A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment

Elastocapillary effects determine early matrix deformation by glioblastoma cell spheroids

During cancer pathogenesis, cell-generated mechanical stresses lead to dramatic alterations in the mechanical and organizational properties of the extracellular matrix (ECM). To date, contraction of the ECM is largely attributed to local mechanical stresses generated during cell invasion, but the impact of "elastocapillary" effects from surface tension on the tumor periphery has not been examined. Here, we embed glioblastoma cell spheroids within collagen gels, as a model of tumors within the ECM. We then modulate the surface tension of the spheroids, such that the spheroid contracts or expands. Surprisingly, in both cases, at the far-field, the ECM is contracted toward the spheroids prior to cellular migration from the spheroid into the ECM. Through computational simulation, we demonstrate that contraction of the ECM arises from a balance of spheroid surface tension, cell-ECM interactions, and time-dependent, poroelastic effects of the gel. This leads to the accumulation of ECM near the periphery of the spheroid and the contraction of the ECM without regard to the expansion or contraction of the spheroid. These results highlight the role of tissue-level surface stresses and fluid flow within the ECM in the regulation of cell-ECM interactions.

Cancer cell sedimentation in 3D cultures reveals active migration regulated by self-generated gradients and adhesion sites

Cell sedimentation in 3D hydrogel cultures refers to the vertical migration of cells towards the bottom of the space. Understanding this poorly examined phenomenon may allow us to design better protocols to prevent it, as well as provide insights into the mechanobiology of cancer development. We conducted a multiscale experimental and mathematical examination of 3D cancer growth in triple negative breast cancer cells. Migration was examined in the presence and absence of Paclitaxel, in high and low adhesion environments and in the presence of fibroblasts. The observed behaviour was modeled by hypothesizing active migration due to self-generated chemotactic gradients. Our results did not reject this hypothesis, whereby migration was likely to be regulated by the MAPK and TGF-β pathways. The mathematical model enabled us to describe the experimental data in absence (normalized error<40%) and presence of Paclitaxel (normalized error<10%), suggesting inhibition of random motion and advection in the latter case. Inhibition of sedimentation in low adhesion and co-culture experiments further supported the conclusion that cells actively migrated downwards due to the presence of signals produced by cells already attached to the adhesive glass surface.

Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics

We here propose a hybrid computational framework to reproduce and analyze aspects of the avascular progression of a generic solid tumor. Our method first employs an individual-based approach to represent the population of tumor cells, which are distinguished in viable and necrotic agents. The active part of the disease is in turn differentiated according to a set of metabolic states. We then describe the spatio-temporal evolution of the concentration of oxygen and of tumor-secreted proteolytic enzymes using partial differential equations (PDEs). A differential equation finally governs the local degradation of the extracellular matrix (ECM) by the malignant mass. Numerical realizations of the model are run to reproduce tumor growth and invasion in a number scenarios that differ for cell properties (adhesiveness, duplication potential, proteolytic activity) and/or environmental conditions (level of tissue oxygenation and matrix density pattern). In particular, our simulations suggest that tumor aggressiveness, in terms of invasive depth and extension of necrotic tissue, can be reduced by (i) stable cell-cell contact interactions, (ii) poor tendency of malignant agents to chemotactically move upon oxygen gradients, and (iii) presence of an overdense matrix, if coupled by a disrupted proteolytic activity of the disease.

In situtumor model for longitudinal in silico imaging trials

Objective.In this article, we introduce a computational model for simulating the growth of breast cancer lesions accounting for the stiffness of surrounding anatomical structures.Approach.In our model, ligaments are classified as the most rigid structures while the softer parts of the breast are occupied by fat and glandular tissues As a result of these variations in tissue elasticity, the rapidly proliferating tumor cells are met with differential resistance. It is found that these cells are likely to circumvent stiffer terrains such as ligaments, instead electing to proliferate preferentially within the more yielding confines of the breast's soft topography. By manipulating the interstitial tumor pressure in direct proportion to the elastic constants of the tissues surrounding the tumor, this model thus creates the potential for realizing a database of unique lesion morphology sculpted by the distinctive topography of each local anatomical infrastructure. We modeled the growth of simulated lesions within volumes extracted from fatty breast models, developed by Graffet alwith a resolution of 50μm generated with the open-source and readily available Virtual Imaging Clinical Trials for Regulatory Evaluation (VICTRE) imaging pipeline. To visualize and validate the realism of the lesion models, we leveraged the imaging component of the VICTRE pipeline, which replicates the siemens mammomat inspiration mammography system in a digital format. This system was instrumental in generating digital mammogram (DM) images for each breast model containing the simulated lesions.Results.By utilizing the DM images, we were able to effectively illustrate the imaging characteristics of the lesions as they integrated with the anatomical backgrounds. Our research also involved a reader study that compared 25 simulated DM regions of interest (ROIs) with inserted lesions from our models with DM ROIs from the DDSM dataset containing real manifestations of breast cancer. In general the simulation time for the lesions was approximately 2.5 hours, but it varied depending on the lesion's local environment.Significance.The lesion growth model will facilitate and enhance longitudinal in silico trials investigating the progression of breast cancer.

A hybrid physics-based and data-driven framework for cellular biological systems: Application to the morphogenesis of organoids

How cells orchestrate their cellular functions remains a crucial question to unravel how they organize in different patterns. We present a framework based on artificial intelligence to advance the understanding of how cell functions are coordinated spatially and temporally in biological systems. It consists of a hybrid physics-based model that integrates both mechanical interactions and cell functions with a data-driven model that regulates the cellular decision-making process through a deep learning algorithm trained on image data metrics. To illustrate our approach, we used data from 3D cultures of murine pancreatic ductal adenocarcinoma cells (PDAC) grown in Matrigel as tumor organoids. Our approach allowed us to find the underlying principles through which cells activate different cell processes to self-organize in different patterns according to the specific microenvironmental conditions. The framework proposed here expands the tools for simulating biological systems at the cellular level, providing a novel perspective to unravel morphogenetic patterns.

Advanced 3D Models of Human Brain Tissue Using Neural Cell Lines: State-of-the-Art and Future Prospects

Human-relevant three-dimensional (3D) models of cerebral tissue can be invaluable tools to boost our understanding of the cellular mechanisms underlying brain pathophysiology. Nowadays, the accessibility, isolation and harvesting of human neural cells represents a bottleneck for obtaining reproducible and accurate models and gaining insights in the fields of oncology, neurodegenerative diseases and toxicology. In this scenario, given their low cost, ease of culture and reproducibility, neural cell lines constitute a key tool for developing usable and reliable models of the human brain. Here, we review the most recent advances in 3D constructs laden with neural cell lines, highlighting their advantages and limitations and their possible future applications.

Traveling wave speed and profile of a "go or grow" glioblastoma multiforme model

Glioblastoma multiforme (GBM) is a fast-growing and deadly brain tumor due to its ability to aggressively invade the nearby brain tissue. A host of mathematical models in the form of reaction-diffusion equations have been formulated and studied in order to assist clinical assessment of GBM growth and its treatment prediction. To better understand the speed of GBM growth and form, we propose a two population reaction-diffusion GBM model based on the 'go or grow' hypothesis. Our model is validated by in vitro data and assumes that tumor cells are more likely to leave and search for better locations when resources are more limited at their current positions. Our findings indicate that the tumor progresses slower than the simpler Fisher model, which is known to overestimate GBM progression. Moreover, we obtain accurate estimations of the traveling wave solution profiles under several plausible GBM cell switching scenarios by applying the approximation method introduced by Canosa.

