A mesoscopic simulator to uncover heterogeneity and evolutionary dynamics in tumors.

Increasingly complex in silico modeling approaches offer a way to simultaneously access cancerous processes at different spatio-temporal scales. High-level models, such as those based on partial differential equations, are computationally affordable and allow large tumor sizes and long temporal windows to be studied, but miss the discrete nature of many key underlying cellular processes. Individual-based approaches provide a much more detailed description of tumors, but have difficulties when trying to handle full-sized real cancers. Thus, there exists a trade-off between the integration of macroscopic and microscopic information, now widely available, and the ability to attain clinical tumor sizes. In this paper we put forward a stochastic mesoscopic simulation framework that incorporates key cellular processes during tumor progression while keeping computational costs to a minimum. Our framework captures a physical scale that allows both the incorporation of microscopic information, tracking the spatio-temporal emergence of tumor heterogeneity and the underlying evolutionary dynamics, and the reconstruction of clinically sized tumors from high-resolution medical imaging data, with the additional benefit of low computational cost. We illustrate the functionality of our modeling approach for the case of glioblastoma, a paradigm of tumor heterogeneity that remains extremely challenging in the clinical setting.

Mitochondria transfer from tumor-activated stromal cells (TASC) to primary Glioblastoma cells.

The tumor microenvironment (TME) controls many aspects of cancer development but little is known about its effect in Glioblastoma (GBM), the main brain tumor in adults. Tumor-activated stromal cell (TASC) population, a component of TME in GBM, was induced in vitro by incubation of MSCs with culture media conditioned by primary cultures of GBM under 3D/organoid conditions. We observed mitochondrial transfer by Tunneling Nanotubes (TNT), extracellular vesicles (EV) and cannibalism from the TASC to GBM and analyzed its effect on both proliferation and survival. We created primary cultures of GBM or TASC in which we have eliminated mitochondrial DNA [Rho 0 (ρ0) cells]. We found that TASC, as described in other cancers, increased GBM proliferation and resistance to standard treatments (radiotherapy and chemotherapy). We analyzed the incorporation of purified mitochondria by ρ0 and ρ+ cells and a derived mathematical model taught us that ρ+ cells incorporate more rapidly pure mitochondria than ρ0 cells.

Computational design of improved standardized chemotherapy protocols for grade II oligodendrogliomas.

Here we put forward a mathematical model describing the response of low-grade (WHO grade II) oligodendrogliomas (LGO) to temozolomide (TMZ). The model describes the longitudinal volumetric dynamics of tumor response to TMZ of a cohort of 11 LGO patients treated with TMZ. After finding patient-specific parameters, different therapeutic strategies were tried computationally on the 'in-silico twins' of those patients. Chemotherapy schedules with larger-than-standard rest periods between consecutive cycles had either the same or better long-term efficacy than the standard 28-day cycles. The results were confirmed in a large trial of 2000 virtual patients. These long-cycle schemes would also have reduced toxicity and defer the appearance of resistances. On the basis of those results, a combination scheme consisting of five induction TMZ cycles given monthly plus 12 maintenance cycles given every three months was found to provide substantial survival benefits for the in-silico twins of the 11 LGO patients (median 5.69 years, range: 0.67 to 68.45 years) and in a large virtual trial including 2000 patients. We used 220 sets of experiments in-silico to show that a clinical trial incorporating 100 patients per arm (standard intensive treatment versus 5 + 12 scheme) could demonstrate the superiority of the novel scheme after a follow-up period of 10 years. Thus, the proposed treatment plan could be the basis for a standardized TMZ treatment for LGO patients with survival benefits.

Transfer of Drug Resistance Characteristics Between Cancer Cell Subpopulations: A Study Using Simple Mathematical Models.

Resistance to chemotherapy is a major cause of cancer treatment failure. The processes of resistance induction and selection of resistant cells (due to the over-expression of the membrane transporter P-glycoprotein, P-gp) are well documented in the literature, and a number of mathematical models have been developed. However, another process of transfer of resistant characteristics is less well known and has received little attention in the mathematical literature. In this paper, we discuss the potential of simple mathematical models to describe the process of resistance transfer, specifically P-gp transfer, in mixtures of resistant and sensitive tumor cell populations. Two different biological hypotheses for P-gp transfer are explored: (1) exchange through physical cell-cell connections and (2) through microvessicles released to the culture medium. Two models are developed which fit very well the observed population growth dynamics. The potential and limitations of these simple "global" models to describe the aforementioned biological processes involved are discussed on the basis of the results obtained.

Integrated modeling of labile and glycated hemoglobin with glucose for enhanced diabetes detection and short-term monitoring.

