Computer simulation of glioma growth and morphology

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion

Mathematical modeling to elucidate brain tumor abrogation by immunotherapy with T11 target structure

T11 Target structure (T11TS), a membrane glycoprotein isolated from sheep erythrocytes, reverses the immune suppressed state of brain tumor induced animals by boosting the functional status of the immune cells. This study aims at aiding in the design of more efficacious brain tumor therapies with T11 target structure. We propose a mathematical model for brain tumor (glioma) and the immune system interactions, which aims in designing efficacious brain tumor therapy. The model encompasses considerations of the interactive dynamics of macrophages, cytotoxic T lymphocytes, glioma cells, TGF-$\beta$, IFN-$\gamma$ and the T11TS. The system undergoes sensitivity analysis, that determines which state variables are sensitive to the given parameters and the parameters are estimated from the published data. Computer simulations were used for model verification and validation, which highlight the importance of T11 target structure in brain tumor therapy

Longitudinal Brain Tumor Tracking, Tumor Grading, and Patient Survival Prediction Using MRI

This work aims to develop novel methods for brain tumor classification, longitudinal brain tumor tracking, and patient survival prediction. Consequently, this dissertation proposes three tasks. First, we develop a framework for brain tumor segmentation prediction in longitudinal multimodal magnetic resonance imaging (mMRI) scans, comprising two methods: feature fusion and joint label fusion (JLF). The first method fuses stochastic multi-resolution texture features with tumor cell density features, in order to obtain tumor segmentation predictions in follow-up scans from a baseline pre-operative timepoint. The second method utilizes JLF to combine segmentation labels obtained from (i) the stochastic texture feature-based and Random Forest (RF)-based tumor segmentation method; and (ii) another state-of-the-art tumor growth and segmentation method known as boosted Glioma Image Segmentation and Registration (GLISTRboost, or GB). With the advantages of feature fusion and label fusion, we achieve state-of-the-art brain tumor segmentation prediction. Second, we propose a deep neural network (DNN) learning-based method for brain tumor type and subtype grading using phenotypic and genotypic data, following the World Health Organization (WHO) criteria. In addition, the classification method integrates a cellularity feature which is derived from the morphology of a pathology image to improve classification performance. The proposed method achieves state-of-the-art performance for tumor grading following the new CNS tumor grading criteria. Finally, we investigate brain tumor volume segmentation, tumor subtype classification, and overall patient survival prediction, and then we propose a new context- aware deep learning method, known as the Context Aware Convolutional Neural Network (CANet). Using the proposed method, we participated in the Multimodal Brain Tumor Segmentation Challenge 2019 (BraTS 2019) for brain tumor volume segmentation and overall survival prediction tasks. In addition, we also participated in the Radiology-Pathology Challenge 2019 (CPM-RadPath 2019) for Brain Tumor Subtype Classification, organized by the Medical Image Computing & Computer Assisted Intervention (MICCAI) Society. The online evaluation results show that the proposed methods offer competitive performance from their use of state-of-the-art methods in tumor volume segmentation, promising performance on overall survival prediction, and state-of-the-art performance on tumor subtype classification. Moreover, our result was ranked second place in the testing phase of the CPM-RadPath 2019

Global existence for a degenerate haptotaxis model of tumor invasion under the go-or-grow dichotomy hypothesis

We propose and study a strongly coupled PDE-ODE-ODE system modeling cancer cell invasion through a tissue network under the go-or-grow hypothesis asserting that cancer cells can either move or proliferate. Hence our setting features two interacting cell populations with their mutual transitions and involves tissue-dependent degenerate diffusion and haptotaxis for the moving subpopulation. The proliferating cells and the tissue evolution are characterized by way of ODEs for the respective densities. We prove the global existence of weak solutions and illustrate the model behaviour by numerical simulations in a two-dimensional setting.Comment: arXiv admin note: text overlap with arXiv:1512.0428

The Impact of Phenotypic Switching on Glioblastoma Growth and Invasion

The brain tumour glioblastoma is characterised by diffuse and infiltrative growth into surrounding brain tissue. At the macroscopic level, the progression speed of a glioblastoma tumour is determined by two key factors: the cell proliferation rate and the cell migration speed. At the microscopic level, however, proliferation and migration appear to be mutually exclusive phenotypes, as indicated by recent in vivo imaging data. Here, we develop a mathematical model to analyse how the phenotypic switching between proliferative and migratory states of individual cells affects the macroscopic growth of the tumour. For this, we propose an individual-based stochastic model in which glioblastoma cells are either in a proliferative state, where they are stationary and divide, or in motile state in which they are subject to random motion. From the model we derive a continuum approximation in the form of two coupled reaction-diffusion equations, which exhibit travelling wave solutions whose speed of invasion depends on the model parameters. We propose a simple analytical method to predict progression rate from the cell-specific parameters and demonstrate that optimal glioblastoma growth depends on a non-trivial trade-off between the phenotypic switching rates. By linking cellular properties to an in vivo outcome, the model should be applicable to designing relevant cell screens for glioblastoma and cytometry-based patient prognostics

Learning Distributions of Functions on a Continuous Time Domain

This work presents several contributions on the topic of learning representations of function spaces, as well as on learning the dynamics of glioma growth as a particular instance thereof. We begin with two preparatory efforts, showing how expert knowledge can be leveraged efficiently in an interactive segmentation context, and presenting a proof of concept for inferring non-deterministic glioma growth patterns purely from data. The remainder of our work builds upon the framework of Neural Processes. We show how these models represent function spaces and discover that they can implicitly decompose the space into different frequency components, not unlike a Fourier transform. In this context we derive an upper bound on the maximum signal frequency Neural Processes can represent and show how to control the learned representations to only contain certain frequencies. We continue with an improvement of a more recent addition to the Neural Process family called ConvCNP, which we combine with a Gaussian Process to make it non-deterministic and to improve generalization. Finally, we show how to perform segmentation in the Neural Process framework by extending a typical segmentation architecture with spatio-temporal attention. The resulting model can interpolate complex spatial variations of segmentations over time and, applied to glioma growth, it is able to represent multiple temporally consistent growth trajectories, exhibiting realistic and diverse spatial growth patterns