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BackgroundTemozolomide (TMZ) is an oral alkylating agent active against gliomas with a favorable toxicity profile. It is part of the standard of care in the management of glioblastoma, and is commonly used in low-grade gliomas. In-silico mathematical models can potentially be used to personalize treatments and to accelerate the discovery of optimal drug delivery schemes.MethodsAgent-based mathematical models fed with either mouse or patient data were developed for the in-silico studies. The experimental test beds used to confirm the results were: mouse glioma models obtained by retroviral expression of EGFR wt or EGFR vIII in primary progenitors from p16/p19 ko mice and grown in vitro and in vivo in orthotopic allografts, and human glioblastoma U251 cells immobilized in alginate microfibers. The patient data used to parametrize the model were obtained from the TCGA/TCIA databases and the TOG clinical study.ResultsSlow growth ‘virtual’ murine gliomas benefited from increasing TMZ dose separation in silico. In line with the simulation results, improved survival, reduced toxicity, lower expression of resistance factors and reduction of the tumor mesenchymal component were observed in experimental models subject to long-cycle treatment, particularly in slowly-growing tumors. Tissue analysis after long-cycle TMZ treatments revealed epigenetically-driven changes in tumor phenotype, which could explain the reduction in glioma growth speed. In-silico trials provided support for methods of implementation in human patients.ConclusionsIn-silico simulations, and in-vitro and in-vivo studies show that TMZ administration schedules with increased time between doses may reduce toxicity, delay the appearance of resistances and lead to survival benefits mediated by changes in the tumor phenotype in gliomas.IMPORTANCE OF THE STUDYIn-vivo evidence is provided of improvements in survival, resistance, and toxicity from TMZ schemes with long rest periods between doses in slowly-growing GBM mouse models. The results match hypotheses generated in silico using a mathematical model incorporating the main biological features and fed with real patient data. An epigenetically-driven change in tumor phenotype was also revealed experimentally, which could explain the reduction in glioma growth speed under the ‘long cycle’ scheme. To determine the extent to which our results hold for human patients, large sets of simulations were performed on virtual patients. These in-silico trials suggest different ways to bring the benefits observed in experimental models into clinical practice.

Tumor growth is the result of the interplay of complex biological processes in huge numbers of individual cells living in changing environments. Effective simple mathematical laws have been shown to describe tumor growth in vitro, or simple animal models with bounded-growth dynamics accurately. However, results for the growth of human cancers in patients are scarce. Our study mined a large dataset of 1133 brain metastases (BMs) with longitudinal imaging follow-up to find growth laws for untreated BMs and recurrent treated BMs. Untreated BMs showed high growth exponents, most likely related to the underlying evolutionary dynamics, with experimental tumors in mice resembling accurately the disease. Recurrent BMs growth exponents were smaller, most probably due to a reduction in tumor heterogeneity after treatment, which may limit the tumor evolutionary capabilities. In silico simulations using a stochastic discrete mesoscopic model with basic evolutionary dynamics led to results in line with the observed data.

