage potential and cell volume can provide an explanation. The second article deals with a new model of cell electroporation essentially based on the experimental results of the I.G.R. In this paper we describe precisely the model, which takes into account the main experimental results in the electroporation process, and we present a variationnal formulation inherent to the model that leads to new efficient schemes in order to numerically solve the involved P.D.E.

  The article describing a new electrical model of classical has been published in Journal of Math Biology. This new phenomenological model involves much less parameters than the usual models, but it still provides the qualitatively good description of the electroporation. The main feature of this model lies in the fact that it provides an intrinsic behavior of the cell membrane, which seems in accordance with the preliminary experimental results of the IGR partner. We also adapted the finite difference method developed by L. Weynans and M. Cisternino for elliptic interface problems to the electropermeabilization model developed recently by C. Poignard with O. Kavian. The new method has been validated by convergence tests and comparison with other models. We have proven that in one dimension the numerical solution converges to the solution of the exact problem. A paper describing these results has been submitted. A second-order Cartesian method for the simulation of electropermeabilization cell models, Leguebe M., Poignard C., Weynans L., Inria Resaerch Report RR-8302).

• Cell Migration modelling:

  The collaboration with IECB (University of Bordeaux) has continued with the postdocatoral position of Julie Joie. We have obtain a continuous model of cell density evolving on micropatterned polymers. The research report RR 7998 will be published in Math. Biosci. and Eng. A discrete model describing the single cells motility is being written.

  We also have started a collaboration with the University of Osaka (Japan), thanks to a PHC Sakura project, on the invadopodia. C. Poignard has been invited at Osaka in february by Prof. Suzuki. A model describing the destruction of the extracellular matrix by the MMP enzyme, and then the cell migration has been obtained. R. Mahumet, a PhD student of Prof. Suzuki is developing a code to simulate the model.

• Adaptive radiotherapy: a new work is also ongoing with Institut Bergonié to quantify the movement and deformations of organs of patients with sarcoma treated with radiotherapy. The preliminary results highlight that these mouvements are much larger than clinicians expected. We are now working on improving our workflow and developing a new segmentation technique to have this monitoring automatically performed (for the time being clinicians have to delineate each structure which is a very time consuming task). The ultimate goal is to change the therapeutical protocol to take these movements into account (which is currently not the case). Preliminary contacts have been made with a company developing a dose computing software to evaluate the efficacy of an adaptive planning of the Radio-Therapy compared to the constant dose plan currently given to the patient.

• Modeling meningioma growth and their responses to radiotherapy: In collaboration with Institut Bergonié, we have started developing new models for studying meningioma. Our model is able to reproduce the characteristic shape of these tumors which is in itself a very satisfactory result. Furthermore, from this model we have derived a simpler non-spatial model able to reproduce the 4 different types of response to radiotherapy observed by clinicians on the more than 70 patients they have selected for this study.

• Theoretical biology of the metastatic process

  We proposed a theoretical study of systemic inhibition of angiogenesis (SIA) in a population of tumors by deriving a model from biophysical considerations and simulating a novel mathematical model able to describe the development of a population of tumors in mutual inhibitory interactions at the organism scale. We showed that the model could explain experimental data on metastatic development and tested the hypothesis of global dormancy (cancer without disease) resulting from the net inhibitory action of stimulatory and inhibitory signaling interactions among the lesions comprising the total tumor burden. We found SIA alone is not sufficient for global dormancy but could suppress the growth of the total metastatic burden. See [41] . The resulting model is a nonlinear partial differential transport equation with nonlocal boundary condition that describes organism-scale population dynamics under the influence of three processes: birth (dissemination of secondary tumors), growth and inhibition (through angiogenesis). The asymptotic behavior of the model was numerically investigated in a second publication [40] and revealed interesting dynamics ranging from convergence to a steady state to bounded non-periodic or periodic behaviors, possibly with complex repeated patterns.

  In link with the previous study and in order to base the modeling on relevant biological data studying the basic phenomenon of growth interactions among tumors, we first performed a rational, quantitative and discriminant analysis of the descriptive and predictive properties of classical ODE-based models for tumor volume kinetics, which has been summarized in a publication that is currently under revision for PloS Computational Biology [42] .

  A collaboration with John Ebos from the Roswell Park Cancer Institute in Buffalo (NY, USA) has been initiated that deals with the objectives to quantify metastatic aggressiveness of several cancer cell linesand to rationally define a neo-adjuvant (i.e., prior to resection of the primary lesion) efficacy score of several anti-cancer chemical agents. The PhD of Etienne Baratchart has been initiated, in close collaboration with the "Angiogenesis and cancer microenvironment laboratory" directed by the Pr Andreas Bikfalvi, about the initiation, development and role of the pre-metastatic and metastatic niche.