Development of a scoring function for comparing simulated and experimental tumor spheroids

Progress continues in the field of cancer biology, yet much remains to be unveiled regarding the mechanisms of cancer invasion. In particular, complex biophysical mechanisms enable a tumor to remodel the surrounding extracellular matrix (ECM), allowing cells to invade alone or collectively. Tumor spheroids cultured in collagen represent a simplified, reproducible 3D model system, which is sufficiently complex to recapitulate the evolving organization of cells and interaction with the ECM that occur during invasion. Recent experimental approaches enable high resolution imaging and quantification of the internal structure of invading tumor spheroids. Concurrently, computational modeling enables simulations of complex multicellular aggregates based on first principles. The comparison between real and simulated spheroids represents a way to fully exploit both data sources, but remains a challenge. We hypothesize that comparing any two spheroids requires first the extraction of basic features from the raw data, and second the definition of key metrics to match such features. Here, we present a novel method to compare spatial features of spheroids in 3D. To do so, we define and extract features from spheroid point cloud data, which we simulated using Cells in Silico (CiS), a high-performance framework for large-scale tissue modeling previously developed by us. We then define metrics to compare features between individual spheroids, and combine all metrics into an overall deviation score. Finally, we use our features to compare experimental data on invading spheroids in increasing collagen densities. We propose that our approach represents the basis for defining improved metrics to compare large 3D data sets. Moving forward, this approach will enable the detailed analysis of spheroids of any origin, one application of which is informing in silico spheroids based on their in vitro counterparts. This will enable both basic and applied researchers to close the loop between modeling and experiments in cancer research.

Utility of the Cerebral Organoid Glioma 'GLICO' Model for Screening Applications

Glioblastoma, a grade IV astrocytoma, is regarded as the most aggressive primary brain tumour with an overall median survival of 16.0 months following the standard treatment regimen of surgical resection, followed by radiotherapy and chemotherapy with temozolomide. Despite such intensive treatment, the tumour almost invariably recurs. This poor prognosis has most commonly been attributed to the initiation, propagation, and differentiation of cancer stem cells. Despite the unprecedented advances in biomedical research over the last decade, the current in vitro models are limited at preserving the inter- and intra-tumoural heterogeneity of primary tumours. The ability to understand and manipulate complex cancers such as glioblastoma requires disease models to be clinically and translationally relevant and encompass the cellular heterogeneity of such cancers. Therefore, brain cancer research models need to aim to recapitulate glioblastoma stem cell function, whilst remaining amenable for analysis. Fortunately, the recent development of 3D cultures has overcome some of these challenges, and cerebral organoids are emerging as cutting-edge tools in glioblastoma research. The opportunity to generate cerebral organoids via induced pluripotent stem cells, and to perform co-cultures with patient-derived cancer stem cells (GLICO model), has enabled the analysis of cancer development in a context that better mimics brain tissue architecture. In this article, we review the recent literature on the use of patient-derived glioblastoma organoid models and their applicability for drug screening, as well as provide a potential workflow for screening using the GLICO model. The proposed workflow is practical for use in most laboratories with accessible materials and equipment, a good first pass, and no animal work required. This workflow is also amenable for analysis, with separate measures of invasion, growth, and viability.

Coupling solid and fluid stresses with brain tumour growth and white matter tract deformations in a neuroimaging-informed model

Brain tumours are among the deadliest types of cancer, since they display a strong ability to invade the surrounding tissues and an extensive resistance to common therapeutic treatments. It is therefore important to reproduce the heterogeneity of brain microstructure through mathematical and computational models, that can provide powerful instruments to investigate cancer progression. However, only a few models include a proper mechanical and constitutive description of brain tissue, which instead may be relevant to predict the progression of the pathology and to analyse the reorganization of healthy tissues occurring during tumour growth and, possibly, after surgical resection. Motivated by the need to enrich the description of brain cancer growth through mechanics, in this paper we present a mathematical multiphase model that explicitly includes brain hyperelasticity. We find that our mechanical description allows to evaluate the impact of the growing tumour mass on the surrounding healthy tissue, quantifying the displacements, deformations, and stresses induced by its proliferation. At the same time, the knowledge of the mechanical variables may be used to model the stress-induced inhibition of growth, as well as to properly modify the preferential directions of white matter tracts as a consequence of deformations caused by the tumour. Finally, the simulations of our model are implemented in a personalized framework, which allows to incorporate the realistic brain geometry, the patient-specific diffusion and permeability tensors reconstructed from imaging data and to modify them as a consequence of the mechanical deformation due to cancer growth.

Simulating the behaviour of glioblastoma multiforme based on patient MRI during treatments

Glioblastoma multiforme is a brain cancer that still shows poor prognosis for patients despite the active research for new treatments. In this work, the goal is to model and simulate the evolution of tumour associated angiogenesis and the therapeutic response to glioblastoma multiforme. Multiple phenomena are modelled in order to fit different biological pathways, such as the cellular cycle, apoptosis, hypoxia or angiogenesis. This leads to a nonlinear system with 4 equations and 4 unknowns: the density of tumour cells, the [Formula: see text] concentration, the density of endothelial cells and the vascular endothelial growth factor concentration. This system is solved numerically on a mesh fitting the geometry of the brain and the tumour of a patient based on a 2D slice of MRI. We show that our numerical scheme is positive, and we give the energy estimates on the discrete solution to ensure its existence. The numerical scheme uses nonlinear control volume finite elements in space and is implicit in time. Numerical simulations have been done using the different standard treatments: surgery, chemotherapy and radiotherapy, in order to conform to the behaviour of a tumour in response to treatments according to empirical clinical knowledge. We find that our theoretical model exhibits realistic behaviours.

Inducing Biomechanical Heterogeneity in Brain Tumor Modeling by MR Elastography: Effects on Tumor Growth, Vascular Density and Delivery of Therapeutics

Simple Summary

Biomechanical forces aggravate brain tumor progression. In this study, magnetic resonance elastography (MRE) is employed to extract tissue biomechanical properties from five glioblastoma patients and a healthy subject, and data are incorporated in a mathematical model that simulates tumor growth. Mathematical modeling enables further understanding of glioblastoma development and allows patient-specific predictions for tumor vascularity and delivery of drugs. Incorporating MRE data results in a more realistic intratumoral distribution of mechanical stress and anisotropic tumor growth and a better description of subsequent events that are closely related to the development of stresses, including heterogeneity of the tumor vasculature and intrapatient variations in tumor perfusion and delivery of drugs.

Abstract

The purpose of this study is to develop a methodology that incorporates a more accurate assessment of tissue mechanical properties compared to current mathematical modeling by use of biomechanical data from magnetic resonance elastography. The elastography data were derived from five glioblastoma patients and a healthy subject and used in a model that simulates tumor growth, vascular changes due to mechanical stresses and delivery of therapeutic agents. The model investigates the effect of tumor-specific biomechanical properties on tumor anisotropic growth, vascular density heterogeneity and chemotherapy delivery. The results showed that including elastography data provides a more realistic distribution of the mechanical stresses in the tumor and induces anisotropic tumor growth. Solid stress distribution differs among patients, which, in turn, induces a distinct functional vascular density distribution—owing to the compression of tumor vessels—and intratumoral drug distribution for each patient. In conclusion, incorporating elastography data results in a more accurate calculation of intratumoral mechanical stresses and enables a better mathematical description of subsequent events, such as the heterogeneous development of the tumor vasculature and intrapatient variations in tumor perfusion and delivery of drugs.