Although children and adolescents with acute lymphoblastic leukaemia (ALL) have high survival rates, approximately 15-20% of patients relapse. Risk of relapse is routinely estimated at diagnosis by biological factors, including flow cytometry data. This high-dimensional data is typically manually assessed by projecting it onto a subset of biomarkers. Cell density and “empty spaces” in 2D projections of the data, i.e. regions devoid of cells, are then used for qualitative assessment. Here, we use topological data analysis (TDA), which quantifies shapes, including empty spaces, in data, to analyse pre-treatment ALL datasets with known patient outcomes. We combine these fully unsupervised analyses with Machine Learning (ML) to identify significant shape characteristics and demonstrate that they accurately predict risk of relapse, particularly for patients previously classified as ‘low risk’. We independently confirm the predictive power of CD10, CD20, CD38, and CD45 as biomarkers for ALL diagnosis. Based on our analyses, we propose three increasingly detailed prognostic pipelines for analysing flow cytometry data from ALL patients depending on technical and technological availability: 1. Visual inspection of specific biological features in biparametric projections of the data; 2. Computation of quantitative topological descriptors of such projections; 3. A combined analysis, using TDA and ML, in the four-parameter space defined by CD10, CD20, CD38 and CD45. Our analyses readily extend to other haematological malignancies.Author summaryAcute lymphoblastic leukaemia (ALL) is a blood cancer which affects predominantly children and adolescents. Therapy typically fails in approximately 20 % of patients, who suffer from relapse. To determine disease status, clinicians assess cell types, their interactions, as well as deviations from normal behaviour. Flow cytometry (FC) is a method that quantifies the intensity of specific cell markers, giving rise to high-dimensional data. This routinely collected information is then reduced to obtain human-interpretable visualisation for prognosis. Topological Data Analysis (TDA) is a field of mathematics that studies shapes in data, considering isolated data islands and empty spaces between them. We showcase how to use TDA to extract shape characteristics in FC data of relapsing patients. We propose three pipelines, of increasing methodological complexity, to aid clinical decisions for risk stratification in ALL. In combination with Machine Learning, TDA enables high-accuracy predictions of relapse to be made at the time of diagnosis.

Human cancers are biologically and morphologically heterogeneous. A variety of clonal populations emerge within these neoplasms and their interaction leads to complex spatio-temporal dynamics during tumor growth. We studied the reshaping of metabolic activity in human cancers by means of continuous and discrete mathematical models, and matched the results to positron emission tomography (PET) imaging data. Our models revealed that the location of increasingly active proliferative cellular spots progressively drifted from the center of the tumor to the periphery, as a result of the competition between gradually more aggressive phenotypes. This computational finding led to the development of a metric, the NPAC, based on the distance from the location of peak activity (proliferation) to the tumor centroid. The NPAC metric can be computed for human patients using 18F-FDG PET/CT images where the voxel of maximum uptake (SUVmax) is taken as the point of peak activity. Two datasets of 18F-FDG PET/CT images were collected, one from 61 breast cancer patients and another from 161 non-small-cell lung cancer patients. In both cohorts, survival analyses were carried out for the NPAC and for other classical PET/CT-based biomarkers, finding that the former had a high prognostic value, outperforming the latter. In summary, our work offers new insights into the evolutionary mechanisms behind tumor progression and provides a PET/CT-based biomarker with clinical applicability.Significance StatementThrough the use of different in silico modeling approaches capturing tumor heterogeneity, we predicted that areas of high metabolic activity would shift towards the periphery as tumors become more malignant. To confirm the prediction and provide clinical value for the finding, we took 18F-FDG PET images of breast cancers and non-small-cell lung cancers, where we measured the distance from the point of maximum activity to the tumor centroid, and normalized it by a surrogate of the volume. We show that this metric has a high prognostic value for both malignancies and outperforms other classical PET-based metabolic biomarkers used in oncology.

Immunotherapies use components of the patient immune system to selectively target cancer cells. The use of CAR T cells to treat B-cell malignancies – leukaemias and lymphomas– is one of the most successful examples, with many patients experiencing long-lasting complete responses to this therapy. This treatment works by extracting the patient’s T cells and adding them the CAR group, which enables them to recognize and target cells carrying the antigen CD19+, that is expressed in these haematological tumors.Here we put forward a mathematical model describing the time response of leukaemias to the injection of CAR T-cells. The model accounts for mature and progenitor B-cells, tumor cells, CAR T cells and side effects by incorporating the main biological processes involved. The model explains the early post-injection dynamics of the different compartments and the fact that the number of CAR T cells injected does not critically affect the treatment outcome. An explicit formula is found that provides the maximum CAR T cell expansion in-vivo and the severity of side effects. Our mathematical model captures other known features of the response to this immunotherapy. It also predicts that CD19+ tumor relapses could be the result of the competition between tumor and CAR T cells analogous to predator-prey dynamics. We discuss this fact on the light of available evidences and the possibility of controlling relapses by early re-challenging of the tumor with stored CAR T cells.