Predicting regrowth of low-grade gliomas after radiotherapy.

Diffuse low grade gliomas are invasive and incurable brain tumors that inevitably transform into higher grade ones. A classical treatment to delay this transition is radiotherapy (RT). Following RT, the tumor gradually shrinks during a period of typically 6 months to 4 years before regrowing. To improve the patient's health-related quality of life and help clinicians build personalized follow-ups, one would benefit from predictions of the time during which the tumor is expected to decrease. The challenge is to provide a reliable estimate of this regrowth time shortly after RT (i.e. with few data), although patients react differently to the treatment. To this end, we analyze the tumor size dynamics from a batch of 20 high-quality longitudinal data, and propose a simple and robust analytical model, with just 4 parameters. From the study of their correlations, we build a statistical constraint that helps determine the regrowth time even for patients for which we have only a few measurements of the tumor size. We validate the procedure on the data and predict the regrowth time at the moment of the first MRI after RT, with precision of, typically, 6 months. Using virtual patients, we study whether some forecast is still possible just three months after RT. We obtain some reliable estimates of the regrowth time in 75% of the cases, in particular for all "fast-responders". The remaining 25% represent cases where the actual regrowth time is large and can be safely estimated with another measurement a year later. These results show the feasibility of making personalized predictions of the tumor regrowth time shortly after RT.

The Effect of Radiotherapy on Diffuse Low-Grade Gliomas Evolution: Confronting Theory with Clinical Data.

Diffuse low-grade gliomas are slowly growing tumors that always recur after treatment. In this paper, we revisit the modeling of the evolution of the tumor radius before and after the radiotherapy process and propose a novel model that is simple yet biologically motivated and that remedies some shortcomings of previously proposed ones. We confront this with clinical data consisting of time series of tumor radii from 43 patient records by using a stochastic optimization technique and obtain very good fits in all cases. Since our model describes the evolution of a tumor from the very first glioma cell, it gives access to the possible age of the tumor. Using the technique of profile likelihood to extract all of the information from the data, we build confidence intervals for the tumor birth age and confirm the fact that low-grade gliomas seem to appear in the late teenage years. Moreover, an approximate analytical expression of the temporal evolution of the tumor radius allows us to explain the correlations observed in the data.

Experimental and modeling study of the formation of cell aggregates with differential substrate adhesion.

The study of cell aggregation in vitro has a tremendous importance these days. In cancer biology, aggregates and spheroids serve as model systems and are considered as pseudo-tumors that are more realistic than 2D cell cultures. Recently, in the context of brain tumors (gliomas), we developed a new poly(ethylene glycol) (PEG)-based hydrogel, with adhesive properties that can be controlled by the addition of poly(L-lysine) (PLL), and a stiffness close to the brain's. This substrate allows the motion of individual cells and the formation of cell aggregates (within one day), and we showed that on a non-adhesive substrate (PEG without PLL is inert for cells), the aggregates are bigger and less numerous than on an adhesive substrate (with PLL). In this article, we present new experimental results on the follow-up of the formation of aggregates on our hydrogels, from the early stages (individual cells) to the late stages (aggregate compaction), in order to compare, for two cell lines (F98 and U87), the aggregation process on the adhesive and non-adhesive substrates. We first show that a spaceless model of perikinetic aggregation can reproduce the experimental evolution of the number of aggregates, but not of the mean area of the aggregates. We thus develop a minimal off-lattice agent-based model, with a few simple rules reproducing the main processes that are at stack during aggregation. Our spatial model can reproduce very well the experimental temporal evolution of both the number of aggregates and their mean area, on adhesive and non-adhesive soft gels and for the two different cell lines. From the fit of the experimental data, we were able to infer the quantitative values of the speed of motion of each cell line, its rate of proliferation in aggregates and its ability to organize in 3D. We also found qualitative differences between the two cell lines regarding the ability of aggregates to compact. These parameters could be inferred for any cell line, and correlated with clinical properties such as aggressiveness and invasiveness.

Modeling the dynamics of oligodendrocyte precursor cells and the genesis of gliomas.

