Speed Switch in Glioblastoma Growth Rate due to Enhanced Hypoxia-Induced Migration

We analyze the wave-speed of the Proliferation Invasion Hypoxia Necro-sis Angiogenesis (PIHNA) model that was previously created and applied to simulate the growth and spread of glioblastoma (GBM), a particularly aggressive primary brain tumor. We extend the PIHNA model by allowing for different hy-poxic and normoxic cell migration rates and study the impact of these differences on the wave-speed dynamics. Through this analysis, we find key variables that drive the outward growth of the simulated GBM. We find a minimum tumor wave-speed for the model; this depends on the migration and proliferation rates of the normoxic cells and is achieved under certain conditions on the migration rates of the normoxic and hypoxic cells. If the hypoxic cell migration rate is greater than the normoxic cell migration rate above a threshold, the wave-speed increases above the predicted minimum. This increase in wave-speed is explored through an eigenvalue and eigenvector analysis of the linearized PIHNA model, which yields an expression for this threshold. The PIHNA model suggests that an inherently faster-diffusing hypoxic cell population can drive the outward growth of a GBM as a whole, and that this effect is more prominent for faster proliferating tumors that recover relatively slowly from a hypoxic phenotype. The findings presented here act as a first step in enabling patient-specific calibration of the PIHNA model

A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma

Glioblastoma (GBM) is the most aggressive primary brain tumor with a short median survival. Tumor recurrence is a clinical expectation of this disease and usually occurs along the resection cavity wall. However, previous clinical observations have suggested that in cases of ischemia following surgery, tumors are more likely to recur distally. Through the use of a previously established mechanistic model of GBM, the Proliferation Invasion Hypoxia Necrosis Angiogenesis (PIHNA) model, we explore the phenotypic drivers of this observed behavior. We have extended the PIHNA model to include a new nutrient-based vascular efficiency term that encodes the ability of local vasculature to provide nutrients to the simulated tumor. The extended model suggests sensitivity to a hypoxic microenvironment and the inherent migration and proliferation rates of the tumor cells are key factors that drive distal recurrence

Integration of Machine Learning and Mechanistic Models Accurately Predicts Variation in Cell Density of Glioblastoma Using Multiparametric MRI

Glioblastoma (GBM) is a heterogeneous and lethal brain cancer. These tumors are followed using magnetic resonance imaging (MRI), which is unable to precisely identify tumor cell invasion, impairing effective surgery and radiation planning. We present a novel hybrid model, based on multiparametric intensities, which combines machine learning (ML) with a mechanistic model of tumor growth to provide spatially resolved tumor cell density predictions. The ML component is an imaging data-driven graph-based semi-supervised learning model and we use the Proliferation-Invasion (PI) mechanistic tumor growth model. We thus refer to the hybrid model as the ML-PI model. The hybrid model was trained using 82 image-localized biopsies from 18 primary GBM patients with pre-operative MRI using a leave-one-patient-out cross validation framework. A Relief algorithm was developed to quantify relative contributions from the data sources. The ML-PI model statistically significantly outperformed (p \u3c 0.001) both individual models, ML and PI, achieving a mean absolute predicted error (MAPE) of 0.106 ± 0.125 versus 0.199 ± 0.186 (ML) and 0.227 ± 0.215 (PI), respectively. Associated Pearson correlation coefficients for ML-PI, ML, and PI were 0.838, 0.518, and 0.437, respectively. The Relief algorithm showed the PI model had the greatest contribution to the result, emphasizing the importance of the hybrid model in achieving the high accuracy

Identifying the spatial and temporal dynamics of molecularly-distinct glioblastoma sub-populations

Glioblastomas (GBMs) are the most aggressive primary brain tumours and have no known cure. Each individual tumour comprises multiple sub-populations of genetically-distinct cells that may respond differently to targeted therapies and may contribute to disappointing clinical trial results. Image-localized biopsy techniques allow multiple biopsies to be taken during surgery and provide information that identifies regions where particular sub-populations occur within an individual GBM, thus providing insight into their regional genetic variability. These sub-populations may also interact with one another in a competitive or cooperative manner; it is important to ascertain the nature of these interactions, as they may have implications for responses to targeted therapies

MultiCellDS: a community-developed standard for curating microenvironment-dependent multicellular data

Exchanging and understanding scientific data and their context represents a significant barrier to advancing research, especially with respect to information siloing. Maintaining information provenance and providing data curation and quality control help overcome common concerns and barriers to the effective sharing of scientific data. To address these problems in and the unique challenges of multicellular systems, we assembled a panel composed of investigators from several disciplines to create the MultiCellular Data Standard (MultiCellDS) with a use-case driven development process. The standard includes (1) digital cell lines, which are analogous to traditional biological cell lines, to record metadata, cellular microenvironment, and cellular phenotype variables of a biological cell line, (2) digital snapshots to consistently record simulation, experimental, and clinical data for multicellular systems, and (3) collections that can logically group digital cell lines and snapshots. We have created a MultiCellular DataBase (MultiCellDB) to store digital snapshots and the 200+ digital cell lines we have generated. MultiCellDS, by having a fixed standard, enables discoverability, extensibility, maintainability, searchability, and sustainability of data, creating biological applicability and clinical utility that permits us to identify upcoming challenges to uplift biology and strategies and therapies for improving human health

MultiCellDS: a standard and a community for sharing multicellular data

Cell biology is increasingly focused on cellular heterogeneity and multicellular systems. To make the fullest use of experimental, clinical, and computational efforts, we need standardized data formats, community-curated "public data libraries", and tools to combine and analyze shared data. To address these needs, our multidisciplinary community created MultiCellDS (MultiCellular Data Standard): an extensible standard, a library of digital cell lines and tissue snapshots, and support software. With the help of experimentalists, clinicians, modelers, and data and library scientists, we can grow this seed into a community-owned ecosystem of shared data and tools, to the benefit of basic science, engineering, and human health

Toward a predictive model of tumor growth

textIn this work, an attempt is made to lay out a framework in which models of tumor growth can be built, calibrated, validated, and differentiated in their level of goodness in such a manner that all the uncertainties associated with each step of the modeling process can be accounted for in the final model prediction. The study can be divided into four basic parts. The first involves the development of a general family of mathematical models of interacting species representing the various constituents of living tissue, which generalizes those previously available in the literature. In this theory, surface effects are introduced by incorporating in the Helmholtz free ` gradients of the volume fractions of the interacting species, thus providing a generalization of the Cahn-Hilliard theory of phase change in binary media and leading to fourth-order, coupled systems of nonlinear evolution equations. A subset of these governing equations is selected as the primary class of models of tumor growth considered in this work. The second component of this study focuses on the emerging and fundamentally important issue of predictive modeling, the study of model calibration, validation, and quantification of uncertainty in predictions of target outputs of models. The Bayesian framework suggested by Babuska, Nobile, and Tempone is employed to embed the calibration and validation processes within the framework of statistical inverse theory. Extensions of the theory are developed which are regarded as necessary for certain scenarios in these methods to models of tumor growth. The third part of the study focuses on the numerical approximation of the diffuse-interface models of tumor growth and on the numerical implementations of the statistical inverse methods at the core of the validation process. A class of mixed finite element models is developed for the considered mass-conservation models of tumor growth. A family of time marching schemes is developed and applied to representative problems of tumor evolution. Finally, in the fourth component of this investigation, a collection of synthetic examples, mostly in two-dimensions, is considered to provide a proof-of-concept of the theory and methods developed in this work.Computational Science, Engineering, and Mathematic