A complete mathematical study of a 3D model of heterogeneous and anisotropic glioma evolution

A Multidisciplinary Hyper-Modeling Scheme in Personalized In Silico Oncology: Coupling Cell Kinetics with Metabolism, Signaling Networks, and Biomechanics as Plug-In Component Models of a Cancer Digital Twin

The massive amount of human biological, imaging, and clinical data produced by multiple and diverse sources necessitates integrative modeling approaches able to summarize all this information into answers to specific clinical questions. In this paper, we present a hypermodeling scheme able to combine models of diverse cancer aspects regardless of their underlying method or scale. Describing tissue-scale cancer cell proliferation, biomechanical tumor growth, nutrient transport, genomic-scale aberrant cancer cell metabolism, and cell-signaling pathways that regulate the cellular response to therapy, the hypermodel integrates mutation, miRNA expression, imaging, and clinical data. The constituting hypomodels, as well as their orchestration and links, are described. Two specific cancer types, Wilms tumor (nephroblastoma) and non-small cell lung cancer, are addressed as proof-of-concept study cases. Personalized simulations of the actual anatomy of a patient have been conducted. The hypermodel has also been applied to predict tumor control after radiotherapy and the relationship between tumor proliferative activity and response to neoadjuvant chemotherapy. Our innovative hypermodel holds promise as a digital twin-based clinical decision support system and as the core of future in silico trial platforms, although additional retrospective adaptation and validation are necessary.

PML Differentially Regulates Growth and Invasion in Brain Cancer

Glioblastoma is the most malignant brain tumor among adults. Despite multimodality treatment, it remains incurable, mainly because of its extensive heterogeneity and infiltration in the brain parenchyma. Recent evidence indicates dysregulation of the expression of the Promyelocytic Leukemia Protein (PML) in primary Glioblastoma samples. PML is implicated in various ways in cancer biology. In the brain, PML participates in the physiological migration of the neural progenitor cells, which have been hypothesized to serve as the cell of origin of Glioblastoma. The role of PML in Glioblastoma progression has recently gained attention due to its controversial effects in overall Glioblastoma evolution. In this work, we studied the role of PML in Glioblastoma pathophysiology using the U87MG cell line. We genetically modified the cells to conditionally overexpress the PML isoform IV and we focused on its dual role in tumor growth and invasive capacity. Furthermore, we targeted a PML action mediator, the Enhancer of Zeste Homolog 2 (EZH2), via the inhibitory drug DZNeP. We present a combined in vitro–in silico approach, that utilizes both 2D and 3D cultures and cancer-predictive computational algorithms, in order to differentiate and interpret the observed biological results. Our overall findings indicate that PML regulates growth and invasion through distinct cellular mechanisms. In particular, PML overexpression suppresses cell proliferation, while it maintains the invasive capacity of the U87MG Glioblastoma cells and, upon inhibition of the PML-EZH2 pathway, the invasion is drastically eliminated. Our in silico simulations suggest that the underlying mechanism of PML-driven Glioblastoma physiology regulates invasion by differential modulation of the cell-to-cell adhesive and diffusive capacity of the cells. Elucidating further the role of PML in Glioblastoma biology could set PML as a potential molecular biomarker of the tumor progression and its mediated pathway as a therapeutic target, aiming at inhibiting cell growth and potentially clonal evolution regarding their proliferative and/or invasive phenotype within the heterogeneous tumor mass.