Oligodendrocyte precursor cells (OPCs) have remarkable properties: they represent the most abundant cycling cell population in the adult normal brain and they manage to achieve a uniform and constant density throughout the adult brain. This equilibrium is obtained by the interplay of four processes: division, differentiation or death, migration and active self-repulsion. They are also strongly suspected to be at the origin of gliomas, when their equilibrium is disrupted. In this article, we present a model of the dynamics of OPCs, first in a normal tissue. This model is based on a cellular automaton and its rules are mimicking the ones that regulate the dynamics of real OPCs. The model is able to reproduce the homeostasis of the cell population, with the maintenance of a constant and uniform cell density and the healing of a lesion. We show that there exists a fair quantitative agreement between the simulated and experimental parameters, such as the cell velocity, the time taken to close a lesion, and the duration of the cell cycle. We present three possible scenarios of disruption of the equilibrium: the appearance of an over-proliferating cell, of a deadless/non-differentiating cell, or of a cell that lost any contact-inhibition. We show that the appearance of an over-proliferating cell is sufficient to trigger the growth of a tumor that has low-grade glioma features: an invasive behaviour, a linear radial growth of the tumor with a corresponding growth velocity of less than 2 mm per year, as well a cell density at the center which exceeds the one in normal tissue by a factor of less than two. The loss of contact inhibition leads to a more high-grade-like glioma. The results of our model contribute to the body of evidence that identify OPCs as possible cells of origin of gliomas.

Quantitative characterization of the imaging limits of diffuse low-grade oligodendrogliomas.

BACKGROUND: Supratentorial diffuse low-grade gliomas in adults extend beyond maximal visible MRI-defined abnormalities, and a gap exists between the imaging signal changes and the actual tumor margins. Direct quantitative comparisons between imaging and histological analyses are lacking to date. However, they are of the utmost importance if one wishes to develop realistic models for diffuse glioma growth. METHODS: In this study, we quantitatively compared the cell concentration and the edema fraction from human histological biopsy samples (BSs) performed inside and outside imaging abnormalities during serial imaging-based stereotactic biopsy of diffuse low-grade gliomas. RESULTS: The cell concentration was significantly higher in BSs located inside (1189 ± 378 cell/mm(2)) than outside (740 ± 124 cell/mm(2)) MRI-defined abnormalities (P = .0003). The edema fraction was significantly higher in BSs located inside (mean, 45% ± 23%) than outside (mean, 5 %± 9%) MRI-defined abnormalities (P < .0001). At borders of the MRI-defined abnormalities, 20% of the tissue surface area was occupied by edema and only 3% by tumor cells. The cycling cell concentration was significantly higher in BSs located inside (10 ± 12 cell/mm(2)), compared with outside (0.5 ± 0.9 cell/mm(2)), MRI-defined abnormalities (P = .0001). CONCLUSIONS: We showed that the margins of T2-weighted signal changes are mainly correlated with the edema fraction. In 62.5% of patients, the cycling tumor cell fraction (defined as the ratio of the cycling tumor cell concentration to the total number of tumor cells) was higher at the limits of the MRI-defined abnormalities than closer to the center of the tumor. In the remaining patients, the cycling tumor cell fraction increased towards the center of the tumor.

Analysis of a minimal model for p53 oscillations.

Oscillatory behaviours in genetic networks are important examples for studying the principles underlying the dynamics of cellular regulation. Recently the team of Alon has reported a surprisingly rich oscillatory response of the p53 tumor suppressor to irradiation stress et al. [Lahav, G., Rosenfeld, N., Sigal, A., Geva-Zatorsky, N., Levine, A.J., Elowitz, M.B., Alon, U., 2004. Dynamics of the p53-Mdm2 feedback loop in individual cells. Nat. Genet. 36 (2), 147-150; Geva-Zatorsky, N., Rosenfeld, N., Itzkovitz, S., Milo, R., Sigal, A., Dekel, E., Yarnitzky, T., Liron, Y., Polak, P., Lahav, G., Alon, U., 2006. Oscillations and variability in the p53 system. Mol. Syst. Biol. 2, 2006.0033]. Several models for this system have been proposed by different groups, based essentially on negative feedback loops. In this paper we investigate in detail oscillations and stability in a deterministic time delayed differential model of the core circuit for p53 expression. This model is representative of a class of modelling approaches of this system, based on a "minimal" set of well-established biomolecular regulations. Depending on the protein degradation rates we show the existence of bifurcations between a stable steady state and oscillations both in presence and absence of stress.