A phenotype-structured model to reproduce the avascular growth of a tumor and its interaction with the surrounding environment

We here propose a one-dimensional spatially explicit phenotype-structured model to analyze selected aspects of avascular tumor progression. In particular, our approach distinguishes viable and necrotic cell fractions. The metabolically active part of the disease is, in turn, differentiated according to a continuous trait, that identifies cell variants with different degrees of motility and proliferation potential. A parabolic partial differential equation (PDE) then governs the spatio-temporal evolution of the phenotypic distribution of active cells within the host tissue. In this respect, active tumor agents are allowed to duplicate, move upon haptotactic and pressure stimuli, and eventually undergo necrosis. The mutual influence between the emerging malignancy and its environment (in terms of molecular landscape) is implemented by coupling the evolution law of the viable tumor mass with a parabolic PDE for oxygen kinetics and a differential equation that accounts for local consumption of extracellular matrix (ECM) elements. The resulting numerical realizations reproduce tumor growth and invasion in a number scenarios that differ for cell properties (i.e., individual migratory behavior, duplication and mutation potential) and environmental conditions (i.e., level of tissue oxygenation and homogeneity in the initial matrix profile). In particular, our simulations show that, in all cases, more mobile cell variants occupy the front edge of the tumor, whereas more proliferative clones are selected at the more internal regions. A necrotic core constantly occupies the bulk of the mass due to nutrient deprivation. This work may eventually suggest some biomedical strategies to partially reduce tumor aggressiveness, i.e., to enhance necrosis of malignant tissue and to promote the presence of more proliferative cell phenotypes over more invasive ones.

Atorvastatin-mediated rescue of cancer-related cognitive changes in combined anticancer therapies

Acute administration of trastuzumab (TZB) may induce various forms of cognitive impairment. These cancer-related cognitive changes (CRCC) are regulated by an adverse biological process involving cancer stem cells (CSCs) and IL-6. Recent studies have reported that atorvastatin (ATV) may change the dynamic of cognitive impairment in a combination (TZB+ATV) therapy. In this study, we investigate the mutual interactions between cancer stem cells and the tumor cells that facilitate cognitive impairment during long term TZB therapy by developing a mathematical model that involves IL-6 and the key apoptotic regulation. These include the densities of tumor cells and CSCs, and the concentrations of intracellular signaling molecules (NFκB, Bcl-2, BAX). We apply the mathematical model to a single or combination (ATV+TZB) therapy used in the experiments to demonstrate that the CSCs can enhance CRCC by secreting IL-6 and ATV may interfere the whole regulation. We show that the model can both reproduce the major experimental observation on onset and prevention of CRCC, and suggest several important predictions to guide future experiments with the goal of the development of new anti-tumor and anti-CRCC strategies. Moreover, using this model, we investigate the fundamental mechanism of onset of cognitive impairment in TZB-treated patients and the impact of alternating therapies on the anti-tumor efficacy and intracellular response to different treatment schedules.

A conventional drug, trastuzumab (TZB), was shown to be an effective weapon in killing cancer cells in brain. However, long term treatment of TZB increases the proportion of cancer stem cells (CSCs) in the tumour microenvironment (TME) and induces up-regulation of pro-tumoral molecules such as IL-6 in TME. These cancer cells then become more resistant to this chemotherapy through the IL-mediated up-regulation of NFκB and CSCs. More importantly, these changes in TME result in a serious side effect, cognitive impairment called cancer-related cognitive changes (CRCC). The detailed mechanism of CRCC is still poorly understood. However, cancer patients with chemotherapy-induced cognitive impairment can have long-term or delayed mental changes. In this study, we investigated the fundamental mechanism of CRCC in cancer patients based on experiments and a mathematical model that describes how tumor cells interact with CSCs in response to chemo drugs. In particular, we investigate how TZB-induced CSCs with modified IL-6 landscapes shape the cognitive functions in cancer patients. We showed that the combination treatment with another drug, atorvastatin (ATV), can abrogate the TZB-induced CRCC and enhance the survival probability of cancer patients by synergistic anti-tumor effect. We demonstrate that the cognitive functions and survival rates in cancer patients depend on the apoptotic signaling pathways via the critical communication and IL-6 landscapes of stimulated CTCs.

Mathematical model of STAT signalling pathways in cancer development and optimal control approaches

In various diseases, the STAT family display various cellular controls over various challenges faced by the immune system and cell death programs. In this study, we investigate how an intracellular signalling network (STAT1, STAT3, Bcl-2 and BAX) regulates important cellular states, either anti-apoptosis or apoptosis of cancer cells. We adapt a mathematical framework to illustrate how the signalling network can generate a bi-stability condition so that it will induce either apoptosis or anti-apoptosis status of tumour cells. Then, we use this model to develop several anti-tumour strategies including IFN-β infusion. The roles of JAK-STATs signalling in regulation of the cell death program in cancer cells and tumour growth are poorly understood. The mathematical model unveils the structure and functions of the intracellular signalling and cellular outcomes of the anti-tumour drugs in the presence of IFN-β and JAK stimuli. We identify the best injection order of IFN-β and DDP among many possible combinations, which may suggest better infusion strategies of multiple anti-cancer agents at clinics. We finally use an optimal control theory in order to maximize anti-tumour efficacy and minimize administrative costs. In particular, we minimize tumour volume and maximize the apoptotic potential by minimizing the Bcl-2 concentration and maximizing the BAX level while minimizing total injection amount of both IFN-β and JAK2 inhibitors (DDP).

Hydrogel-Based Spheroid Models of Glioblastoma for Drug Screening Applications

Glioblastoma multiforme (GBM) is the most aggressive brain tumor, with median patient survival of 12-15 months even after treatment. To facilitate basic research as well as treatment development, bioengineered GBM models that adequately recapitulate aspects of the in vivo tumor microenvironment are greatly needed. Multicellular spheroids are a well-accepted model in tumor biology as well as drug screening because they recapitulate many of the solid tumor characteristics, such as hypoxic core and cell-cell communication. There are multiple approaches for growing GBM cells into tumor spheroids - non-adherent plastic dishes, hanging drop, bioreactors, and hydrogels, amongst others. Suspension spheroid models offer ease of growth, uniformity, and overall lower cost, but neglect the cell-matrix interactions, while hydrogel-based spheroids capture cell-matrix interactions and allow co-cultures with stromal cells. In this review, we summarize various approaches to fabricate GBM spheroid models as well as GBM spheroid characteristics and chemotherapeutic responsiveness as a function of hydrogel matrix encapsulation and properties, in order to advance therapies.

Multiscale modeling of glioma pseudopalisades: contributions from the tumor microenvironment

Gliomas are primary brain tumors with a high invasive potential and infiltrative spread. Among them, glioblastoma multiforme (GBM) exhibits microvascular hyperplasia and pronounced necrosis triggered by hypoxia. Histological samples showing garland-like hypercellular structures (so-called pseudopalisades) centered around the occlusion site of a capillary are typical for GBM and hint on poor prognosis of patient survival. We propose a multiscale modeling approach in the kinetic theory of active particles framework and deduce by an upscaling process a reaction-diffusion model with repellent pH-taxis. We prove existence of a unique global bounded classical solution for a version of the obtained macroscopic system and investigate the asymptotic behavior of the solution. Moreover, we study two different types of scaling and compare the behavior of the obtained macroscopic PDEs by way of simulations. These show that patterns (not necessarily of Turing type), including pseudopalisades, can be formed for some parameter ranges, in accordance with the tumor grade. This is true when the PDEs are obtained via parabolic scaling (undirected tissue), while no such patterns are observed for the PDEs arising by a hyperbolic limit (directed tissue). This suggests that brain tissue might be undirected - at least as far as glioma migration is concerned. We also investigate two different ways of including cell level descriptions of response to hypoxia and the way they are related .

Predicting the results of competition between two breast cancer lines grown in 3-D spheroid culture

This study develops a novel model of a consumer-resource system with mobility included, in order to explain a novel experiment of competition between two breast cancer cell lines grown in 3D in vitro spheroid culture. The model reproduces observed differences in monoculture, such as overshoot phenomena and final size. It also explains both theoretically and through simulation the inevitable triumph of the same cell line in co-culture, independent of initial conditions. The mobility of one cell line (MDA-MB-231) is required to explain both the success and the rapidity with which that species dominates the population and drives the other species (MCF-7) to extinction. It is shown that mobility directly interferes with the other species and that the cost of that mobility is in resource usage rate.

In vitro biomimetic models for glioblastoma-a promising tool for drug response studies

The poor response of glioblastoma to current treatment protocols is a consequence of its intrinsic drug resistance. Resistance to chemotherapy is primarily associated with considerable cellular heterogeneity, and plasticity of glioblastoma cells, alterations in gene expression, presence of specific tumor microenvironment conditions and blood-brain barrier. In an attempt to successfully overcome chemoresistance and better understand the biological behavior of glioblastoma, numerous tri-dimensional (3D) biomimetic models were developed in the past decade. These novel advanced models are able to better recapitulate the spatial organization of glioblastoma in a real time, therefore providing more realistic and reliable evidence to the response of glioblastoma to therapy. Moreover, these models enable the fine-tuning of different tumor microenvironment conditions and facilitate studies on the effects of the tumor microenvironment on glioblastoma chemoresistance. This review outlines current knowledge on the essence of glioblastoma chemoresistance and describes the progress achieved by 3D biomimetic models. Moreover, comprehensive literature assessment regarding the influence of 3D culturing and microenvironment mimicking on glioblastoma gene expression and biological behavior is also provided. The contribution of the blood-brain barrier as well as the blood-tumor barrier to glioblastoma chemoresistance is also reviewed from the perspective of 3D biomimetic models. Finally, the role of mathematical models in predicting 3D glioblastoma behavior and drug response is elaborated. In the future, technological innovations along with mathematical simulations should create reliable 3D biomimetic systems for glioblastoma research that should facilitate the identification and possibly application in preclinical drug testing and precision medicine.

Digital Twins for Tissue Culture Techniques—Concepts, Expectations, and State of the Art

Techniques to provide in vitro tissue culture have undergone significant changes during the last decades, and current applications involve interactions of cells and organoids, three-dimensional cell co-cultures, and organ/body-on-chip tools. Efficient computer-aided and mathematical model-based methods are required for efficient and knowledge-driven characterization, optimization, and routine manufacturing of tissue culture systems. As an alternative to purely experimental-driven research, the usage of comprehensive mathematical models as a virtual in silico representation of the tissue culture, namely a digital twin, can be advantageous. Digital twins include the mechanistic of the biological system in the form of diverse mathematical models, which describe the interaction between tissue culture techniques and cell growth, metabolism, and the quality of the tissue. In this review, current concepts, expectations, and the state of the art of digital twins for tissue culture concepts will be highlighted. In general, DT’s can be applied along the full process chain and along the product life cycle. Due to the complexity, the focus of this review will be especially on the design, characterization, and operation of the tissue culture techniques.

Cell – extracellular matrix interaction in glioma growth. In silico model

The study aims to investigate the role of viscoelastic interactions between cells and extracellular matrix (ECM) in avascular tumor growth. Computer simulations of glioma multicellular tumor spheroid (MTS) growth are being carried out for various conditions. The calculations are based on a continuous model, which simulates oxygen transport into MTS; transitions between three cell phenotypes, cell transport, conditioned by hydrostatic forces in cell–ECM composite system, cell motility and cell adhesion. Visco-elastic cell aggregation and elastic ECM scaffold represent two compressible constituents of the composite. Cell–ECM interactions form a Transition Layer on the spheroid surface, where mechanical characteristics of tumor undergo rapid transition. This layer facilitates tumor progression to a great extent. The study demonstrates strong effects of ECM stiffness, mechanical deformations of the matrix and cell–cell adhesion on tumor progression. The simulations show in particular that at certain, rather high degrees of matrix stiffness a formation of distant multicellular clusters takes place, while at further increase of ECM stiffness subtumors do not form. The model also illustrates to what extent mere mechanical properties of cell–ECM system may contribute into variations of glioma invasion scenarios.

A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis

We propose a model for glioma patterns in a microlocal tumor environment under the influence of acidity, angiogenesis, and tissue anisotropy. The bottom-up model deduction eventually leads to a system of reaction–diffusion–taxis equations for glioma and endothelial cell population densities, of which the former infers flux limitation both in the self-diffusion and taxis terms. The model extends a recently introduced (Kumar, Li and Surulescu, 2020) description of glioma pseudopalisade formation with the aim of studying the effect of hypoxia-induced tumor vascularization on the establishment and maintenance of these histological patterns which are typical for high-grade brain cancer. Numerical simulations of the population level dynamics are performed to investigate several model scenarios containing this and further effects.

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.

Characterization of multicellular breast tumor spheroids using image data-driven biophysical mathematical modeling

Multicellular tumor spheroid (MCTS) systems provide an in vitro cell culture model system which mimics many of the complexities of an in vivo solid tumor and tumor microenvironment, and are often used to study cancer cell growth and drug efficacy. Here, we present a coupled experimental-computational framework to estimate phenotypic growth and biophysical tumor microenvironment properties. This novel framework utilizes standard microscopy imaging of MCTS systems to drive a biophysical mathematical model of MCTS growth and mechanical interactions. By extending our previous in vivo mechanically-coupled reaction–diffusion modeling framework we developed a microscopy image processing framework capable of mechanistic characterization of MCTS systems. Using MDA-MB-231 breast cancer MCTS, we estimated biophysical parameters of cellular diffusion, rate of cellular proliferation, and cellular tractions forces. We found significant differences in these model-based biophysical parameters throughout the treatment time course between untreated and treated MCTS systems, whereas traditional size-based morphometric parameters were inconclusive. The proposed experimental-computational framework estimates mechanistic MCTS growth and invasion parameters with significant potential to assist in better and more precise assessment of in vitro drug efficacy through the development of computational analysis methodologies for three-dimensional cell culture systems to improve the development and evaluation of antineoplastic drugs.

Mathematical modeling of PDGF-driven glioma reveals the dynamics of immune cells infiltrating into tumors

Background: Tumor-infiltrated immune cells compose a significant component of many cancers. They have been observed to have contradictory impacts on tumors. Although the primary reasons for these observations remain elusive, it is important to understand how immune cells infiltrating into tumors is regulated. Recently our group conducted a series of experimental studies, which showed that muIDH1 gliomas have a significant global reduction of immune cells and suggested that the longer survival time of mice with CIMP gliomas may be due to the IDH mutation and its effect on reducing of the tumor-infiltrated immune cells. However, to comprehend how IDH1 mutants regulate infiltration of immune cells into gliomas and how they affect the aggressiveness of gliomas, it is necessary to integrate our experimental data into a dynamical system to acquire a much deeper understanding of subtle regulation of immune cell infiltration. Methods: The method is integration of mathematical modeling and experiments. According to mass conservation laws and assumption that immune cells migrate into the tumor site along a chemotactic gradient field, a mathematical model is formulated. Parameters are estimated from our experiments. Numerical methods are developed to solve the problem. Numerical predictions are compared with experimental results. Results: Our analysis shows that the net rate of increase of immune cells infiltrated into the tumor is approximately proportional to the 4/5 power of the chemoattractant production rate, and it is an increasing function of time while the percentage of immune cells infiltrated into the tumor is a decreasing function of time. Our model predicts that wtIDH1 mice will survive longer if the immune cells are blocked by reducing chemotactic coefficient. For more aggressive gliomas, our model shows that there is little difference in their survivals between wtIDH1 and muIDH1 tumors, and the percentage of immune cells infiltrated into the tumor is much lower. These predictions are verified by our experimental results. In addition, wtIDH1 and muIDH1 can be quantitatively distinguished by their chemoattractant production rates, and the chemotactic coefficient determines possibilities of immune cells migration along chemoattractant gradient fields. Conclusions: The chemoattractant gradient field produced by tumor cells may facilitate immune cells migration to the tumor cite. The chemoattractant production rate may be utilized to classify wtIDH1 and muIDH1 tumors. The dynamics of immune cells infiltrating into tumors is largely determined by tumor cell chemoattractant production rate and chemotactic coefficient.