Metabolic biomarkers, particularly glycated hemoglobin and fasting plasma glucose, are pivotal in the diagnosis and control of diabetes mellitus. Despite their importance, they exhibit limitations in assessing short-term glucose variations. In this study, we propose labile hemoglobin as an additional biomarker, providing insightful perspectives into these fluctuations. By utilizing datasets from 40,652 retrospective general participants and conducting glucose tolerance tests on 60 prospective pediatric subjects, we explored the relationship between plasma glucose and labile hemoglobin. A mathematical model was developed to encapsulate short-term glucose kinetics in the pediatric group. Applying dimensionality reduction techniques, we successfully identified participant subclusters, facilitating the differentiation between diabetic and non-diabetic individuals. Intriguingly, by integrating labile hemoglobin measurements with plasma glucose values, we were able to predict the likelihood of diabetes in pediatric subjects, underscoring the potential of labile hemoglobin as a significant glycemic biomarker for diabetes research.

A Simple 3D Cell Culture Method for Studying the Interactions between Human Mesenchymal Stromal/Stem Cells and Patients Derived Glioblastoma.

We have developed a 3D biosphere model using patient-derived cells (PDCs) from glioblastoma (GBM), the major form of primary brain tumors in adult, plus cancer-activated fibroblasts (CAFs), obtained by culturing mesenchymal stem cells with GBM conditioned media. The effect of MSC/CAFs on the proliferation, cell-cell interactions, and response to treatment of PDCs was evaluated. Proliferation in the presence of CAFs was statistically lower but the spheroids formed within the 3D-biosphere were larger. A treatment for 5 days with Temozolomide (TMZ) and irradiation, the standard therapy for GBM, had a marked effect on cell number in monocultures compared to co-cultures and influenced cancer stem cells composition, similar to that observed in GBM patients. Mathematical analyses of spheroids growth and morphology confirm the similarity with GBM patients. We, thus, provide a simple and reproducible method to obtain 3D cultures from patient-derived biopsies and co-cultures with MSC with a near 100% success. This method provides the basis for relevant in vitro functional models for a better comprehension of the role of tumor microenvironment and, for precision and/or personalized medicine, potentially to predict the response to treatments for each GBM patient.

Optimal Combinations of Chemotherapy and Radiotherapy in Low-Grade Gliomas: A Mathematical Approach.

Low-grade gliomas (LGGs) are brain tumors characterized by their slow growth and infiltrative nature. Treatment options for these tumors are surgery, radiation therapy and chemotherapy. The optimal use of radiation therapy and chemotherapy is still under study. In this paper, we construct a mathematical model of LGG response to combinations of chemotherapy, specifically to the alkylating agent temozolomide and radiation therapy. Patient-specific parameters were obtained from longitudinal imaging data of the response of real LGG patients. Computer simulations showed that concurrent cycles of radiation therapy and temozolomide could provide the best therapeutic efficacy in-silico for the patients included in the study. The patient cohort was extended computationally to a set of 3000 virtual patients. This virtual cohort was subject to an in-silico trial in which matching the doses of radiotherapy to those of temozolomide in the first five days of each cycle improved overall survival over concomitant radio-chemotherapy according to RTOG 0424. Thus, the proposed treatment schedule could be investigated in a clinical setting to improve combination treatments in LGGs with substantial survival benefits.

Influence of Coating and Size of Magnetic Nanoparticles on Cellular Uptake for In Vitro MRI.

Iron oxide nanoparticles (IONPs) are suitable materials for contrast enhancement in magnetic resonance imaging (MRI). Their potential clinical applications range from diagnosis to therapy and follow-up treatments. However, a deeper understanding of the interaction between IONPs, culture media and cells is necessary for expanding the application of this technology to different types of cancer therapies. To achieve new insights of these interactions, a set of IONPs were prepared with the same inorganic core and five distinct coatings, to study their aggregation and interactions in different physiological media, as well as their cell labelling efficiency. Then, a second set of IONPs, with six different core sizes and the same coating, were used to study how the core size affects cell labelling and MRI in vitro. Here, IONPs suspended in biological media experience a partial removal of the coating and adhesion of molecules. The FBS concentration alters the labelling of all types of IONPs and hydrodynamic sizes ≥ 300 nm provide the greatest labelling using the centrifugation-mediated internalization (CMI). The best contrast for MRI results requires a core size range between 12-14 nm coated with dimercaptosuccinic acid (DMSA) producing R2* values of 393.7 s-1 and 428.3 s-1, respectively. These findings will help to bring IONPs as negative contrast agents into clinical settings.

Identification of a transient state during the acquisition of temozolomide resistance in glioblastoma.

Drug resistance limits the therapeutic efficacy in cancers and leads to tumor recurrence through ill-defined mechanisms. Glioblastoma (GBM) are the deadliest brain tumors in adults. GBM, at diagnosis or after treatment, are resistant to temozolomide (TMZ), the standard chemotherapy. To better understand the acquisition of this resistance, we performed a longitudinal study, using a combination of mathematical models, RNA sequencing, single cell analyses, functional and drug assays in a human glioma cell line (U251). After an initial response characterized by cell death induction, cells entered a transient state defined by slow growth, a distinct morphology and a shift of metabolism. Specific genes expression associated to this population revealed chromatin remodeling. Indeed, the histone deacetylase inhibitor trichostatin (TSA), specifically eliminated this population and thus prevented the appearance of fast growing TMZ-resistant cells. In conclusion, we have identified in glioblastoma a population with tolerant-like features, which could constitute a therapeutic target.