Modeling How Heterogeneity in Cell Cycle Length Affects Cancer Cell Growth Dynamics in Response to Treatment

Tumors are complex, dynamic, and adaptive biological systems characterized by high heterogeneity at genetic, epigenetic, phenotypic, as well as tissue microenvironmental level. In this work, utilizing cellular automata methods, we focus on intrinsic heterogeneity with respect to cell cycle duration and explore whether and to what extent this heterogeneity affects cancer cell growth dynamics when cytotoxic treatment is applied. We assume that treatment acts on cancer cells specifically during mitosis and compare it with a (cell cycle-non-specific) cytotoxic treatment that acts randomly regardless of the cell cycle phase. We simulate the spatiotemporal evolution of tumor cells with different initial spatial configurations and different cell length probability distributions. We observed that in heterogeneous populations, strong selection forces act on cancer cells favoring the faster cells, when the death rates are lower than the proliferation rates. However, at higher mitotic death rates, selection of the slower proliferative cells is favored, leading to slower post-treatment regrowth rates, as compared to untreated growth. Of note, random cell death progressively eliminates the slower proliferative cells, consistently, favoring highly proliferative phenotypes. Interestingly, compared to the monoclonal populations that exhibit complete response at high random death rates, emergent resistance arises naturally in heterogeneous populations during treatment. As divergent selection forces may act on a heterogeneous cancer cell population, we argue that treatment plan selection can considerably alter the post-treatment tumor dynamics, cell survival, and emergence of resistance, proving its significant biological and therapeutic impact.

In Vitro/In Silico Study on the Role of Doubling Time Heterogeneity among Primary Glioblastoma Cell Lines

The application of accurate cancer predictive algorithms validated with experimental data is a field concerning both basic researchers and clinicians, especially regarding a highly aggressive form of cancer, such as Glioblastoma. In an aim to enhance prediction accuracy in realistic patient-specific environments, accounting for both inter- and intratumoral heterogeneity, we use patient-derived Glioblastoma cells from different patients. We focus on cell proliferation using in vitro experiments to estimate cell doubling times and sizes for established primary Glioblastoma cell lines. A preclinically driven mathematical model parametrization is accomplished by taking into account the experimental measurements. As a control cell line we use the well-studied U87MG cells. Both in vitro and in silico results presented support that the variance between tumor staging can be attributed to the differential proliferative capacity of the different Glioblastoma cells. More specifically, the intratumoral heterogeneity together with the overall proliferation reflected in both the proliferation rate and the mechanical cell contact inhibition can predict the in vitro evolution of different Glioblastoma cell lines growing under the same conditions. Undoubtedly, additional imaging techniques capable of providing spatial information of tumor cell physiology and microenvironment will enhance our understanding regarding Glioblastoma nature and verify and further improve our predictability.

Mathematical modelling of spatio-temporal glioma evolution

Background

Gliomas are the most common types of brain cancer, well known for their aggressive proliferation and the invasive behavior leading to a high mortality rate. Several mathematical models have been developed for identifying the interactions between glioma cells and tissue microenvironment, which play an important role in the mechanism of the tumor formation and progression.

Methods

Building and expanding on existing approaches, this paper develops a continuous three-dimensional model of avascular glioma spatio-temporal evolution. The proposed spherical model incorporates the interactions between the populations of four different glioma cell phenotypes (proliferative, hypoxic, hypoglychemic and necrotic) and their tissue microenvironment, in order to investigate how they affect tumor growth and invasion in an isotropic and homogeneous medium. The model includes two key variables involved in the proliferation and invasion processes of cancer cells; i.e. the extracellular matrix and the matrix-degradative enzymes concentrations inside the tumor and its surroundings. Additionally, the proposed model focuses on innovative features, such as the separate and independent impact of two vital nutrients, namely oxygen and glucose, in tumor growth, leading to the formation of cell populations with different metabolic profiles. The model implementation takes under consideration the variations of particular factors, such as the local cell proliferation rate, the variable conversion rates of cells from one category to another and the nutrient-dependent thresholds of conversion. All model variables (cell densities, ingredients concentrations) are continuous and described by reaction-diffusion equations.

Results

Several simulations were performed using combinations of growth and invasion rates, for different evolution times. The model results were evaluated by medical experts and validated on experimental glioma models available in the literature, revealing high agreement between simulated and experimental results.

Conclusions

Based on the experimental validation, as well as the evaluation by clinical experts, the proposed model may provide an essential tool for the patient-specific simulation of different tumor evolution scenarios and reliable prognosis of glioma spatio-temporal progression.

Simulating radiotherapy effect in high-grade glioma by using diffusive modeling and brain atlases

Applying diffusive models for simulating the spatiotemporal change of concentration of tumour cells is a modern application of predictive oncology. Diffusive models are used for modelling glioblastoma, the most aggressive type of glioma. This paper presents the results of applying a linear quadratic model for simulating the effects of radiotherapy on an advanced diffusive glioma model. This diffusive model takes into consideration the heterogeneous velocity of glioma in gray and white matter and the anisotropic migration of tumor cells, which is facilitated along white fibers. This work uses normal brain atlases for extracting the proportions of white and gray matter and the diffusion tensors used for anisotropy. The paper also presents the results of applying this glioma model on real clinical datasets.

In-depth analysis and evaluation of diffusive glioma models

Glioma is one of the most aggressive types of brain tumor. Several mathematical models have been developed during the past two decades, toward simulating the mechanisms that govern the development of glioma. The most common models use the diffusion-reaction equation (DRE) for simulating the spatiotemporal variation of tumor cell concentration. Nevertheless, despite the applications presented, there has been little work on studying the details of the mathematical solution and implementation of the 3-D diffusion model and presenting a qualitative analysis of the algorithmic results. This paper presents a complete mathematical framework on the solution of the DRE using different numerical schemes. This framework takes into account all characteristics of the latest models, such as brain tissue heterogeneity, anisotropic tumor cell migration, chemotherapy, and resection modeling. The different numerical schemes presented have been evaluated based upon the degree to which the DRE exact solution is approximated. Experiments have been conducted both on real datasets and a test case for which there is a known algebraic expression of the solution. Thus, it is possible to calculate the accuracy of the different models.

High-grade glioma diffusive modeling using statistical tissue information and diffusion tensors extracted from atlases

Glioma, especially glioblastoma, is a leading cause of brain cancer fatality involving highly invasive and neoplastic growth. Diffusive models of glioma growth use variations of the diffusion-reaction equation in order to simulate the invasive patterns of glioma cells by approximating the spatiotemporal change of glioma cell concentration. The most advanced diffusive models take into consideration the heterogeneous velocity of glioma in gray and white matter, by using two different discrete diffusion coefficients in these areas. Moreover, by using diffusion tensor imaging (DTI), they simulate the anisotropic migration of glioma cells, which is facilitated along white fibers, assuming diffusion tensors with different diffusion coefficients along each candidate direction of growth. Our study extends this concept by fully exploiting the proportions of white and gray matter extracted by normal brain atlases, rather than discretizing diffusion coefficients. Moreover, the proportions of white and gray matter, as well as the diffusion tensors, are extracted by the respective atlases; thus, no DTI processing is needed. Finally, we applied this novel glioma growth model on real data and the results indicate that prognostication rates can be improved.

DoctorEye: A clinically driven multifunctional platform, for accurate processing of tumors in medical images

This paper presents a novel, open access interactive platform for 3D medical image analysis, simulation and visualization, focusing in oncology images. The platform was developed through constant interaction and feedback from expert clinicians integrating a thorough analysis of their requirements while having an ultimate goal of assisting in accurately delineating tumors. It allows clinicians not only to work with a large number of 3D tomographic datasets but also to efficiently annotate multiple regions of interest in the same session. Manual and semi-automatic segmentation techniques combined with integrated correction tools assist in the quick and refined delineation of tumors while different users can add different components related to oncology such as tumor growth and simulation algorithms for improving therapy planning. The platform has been tested by different users and over large number of heterogeneous tomographic datasets to ensure stability, usability, extensibility and robustness with promising results.

AVAILABILITY

the platform, a manual and tutorial videos are available at: http://biomodeling.ics.forth.gr. it is free to use under the GNU General Public License.