Integrated Biophysical Modeling and Image Analysis: Application to Neuro-Oncology

Central nervous system (CNS) tumors come with vastly heterogeneous histologic, molecular, and radiographic landscapes, rendering their precise characterization challenging. The rapidly growing fields of biophysical modeling and radiomics have shown promise in better characterizing the molecular, spatial, and temporal heterogeneity of tumors. Integrative analysis of CNS tumors, including clinically acquired multi-parametric magnetic resonance imaging (mpMRI) and the inverse problem of calibrating biophysical models to mpMRI data, assists in identifying macroscopic quantifiable tumor patterns of invasion and proliferation, potentially leading to improved (a) detection/segmentation of tumor subregions and (b) computer-aided diagnostic/prognostic/predictive modeling. This article presents a summary of (a) biophysical growth modeling and simulation,(b) inverse problems for model calibration, (c) these models' integration with imaging workflows, and (d) their application to clinically relevant studies. We anticipate that such quantitative integrative analysis may even be beneficial in a future revision of the World Health Organization (WHO) classification for CNS tumors, ultimately improving patient survival prospects.

Towards Personalized Diagnosis of Glioblastoma in Fluid-Attenuated Inversion Recovery (FLAIR) by Topological Interpretable Machine Learning

Glioblastoma multiforme (GBM) is a fast-growing and highly invasive brain tumor, which tends to occur in adults between the ages of 45 and 70 and it accounts for 52 percent of all primary brain tumors. Usually, GBMs are detected by magnetic resonance images (MRI). Among MRI, a fluid-attenuated inversion recovery (FLAIR) sequence produces high quality digital tumor representation. Fast computer-aided detection and segmentation techniques are needed for overcoming subjective medical doctors (MDs) judgment. This study has three main novelties for demonstrating the role of topological features as new set of radiomics features which can be used as pillars of a personalized diagnostic systems of GBM analysis from FLAIR. For the first time topological data analysis is used for analyzing GBM from three complementary perspectives—tumor growth at cell level, temporal evolution of GBM in follow-up period and eventually GBM detection. The second novelty is represented by the definition of a new Shannon-like topological entropy, the so-called Generator Entropy. The third novelty is the combination of topological and textural features for training automatic interpretable machine learning. These novelties are demonstrated by three numerical experiments. Topological Data Analysis of a simplified 2D tumor growth mathematical model had allowed to understand the bio-chemical conditions that facilitate tumor growth—the higher the concentration of chemical nutrients the more virulent the process. Topological data analysis was used for evaluating GBM temporal progression on FLAIR recorded within 90 days following treatment completion and at progression. The experiment had confirmed that persistent entropy is a viable statistics for monitoring GBM evolution during the follow-up period. In the third experiment we developed a novel methodology based on topological and textural features and automatic interpretable machine learning for automatic GBM classification on FLAIR. The algorithm reached a classification accuracy up to 97%.

Morphological quantification of proliferation-to-invasion transition in tumor spheroids

BACKGROUND

Metastasis determines the lethality of cancer. In most clinical cases, patients are able to live with tumor proliferation before metastasis. Thus, the transition from tumor proliferation to metastasis/invasion is essential. However, the mechanism is still unclear and especially, the proliferation-to-metastasis/invasion transition point has not been well defined. Therefore, quantitative characterization of this transition is urgently needed.

METHODS

We have successfully developed a home-built living-cell incubation system combined with an inverted optical microscope, and a systematic, quantitative approach to describing the major characteristic morphological parameters for the identification of the critical transition points for tumor-cell spheroids in a collagen fiber scaffold.

RESULTS

The system focuses on in vitro tumor modeling, e.g. the development of tumor-cell spheroids in a collagen fiber scaffold and the monitoring of cell transition from proliferation to invasion. By applying this approach to multiple tumor spheroid models, such as U87 (glioma tumor), H1299 (lung cancer), and MDA-MB-231 (breast cancer) cells, we have obtained quantitative morphological references to evaluate the proliferation-to-invasion transition time, as well as differentiating the invasion potential of tumor cells upon environmental changes, i.e. drug application.

CONCLUSIONS

Our quantitative approach provides a feasible clarification for the proliferation-to-invasion transition of in vitro tumor models (spheroids). Moreover, the transition time is a useful reference for the invasive potential of tumor cells.

GENERAL SIGNIFICANCE

This quantitative approach is potentially applicable to primary tumor cells, and thus has potential applications in the fields of cancer metastasis investigations and clinical diagnostics.

Three-dimensional tumor growth in time-varying chemical fields: a modeling framework and theoretical study

Background

Contemporary biological observations have revealed a large variety of mechanisms acting during the expansion of a tumor. However, there are still many qualitative and quantitative aspects of the phenomenon that remain largely unknown. In this context, mathematical and computational modeling appears as an invaluable tool providing the means for conducting in silico experiments, which are cheaper and less tedious than real laboratory experiments.

Results

This paper aims at developing an extensible and computationally efficient framework for in silico modeling of tumor growth in a 3-dimensional, inhomogeneous and time-varying chemical environment. The resulting model consists of a set of mathematically derived and algorithmically defined operators, each one addressing the effects of a particular biological mechanism on the state of the system. These operators may be extended or re-adjusted, in case a different set of starting assumptions or a different simulation scenario needs to be considered.

Conclusion

In silico modeling provides an alternative means for testing hypotheses and simulating scenarios for which exact biological knowledge remains elusive. However, finer tuning of pertinent methods presupposes qualitative and quantitative enrichment of available biological evidence. Validation in a strict sense would further require comprehensive, case-specific simulations and detailed comparisons with biomedical observations.

A Biomechanical Model of Tumor-Induced Intracranial Pressure and Edema in Brain Tissue

Brain tumor growth and tumor-induced edema result in increased intracranial pressure (ICP), which, in turn, is responsible for conditions as benign as headaches and vomiting or as severe as seizures, neurological damage, or even death. Therefore, it has been hypothesized that tracking ICP dynamics may offer improved prognostic potential in terms of early detection of brain cancer and better delimitation of the tumor boundary. However, translating such theory into clinical practice remains a challenge, in part because of an incomplete understanding of how ICP correlates with tumor grade. Here, we propose a multiphase mixture model that describes the biomechanical response of healthy brain tissue-in terms of changes in ICP and edema-to a growing tumor. The model captures ICP dynamics within the diseased brain and accounts for the ability/inability of healthy tissue to compensate for this pressure. We propose parameter regimes that distinguish brain tumors by grade, thereby providing critical insight into how ICP dynamics vary by severity of disease. In particular, we offer an explanation for clinically observed phenomena, such as a lack of symptoms in low-grade glioma patients versus a rapid onset of symptoms in those with malignant tumors. Our model also takes into account the effects tumor-derived proteases may have on ICP levels and the extent of tumor invasion. This work represents an important first step toward understanding the mechanisms that underlie the onset of edema and ICP in cancer-afflicted brains. Continued modeling effort in this direction has the potential to make an impact in the field of brain cancer diagnostics.

Strategies in regulating glioblastoma signaling pathways and anti-invasion therapy

Glioblastoma multiforme is one of the most invasive type of glial tumors, which rapidly grows and commonly spreads into nearby brain tissue. It is a devastating brain cancer that often results in death within approximately 12 to 15 months after diagnosis. In this work, optimal control theory was applied to regulate intracellular signaling pathways of miR-451–AMPK–mTOR–cell cycle dynamics via glucose and drug intravenous administration infusions. Glucose level is controlled to activate miR-451 in the up-stream pathway of the model. A potential drug blocking the inhibitory pathway of mTOR by AMPK complex is incorporated to explore regulation of the down-stream pathway to the cell cycle. Both miR-451 and mTOR levels are up-regulated inducing cell proliferation and reducing invasion in the neighboring tissues. Concomitant and alternating glucose and drug infusions are explored under various circumstances to predict best clinical outcomes with least administration costs.

Role of tumor-associated neutrophils in regulation of tumor growth in lung cancer development: A mathematical model

Neutrophils display rapid and potent innate immune responses in various diseases. Tumor-associated neutrophils (TANs) however either induce or overcome immunosuppressive functions of the tumor microenvironment through complex tumor-stroma crosstalk. We developed a mathematical model to address the question of how phenotypic alterations between tumor suppressive N1 TANS, and tumor promoting N2 TANs affect nonlinear tumor growth in a complex tumor microenvironment. The model provides a visual display of the complex behavior of populations of TANs and tumors in response to various TGF-β and IFN-β stimuli. In addition, the effect of anti-tumor drug administration is incorporated in the model in an effort to achieve optimal anti-tumor efficacy. The simulation results from the mathematical model were in good agreement with experimental data. We found that the N2-to-N1 ratio (N21R) index is positively correlated with aggressive tumor growth, suggesting that this may be a good prognostic factor. We also found that the antitumor efficacy increases when the relative ratio (Dap) of delayed apoptotic cell death of N1 and N2 TANs is either very small or relatively large, providing a basis for therapeutically targeting prometastatic N2 TANs.

Differentiation of Glioblastoma and Solitary Brain Metastasis by Gradient of Relative Cerebral Blood Volume in the Peritumoral Brain Zone Derived from Dynamic Susceptibility Contrast Perfusion Magnetic Resonance Imaging

OBJECTIVE

The purpose of our study was to evaluate the efficacy of the relative cerebral blood volume (rCBV) gradient in the peritumoral brain zone (PBZ)-the difference in the rCBV values from the area closest to the enhancing lesion to the area closest to the healthy white matter-in differentiating glioblastoma (GB) from solitary brain metastasis (MET).

METHODS

A 3.0-T magnetic resonance imaging (MRI) machine was used to perform dynamic susceptibility contrast perfusion MRI (DSC-MRI) on 43 patients with a solitary brain tumor (24 GB, 19 MET). The rCBV ratios were acquired by DSC-MRI data in 3 regions of the PBZ (near the enhancing tumor, G1; intermediate distance from the enhancing tumor, G2; far from the enhancing tumor, G3). The maximum rCBV ratios in the PBZ (rCBVp) and the enhancing tumor were also calculated, respectively. The perfusion parameters were evaluated using the nonparametric Mann-Whitney test. The sensitivity, specificity, accuracy, and the area under the receiver operating characteristic curve were identified.

RESULTS

The rCBVp ratios and rCBV gradient in the PBZ were significantly higher in GB compared with MET (P < 0.05 for both rCBVp ratios and rCBV gradient). The threshold values of 0.50 or greater for rCBVp ratios provide sensitivity and specificity of 57.69% and 79.17%, respectively, for differentiation of GB from MET. Compared with rCBVp ratios, rCBV gradient had higher sensitivity (94.44%) and specificity (91.67%) using the threshold value of greater than 0.06.

CONCLUSIONS

The parameter of rCBV gradient derived from DSC-MRI in the PBZ seems to be the most efficient parameter to differentiate GB from METs.

Modeling three-dimensional invasive solid tumor growth in heterogeneous microenvironment under chemotherapy

A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid three-dimensional (3D) computational model that integrates pharmacokinetic model, continuum diffusion-reaction model and discrete cell automaton model to investigate 3D invasive solid tumor growth in heterogeneous microenvironment under chemotherapy. Specifically, we consider the effects of heterogeneous environment on drug diffusion, tumor growth, invasion and the drug-tumor interaction on individual cell level. We employ the hybrid model to investigate the evolution and growth dynamics of avascular invasive solid tumors under different chemotherapy strategies. Our simulations indicate that constant dosing is generally more effective in suppressing primary tumor growth than periodic dosing, due to the resulting continuous high drug concentration. In highly heterogeneous microenvironment, the malignancy of the tumor is significantly enhanced, leading to inefficiency of chemotherapies. The effects of geometrically-confined microenvironment and non-uniform drug dosing are also investigated. Our computational model, when supplemented with sufficient clinical data, could eventually lead to the development of efficient in silico tools for prognosis and treatment strategy optimization.

Quantifying cancer cell receptors with paired-agent fluorescent imaging: a novel method to account for tissue optical property effects

Dynamic fluorescence imaging approaches can be used to estimate the concentration of cell surface receptors in vivo. Kinetic models are used to generate the final estimation by taking the targeted imaging agent concentration as a function of time. However, tissue absorption and scattering properties cause the final readout signal to be on a different scale than the real fluorescent agent concentration. In paired-agent imaging approaches, simultaneous injection of a suitable control imaging agent with a targeted one can account for non-specific uptake and retention of the targeted agent. Additionally, the signal from the control agent can be a normalizing factor to correct for tissue optical property differences. In this study, the kinetic model used for paired-agent imaging analysis (i.e., simplified reference tissue model) is modified and tested in simulation and experimental data in a way that accounts for the scaling correction within the kinetic model fit to the data to ultimately extract an estimate of the targeted biomarker concentration.

Engineered 3D tumour model for study of glioblastoma aggressiveness and drug evaluation on a detachably assembled microfluidic device

3D models of tumours have emerged as an advanced technique in pharmacology and tumour cell biology, in particular for studying malignant tumours such as glioblastoma multiforme (GBM). Herein, we developed a 3D GBM model on a detachably assembled microfluidic device, which could be used to study GBM aggressiveness and for anti-GBM drug testing. Fundamental characteristics of the GBM microenvironment in terms of 3D tissue organisation, extracellular matrices and blood flow were reproduced in vitro by serial manipulations in the integrated microfluidic device, including GBM spheroid self-assembly, embedding in a collagen matrix, and continuous perfusion culture, respectively. We could realize multiple spheroids parallel manipulation, whilst, compartmentalized culture, in a highly flexible manner. This method facilitated investigations into the viability, proliferation, invasiveness and phenotype transition of GBM in a 3D microenvironment and under continuous stimulation by drugs. Anti-invasion effect of resveratrol, a naturally isolated polyphenol, was innovatively evaluated using this in vitro 3D GBM model. Temozolomide and the combination of resveratrol and temozolomide were also evaluated as control. This scalable model enables research into GBM in a more physiologically relevant microenvironment, which renders it promising for use in translational or personalised medicine to examine the impact of, or identify combinations of, therapeutic agents.

Mechanical confinement via a PEG/Collagen interpenetrating network inhibits behavior characteristic of malignant cells in the triple negative breast cancer cell line MDA.MB.231

To decouple the effects of collagen fiber density and network mechanics on cancer cell behavior, we describe a highly tunable in vitro 3D interpenetrating network (IPN) consisting of a primary fibrillar collagen network reinforced by a secondary visible light-mediated thiol-ene poly(ethylene glycol) (PEG) network. This PEG/Collagen IPN platform is cytocompatible, inherently bioactive via native cellular adhesion sites, and mechanically tunable over several orders of magnitude-mimicking both healthy and cancerous breast tissue. Furthermore, we use the PEG/Collagen IPN platform to investigate the effect of mechanical confinement on cancer cell behavior as it is hypothesized that cells within tumors that have yet to invade into the surrounding tissue experience mechanical confinement. We find that mechanical confinement via the IPN impairs behavior characteristic of malignant cells (i.e., viability, proliferation, and cellular motility) in the triple negative breast cancer cell line MDA.MB.231, and is more effective than removal of soluble growth signals. The PEG/Collagen IPN platform is a useful tool for studying mechanotransductive signaling pathways and motivates further investigation into the role of mechanical confinement in cancer progression.

STATEMENT OF SIGNIFICANCE

In this study, we have developed, optimized, and applied a novel 3D in vitro cell culture platform composed of an interpenetrating network (IPN) that is both mechanically tunable and inherently bioactive. The IPN consists of a primary fibrillar collagen type-1 network reinforced by a secondary thiol-ene poly(ethylene glycol) (PEG) network. The IPNs are formed via a novel strategy in which cell-laden collagen gels are formed first, and soluble PEG monomers are added later and crosslinked via visible light. This approach ensures that the collagen gels contain a fibrillar architecture similar to the collagen architecture present in vivo. We applied our IPN platform to study the effect of mechanical confinement on cancer cell behavior and found that it inhibits malignant-like behavior.

Towards patient-specific modeling of brain tumor growth and formation of secondary nodes guided by DTI-MRI

Previous studies to simulate brain tumor progression, often investigate either temporal changes in cancer cell density or the overall tissue-level growth of the tumor mass. Here, we developed a computational model to bridge these two approaches. The model incorporates the tumor biomechanical response at the tissue level and accounts for cellular events by modeling cancer cell proliferation, infiltration to surrounding tissues, and invasion to distant locations. Moreover, acquisition of high resolution human data from anatomical magnetic resonance imaging, diffusion tensor imaging and perfusion imaging was employed within the simulations towards a realistic and patient specific model. The model predicted the intratumoral mechanical stresses to range from 20 to 34 kPa, which caused an up to 4.5 mm displacement to the adjacent healthy tissue. Furthermore, the model predicted plausible cancer cell invasion patterns within the brain along the white matter fiber tracts. Finally, by varying the tumor vascular density and its invasive outer ring thickness, our model showed the potential of these parameters for guiding the timing (83–90 days) of cancer cell distant invasion as well as the number (0–2 sites) and location (temportal and/or parietal lobe) of the invasion sites.

The biology and mathematical modelling of glioma invasion: a review

Adult gliomas are aggressive brain tumours associated with low patient survival rates and limited life expectancy. The most important hallmark of this type of tumour is its invasive behaviour, characterized by a markedly phenotypic plasticity, infiltrative tumour morphologies and the ability of malignant progression from low- to high-grade tumour types. Indeed, the widespread infiltration of healthy brain tissue by glioma cells is largely responsible for poor prognosis and the difficulty of finding curative therapies. Meanwhile, mathematical models have been established to analyse potential mechanisms of glioma invasion. In this review, we start with a brief introduction to current biological knowledge about glioma invasion, and then critically review and highlight future challenges for mathematical models of glioma invasion.

THE PROHOROV METRIC FRAMEWORK AND AGGREGATE DATA INVERSE PROBLEMS FOR RANDOM PDEs

We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [24, 5, 12, 28, 16]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random PDEs.

The role of cerebral blood flow gradient in peritumoral edema for differentiation of glioblastomas from solitary metastatic lesions

OBJECTIVE

Differentiation of glioblastomas from solitary brain metastases using conventional MRI remains an important unsolved problem. In this study, we introduced the conception of the cerebral blood flow (CBF) gradient in peritumoral edema-the difference in CBF values from the proximity of the enhancing tumor to the normal-appearing white matter, and investigated the contribution of perfusion metrics on the discrimination of glioblastoma from a metastatic lesion.

MATERIALS AND METHODS

Fifty-two consecutive patients with glioblastoma or a solitary metastatic lesion underwent three-dimensional arterial spin labeling (3D-ASL) before surgical resection. The CBF values were measured in the peritumoral edema (near: G1; Intermediate: G2; Far: G3). The CBF gradient was calculated as the subtractions CBFG1 -CBFG3, CBFG1 - CBFG2 and CBFG2 - CBFG3. A receiver operating characteristic (ROC) curve analysis was used to seek for the best cutoff value permitting discrimination between these two tumors.

RESULTS

The absolute/related CBF values and the CBF gradient in the peritumoral regions of glioblastomas were significantly higher than those in metastases(P < 0.038). ROC curve analysis reveals, a cutoff value of 1.92 ml/100g for the CBF gradient of CBFG1 -CBFG3 generated the best combination of sensitivity (92.86%) and specificity (100.00%) for distinguishing between a glioblastoma and metastasis.

CONCLUSION

The CBF gradient in peritumoral edema appears to be a more promising ASL perfusion metrics in differentiating high grade glioma from a solitary metastasis.

Glioma growth modeling based on the effect of vital nutrients and metabolic products

Glioma brain tumors exhibit considerably aggressive behavior leading to high mortality rates. Mathematical modeling of tumor growth aims to explore the interactions between glioma cells and tissue microenvironment, which affect tumor evolution. Leveraging this concept, we present a three-dimensional model of glioma spatio-temporal evolution based on existing continuum approaches, yet incorporating novel factors of the phenomenon. The proposed model involves the interactions between different tumor cell phenotypes and their microenvironment, investigating how tumor growth is affected by complex biological exchanges. It focuses on the separate and combined effect of vital nutrients and cellular wastes on tumor expansion, leading to the formation of cell populations with different metabolic, proliferative, and diffusive profiles. Several simulations were performed on a virtual and a real glioma, using combinations of proliferation and diffusion rates for different evolution times. The model results were validated on a glioma model available in the literature and a real case of tumor progression. The experimental observations indicate that our model estimates quite satisfactorily the expansion of each region and the overall tumor growth. Based on the individual results, the proposed model may provide an important research tool for patient-specific simulation of different tumor evolution scenarios and reliable estimation of glioma evolution. Graphical Abstract Outline of the mathematical model functionality and application to glioma growth with indicative results.

A Brownian dynamics tumor progression simulator with application to glioblastoma

Tumor progression modeling offers the potential to predict tumor-spreading behavior to improve prognostic accuracy and guide therapy development. Common simulation methods include continuous reaction-diffusion (RD) approaches that capture mean spatio-temporal tumor spreading behavior and discrete agent-based (AB) approaches which capture individual cell events such as proliferation or migration. The brain cancer glioblastoma (GBM) is especially appropriate for such proliferation-migration modeling approaches because tumor cells seldom metastasize outside of the central nervous system and cells are both highly proliferative and migratory. In glioblastoma research, current RD estimates of proliferation and migration parameters are derived from computed tomography or magnetic resonance images. However, these estimates of glioblastoma cell migration rates, modeled as a diffusion coefficient, are approximately 1-2 orders of magnitude larger than single-cell measurements in animal models of this disease. To identify possible sources for this discrepancy, we evaluated the fundamental RD simulation assumptions that cells are point-like structures that can overlap. To give cells physical size (~10 μm), we used a Brownian dynamics approach that simulates individual single-cell diffusive migration, growth, and proliferation activity via a gridless, off-lattice, AB method where cells can be prohibited from overlapping each other. We found that for realistic single-cell parameter growth and migration rates, a non-overlapping model gives rise to a jammed configuration in the center of the tumor and a biased outward diffusion of cells in the tumor periphery, creating a quasi-ballistic advancing tumor front. The simulations demonstrate that a fast-progressing tumor can result from minimally diffusive cells, but at a rate that is still dependent on single-cell diffusive migration rates. Thus, modeling with the assumption of physically-grounded volume conservation can account for the apparent discrepancy between estimated and measured diffusion of GBM cells and provide a new theoretical framework that naturally links single-cell growth and migration dynamics to tumor-level progression.