Universal scaling laws rule explosive growth in human cancers.

Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a measure of the size of the system. Here we describe the discovery of universal superlinear metabolic scaling laws in human cancers. This dependence underpins increasing tumour aggressiveness, due to evolutionary dynamics, which leads to an explosive growth as the disease progresses. We validated this dynamic using longitudinal volumetric data of different histologies from large cohorts of cancer patients. To explain our observations we put forward increasingly-complex biologically-inspired mathematical models that captured the key processes governing tumor growth. Our models predicted that the emergence of superlinear allometric scaling laws is an inherently three-dimensional phenomenon. Moreover, the scaling laws thereby identified allowed us to define a set of metabolic metrics with prognostic value, thus providing added clinical utility to the base findings.

Interplay of Darwinian Selection, Lamarckian Induction and Microvesicle Transfer on Drug Resistance in Cancer.

Development of drug resistance in cancer has major implications for patients' outcome. It is related to processes involved in the decrease of drug efficacy, which are strongly influenced by intratumor heterogeneity and changes in the microenvironment. Heterogeneity arises, to a large extent, from genetic mutations analogously to Darwinian evolution, when selection of tumor cells results from the adaptation to the microenvironment, but could also emerge as a consequence of epigenetic mutations driven by stochastic events. An important exogenous source of alterations is the action of chemotherapeutic agents, which not only affects the signalling pathways but also the interactions among cells. In this work we provide experimental evidence from in vitro assays and put forward a mathematical kinetic transport model to describe the dynamics displayed by a system of non-small-cell lung carcinoma cells (NCI-H460) which, depending on the effect of a chemotherapeutic agent (doxorubicin), exhibits a complex interplay between Darwinian selection, Lamarckian induction and the nonlocal transfer of extracellular microvesicles. The role played by all of these processes to multidrug resistance in cancer is elucidated and quantified.

Changes in the retreatment radiation tolerance of the spinal cord with time after the initial treatment.

PURPOSE: To estimate, from experimental data, the retreatment radiation 'tolerances' of the spinal cord at different times after initial treatment. MATERIALS AND METHODS: A model was developed to show the relationship between the biological effective doses (BEDs) for two separate courses of treatment with the BED of each course being expressed as a percentage of the designated 'retreatment tolerance' BED value, denoted [Formula: see text] and [Formula: see text]. The primate data of Ang et al. ( 2001 ) were used to determine the fitted parameters. However, based on rodent data, recovery was assumed to commence 70 days after the first course was complete, and with a non-linear relationship to the magnitude of the initial BED (BEDinit). RESULTS: The model, taking into account the above processes, provides estimates of the retreatment tolerance dose after different times. Extrapolations from the experimental data can provide conservative estimates for the clinic, with a lower acceptable myelopathy incidence. Care must be taken to convert the predicted [Formula: see text] value into a formal BED value and then a practical dose fractionation schedule. CONCLUSIONS: Used with caution, the proposed model allows estimations of retreatment doses with elapsed times ranging from 70 days up to three years after the initial course of treatment.

Delay effects in the response of low-grade gliomas to radiotherapy: a mathematical model and its therapeutical implications.

Low-grade gliomas (LGGs) are a group of primary brain tumours usually encountered in young patient populations. These tumours represent a difficult challenge because many patients survive a decade or more and may be at a higher risk for treatment-related complications. Specifically, radiation therapy is known to have a relevant effect on survival but in many cases it can be deferred to avoid side effects while maintaining its beneficial effect. However, a subset of LGGs manifests more aggressive clinical behaviour and requires earlier intervention. Moreover, the effectiveness of radiotherapy depends on the tumour characteristics. Recently Pallud et al. (2012. Neuro-Oncology, 14: , 1-10) studied patients with LGGs treated with radiation therapy as a first-line therapy and obtained the counterintuitive result that tumours with a fast response to the therapy had a worse prognosis than those responding late. In this paper, we construct a mathematical model describing the basic facts of glioma progression and response to radiotherapy. The model provides also an explanation to the observations of Pallud et al. Using the model, we propose radiation fractionation schemes that might be therapeutically useful by helping to evaluate tumour malignancy while at the same time reducing the toxicity associated to the treatment.

Bright solitary waves in malignant gliomas.

We put forward a nonlinear wave model describing the fundamental dynamical features of an aggressive type of brain tumors. Our model accounts for the invasion of normal tissue by a proliferating and propagating rim of active glioma cancer cells in the tumor boundary and the subsequent formation of a necrotic core. By resorting to numerical simulations, phase space analysis, and exact solutions we prove that bright solitary tumor waves develop in such systems. Possible implications of our model as a tool to extract relevant patient specific tumor parameters in combination with standard preoperative clinical imaging are also discussed.

Localized nonlinear waves in systems with time- and space-modulated nonlinearities.

Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schrödinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.

Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities.

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves.