Mathematic Modeling at Micro and Macroscopic Level of Primary Central Nervous System Lymphomas (PCNSL)

Primary central nervous system lymphomas (PCNSL) are extra-nodal, malignant non-Hodgkin lymphomas of diffuse large B-cell type confined to the CNS or eyes without evidence of systemic spread. PCNSL account for up to 1% of all lymphomas and 3% of primary brain tumors. Despite recent progress in PCNSL treatment, remissions are short lasting and the outcome remains poor with a minority of long-term survivors (20%). Moreover, treatments expose patients to a high risk of neurotoxicity. Even though PCNSL has been extensively studied, the pathogenic mechanisms underlying its remarkable tropism and its peculiar clinical behaviour are not well elucidated. Since 2010, the French National Institute of Cancer (INCa) has supported the creation of medical networks dedicated to rare cancers, including PCNSL (LOC network). LOC has developed a national clinical database of newly diagnosed PCNSL with a virtual tumor database to perform translational studies. Furthermore, LOC has launched several prospective trials including a phase III clinical trial (BLOCAGE - PHRC 2014) with an expected sample size of 300 patients to perform ancillary analysis. Modeling malignant extracerebral/systemic non-Hodgkin lymphoma therapy and outcome has been previously performed, however due to its peculiar anatomical and immunoprivileged microenvironment, and its specific therapeutic management, specific modeling of PCNSL is required. Interestingly, in glioblastoma, another primary brain tumor, a model prediction of expected tumor burden provided a personalized assessment of a therapy's effectiveness. Therefore, a comprehensive mechanistic view of mathematical modeling of PCNSL growth and treatment response could be used to better stratify PCNSL evolution and to predict the best treatment options. From a radiological point of view, PCNSL often display a characteristic presentation with periventricular contrast enhancing lesions. This is due to its hypercellularity, high nuclear/cytoplasmic ratio, disruption of the blood-brain barrier, and its predilection for the periventricular and superficial regions often in contact with ventricular or meningeal surface. Interestingly, some small studies suggest that the integration of radiological and high-throughput data would help to stratify the prognosis of PCNSL. In addition, MRI assesses therapeutic response but this evaluation lacks of sensitivity to detect non-enhancing lesions. Radiomics is a promising new paradigm for extending clinical imaging into the era of molecular and genomic imaging. Interesting results using MRI and molecular phenotypes have been obtained in different cancers and very recently in glioblastomas4. However, there is only some evidence suggesting that molecular phenotype of PCNSL could be related to some particular imaging morphophenotypes. Interestingly, our team has recently identified a potential molecular-radiological association between the presence of TERT promoter mutations and the localization of PCNSL within corpus callosum. Furthermore, using MRI data (macroscopic data) will be also used to explore predictors of MRI patterns in a multivariate framework, we will develop a linear modeling approach that measures the association of MRI patterns with a number of potential predictors, including expression levels on a gene-by-gene basis, driver mutations and clinical variables. Somatically acquired mutation and cytogenetic lesion will be encoded as being present/absent. We choose a linear model due to its interpretability and established statistical methods, enabling us to test which MRI morphological pattern are associated with deregulated transcripts in the presence of specific alterations after correcting for other confounding factors and other clinical variables and coexisting driver mutations. The total variance in the MRI data will be studied and dissected using data from selected driver genes, cytogenetic lesion and the most relevant principal components of MRI data will be analyzed in a Least Absolute Shrinkage and Selection Operator (LASSO) penalized model. The optimal model maximizes the explained variance R2.

We will evaluate prognosis accuracy of survival models using Harrel's C statistic, as implemented in Hmisc R package. This statistic measures the fraction of pairs of patients with concordant risk predictions, and outcome similarly to the area under the receiver operating characteristic curve. To reduce the bias of estimated risk, we will use a fivefold cross-validating scheme. In addition, we will also analyze survival impact of this multidimensional data using random forest as an alternative approach for predicting outcome and measuring variable importance. These are implemented in the randomForesetSRC R package. the preliminary results obtained on a sub sample of patient showed that the 100 patient cohort will be sufficient to build and assess the predictive values of the models we will study. Tools to integrate multiple sources data set described above for a small subset will be scaled up using all the variables available from the complete dataset: non negative matrix co-factorization and regularized generalized canonical correlation analysis.

Patient prognosis may tightly correlate with a characteristic morphological tumor phenotype on the histological level and with tumor shape, which itself may correlate with the gene expression pattern. For this reason, macro-level growth simulations with the above statistical model will be complemented by simulations with mechanistic models at the histological level, and at whole tumor level. The histological-level model will be calibrated with experiments using diffuse large B cell lymphoma (DLBCL) cell lines co-cultured with other microenvironment cells like glial cells, and with murine experiments. This model shall shed light on the mechanisms at cell level capable of explaining the observed cell proliferation and multicellular arrangement pattern.