Automated contour analysis of multi-cellular spheroids spreading through high content imaging

The morphology of 2D cell colonies has been studied to understand tumor metastasis in the past decades. However, 2D cell cultures are lacking many features of 3D tissues, and their physiological behaviors are quite different from solid tumors in vivo. In this work, we studied the multi-cellular tumor spheroid (MCTS) spreading on the substrate, which keeps parts of 3D tissue characteristics and facilitates cell tracking through 2D imaging. By using a high content imaging system (HCS), we tracked multiple spheroids in one single 96-well plate for 36 h. An automated algorithm based on Otsu's method was developed to investigate the morphological details of spheroids through the quantification of radius length and its coefficients of variation. Spheroid spreading is altered by the PIP-platin, which was a novel platinum based drug previously reported by us with an inhibitory effect on cell migration. All parameters showed dose dependent decreases when PIP-platin concentration increased, indicating the inhibition of spheroid expansion by this compound. To investigate the surface roughness of spheroids affected by the drug, we applied the Fourier parameter β and the normalized standard deviation of the radius STD _r / [Formula: see text], which were found inversely proportional to the concentrations of PIP-platin. Particularly at the low drug concentrations, the indices of contour roughness appeared to be more sensitive than spheroid sizes, which could be the potential morphological markers for high content screening of drugs.

Role of Microenvironment in Glioma Invasion: What We Learned from In Vitro Models

The invasion properties of glioblastoma hamper a radical surgery and are responsible for its recurrence. Understanding the invasion mechanisms is thus critical to devise new therapeutic strategies. Therefore, the creation of in vitro models that enable these mechanisms to be studied represents a crucial step. Since in vitro models represent an over-simplification of the in vivo system, in these years it has been attempted to increase the level of complexity of in vitro assays to create models that could better mimic the behaviour of the cells in vivo. These levels of complexity involved: 1. The dimension of the system, moving from two-dimensional to three-dimensional models; 2. The use of microfluidic systems; 3. The use of mixed cultures of tumour cells and cells of the tumour micro-environment in order to mimic the complex cross-talk between tumour cells and their micro-environment; 4. And the source of cells used in an attempt to move from commercial lines to patient-based models. In this review, we will summarize the evidence obtained exploring these different levels of complexity and highlighting advantages and limitations of each system used.

A simple and accurate rule-based modeling framework for simulation of autocrine/paracrine stimulation of glioblastoma cell motility and proliferation by L1CAM in 2-D culture

Background

Glioblastoma multiforme (GBM) is a devastating brain cancer for which there is no known cure. Its malignancy is due to rapid cell division along with high motility and invasiveness of cells into the brain tissue. Simple 2-dimensional laboratory assays (e.g., a scratch assay) commonly are used to measure the effects of various experimental perturbations, such as treatment with chemical inhibitors. Several mathematical models have been developed to aid the understanding of the motile behavior and proliferation of GBM cells. However, many are mathematically complicated, look at multiple interdependent phenomena, and/or use modeling software not freely available to the research community. These attributes make the adoption of models and simulations of even simple 2-dimensional cell behavior an uncommon practice by cancer cell biologists.

Results

Herein, we developed an accurate, yet simple, rule-based modeling framework to describe the in vitro behavior of GBM cells that are stimulated by the L1CAM protein using freely available NetLogo software. In our model L1CAM is released by cells to act through two cell surface receptors and a point of signaling convergence to increase cell motility and proliferation. A simple graphical interface is provided so that changes can be made easily to several parameters controlling cell behavior, and behavior of the cells is viewed both pictorially and with dedicated graphs. We fully describe the hierarchical rule-based modeling framework, show simulation results under several settings, describe the accuracy compared to experimental data, and discuss the potential usefulness for predicting future experimental outcomes and for use as a teaching tool for cell biology students.

Conclusions

It is concluded that this simple modeling framework and its simulations accurately reflect much of the GBM cell motility behavior observed experimentally in vitro in the laboratory. Our framework can be modified easily to suit the needs of investigators interested in other similar intrinsic or extrinsic stimuli that influence cancer or other cell behavior. This modeling framework of a commonly used experimental motility assay (scratch assay) should be useful to both researchers of cell motility and students in a cell biology teaching laboratory.

Electronic supplementary material

The online version of this article (10.1186/s12918-017-0516-z) contains supplementary material, which is available to authorized users.

Emerging tumor spheroids technologies for 3D in vitro cancer modeling

Cancer is a leading cause of mortality and morbidity worldwide. Around 90% of deaths are caused by metastasis and just 10% by primary tumor. The advancement of treatment approaches is not at the same rhythm of the disease; making cancer a focal target of biomedical research. To enhance the understanding and prompts the therapeutic delivery; concepts of tissue engineering are applied in the development of in vitro models that can bridge between 2D cell culture and animal models, mimicking tissue microenvironment. Tumor spheroid represents highly suitable 3D organoid-like framework elucidating the intra and inter cellular signaling of cancer, like that formed in physiological niche. However, spheroids are of limited value in studying critical biological phenomenon such as tumor-stroma interactions involving extra cellular matrix or immune system. Therefore, a compelling need of tailoring spheroid technologies with physiologically relevant biomaterials or in silico models, is ever emerging. The diagnostic and prognostic role of spheroids rearrangements within biomaterials or microfluidic channel is indicative of patient management; particularly for the decision of targeted therapy. Fragmented information on available in vitro spheroid models and lack of critical analysis on transformation aspects of these strategies; pushes the urge to comprehensively overview the recent technological advancements (e.g. bioprinting, micro-fluidic technologies or use of biomaterials to attain the third dimension) in the shed of translationable cancer research. In present article, relationships between current models and their possible exploitation in clinical success is explored with the highlight of existing challenges in defining therapeutic targets and screening of drug efficacy.

The microenvironment induces collective migration in SDHB-silenced mouse pheochromocytoma spheroids

Pheochromocytomas (Pheos) and paragangliomas (PGLs) are neuroendocrine tumors. Approximately 30-40% of Pheos/PGLs are due to germline mutations in one of the susceptibility genes, including those encoding the succinate dehydrogenase subunits A-D (SDHA-D). Up to 2/3 of patients affected by SDHB mutated Pheo/PGL develop metastatic disease with no successful cure at present. Here, for the first time, we evaluated the effects of SDHB silencing in a three dimension (3D) culture using spheroids of a mouse Pheo cell line silenced or not (wild type/wt/control) for the SDHB subunit. We investigated the role of the microenvironment on spheroid growth and migration/invasion by co-culturing SDHB-silenced or wt spheroids with primary cancer-activated fibroblasts (CAFs). When spheroids were co-cultured with fibroblasts, SDHB-silenced cells showed a significant increase in matrigel invasion as demonstrated by the computation of the migratory areas (P < 0.001). Moreover, cells detaching from the SDHB-silenced spheroids moved collectively, unlike the cells of wt spheroids that moved individually. Additionally, SDHB-silenced spheroids developed long filamentous formations along which clusters of cells migrated far away from the spheroid, whereas these structures were not present in wt spheroids. We found that lactate, largely secreted by CAFs, plays a specific role in promoting migration only of SDHB-silenced cells. In this study, we demonstrated that SDHB silencing per se increases tumor cell migration/invasion and that microenvironment, as represented by CAFs, plays a pivotal role in enhancing collective migration/invasion in Pheo SDHB-silenced tumor cells, suggesting their role in increasing the tumor metastasizing potential.